http://www.ingmardeboer.nl/api.php?action=feedcontributions&user=Ingmardb&feedformat=atomIngmar de Boer - User contributions [en]2024-03-28T16:45:45ZUser contributionsMediaWiki 1.26.0http://www.ingmardeboer.nl/index.php?title=Secret_Doctrine_Articles&diff=1308Secret Doctrine Articles2023-10-24T22:13:31Z<p>Ingmardb: </p>
<hr />
<div>Below is a list of links to most of my contributions to the [http://prajnaquest.fr/blog/ Book of Dzyan] web site. <br />
<br />
Latest articles on Fohat:<br />
<br />
* [http://prajnaquest.fr/blog/who-were-the-turanians-of-the-secret-doctrine/ Who were the Turanians of The Secret Doctrine?]<br />
<br />
* [http://prajnaquest.fr/blog/on-the-etymology-of-the-term-fohat/ On the Etymology of the Term Fohat]<br />
<br />
* [http://prajnaquest.fr/blog/the-book-of-dzyan-some-themes-related-to-chinese-traditional-religion/ The Book of Dzyan: Some Themes Related to Chinese Traditional Religion]<br />
<br />
Other articles:<br />
<br />
* [http://prajnaquest.fr/blog/the-three-logoi-1/ The Three Logoi (in three parts)]<br />
<br />
* [http://prajnaquest.fr/blog/two-aspects-of-the-absolute/ Two Aspects of the Absolute]<br />
<br />
* [http://prajnaquest.fr/blog/on-the-summary-to-the-first-fundamental-proposition/ On the Summary to the First Fundamental Proposition]<br />
<br />
* [http://prajnaquest.fr/blog/kara%e1%b9%87a-the-causeless-cause/ Karana, the Causeless Cause]<br />
<br />
* [http://prajnaquest.fr/blog/on-the-eternal-germ/ On the Eternal Germ]<br />
<br />
* [http://prajnaquest.fr/blog/the-orthography-of-kwan-yin-tien/ The Orthography of Kwan Yin Tien]<br />
<br />
* [http://prajnaquest.fr/blog/the-orthography-of-sien-tchan/ The Orthography of Sien Tchan]<br />
<br />
* [http://prajnaquest.fr/blog/alaya-in-the-la%e1%b9%85kavatarasutra-part-i/ Alaya in the Lankavatarasutra - Part I "Philological"]<br />
<br />
* [http://prajnaquest.fr/blog/alaya-in-the-la%e1%b9%85kavatarasutra-part-ii/ Alaya in the Lankavatarasutra - Part II "Philosophical"]<br />
<br />
* [http://prajnaquest.fr/blog/the-three-svabhavas-in-the-secret-doctrine/ The Three Svabhavas in the Secret Doctrine]<br />
<br />
* [http://prajnaquest.fr/blog/the-universal-over-soul/ The Universal Over-Soul]<br />
<br />
* [http://prajnaquest.fr/blog/the-orthography-of-dgyu-or-dzyu/ The Orthography of Dgyu or Dzyu]<br />
<br />
* [http://prajnaquest.fr/blog/the-sacred-four-and-the-emanation-of-the-primordial-seven/ The Sacred Four and the Emanation of the Primordial Seven]<br />
<br />
* [http://prajnaquest.fr/blog/the-orthography-and-pronunciation-of-koot-hoomi/ The Orthography and Pronunciation of "Koot Hoomi"]<br />
<br />
* [http://prajnaquest.fr/blog/the-signature-of-koot-hoomi-in-mahatma-letter-iv/ The Signature of Koot Hoomi in Mahatma Letter IV]<br />
<br />
* [http://prajnaquest.fr/blog/svabhava-as-prima-materia-v-4/ Svabhava as Prima-Materia]<br />
<br />
* [http://prajnaquest.fr/blog/a-digital-index-of-the-secret-doctrine/ A Digital Index of the Secret Doctrine]</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Secret_Doctrine_Articles&diff=1307Secret Doctrine Articles2023-10-24T22:12:44Z<p>Ingmardb: </p>
<hr />
<div>Please find here the links to most of my contributions to the [http://prajnaquest.fr/blog/ Book of Dzyan] web site. <br />
<br />
Latest articles on Fohat:<br />
<br />
* [http://prajnaquest.fr/blog/who-were-the-turanians-of-the-secret-doctrine/ Who were the Turanians of The Secret Doctrine?]<br />
<br />
* [http://prajnaquest.fr/blog/on-the-etymology-of-the-term-fohat/ On the Etymology of the Term Fohat]<br />
<br />
* [http://prajnaquest.fr/blog/the-book-of-dzyan-some-themes-related-to-chinese-traditional-religion/ The Book of Dzyan: Some Themes Related to Chinese Traditional Religion]<br />
<br />
Other articles:<br />
<br />
* [http://prajnaquest.fr/blog/the-three-logoi-1/ The Three Logoi (in three parts)]<br />
<br />
* [http://prajnaquest.fr/blog/two-aspects-of-the-absolute/ Two Aspects of the Absolute]<br />
<br />
* [http://prajnaquest.fr/blog/on-the-summary-to-the-first-fundamental-proposition/ On the Summary to the First Fundamental Proposition]<br />
<br />
* [http://prajnaquest.fr/blog/kara%e1%b9%87a-the-causeless-cause/ Karana, the Causeless Cause]<br />
<br />
* [http://prajnaquest.fr/blog/on-the-eternal-germ/ On the Eternal Germ]<br />
<br />
* [http://prajnaquest.fr/blog/the-orthography-of-kwan-yin-tien/ The Orthography of Kwan Yin Tien]<br />
<br />
* [http://prajnaquest.fr/blog/the-orthography-of-sien-tchan/ The Orthography of Sien Tchan]<br />
<br />
* [http://prajnaquest.fr/blog/alaya-in-the-la%e1%b9%85kavatarasutra-part-i/ Alaya in the Lankavatarasutra - Part I "Philological"]<br />
<br />
* [http://prajnaquest.fr/blog/alaya-in-the-la%e1%b9%85kavatarasutra-part-ii/ Alaya in the Lankavatarasutra - Part II "Philosophical"]<br />
<br />
* [http://prajnaquest.fr/blog/the-three-svabhavas-in-the-secret-doctrine/ The Three Svabhavas in the Secret Doctrine]<br />
<br />
* [http://prajnaquest.fr/blog/the-universal-over-soul/ The Universal Over-Soul]<br />
<br />
* [http://prajnaquest.fr/blog/the-orthography-of-dgyu-or-dzyu/ The Orthography of Dgyu or Dzyu]<br />
<br />
* [http://prajnaquest.fr/blog/the-sacred-four-and-the-emanation-of-the-primordial-seven/ The Sacred Four and the Emanation of the Primordial Seven]<br />
<br />
* [http://prajnaquest.fr/blog/the-orthography-and-pronunciation-of-koot-hoomi/ The Orthography and Pronunciation of "Koot Hoomi"]<br />
<br />
* [http://prajnaquest.fr/blog/the-signature-of-koot-hoomi-in-mahatma-letter-iv/ The Signature of Koot Hoomi in Mahatma Letter IV]<br />
<br />
* [http://prajnaquest.fr/blog/svabhava-as-prima-materia-v-4/ Svabhava as Prima-Materia]<br />
<br />
* [http://prajnaquest.fr/blog/a-digital-index-of-the-secret-doctrine/ A Digital Index of the Secret Doctrine]</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Book_of_Dzyan&diff=1306Book of Dzyan2023-10-24T22:09:12Z<p>Ingmardb: Redirected page to Secret Doctrine Articles</p>
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<div>#REDIRECT [[Secret Doctrine Articles]]</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Book_of_Dzyan&diff=1305Book of Dzyan2023-10-24T22:08:36Z<p>Ingmardb: </p>
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<div>#REDIRECT [Secret Doctrine Articles]</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Book_of_Dzyan&diff=1304Book of Dzyan2023-10-24T22:07:42Z<p>Ingmardb: </p>
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<div>#REDIRECT Secret Doctrine</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=File:Tree_of_Science_-_3_-_1.pdf&diff=1303File:Tree of Science - 3 - 1.pdf2023-10-10T18:22:01Z<p>Ingmardb: </p>
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<div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1302Tree of Science2023-10-10T18:19:55Z<p>Ingmardb: </p>
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<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3.1</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3_-_1.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the <i>Messenger Lectures</i> [1]. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists proclaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the <i>Principia</i> (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find [2]<br />
<br />
<ul><i>I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.</i></ul><br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena involved. Feynman also remarks that having criticism of the old is easy, while creating the new is difficult. Of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant example in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work <i>De revolutionibus orbium caelestium</i>. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First, perhaps we should acknowledge that the heliocentric world view was not completely new at the time. Copernicus had already studied several ancient Greek texts mentioning the heliocentric worldview texts. One of these texts was Claudius Ptolemy's <i>Almagest</i>. In the days of Ptolemy however, heliocentrism was already a controversial point of view. Copernicus realised perfectly well how controversial his work would be in his day, and he chose wisely to arrange for the book to be published after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it all the same, despite the controversy it would stir. In his foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
So how could Copernicus be so sure that the earth was not at the centre of the solar system, if it was not on the basis of a proven hypothesis? In <i>De revolutionibus</i> he gives two "facts" which are, as he formulates it, "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" while the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time, there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between the movements of the inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis [3]):<br />
<br />
<ul><i>For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.</i></ul><br />
<br />
<p style="margin-top: 30px; margin-bottom: 30px;"><br />
<gallery widths=300px heights=300px><br />
File:Mars-Sun-geocentric.png <br />
File:Mars-Sun-heliocentric.png <br />
</gallery><br />
</p><br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
<p style="margin-top: 30px; margin-bottom: 30px;"><br />
[[File:Trees.png|border|550px]]<br />
</p><br />
<br />
[[File:Arbor_-_1.png|right|border|240px]] This idea has also been recognised by several of the earlier philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work <i>l'Arbre de Ciència</i> [4] already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon also compared the progression of science to a tree. In <i>The Advancement of Learning</i> [5] (1605), and the enlarged Latin version of the same work <i>De augmentis scientiarum</i> [5] (1623), the trunk representing the unified theory he calls the <i>philosophiae prima</i>, the primary philosophy, or the <i>summary</i> of philosophy.<br />
<br />
Particularly in natural science, advancement is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon, to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as "answering a why-question": why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that at least one of the most important advances in science was decided by the criterium of having a better insight into the nature of things. Advancement is in this case primarily an advancement in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now, has this all changed with the advent of quantum mechanics in the twentieth century? Is there something special going on in modern physics causing that our why-questions, our urge to understand things, are suddenly not good enough anymore? In the same series of lectures6, there is another well-known quote from Feynman, perhaps his most famous one, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the "trunk" of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1301Tree of Science2023-10-10T18:18:16Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3.1</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3_-_1.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures [1]. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find [2]<br />
<br />
<ul><i>I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.</i></ul><br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena involved. Feynman also remarks that having criticism of the old is easy, while creating the new is difficult. Of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant example in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work <i>De revolutionibus orbium caelestium</i>. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First, perhaps we should acknowledge that the heliocentric world view was not completely new at the time. Copernicus had already studied several ancient Greek texts mentioning the heliocentric worldview texts. One of these texts was Claudius Ptolemy's <i>Almagest</i>. In the days of Ptolemy however, heliocentrism was already a controversial point of view. Copernicus realised perfectly well how controversial his work would be in his day, and he chose wisely to arrange for the book to be published after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it all the same, despite the controversy it would stir. In his foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
So how could Copernicus be so sure that the earth was not at the centre of the solar system, if it was not on the basis of a proven hypothesis? In <i>De revolutionibus</i> he gives two "facts" which are, as he formulates it, "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" while the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time, there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between the movements of the inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis [3]):<br />
<br />
<ul><i>For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.</i></ul><br />
<br />
<p style="margin-top: 30px; margin-bottom: 30px;"><br />
<gallery widths=300px heights=300px><br />
File:Mars-Sun-geocentric.png <br />
File:Mars-Sun-heliocentric.png <br />
</gallery><br />
</p><br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
<p style="margin-top: 30px; margin-bottom: 30px;"><br />
[[File:Trees.png|border|550px]]<br />
</p><br />
<br />
[[File:Arbor_-_1.png|right|border|240px]] This idea has also been recognised by several of the earlier philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work <i>l'Arbre de Ciència</i> [4] already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon also compared the progression of science to a tree. In <i>The Advancement of Learning</i> [5] (1605), and the enlarged Latin version of the same work <i>De augmentis scientiarum</i> [5] (1623), the trunk representing the unified theory he calls the <i>philosophiae prima</i>, the primary philosophy, or the <i>summary</i> of philosophy.<br />
<br />
Particularly in natural science, advancement is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon, to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as "answering a why-question": why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that at least one of the most important advances in science was decided by the criterium of having a better insight into the nature of things. Advancement is in this case primarily an advancement in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now, has this all changed with the advent of quantum mechanics in the twentieth century? Is there something special going on in modern physics causing that our why-questions, our urge to understand things, are suddenly not good enough anymore? In the same series of lectures6, there is another well-known quote from Feynman, perhaps his most famous one, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the "trunk" of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1300Tree of Science2023-10-10T18:17:58Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3_-_1.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures [1]. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find [2]<br />
<br />
<ul><i>I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.</i></ul><br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena involved. Feynman also remarks that having criticism of the old is easy, while creating the new is difficult. Of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant example in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work <i>De revolutionibus orbium caelestium</i>. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First, perhaps we should acknowledge that the heliocentric world view was not completely new at the time. Copernicus had already studied several ancient Greek texts mentioning the heliocentric worldview texts. One of these texts was Claudius Ptolemy's <i>Almagest</i>. In the days of Ptolemy however, heliocentrism was already a controversial point of view. Copernicus realised perfectly well how controversial his work would be in his day, and he chose wisely to arrange for the book to be published after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it all the same, despite the controversy it would stir. In his foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
So how could Copernicus be so sure that the earth was not at the centre of the solar system, if it was not on the basis of a proven hypothesis? In <i>De revolutionibus</i> he gives two "facts" which are, as he formulates it, "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" while the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time, there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between the movements of the inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis [3]):<br />
<br />
<ul><i>For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.</i></ul><br />
<br />
<p style="margin-top: 30px; margin-bottom: 30px;"><br />
<gallery widths=300px heights=300px><br />
File:Mars-Sun-geocentric.png <br />
File:Mars-Sun-heliocentric.png <br />
</gallery><br />
</p><br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
<p style="margin-top: 30px; margin-bottom: 30px;"><br />
[[File:Trees.png|border|550px]]<br />
</p><br />
<br />
[[File:Arbor_-_1.png|right|border|240px]] This idea has also been recognised by several of the earlier philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work <i>l'Arbre de Ciència</i> [4] already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon also compared the progression of science to a tree. In <i>The Advancement of Learning</i> [5] (1605), and the enlarged Latin version of the same work <i>De augmentis scientiarum</i> [5] (1623), the trunk representing the unified theory he calls the <i>philosophiae prima</i>, the primary philosophy, or the <i>summary</i> of philosophy.<br />
<br />
Particularly in natural science, advancement is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon, to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as "answering a why-question": why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that at least one of the most important advances in science was decided by the criterium of having a better insight into the nature of things. Advancement is in this case primarily an advancement in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now, has this all changed with the advent of quantum mechanics in the twentieth century? Is there something special going on in modern physics causing that our why-questions, our urge to understand things, are suddenly not good enough anymore? In the same series of lectures6, there is another well-known quote from Feynman, perhaps his most famous one, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the "trunk" of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1299Tree of Science2023-10-10T18:05:32Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3_-_1.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures [1]. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find [2]:<br />
<br />
<ul><i>I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.</i></ul><br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis [3]):<br />
<br />
<ul><i>For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.</i></ul><br />
<br />
<p style="margin-top: 30px; margin-bottom: 30px;"><br />
<gallery widths=300px heights=300px><br />
File:Mars-Sun-geocentric.png <br />
File:Mars-Sun-heliocentric.png <br />
</gallery><br />
</p><br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
<p style="margin-top: 30px; margin-bottom: 30px;"><br />
[[File:Trees.png|border|550px]]<br />
</p><br />
<br />
[[File:Arbor_-_1.png|right|border|240px]] In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència [4] already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning [5] (1605), and the enlarged Latin version of the same work De augmentis scientiarum [5] (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures [6], where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Main_Page&diff=1297Main Page2023-10-01T00:00:50Z<p>Ingmardb: /* T */</p>
<hr />
<div><p style="margin-top: 25px; margin-bottom: 20px;"><br />
[[#A|A]] [[#B|B]] [[#C|C]] [[#D|D]] [[#E|E]] [[#F|F]] [[#G|G]] [[#H|H]] [[#I|I]] [[#J|J]] [[#K|K]] [[#L|L]] [[#M|M]] [[#N|N]] [[#O|O]] [[#P|P]] [[#Q|Q]] [[#R|R]] [[#S|S]] [[#T|T]] [[#U|U]] [[#V|V]] [[#W|W]] [[#X|X]] [[#Y|Y]] [[#Z|Z]]<br />
</p><br />
{| cellpadding="10" cellspacing="10" style="background-color: #f4f4f4; border: 1px; border-color: #b4b4b4; border-style: outset; padding: 0px; margin-left: -2px; width: 80%;"<br />
|- <br />
| style="width: 50%; vertical-align:top;"|<br />
<h1 style="margin-top: 0px;">A</h1><br />
__NOTOC__ <br />
[[APC Houses]]<br /><br />
[[Asanga]]<br /><br />
[[Ascendant-Parallelcirkelsysteem]] [[File:Dutch.gif]]<br/><br />
[[Astrologen doen maar wat]] [[File:Dutch.gif]]<br /><br />
[[Astrology]]<br /><br />
[[Authorship Attribution Method]], Applied to the Buddhist Scriptures of Ārya Asaṅga, A Statistical -<br />
<br />
=B=<br />
<br />
[[Buddhism]], some links<br /><br />
[[Book of Dzyan]] web site <br /><br />
[[Book of the Universe]] The, - (On Max Tegmark's Mathematical Universe Hypothesis)<br />
<br />
=C=<br />
<br />
[[Circle]], The -, or the Unreasonable Effectiveness of Mathematics<br /><br />
[[Contact]]<br /><br />
[[Cosmografie]] voor astrologen [[File:Dutch.gif]]<br /><br />
<br />
=D=<br />
<br />
[[Diagram of Meditation]] dictated by H.P. Blavatsky to E.T. Sturdy around 1887<br /><br />
[[Dierenriem]] [[File:Dutch.gif]]<br /><br />
[[Dzyan]], A Diagram on the Origin of the Book of -<br /><br />
<br />
=E=<br />
<br />
[[Eckhart]] De Drieheid: Johannes Eckhart, proeve van vertaling [[File:Dutch.gif]]<br />
<br />
=F=<br />
<br />
[[Facebook]] pages <br /><br />
[[Feynman]], Richard - (the physicist)<br /><br />
<br />
=G=<br />
<br />
=H=<br />
[[Hypothetische Planeten]], De posities van de - [[File:Dutch.gif]]<br /><br />
<br />
=I=<br />
<br />
=J=<br />
<br />
=K=<br />
<br />
<!--[[Kalacakra]] Notes on the chronology of the Kalacakratantra<br /--><br />
[[Krisnamurti]]'s "keuzeloos gewaarzijn" [[File:Dutch.gif]] <br /><br />
<br />
=L=<br />
<br />
[[Labout]], L.W.J., tekening De Zeven Evolutiesystemen van het Zonnestelsel [[File:Dutch.gif]] <br><br />
[[Lamp]] Sri Ram, Een - te zijn voor jezelf: de praktijk van mindfulness [[File:Dutch.gif]] <br><br />
[[Licht van Azië]] (fragment om voor te lezen) [[File:Dutch.gif]] <br><br />
<br />
=M=<br />
<br />
=N=<br />
<br />
[[Natuurkunde in de theosofische literatuur]] [[File:Dutch.gif]]<br><br />
<br />
=O=<br />
<br />
=P=<br />
[[Pranavavada]] Manuscripts<br /><br />
<br />
=Q=<br />
<br />
=R=<br />
<br />
=S=<br />
[http://vps.ingmardeboer.nl Sanskrit Dictionary] Monier Williams and other DICT dictionaries<br /><br />
[[Secret Doctrine Articles|Secret Doctrine]] articles for the Book of Dzyan Blog<br /><br />
[[Semiotische driehoek]], De - [[File:Dutch.gif]]<br /><br />
[[Stem van de Stilte]], De Wereld achter het Werk [[File:Dutch.gif]]<br /><br />
<br />
=T=<br />
<br />
[[Theosophical History (Diagrams)]]<br /><br />
[[Thierens]] A.E., "founder of astrology in the Netherlands"<br /><br />
[[Topocentrische plaatsbepaling]] [[File:Dutch.gif]]<br><br />
[[Tree of Science]], Asking "Why, why, why?" or the - (on Richard Feynman and the advancement of science)<br><br />
<br />
=U=<br />
<br />
[[Unicode]] transliteration standard for Sanskrit<br /><br />
<br />
=V=<br />
<br />
[[Verwondering]], Momenten van - [[File:Dutch.gif]]<br><br />
<br />
=W=<br />
[[Wiskunde]], Waarom is - zo'n effectief middel in het beschrijven van natuurkundige verschijnselen? [[File:Dutch.gif]]<br />
<br />
=Y=<br />
<br />
[[Yoga Sutra]]'s, Het hart van Patañjali's - [[File:Dutch.gif]]<br /><br />
<br />
=Z=</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Main_Page&diff=1296Main Page2023-10-01T00:00:32Z<p>Ingmardb: /* T */</p>
<hr />
<div><p style="margin-top: 25px; margin-bottom: 20px;"><br />
[[#A|A]] [[#B|B]] [[#C|C]] [[#D|D]] [[#E|E]] [[#F|F]] [[#G|G]] [[#H|H]] [[#I|I]] [[#J|J]] [[#K|K]] [[#L|L]] [[#M|M]] [[#N|N]] [[#O|O]] [[#P|P]] [[#Q|Q]] [[#R|R]] [[#S|S]] [[#T|T]] [[#U|U]] [[#V|V]] [[#W|W]] [[#X|X]] [[#Y|Y]] [[#Z|Z]]<br />
</p><br />
{| cellpadding="10" cellspacing="10" style="background-color: #f4f4f4; border: 1px; border-color: #b4b4b4; border-style: outset; padding: 0px; margin-left: -2px; width: 80%;"<br />
|- <br />
| style="width: 50%; vertical-align:top;"|<br />
<h1 style="margin-top: 0px;">A</h1><br />
__NOTOC__ <br />
[[APC Houses]]<br /><br />
[[Asanga]]<br /><br />
[[Ascendant-Parallelcirkelsysteem]] [[File:Dutch.gif]]<br/><br />
[[Astrologen doen maar wat]] [[File:Dutch.gif]]<br /><br />
[[Astrology]]<br /><br />
[[Authorship Attribution Method]], Applied to the Buddhist Scriptures of Ārya Asaṅga, A Statistical -<br />
<br />
=B=<br />
<br />
[[Buddhism]], some links<br /><br />
[[Book of Dzyan]] web site <br /><br />
[[Book of the Universe]] The, - (On Max Tegmark's Mathematical Universe Hypothesis)<br />
<br />
=C=<br />
<br />
[[Circle]], The -, or the Unreasonable Effectiveness of Mathematics<br /><br />
[[Contact]]<br /><br />
[[Cosmografie]] voor astrologen [[File:Dutch.gif]]<br /><br />
<br />
=D=<br />
<br />
[[Diagram of Meditation]] dictated by H.P. Blavatsky to E.T. Sturdy around 1887<br /><br />
[[Dierenriem]] [[File:Dutch.gif]]<br /><br />
[[Dzyan]], A Diagram on the Origin of the Book of -<br /><br />
<br />
=E=<br />
<br />
[[Eckhart]] De Drieheid: Johannes Eckhart, proeve van vertaling [[File:Dutch.gif]]<br />
<br />
=F=<br />
<br />
[[Facebook]] pages <br /><br />
[[Feynman]], Richard - (the physicist)<br /><br />
<br />
=G=<br />
<br />
=H=<br />
[[Hypothetische Planeten]], De posities van de - [[File:Dutch.gif]]<br /><br />
<br />
=I=<br />
<br />
=J=<br />
<br />
=K=<br />
<br />
<!--[[Kalacakra]] Notes on the chronology of the Kalacakratantra<br /--><br />
[[Krisnamurti]]'s "keuzeloos gewaarzijn" [[File:Dutch.gif]] <br /><br />
<br />
=L=<br />
<br />
[[Labout]], L.W.J., tekening De Zeven Evolutiesystemen van het Zonnestelsel [[File:Dutch.gif]] <br><br />
[[Lamp]] Sri Ram, Een - te zijn voor jezelf: de praktijk van mindfulness [[File:Dutch.gif]] <br><br />
[[Licht van Azië]] (fragment om voor te lezen) [[File:Dutch.gif]] <br><br />
<br />
=M=<br />
<br />
=N=<br />
<br />
[[Natuurkunde in de theosofische literatuur]] [[File:Dutch.gif]]<br><br />
<br />
=O=<br />
<br />
=P=<br />
[[Pranavavada]] Manuscripts<br /><br />
<br />
=Q=<br />
<br />
=R=<br />
<br />
=S=<br />
[http://vps.ingmardeboer.nl Sanskrit Dictionary] Monier Williams and other DICT dictionaries<br /><br />
[[Secret Doctrine Articles|Secret Doctrine]] articles for the Book of Dzyan Blog<br /><br />
[[Semiotische driehoek]], De - [[File:Dutch.gif]]<br /><br />
[[Stem van de Stilte]], De Wereld achter het Werk [[File:Dutch.gif]]<br /><br />
<br />
=T=<br />
<br />
[[Theosophical History (Diagrams)]]<br /><br />
[[Thierens]] A.E., "founder of astrology in the Netherlands"<br /><br />
[[Topocentrische plaatsbepaling]] [[File:Dutch.gif]]<br><br />
[[Tree of Science]], Asking "Why, why, why?" or the -, on Richard Feynman and the advancement of science<br><br />
<br />
=U=<br />
<br />
[[Unicode]] transliteration standard for Sanskrit<br /><br />
<br />
=V=<br />
<br />
[[Verwondering]], Momenten van - [[File:Dutch.gif]]<br><br />
<br />
=W=<br />
[[Wiskunde]], Waarom is - zo'n effectief middel in het beschrijven van natuurkundige verschijnselen? [[File:Dutch.gif]]<br />
<br />
=Y=<br />
<br />
[[Yoga Sutra]]'s, Het hart van Patañjali's - [[File:Dutch.gif]]<br /><br />
<br />
=Z=</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Main_Page&diff=1295Main Page2023-10-01T00:00:12Z<p>Ingmardb: /* F */</p>
<hr />
<div><p style="margin-top: 25px; margin-bottom: 20px;"><br />
[[#A|A]] [[#B|B]] [[#C|C]] [[#D|D]] [[#E|E]] [[#F|F]] [[#G|G]] [[#H|H]] [[#I|I]] [[#J|J]] [[#K|K]] [[#L|L]] [[#M|M]] [[#N|N]] [[#O|O]] [[#P|P]] [[#Q|Q]] [[#R|R]] [[#S|S]] [[#T|T]] [[#U|U]] [[#V|V]] [[#W|W]] [[#X|X]] [[#Y|Y]] [[#Z|Z]]<br />
</p><br />
{| cellpadding="10" cellspacing="10" style="background-color: #f4f4f4; border: 1px; border-color: #b4b4b4; border-style: outset; padding: 0px; margin-left: -2px; width: 80%;"<br />
|- <br />
| style="width: 50%; vertical-align:top;"|<br />
<h1 style="margin-top: 0px;">A</h1><br />
__NOTOC__ <br />
[[APC Houses]]<br /><br />
[[Asanga]]<br /><br />
[[Ascendant-Parallelcirkelsysteem]] [[File:Dutch.gif]]<br/><br />
[[Astrologen doen maar wat]] [[File:Dutch.gif]]<br /><br />
[[Astrology]]<br /><br />
[[Authorship Attribution Method]], Applied to the Buddhist Scriptures of Ārya Asaṅga, A Statistical -<br />
<br />
=B=<br />
<br />
[[Buddhism]], some links<br /><br />
[[Book of Dzyan]] web site <br /><br />
[[Book of the Universe]] The, - (On Max Tegmark's Mathematical Universe Hypothesis)<br />
<br />
=C=<br />
<br />
[[Circle]], The -, or the Unreasonable Effectiveness of Mathematics<br /><br />
[[Contact]]<br /><br />
[[Cosmografie]] voor astrologen [[File:Dutch.gif]]<br /><br />
<br />
=D=<br />
<br />
[[Diagram of Meditation]] dictated by H.P. Blavatsky to E.T. Sturdy around 1887<br /><br />
[[Dierenriem]] [[File:Dutch.gif]]<br /><br />
[[Dzyan]], A Diagram on the Origin of the Book of -<br /><br />
<br />
=E=<br />
<br />
[[Eckhart]] De Drieheid: Johannes Eckhart, proeve van vertaling [[File:Dutch.gif]]<br />
<br />
=F=<br />
<br />
[[Facebook]] pages <br /><br />
[[Feynman]], Richard - (the physicist)<br /><br />
<br />
=G=<br />
<br />
=H=<br />
[[Hypothetische Planeten]], De posities van de - [[File:Dutch.gif]]<br /><br />
<br />
=I=<br />
<br />
=J=<br />
<br />
=K=<br />
<br />
<!--[[Kalacakra]] Notes on the chronology of the Kalacakratantra<br /--><br />
[[Krisnamurti]]'s "keuzeloos gewaarzijn" [[File:Dutch.gif]] <br /><br />
<br />
=L=<br />
<br />
[[Labout]], L.W.J., tekening De Zeven Evolutiesystemen van het Zonnestelsel [[File:Dutch.gif]] <br><br />
[[Lamp]] Sri Ram, Een - te zijn voor jezelf: de praktijk van mindfulness [[File:Dutch.gif]] <br><br />
[[Licht van Azië]] (fragment om voor te lezen) [[File:Dutch.gif]] <br><br />
<br />
=M=<br />
<br />
=N=<br />
<br />
[[Natuurkunde in de theosofische literatuur]] [[File:Dutch.gif]]<br><br />
<br />
=O=<br />
<br />
=P=<br />
[[Pranavavada]] Manuscripts<br /><br />
<br />
=Q=<br />
<br />
=R=<br />
<br />
=S=<br />
[http://vps.ingmardeboer.nl Sanskrit Dictionary] Monier Williams and other DICT dictionaries<br /><br />
[[Secret Doctrine Articles|Secret Doctrine]] articles for the Book of Dzyan Blog<br /><br />
[[Semiotische driehoek]], De - [[File:Dutch.gif]]<br /><br />
[[Stem van de Stilte]], De Wereld achter het Werk [[File:Dutch.gif]]<br /><br />
<br />
=T=<br />
<br />
[[Theosophical History (Diagrams)]]<br /><br />
[[Thierens]] A.E., "founder of astrology in the Netherlands"<br /><br />
[[Topocentrische plaatsbepaling]] [[File:Dutch.gif]]<br><br />
[[Tree of Science]] Asking "Why, why, why?" or the -, on Richard Feynman and the advancement of science<br><br />
<br />
=U=<br />
<br />
[[Unicode]] transliteration standard for Sanskrit<br /><br />
<br />
=V=<br />
<br />
[[Verwondering]], Momenten van - [[File:Dutch.gif]]<br><br />
<br />
=W=<br />
[[Wiskunde]], Waarom is - zo'n effectief middel in het beschrijven van natuurkundige verschijnselen? [[File:Dutch.gif]]<br />
<br />
=Y=<br />
<br />
[[Yoga Sutra]]'s, Het hart van Patañjali's - [[File:Dutch.gif]]<br /><br />
<br />
=Z=</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Main_Page&diff=1294Main Page2023-09-30T23:59:48Z<p>Ingmardb: /* K */</p>
<hr />
<div><p style="margin-top: 25px; margin-bottom: 20px;"><br />
[[#A|A]] [[#B|B]] [[#C|C]] [[#D|D]] [[#E|E]] [[#F|F]] [[#G|G]] [[#H|H]] [[#I|I]] [[#J|J]] [[#K|K]] [[#L|L]] [[#M|M]] [[#N|N]] [[#O|O]] [[#P|P]] [[#Q|Q]] [[#R|R]] [[#S|S]] [[#T|T]] [[#U|U]] [[#V|V]] [[#W|W]] [[#X|X]] [[#Y|Y]] [[#Z|Z]]<br />
</p><br />
{| cellpadding="10" cellspacing="10" style="background-color: #f4f4f4; border: 1px; border-color: #b4b4b4; border-style: outset; padding: 0px; margin-left: -2px; width: 80%;"<br />
|- <br />
| style="width: 50%; vertical-align:top;"|<br />
<h1 style="margin-top: 0px;">A</h1><br />
__NOTOC__ <br />
[[APC Houses]]<br /><br />
[[Asanga]]<br /><br />
[[Ascendant-Parallelcirkelsysteem]] [[File:Dutch.gif]]<br/><br />
[[Astrologen doen maar wat]] [[File:Dutch.gif]]<br /><br />
[[Astrology]]<br /><br />
[[Authorship Attribution Method]], Applied to the Buddhist Scriptures of Ārya Asaṅga, A Statistical -<br />
<br />
=B=<br />
<br />
[[Buddhism]], some links<br /><br />
[[Book of Dzyan]] web site <br /><br />
[[Book of the Universe]] The, - (On Max Tegmark's Mathematical Universe Hypothesis)<br />
<br />
=C=<br />
<br />
[[Circle]], The -, or the Unreasonable Effectiveness of Mathematics<br /><br />
[[Contact]]<br /><br />
[[Cosmografie]] voor astrologen [[File:Dutch.gif]]<br /><br />
<br />
=D=<br />
<br />
[[Diagram of Meditation]] dictated by H.P. Blavatsky to E.T. Sturdy around 1887<br /><br />
[[Dierenriem]] [[File:Dutch.gif]]<br /><br />
[[Dzyan]], A Diagram on the Origin of the Book of -<br /><br />
<br />
=E=<br />
<br />
[[Eckhart]] De Drieheid: Johannes Eckhart, proeve van vertaling [[File:Dutch.gif]]<br />
<br />
=F=<br />
<br />
[[Facebook]] pages <br /><br />
[[Feynman]] Richard - (the physicist)<br /><br />
<br />
=G=<br />
<br />
=H=<br />
[[Hypothetische Planeten]], De posities van de - [[File:Dutch.gif]]<br /><br />
<br />
=I=<br />
<br />
=J=<br />
<br />
=K=<br />
<br />
<!--[[Kalacakra]] Notes on the chronology of the Kalacakratantra<br /--><br />
[[Krisnamurti]]'s "keuzeloos gewaarzijn" [[File:Dutch.gif]] <br /><br />
<br />
=L=<br />
<br />
[[Labout]], L.W.J., tekening De Zeven Evolutiesystemen van het Zonnestelsel [[File:Dutch.gif]] <br><br />
[[Lamp]] Sri Ram, Een - te zijn voor jezelf: de praktijk van mindfulness [[File:Dutch.gif]] <br><br />
[[Licht van Azië]] (fragment om voor te lezen) [[File:Dutch.gif]] <br><br />
<br />
=M=<br />
<br />
=N=<br />
<br />
[[Natuurkunde in de theosofische literatuur]] [[File:Dutch.gif]]<br><br />
<br />
=O=<br />
<br />
=P=<br />
[[Pranavavada]] Manuscripts<br /><br />
<br />
=Q=<br />
<br />
=R=<br />
<br />
=S=<br />
[http://vps.ingmardeboer.nl Sanskrit Dictionary] Monier Williams and other DICT dictionaries<br /><br />
[[Secret Doctrine Articles|Secret Doctrine]] articles for the Book of Dzyan Blog<br /><br />
[[Semiotische driehoek]], De - [[File:Dutch.gif]]<br /><br />
[[Stem van de Stilte]], De Wereld achter het Werk [[File:Dutch.gif]]<br /><br />
<br />
=T=<br />
<br />
[[Theosophical History (Diagrams)]]<br /><br />
[[Thierens]] A.E., "founder of astrology in the Netherlands"<br /><br />
[[Topocentrische plaatsbepaling]] [[File:Dutch.gif]]<br><br />
[[Tree of Science]] Asking "Why, why, why?" or the -, on Richard Feynman and the advancement of science<br><br />
<br />
=U=<br />
<br />
[[Unicode]] transliteration standard for Sanskrit<br /><br />
<br />
=V=<br />
<br />
[[Verwondering]], Momenten van - [[File:Dutch.gif]]<br><br />
<br />
=W=<br />
[[Wiskunde]], Waarom is - zo'n effectief middel in het beschrijven van natuurkundige verschijnselen? [[File:Dutch.gif]]<br />
<br />
=Y=<br />
<br />
[[Yoga Sutra]]'s, Het hart van Patañjali's - [[File:Dutch.gif]]<br /><br />
<br />
=Z=</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Main_Page&diff=1293Main Page2023-09-30T23:59:28Z<p>Ingmardb: /* K */</p>
<hr />
<div><p style="margin-top: 25px; margin-bottom: 20px;"><br />
[[#A|A]] [[#B|B]] [[#C|C]] [[#D|D]] [[#E|E]] [[#F|F]] [[#G|G]] [[#H|H]] [[#I|I]] [[#J|J]] [[#K|K]] [[#L|L]] [[#M|M]] [[#N|N]] [[#O|O]] [[#P|P]] [[#Q|Q]] [[#R|R]] [[#S|S]] [[#T|T]] [[#U|U]] [[#V|V]] [[#W|W]] [[#X|X]] [[#Y|Y]] [[#Z|Z]]<br />
</p><br />
{| cellpadding="10" cellspacing="10" style="background-color: #f4f4f4; border: 1px; border-color: #b4b4b4; border-style: outset; padding: 0px; margin-left: -2px; width: 80%;"<br />
|- <br />
| style="width: 50%; vertical-align:top;"|<br />
<h1 style="margin-top: 0px;">A</h1><br />
__NOTOC__ <br />
[[APC Houses]]<br /><br />
[[Asanga]]<br /><br />
[[Ascendant-Parallelcirkelsysteem]] [[File:Dutch.gif]]<br/><br />
[[Astrologen doen maar wat]] [[File:Dutch.gif]]<br /><br />
[[Astrology]]<br /><br />
[[Authorship Attribution Method]], Applied to the Buddhist Scriptures of Ārya Asaṅga, A Statistical -<br />
<br />
=B=<br />
<br />
[[Buddhism]], some links<br /><br />
[[Book of Dzyan]] web site <br /><br />
[[Book of the Universe]] The, - (On Max Tegmark's Mathematical Universe Hypothesis)<br />
<br />
=C=<br />
<br />
[[Circle]], The -, or the Unreasonable Effectiveness of Mathematics<br /><br />
[[Contact]]<br /><br />
[[Cosmografie]] voor astrologen [[File:Dutch.gif]]<br /><br />
<br />
=D=<br />
<br />
[[Diagram of Meditation]] dictated by H.P. Blavatsky to E.T. Sturdy around 1887<br /><br />
[[Dierenriem]] [[File:Dutch.gif]]<br /><br />
[[Dzyan]], A Diagram on the Origin of the Book of -<br /><br />
<br />
=E=<br />
<br />
[[Eckhart]] De Drieheid: Johannes Eckhart, proeve van vertaling [[File:Dutch.gif]]<br />
<br />
=F=<br />
<br />
[[Facebook]] pages <br /><br />
[[Feynman]] Richard - (the physicist)<br /><br />
<br />
=G=<br />
<br />
=H=<br />
[[Hypothetische Planeten]], De posities van de - [[File:Dutch.gif]]<br /><br />
<br />
=I=<br />
<br />
=J=<br />
<br />
=K=<br />
<br />
#[[Kalacakra]] Notes on the chronology of the Kalacakratantra<br /><br />
[[Krisnamurti]]'s "keuzeloos gewaarzijn" [[File:Dutch.gif]] <br /><br />
<br />
=L=<br />
<br />
[[Labout]], L.W.J., tekening De Zeven Evolutiesystemen van het Zonnestelsel [[File:Dutch.gif]] <br><br />
[[Lamp]] Sri Ram, Een - te zijn voor jezelf: de praktijk van mindfulness [[File:Dutch.gif]] <br><br />
[[Licht van Azië]] (fragment om voor te lezen) [[File:Dutch.gif]] <br><br />
<br />
=M=<br />
<br />
=N=<br />
<br />
[[Natuurkunde in de theosofische literatuur]] [[File:Dutch.gif]]<br><br />
<br />
=O=<br />
<br />
=P=<br />
[[Pranavavada]] Manuscripts<br /><br />
<br />
=Q=<br />
<br />
=R=<br />
<br />
=S=<br />
[http://vps.ingmardeboer.nl Sanskrit Dictionary] Monier Williams and other DICT dictionaries<br /><br />
[[Secret Doctrine Articles|Secret Doctrine]] articles for the Book of Dzyan Blog<br /><br />
[[Semiotische driehoek]], De - [[File:Dutch.gif]]<br /><br />
[[Stem van de Stilte]], De Wereld achter het Werk [[File:Dutch.gif]]<br /><br />
<br />
=T=<br />
<br />
[[Theosophical History (Diagrams)]]<br /><br />
[[Thierens]] A.E., "founder of astrology in the Netherlands"<br /><br />
[[Topocentrische plaatsbepaling]] [[File:Dutch.gif]]<br><br />
[[Tree of Science]] Asking "Why, why, why?" or the -, on Richard Feynman and the advancement of science<br><br />
<br />
=U=<br />
<br />
[[Unicode]] transliteration standard for Sanskrit<br /><br />
<br />
=V=<br />
<br />
[[Verwondering]], Momenten van - [[File:Dutch.gif]]<br><br />
<br />
=W=<br />
[[Wiskunde]], Waarom is - zo'n effectief middel in het beschrijven van natuurkundige verschijnselen? [[File:Dutch.gif]]<br />
<br />
=Y=<br />
<br />
[[Yoga Sutra]]'s, Het hart van Patañjali's - [[File:Dutch.gif]]<br /><br />
<br />
=Z=</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Feynman&diff=1292Feynman2023-09-30T23:57:22Z<p>Ingmardb: Redirected page to Tree of Science</p>
<hr />
<div>#REDIRECT [[Tree of Science]]</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Main_Page&diff=1291Main Page2023-09-30T23:55:46Z<p>Ingmardb: </p>
<hr />
<div><p style="margin-top: 25px; margin-bottom: 20px;"><br />
[[#A|A]] [[#B|B]] [[#C|C]] [[#D|D]] [[#E|E]] [[#F|F]] [[#G|G]] [[#H|H]] [[#I|I]] [[#J|J]] [[#K|K]] [[#L|L]] [[#M|M]] [[#N|N]] [[#O|O]] [[#P|P]] [[#Q|Q]] [[#R|R]] [[#S|S]] [[#T|T]] [[#U|U]] [[#V|V]] [[#W|W]] [[#X|X]] [[#Y|Y]] [[#Z|Z]]<br />
</p><br />
{| cellpadding="10" cellspacing="10" style="background-color: #f4f4f4; border: 1px; border-color: #b4b4b4; border-style: outset; padding: 0px; margin-left: -2px; width: 80%;"<br />
|- <br />
| style="width: 50%; vertical-align:top;"|<br />
<h1 style="margin-top: 0px;">A</h1><br />
__NOTOC__ <br />
[[APC Houses]]<br /><br />
[[Asanga]]<br /><br />
[[Ascendant-Parallelcirkelsysteem]] [[File:Dutch.gif]]<br/><br />
[[Astrologen doen maar wat]] [[File:Dutch.gif]]<br /><br />
[[Astrology]]<br /><br />
[[Authorship Attribution Method]], Applied to the Buddhist Scriptures of Ārya Asaṅga, A Statistical -<br />
<br />
=B=<br />
<br />
[[Buddhism]], some links<br /><br />
[[Book of Dzyan]] web site <br /><br />
[[Book of the Universe]] The, - (On Max Tegmark's Mathematical Universe Hypothesis)<br />
<br />
=C=<br />
<br />
[[Circle]], The -, or the Unreasonable Effectiveness of Mathematics<br /><br />
[[Contact]]<br /><br />
[[Cosmografie]] voor astrologen [[File:Dutch.gif]]<br /><br />
<br />
=D=<br />
<br />
[[Diagram of Meditation]] dictated by H.P. Blavatsky to E.T. Sturdy around 1887<br /><br />
[[Dierenriem]] [[File:Dutch.gif]]<br /><br />
[[Dzyan]], A Diagram on the Origin of the Book of -<br /><br />
<br />
=E=<br />
<br />
[[Eckhart]] De Drieheid: Johannes Eckhart, proeve van vertaling [[File:Dutch.gif]]<br />
<br />
=F=<br />
<br />
[[Facebook]] pages <br /><br />
[[Feynman]] Richard - (the physicist)<br /><br />
<br />
=G=<br />
<br />
=H=<br />
[[Hypothetische Planeten]], De posities van de - [[File:Dutch.gif]]<br /><br />
<br />
=I=<br />
<br />
=J=<br />
<br />
=K=<br />
<br />
[[Kalacakra]] Notes on the chronology of the Kalacakratantra<br /><br />
[[Krisnamurti]]'s "keuzeloos gewaarzijn" [[File:Dutch.gif]] <br /><br />
<br />
=L=<br />
<br />
[[Labout]], L.W.J., tekening De Zeven Evolutiesystemen van het Zonnestelsel [[File:Dutch.gif]] <br><br />
[[Lamp]] Sri Ram, Een - te zijn voor jezelf: de praktijk van mindfulness [[File:Dutch.gif]] <br><br />
[[Licht van Azië]] (fragment om voor te lezen) [[File:Dutch.gif]] <br><br />
<br />
=M=<br />
<br />
=N=<br />
<br />
[[Natuurkunde in de theosofische literatuur]] [[File:Dutch.gif]]<br><br />
<br />
=O=<br />
<br />
=P=<br />
[[Pranavavada]] Manuscripts<br /><br />
<br />
=Q=<br />
<br />
=R=<br />
<br />
=S=<br />
[http://vps.ingmardeboer.nl Sanskrit Dictionary] Monier Williams and other DICT dictionaries<br /><br />
[[Secret Doctrine Articles|Secret Doctrine]] articles for the Book of Dzyan Blog<br /><br />
[[Semiotische driehoek]], De - [[File:Dutch.gif]]<br /><br />
[[Stem van de Stilte]], De Wereld achter het Werk [[File:Dutch.gif]]<br /><br />
<br />
=T=<br />
<br />
[[Theosophical History (Diagrams)]]<br /><br />
[[Thierens]] A.E., "founder of astrology in the Netherlands"<br /><br />
[[Topocentrische plaatsbepaling]] [[File:Dutch.gif]]<br><br />
[[Tree of Science]] Asking "Why, why, why?" or the -, on Richard Feynman and the advancement of science<br><br />
<br />
=U=<br />
<br />
[[Unicode]] transliteration standard for Sanskrit<br /><br />
<br />
=V=<br />
<br />
[[Verwondering]], Momenten van - [[File:Dutch.gif]]<br><br />
<br />
=W=<br />
[[Wiskunde]], Waarom is - zo'n effectief middel in het beschrijven van natuurkundige verschijnselen? [[File:Dutch.gif]]<br />
<br />
=Y=<br />
<br />
[[Yoga Sutra]]'s, Het hart van Patañjali's - [[File:Dutch.gif]]<br /><br />
<br />
=Z=</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Main_Page&diff=1290Main Page2023-09-30T23:55:14Z<p>Ingmardb: /* F */</p>
<hr />
<div><p style="margin-top: 25px; margin-bottom: 20px;"><br />
[[#A|A]] [[#B|B]] [[#C|C]] [[#D|D]] [[#E|E]] [[#F|F]] [[#G|G]] [[#H|H]] [[#I|I]] [[#J|J]] [[#K|K]] [[#L|L]] [[#M|M]] [[#N|N]] [[#O|O]] [[#P|P]] [[#Q|Q]] [[#R|R]] [[#S|S]] [[#T|T]] [[#U|U]] [[#V|V]] [[#W|W]] [[#X|X]] [[#Y|Y]] [[#Z|Z]]<br />
</p><br />
{| cellpadding="10" cellspacing="10" style="background-color: #f4f4f4; border: 1px; border-color: #b4b4b4; border-style: outset; padding: 0px; margin-left: -2px; width: 80%;"<br />
|- <br />
| style="width: 50%; vertical-align:top;"|<br />
<h1 style="margin-top: 0px;">A</h1><br />
__NOTOC__ <br />
[[APC Houses]]<br /><br />
[[Asanga]]<br /><br />
[[Ascendant-Parallelcirkelsysteem]] [[File:Dutch.gif]]<br/><br />
[[Astrologen doen maar wat]] [[File:Dutch.gif]]<br /><br />
[[Astrology]]<br /><br />
[[Authorship Attribution Method]], Applied to the Buddhist Scriptures of Ārya Asaṅga, A Statistical -<br />
<br />
=B=<br />
<br />
[[Buddhism]], some links<br /><br />
[[Book of Dzyan]] web site <br /><br />
[[Book of the Universe]] The, - (On Max Tegmark's Mathematical Universe Hypothesis)<br />
<br />
=C=<br />
<br />
[[Circle]], The -, or the Unreasonable Effectiveness of Mathematics<br /><br />
[[Contact]]<br /><br />
[[Cosmografie]] voor astrologen [[File:Dutch.gif]]<br /><br />
<br />
=D=<br />
<br />
[[Diagram of Meditation]] dictated by H.P. Blavatsky to E.T. Sturdy around 1887<br /><br />
[[Dierenriem]] [[File:Dutch.gif]]<br /><br />
[[Dzyan]], A Diagram on the Origin of the Book of -<br /><br />
<br />
=E=<br />
<br />
[[Eckhart]] De Drieheid: Johannes Eckhart, proeve van vertaling [[File:Dutch.gif]]<br />
<br />
=F=<br />
<br />
[[Facebook]] pages<br />
[[Feynman]] Richard - (the physicist)<br />
<br />
=G=<br />
<br />
=H=<br />
[[Hypothetische Planeten]], De posities van de - [[File:Dutch.gif]]<br /><br />
<br />
=I=<br />
<br />
=J=<br />
<br />
=K=<br />
<br />
[[Kalacakra]] Notes on the chronology of the Kalacakratantra<br /><br />
[[Krisnamurti]]'s "keuzeloos gewaarzijn" [[File:Dutch.gif]] <br /><br />
<br />
=L=<br />
<br />
[[Labout]], L.W.J., tekening De Zeven Evolutiesystemen van het Zonnestelsel [[File:Dutch.gif]] <br><br />
[[Lamp]] Sri Ram, Een - te zijn voor jezelf: de praktijk van mindfulness [[File:Dutch.gif]] <br><br />
[[Licht van Azië]] (fragment om voor te lezen) [[File:Dutch.gif]] <br><br />
<br />
=M=<br />
<br />
=N=<br />
<br />
[[Natuurkunde in de theosofische literatuur]] [[File:Dutch.gif]]<br><br />
<br />
=O=<br />
<br />
=P=<br />
[[Pranavavada]] Manuscripts<br /><br />
<br />
=Q=<br />
<br />
=R=<br />
<br />
=S=<br />
[http://vps.ingmardeboer.nl Sanskrit Dictionary] Monier Williams and other DICT dictionaries<br /><br />
[[Secret Doctrine Articles|Secret Doctrine]] articles for the Book of Dzyan Blog<br /><br />
[[Semiotische driehoek]], De - [[File:Dutch.gif]]<br /><br />
[[Stem van de Stilte]], De Wereld achter het Werk [[File:Dutch.gif]]<br /><br />
<br />
=T=<br />
<br />
[[Theosophical History (Diagrams)]]<br /><br />
[[Thierens]] A.E., "founder of astrology in the Netherlands"<br /><br />
[[Topocentrische plaatsbepaling]] [[File:Dutch.gif]]<br><br />
[[Tree of Science]] Asking "Why, why, why?" or the -, on Richard Feynman and the advancement of science<br><br />
<br />
=U=<br />
<br />
[[Unicode]] transliteration standard for Sanskrit<br /><br />
<br />
=V=<br />
<br />
[[Verwondering]], Momenten van - [[File:Dutch.gif]]<br><br />
<br />
=W=<br />
[[Wiskunde]], Waarom is - zo'n effectief middel in het beschrijven van natuurkundige verschijnselen? [[File:Dutch.gif]]<br />
<br />
=Y=<br />
<br />
[[Yoga Sutra]]'s, Het hart van Patañjali's - [[File:Dutch.gif]]<br /><br />
<br />
=Z=</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1289Tree of Science2023-09-30T23:52:53Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures [1]. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find [2]:<br />
<br />
<ul><i>I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.</i></ul><br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis [3]):<br />
<br />
<ul><i>For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.</i></ul><br />
<br />
<p style="margin-top: 30px; margin-bottom: 30px;"><br />
<gallery widths=300px heights=300px><br />
File:Mars-Sun-geocentric.png <br />
File:Mars-Sun-heliocentric.png <br />
</gallery><br />
</p><br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
<p style="margin-top: 30px; margin-bottom: 30px;"><br />
[[File:Trees.png|border|550px]]<br />
</p><br />
<br />
[[File:Arbor_-_1.png|right|border|240px]] In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència [4] already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning [5] (1605), and the enlarged Latin version of the same work De augmentis scientiarum [5] (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures [6], where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1288Tree of Science2023-09-30T23:51:55Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures [1]. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find [2]:<br />
<br />
<ul><i>I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.</i></ul><br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis [3]):<br />
<br />
<ul><i>For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.</i></ul><br />
<br />
<p style="margin-top: 30px; margin-bottom: 30px;"><br />
<gallery widths=350px heights=350px><br />
File:Mars-Sun-geocentric.png <br />
File:Mars-Sun-heliocentric.png <br />
</gallery><br />
</p><br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
<p style="margin-top: 30px; margin-bottom: 30px;"><br />
[[File:Trees.png|border|500px]]<br />
</p><br />
<br />
[[File:Arbor_-_1.png|right|border|240px]] In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència [4] already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning [5] (1605), and the enlarged Latin version of the same work De augmentis scientiarum [5] (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures [6], where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1287Tree of Science2023-09-30T23:51:04Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures [1]. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find [2]:<br />
<br />
<ul><i>I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.</i></ul><br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis [3]):<br />
<br />
<ul><i>For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.</i></ul><br />
<br />
<p style="margin-top: 30px; margin-bottom: 30px;"><br />
<gallery widths=350px heights=350px><br />
File:Mars-Sun-geocentric.png <br />
File:Mars-Sun-heliocentric.png <br />
</gallery><br />
</p><br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
[[File:Trees.png|border|500px]]<br />
<br />
[[File:Arbor_-_1.png|right|border|240px]] In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència [4] already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning [5] (1605), and the enlarged Latin version of the same work De augmentis scientiarum [5] (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures [6], where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1286Tree of Science2023-09-30T23:50:31Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures [1]. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find [2]:<br />
<br />
<ul><i>I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.</i></ul><br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis [3]):<br />
<br />
<ul><i>For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.</i></ul><br />
<br />
<p style="top: 20px; bottom: 20px;"><br />
<gallery widths=350px heights=350px><br />
File:Mars-Sun-geocentric.png <br />
File:Mars-Sun-heliocentric.png <br />
</gallery><br />
</p><br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
[[File:Trees.png|border|500px]]<br />
<br />
[[File:Arbor_-_1.png|right|border|240px]] In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència [4] already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning [5] (1605), and the enlarged Latin version of the same work De augmentis scientiarum [5] (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures [6], where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1285Tree of Science2023-09-30T23:49:19Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures [1]. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find [2]:<br />
<br />
<ul><i>I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.</i></ul><br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis [3]):<br />
<br />
<ul><i>For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.</i></ul><br />
<br />
<div><br />
<gallery widths=350px heights=350px><br />
File:Mars-Sun-geocentric.png <br />
File:Mars-Sun-heliocentric.png <br />
</gallery><br />
</div><br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
[[File:Trees.png|border|500px]]<br />
<br />
[[File:Arbor_-_1.png|right|border|240px]] In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència [4] already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning [5] (1605), and the enlarged Latin version of the same work De augmentis scientiarum [5] (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures [6], where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1284Tree of Science2023-09-30T23:48:56Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures [1]. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find [2]:<br />
<br />
<ul><i>I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.</i></ul><br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis [3]):<br />
<br />
<ul><i>For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.</i></ul><br />
<br />
<p><br />
<gallery widths=350px heights=350px><br />
File:Mars-Sun-geocentric.png <br />
File:Mars-Sun-heliocentric.png <br />
</gallery><br />
</p><br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
[[File:Trees.png|border|500px]]<br />
<br />
[[File:Arbor_-_1.png|right|border|240px]] In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència [4] already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning [5] (1605), and the enlarged Latin version of the same work De augmentis scientiarum [5] (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures [6], where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1283Tree of Science2023-09-30T23:48:04Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures [1]. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find [2]:<br />
<br />
<ul><i>I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.</i></ul><br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis [3]):<br />
<br />
<ul><i>For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.</i></ul><br />
<br />
<gallery widths=350px heights=350px><br />
File:Mars-Sun-geocentric.png <br />
File:Mars-Sun-heliocentric.png <br />
</gallery><br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
[[File:Trees.png|border|500px]]<br />
<br />
[[File:Arbor_-_1.png|right|border|240px]] In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència [4] already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning [5] (1605), and the enlarged Latin version of the same work De augmentis scientiarum [5] (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures [6], where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1282Tree of Science2023-09-30T23:46:30Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures [1]. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find [2]:<br />
<br />
<ul>I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.</ul><br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis [3]):<br />
<br />
<ul>For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.</ul><br />
<br />
<gallery widths=350px heights=350px><br />
File:Mars-Sun-geocentric.png <br />
File:Mars-Sun-heliocentric.png <br />
</gallery><br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
[[File:Trees.png|border|500px]]<br />
<br />
[[File:Arbor_-_1.png|right|border|240px]] In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència [4] already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning [5] (1605), and the enlarged Latin version of the same work De augmentis scientiarum [5] (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures [6], where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1281Tree of Science2023-09-30T23:41:16Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures1. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find2:<br />
<br />
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.<br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis3):<br />
<br />
For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.<br />
<br />
<gallery widths=350px heights=350px><br />
File:Mars-Sun-geocentric.png <br />
File:Mars-Sun-heliocentric.png <br />
</gallery><br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
[[File:Trees.png|border|500px]]<br />
<br />
[[File:Arbor_-_1.png|right|border|240px]] In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència4 already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning5 (1605), and the enlarged Latin version of the same work De augmentis scientiarum5 (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures6, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1280Tree of Science2023-09-30T23:40:42Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures1. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find2:<br />
<br />
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.<br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis3):<br />
<br />
For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.<br />
<br />
<gallery widths=350px heights=350px><br />
File:Mars-Sun-geocentric.png <br />
File:Mars-Sun-heliocentric.png <br />
</gallery><br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
[[File:Trees.png|border|500px]]<br />
<br />
[[File:Arbor_-_1.png|right|border|220px]] In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència4 already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning5 (1605), and the enlarged Latin version of the same work De augmentis scientiarum5 (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures6, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1279Tree of Science2023-09-30T23:39:22Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures1. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find2:<br />
<br />
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.<br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis3):<br />
<br />
For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.<br />
<br />
<gallery widths=350px heights=350px><br />
File:Mars-Sun-geocentric.png <br />
File:Mars-Sun-heliocentric.png <br />
</gallery><br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
[[File:Trees.png|border|600px]]<br />
<br />
[[File:Arbor_-_1.png|right|border|220px]] In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència4 already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning5 (1605), and the enlarged Latin version of the same work De augmentis scientiarum5 (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures6, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1278Tree of Science2023-09-30T23:35:45Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures1. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find2:<br />
<br />
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.<br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis3):<br />
<br />
For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.<br />
<br />
<gallery widths=400px heights=400px><br />
File:Mars-Sun-geocentric.png <br />
File:Mars-Sun-heliocentric.png <br />
</gallery><br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
[[File:Trees.png|border|800px]]<br />
<br />
In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència4 already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning5 (1605), and the enlarged Latin version of the same work De augmentis scientiarum5 (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures6, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1277Tree of Science2023-09-30T23:30:39Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures1. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find2:<br />
<br />
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.<br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis3):<br />
<br />
For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.<br />
<br />
[[File:Mars-Sun-geocentric.png|border|400px]][[File:Mars-Sun-heliocentric.png|border|400px]]<br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
[[File:Trees.png|border|800px]]<br />
<br />
In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència4 already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning5 (1605), and the enlarged Latin version of the same work De augmentis scientiarum5 (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures6, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1276Tree of Science2023-09-30T23:30:10Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures1. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find2:<br />
<br />
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.<br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis3):<br />
<br />
For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.<br />
<br />
[[File:Mars-Sun-geocentric.png|400px]][[File:Mars-Sun-heliocentric.png|400px]]<br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
[[File:Trees.png|border|800px]]<br />
<br />
In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència4 already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning5 (1605), and the enlarged Latin version of the same work De augmentis scientiarum5 (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures6, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1275Tree of Science2023-09-30T23:27:12Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures1. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find2:<br />
<br />
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.<br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis3):<br />
<br />
For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.<br />
<br />
[[File:Mars-Sun-geocentric.png|400px]][[File:Mars-Sun-heliocentric.png|400px]]<br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
[[File:Trees.png|800px|frame]]<br />
<br />
In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència4 already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning5 (1605), and the enlarged Latin version of the same work De augmentis scientiarum5 (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures6, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1274Tree of Science2023-09-30T23:25:27Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures1. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find2:<br />
<br />
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.<br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis3):<br />
<br />
For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.<br />
<br />
[[File:Mars-Sun-heliocentric.png|400px]][[File:Mars-Sun-geocentric.png|400px]]<br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
[[File:Trees.png|800px]]<br />
<br />
In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència4 already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning5 (1605), and the enlarged Latin version of the same work De augmentis scientiarum5 (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures6, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<small><br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
</small><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1273Tree of Science2023-09-30T23:23:08Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures1. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find2:<br />
<br />
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.<br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis3):<br />
<br />
For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.<br />
<br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
[[File:Mars-Sun-heliocentric.png|400px]][[File:Mars-Sun-geocentric.png|400px]]<br />
<br />
<br />
In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència4 already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning5 (1605), and the enlarged Latin version of the same work De augmentis scientiarum5 (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures6, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=File:Mars_retrograde_-_2.png&diff=1272File:Mars retrograde - 2.png2023-09-30T23:21:14Z<p>Ingmardb: </p>
<hr />
<div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=File:Mars-Sun-geocentric.png&diff=1271File:Mars-Sun-geocentric.png2023-09-30T23:17:30Z<p>Ingmardb: </p>
<hr />
<div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=File:Mars-Sun-heliocentric.png&diff=1270File:Mars-Sun-heliocentric.png2023-09-30T23:17:15Z<p>Ingmardb: </p>
<hr />
<div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=File:Trees.png&diff=1269File:Trees.png2023-09-30T23:15:38Z<p>Ingmardb: </p>
<hr />
<div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=File:Arbor_-_1.png&diff=1268File:Arbor - 1.png2023-09-30T23:14:00Z<p>Ingmardb: </p>
<hr />
<div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1267Tree of Science2023-09-30T22:42:53Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures1. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find2:<br />
<br />
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.<br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis3):<br />
<br />
For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.<br />
<br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
<br />
In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència4 already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning5 (1605), and the enlarged Latin version of the same work De augmentis scientiarum5 (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures6, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
<strong>Notes</strong><br />
<ol><br />
<li>Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
<li>In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
<li>Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
<li>Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
<li>Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
<li>In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
</ol><br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1266Tree of Science2023-09-30T22:41:46Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science ]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures1. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find2:<br />
<br />
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.<br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis3):<br />
<br />
For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.<br />
<br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
<br />
In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència4 already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning5 (1605), and the enlarged Latin version of the same work De augmentis scientiarum5 (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures6, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
Notes<br />
<br />
1. Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
2. In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
3. Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
4. Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
5. Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
6. In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
<br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1265Tree of Science2023-09-30T22:40:15Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or The Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or The Tree of Science (v. 3)]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures1. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find2:<br />
<br />
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.<br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis3):<br />
<br />
For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
<br />
In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència4 already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning5 (1605), and the enlarged Latin version of the same work De augmentis scientiarum5 (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures6, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
Notes<br />
<br />
1. Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
2. In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
3. Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
4. Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
5. Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
6. In the sixth lecture at 8:10. In my book on page 129. (see note 1)<br />
<br />
<br />
</div></div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1264Tree of Science2023-09-30T22:37:44Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or the Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
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* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or the Tree of Science (v. 3)]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures1. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find2:<br />
<br />
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.<br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis3):<br />
<br />
For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
<br />
In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència4 already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning5 (1605), and the enlarged Latin version of the same work De augmentis scientiarum5 (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures6, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
Notes<br />
<br />
1. Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
2. In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
3. Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
4. Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
5. Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
6. In the sixth lecture at 8:10. In my book on page 129. (see note 1)</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1263Tree of Science2023-09-30T22:37:26Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or the Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
{| class="wikitable" style="background-color: #ffffff; width: 100%;" <br />
|style="padding: 20px;"|<br />
* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or the Tree of Science (v. 3)]] [[File:Pdf3.gif]] <br />
|}__NOTOC__ <br />
<br />
Asking "Why, why, why?" or the Tree of Science (v. 3)<br />
<br />
Ingmar de Boer<br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures1. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find2:<br />
<br />
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.<br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis3):<br />
<br />
For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
<br />
In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència4 already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning5 (1605), and the enlarged Latin version of the same work De augmentis scientiarum5 (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures6, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
Notes<br />
<br />
1. Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
2. In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
3. Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
4. Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
5. Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
6. In the sixth lecture at 8:10. In my book on page 129. (see note 1)</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Tree_of_Science&diff=1262Tree of Science2023-09-30T22:37:07Z<p>Ingmardb: </p>
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<H1 style="margin-top: 0px;">Asking "Why, why, why?" or the Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
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Asking "Why, why, why?" or the Tree of Science (v. 3)<br />
<br />
Ingmar de Boer<br />
<br />
Richard Feynman explains to his student audience how they should go about integrating their newly acquired knowledge on quantum mechanics in the sixth of the 1964 series of lectures called the Messenger Lectures1. When he was asked in an interview how magnets attract or repel each other, he answers "they just do". We could ask "why, why, why" ad infinitum without being satisfied, he says. On other occasions he defends the position that science is about knowledge, about being able to make accurate predictions, and not about understanding. I will argue here, that from a more general perspective, this idea about science is not in accordance with historical reality and will most likely not be in the future.<br />
<br />
If we take a look at the history of science, we can see that in essence the great advancements in science amounted to a better understanding of nature. Describing or modelling reality is only a part of the process of scientific discovery. Understanding may be seen as being able to describe phenomena in terms of a more general model, and that seems to (temporarily) satisfy our need for understanding the world around us. Explaining and understanding may be seen as two sides of the same coin. Science is almost never fully experimental, although some scientists procaim it to be so. Generally, hypotheses are formulated using our understanding of what could be a better explanation than the one we already know, otherwise we would be condemned to blind guesswork, which would result in a very ineffective process of scientific discovery. <br />
<br />
One of the most well-known statements by Isaac Newton on this subject is made in the last scholium of the Principia (in the third edition of 1726), where he says that he "does not think up hypotheses", "Hypotheses non fingo". Often it is thought that he meant by this, that hypotheses should be built upon observations, but, interestingly, that is in contrast to what Newton actually declares in the scholium. In the 1999 translation by Cohen and Whitman we find2:<br />
<br />
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.<br />
<br />
Apparently Newton is of the opinion that empirical research is done on the basis of deduction instead of guessing. What he calls hypothesis here, is indeed no more than a guess, as it is thought up without any logical connection to the phenomena at hand. Having criticism of the old is easy, while creating the new is difficult, Feynman also remarks, and of course at first glance it seems he is right, certainly from his perspective, where guessing is the only possible option left. On the other hand, Newton makes it look like it should be possible to directly deduce the new from the old.<br />
<br />
We could take a look here at an example from the history of science, perhaps even the most significant in the whole of its history, of the shift from the geocentric to the heliocentric worldview, as it was presented by Nicolaus Copernicus in his work De revolutionibus orbium caelestium. (On the Revolutions of the Heavenly Spheres) How did he come up with his completely new view of the universe? First perhaps we should acknowledge that the heliocentric world view was not completely new at all. Apart from Claudius Ptolemy's Almagest, Copernicus studied ancient Greek texts speaking about the heliocentric worldview. In the days of Ptolemy however, heliocentrism was already controversial. Copernicus realised perfectly well how controversial his work would be in his day, but nevertheless he arranged the publication of the book, be it after his death. In his foreword he addressed Pope Paul III directly, explaining why he published it despite the controversy it would stir. In the foreword, his ideas are presented as a hypothesis, but in the chapters of the work itself, he shows that he is strongly convinced that the view he presents is the best explanation of the data which were at his disposal at the time.<br />
<br />
How could he be so sure that the earth was not at the centre of the universe if it was not on the basis of a proven hypothesis? In De revolutionibus he gives two "facts" which are "enough to show" that the centre of all known (then circular) planetary orbits is the sun, and not the earth. His first argument is the "apparent nonuniform motion of the planets" and the second is that their distance from the earth varies significantly. Both these observations are inconsistent with the sun and the planets moving in concentric circles around the earth. At that time there was no proper explanation for the retrograde movements of the planets, and it was unclear why the sun and moon did not show any retrograde movement. Also the differences between inner and outer planets were not properly understood. He writes (English translation by Charles Glen Wallis3):<br />
<br />
For [these outer planets] are always closest to the earth, as is well known, about the time of their evening rising, that is, when they are in opposition to the sun, with the earth between them and the sun. On the other hand, they are at their farthest from the earth at the time of their evening setting, when they become invisible in the vincinity of the sun, namely when we have the sun between them and the earth.<br />
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In the two figures above, we can see how Mars in the geocentric model always has more or less the same distance to the earth, while in the heliocentric model, the distance varies between the longest distance around the conjunction with the sun, and the shortest distance around the opposition, when Mars is in the middle of its retrograde movement. This behaviour can be explained by the heliocentric, but not with the geocentric model. There were enough data at his disposal, so that on the basis of these data Copernicus could deduce with great certainty that the heliocentric model was superior.<br />
<br />
However, at that time the predictive value of the heliocentric model did not surpass that of the Ptolemaean model: the results of its calculations were not particularly more accurate. Still, in our days we consider Copernicus' work the epitome of revolutionary scientific achievement. To cut it short, its significance lies in our better understanding of, in this case, the solar system. So what does it actually mean that we understand something? Is it perhaps some esoteric or unscientifc principle at work?<br />
<br />
Most people working in the area of natural science will be able to confirm that creating hypotheses is not just blind guesswork. Of course creating hypotheses is a complex process, but at least one clue to what may often be happening is actually given by Feynman himself, when he argues that one should not be using examples or analogies which explain a phenomenon in terms of something more commonly known to clarify physical phenomena, in particular in case of the "strange" phenomena of quantum mechanics. One of the ways science moves forward is that someone discovers that the model which is currently in use is wrong, often because it refers to known phenomena. We can think of many examples of this in the history of science, a simple one being the idea that objects only move when a force is exterted upon them, as for example Aristotle believed. Newton, in his First Law of Motion, states that objects without any force acting upon them will move with constant or zero velocity. The former idea has its origin in observing from a human perspective, living on the earth's surface, where objects are stopped by the earth when they are falling, or by its resistance when they are moving on its surface. This is often called an anthropocentric or humanocentric bias. Also in the case of Copernicus' discoveries the same principle is at work, in a most exemplary way. We could systematically search our present-day models for this type of bias, and try to take a different, universal, viewpoint, and try to cleanse physics from this type of models, and also in modern times scientists have done so. Discovering the too narrow-minded worldviews of today obviously presupposes specific abilities, which may not be present in all of us, or may perhaps be developed over time, but exactly those abilities served as a key ingredient for the most significant discoveries in the history of science. An important part of the advancement of science is apparently the careful examination of existing models, perhaps from a philosophical therapeutical standpoint, or perhaps even a psychological one. Of course there are more types of bias we can examine to learn about weak spots in the current way of looking at things.<br />
<br />
We can ask ourselves: how does science actually advance? Either by deduction or by hypothesis, what does it mean to better understand the world around us? We could think that perhaps explaining or understanding things leads to unification of models. If we are able to describe a phenomenon A in terms of phenomenon B, it makes a separate model of A superfluous, unifying the two models. This process eventually ends in a single "unified theory". Such a theory can be described in two dimensions as a Venn-diagram of collections, containing—but never crossing—each other. In three dimensions we can describe it as a tree, where the final unified theory is represented by the trunk, and the most fundamental problems as large branches. Alternatively, such a tree may be seen as a model of the history of science, or a superstructure of different areas of science. In the following figure, the analogy is shown of a Venn-diagram of collections containing each other, and a tree diagram.<br />
<br />
<br />
In the past, this idea has also been recognised by several early philosophers of science. For example, in 1297 the well-known Catalan philosopher and alchemist Ramon Llull, in his encyclopedic work l'Arbre de Ciència4 already described the interconnections of different areas of knowledge as a tree structure. A few centuries later, Francis Bacon, in The Advancement of Learning5 (1605), and the enlarged Latin version of the same work De augmentis scientiarum5 (1623), also compared science to a tree. He calls the trunk, the unified theory, the philosophiae prima, the primary philosophy, or the summary of philosophy.<br />
<br />
Particularly in natural science, development is driven by explaining effects in terms of their causes. Empirical research generally tries to produce effects by setting up presumed causes, and if in a certain number of a series of experiments the desired effect is produced, the principle of induction is called upon to declare that the presumed causes are indeed responsible for this effect. We may call this causal relation "proven", or we may say that the phenomenon is "explained". This basic process may also be characterised as answering a why-question. Why does the phenomenon take place, or what causes it? What we call natural science is essentially formed by asking why-questions, perhaps not ad infinitum as Feynman suggests, but repeatedly and systematically.<br />
<br />
Let us now return to Feynman's lecture. We have seen that some of the most important advances in science were decided by the criterium of having a better insight into the nature of things. They were primarily advancements in understanding. They were not so much based on guessing hypotheses, as they were on trying to correctly model the available data. Looking for explanations was the most important driving force, that is, asking the important why-questions. Now has this all changed with the advent of quantum mechanics in the twentieth century? What is going on in modern physics that our why-questions, our urge to understand things, is suddenly not good enough anymore? There is another quote from Feynman, perhaps his most well-known, from the same series of lectures6, where he says "I think I can safely say that nobody understands quantum mechanics". For him it is safe to say that, because as one of the greatest experts in the field he is well aware that quantum mechanics does not have a connection with a more abstract layer of knowledge, in terms of which it can be explained. It cannot be explained in terms of more familiar concepts, higher up in the tree of knowledge, but the trunk of physics, or a connection with any existing trunk, or "primary philosophy", is still to be found.<br />
<br />
Feynman, a Nobel-prize laureate, was indeed left with guessing hypotheses and was not able to deduce a new model from the available data or find a relevant bias to see through. His visible irritation with why-questions is a reflection of that, of his ambition, or his deep personal quest for the great answers.⏹<br />
<br />
Notes<br />
<br />
1. Videos of all seven Messenger Lectures held by Feynman at Cornell University in 1964 are to be found here: https://www.feynmanlectures.caltech.edu/messenger.html They were published as a book under the title The Character of Physical Law by British Broadcasting Corporation, 1965. My 2017 copy is by The MIT Press, and has ISBN 9780262533416.<br />
2. In the 1999 translation of Newton's Principia Mathematica by Cohen and Whitman, published as The Principia, Oakland: University of California Press, we find this quote on p. 589, and in the 974 page edition on p. 943. <br />
3. Nicolaus Copernicus (tr. C.G. Wallis), On the Revolutions of the Heavenly Spheres, Encyclopaedia Britannica, Chicago [etc.], [1955], p. 17-20. The Latin first edition is Nicolaus Copernicus, De revolutionibus omnium coelestium, Neurenberg: Johannes Petreius, 1543 ed., p. 7r-8v. "Constat enim propinquiores esse terrae semper circa vespertinum exortum, hoc est, quando Soli opponentur, mediante inter illos et Solem terra: remotissimus autem à terra occasu vespertino, quando circa Solem occultantur, dum videlicet inter eos atque terram Solem habemus." The diagram of the retrograde motion of Mars is taken from Johannes Kepler, Astronomia Nova, 1st ed. 1609, p. 4<br />
4. Ramon Llull, Arbor Scientiae, [1297] The tree is from the 1635 Leiden edition by Ioannes Pillehotte.<br />
5. Francis Bacon, The Advancement of Learning, 1605. The enlarged Latin version of the same work is De augmentis scientiarum, 1623. I used the Latin edition by Joannis Ravenstein, Amsterdam, 1662 ("Lib. IX"), where the fragment is to be found on pages 179-180.<br />
6. In the sixth lecture at 8:10. In my book on page 129. (see note 1)</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Book_of_the_Universe&diff=1261Book of the Universe2023-09-30T22:36:00Z<p>Ingmardb: </p>
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<H1 style="margin-top: 0px;">The Book of the Universe</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
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<i>Philosophy is written in this grand book, which is continually open before our eyes (I call it the Universe) but cannot be understood, if one does not first learn to understand the language, and knows the signs, in which it is written. It is written in the language of mathematics, and the signs are triangles, circles, and other geometrical figures, without which means it is humanly impossible to understand one word of it; without these, one is wandering through a dark labyrinth in vain.</i> (Galileo Galilei, in Il Saggiatore, p. 285 in the 1623 ed., Engl. IdB)<br />
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<ul><i>La Filoſofia è ſcritta in queſto grandiſſimo libro, che continuamente ci ſta aperto innanzi agli occhi (io dico l’ Univerſo) ma non ſi può intendere, ſe prima non s'impara a intender la lingua, e conoſcer i caratteri, ne' quali è ſcritto. Egli è ſcritto in lingua matematica, e i caratteri ſon triangoli, cerchi, ed altre figure Geometriche, ſenza i quali mezzi è impoſſibile intenderne umanamente parola; ſenza queſti è un aggirarſi vanamente per un oſcuro laberinto.</i></ul><br />
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<h3>Introduction</h3><br />
<br />
In his 1623 work Il Saggiatore (The Assayer), Galilei responds to various points of critique on his earlier work. The cited fragment is considered an important statement in the history of science, since it is thought to be the first time in history when the universe is seen as essentially "mathematical". Let us sum up the picture Galilei has painted for us.<br />
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<ol><br />
<li>The universe is compared metaphorically to a book in which philosophy is encoded.<br />
<li>The book can only be understood knowing its language, that of mathematics.<br />
<li>The signs of the language are geometrical figures.<br />
</ol><br />
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Due to this metaphore, this fragment seems to reflect at the same time two different opinions about mathematics, the first being the idea that mathematics is a language, and the second that mathematics is inherently part of reality itself. Further, we could argue that if mathematics is a language, it cannot be an inherent part of nature, since language originates in the human mind. It is part of culture instead of nature, and it depends entirely on collective agreements. It is therefore not part of "the world outside". Language is not discovered, but invented, or perhaps defined. Vice versa, if mathematics is embedded in reality, it cannot be a language, since in that case it originates in the outside world, and is discovered, instead of invented by man.<br />
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<h3>The Mathematical Universe</h3><br />
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In his 2014 work Our Mathematical Universe, as well as the 2007 article The Mathematical Universe, the sympathetic Max Tegmark is putting forward the same idea as Galilei. His theory is presented as the mathematical universe hypothesis (MUH), stating in brief, that "our external physical reality is a mathematical structure". (see p. 207 of the book) The problem here, is that the term "mathematical" is used loosely (and not metaphorically), not only as the language of mathematics, as the scientific area of research, but also as the order, the regularities found in nature. Structures in reality are strictly speaking not mathematical but physical structures, and the scientific discipline which studies them is called physics. For example, Tegmark speaks of symmetry as a mathematical property (p. 265), and of course in everyday speech we would call it that, but strictly speaking it is not a property of mathematics, but of physics. According to Tegmark, the definition of mathematics should be taken "broad enough" to encompass the whole of physical reality. (p. 271) He then goes even a step further when he says that everything which exists in mathematics should also exist in reality. This seems easily to be falsified by creating a mathematical fantasy which does not correspond to anything in any reality. However, if we predefine any mathematical reality as ontological reality, it becomes unfalsifiable, introducing an even greater problem. Again, it cannot be both at the same time.<br />
<br />
To support his argument he defines a hypothesis, the external reality hypothesis (ERH), which is "accepted by most but not all physicists". This is of course not completely true, if it were only because no physicist had heard of this hypothesis before Tegmark defined it himself. Further, it seems strange that "most but not all physicists" would "accept" a hypothesis without any proof: hypotheses are not things to be accepted, but things to be proven or disproven. Obviously this is again a loose way of formulating.<br />
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In mainstream western philosophy there has been an ancient debate about the existence or non-existence of external reality. In physics however, the existence of external reality is not generally put up for discussion. One reason for this is, not that physicists are accepting a hypothesis without proof, but that physicists usually leave this kind of problems to philosophers, and that philosophy's judgement on the "mind-only" world is not very favourable. Solipsism, as it is called there, is often seen as an untenable or particularly unproductive worldview, and for that reason it does not attract a lot of interest from philosophers today. <br />
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Another reason for not doubting external reality in physics, is related to the essence of natural science itself. The larger problem which is the reason of existence of natural sciences is that external reality is only known to us by the grace of the senses, and not by mathematical discovery or imagination. This is why we have to measure things in the external world and design experiments to discover relations between what we have measured. These relations are strictly speaking, again, not mathematical but physical, however there is perhaps a case to be made for calling these both mathematical and physical. Summarising: if the universe was really "mathematical", there would not have existed any form of natural science, neither would there have been any need for it.<br />
<br />
<h3>The World Described by a Subset of Possible Descriptions</h3><br />
<br />
Let us return to the point of view that mathematics would be a language. What can be said in most languages is much more than what we can perceive, or vice versa: reality corresponds to only a subset of what we can describe. For example, we can state that Edward is the son of Henry and Jane as well as of Albert and Victoria, but it is clear that if we are speaking of the same Edward, this cannot be true. Nevertheless, as a sentence there is nothing wrong with it. The language of mathematics is in that respect not different from natural languages, as it is also able to describe much more than what could exist in reality. <br />
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A telling example in natural science is the mathematical invention of complex numbers. In technical applications complex numbers seem to function well, and they are even very important in many areas of physics and engineering, but we do not have any idea what they refer to in reality. A "physicalist" would perhaps argue that as long as we are not able to investigate their reality by means of the methods of natural science, they cannot be real. They do exist in mathematics but do not have any counterpart in reality. For this reason physicists have investigated if the use complex numbers (or at least their imaginary parts) might be eliminated from physics.<br />
<br />
<h3>Platonism in Mathematics</h3><br />
<br />
Following the 1934 lecture by Paul Bernays Sur le platonisme dans les mathematiques, the term Platonism is used (in a strict or less strict sense) in western philosophy to indicate the idea that mathematical entities exist in reality. In fact, in the English version of the article produced from the lecture text, Bernays formulates it as follows:<br />
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<ul><i>[...] the tendency of which we are speaking consists in viewing the objects as cut off from all links with the reflecting subject. Since this tendency asserted itself especially in the philosophy of Plato, allow me to call it "platonism".</i></ul><br />
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The term does not do justice to the great philosopher, since his thoughts about mathematics were probably almost the exact opposite of what Bernays is suggesting here. According to the actual Platonists, mathematics belonged primarily to the "world of ideas", which is not an objective world which is "cut off from the reflecting subject". Around 2000 years later, Immanuel Kant also interpreted this the same way: in chapter I.2.1.2.3 of his Kritik der Reinen Vernunft, he associates the world of ideas, the noumenal, with the domain of reason. <br />
<br />
On the other hand, we know the discoveries of mathematics are not only subjective in nature. Mathematics is not based on introspection in the sense that its discoveries are only of value to the person who observes them in his own subjective inner world. This duality between "inner" knowledge and objectivity makes the status of mathematics as a science hard to understand, at least at first glance. We may think that the progression of neuroscience can shed definitive light on this.<br />
<br />
<h3>The Structure of Reality</h3><br />
<br />
Perhaps things will become clearer if we investigate the role of mathematics in more detail here. Despite Galilei's sincere argument, actual triangles or circles are not found in nature. The language of geometry, of triangles and circles—or anything else we have learnt for that matter—may serve as a tool to model natural phenomena, but they cannot be building blocks of the phenomenal world, since they do not exist in that world. If one considers triangles and circles to be parts of a language, of geometry, and not of reality, then mathematics should also be considered to be a type of language, or perhaps a set of modelling tools, but not the structure of reality. The structure of the universe is therefore not "mathematical". Mathematics is a way for us to perceive, analyse, or define the structure of reality. Certainly, we should not be calling something mathematics/mathematical from now on, which has been called physics/physical for centuries, and think that that in itself will solve any fundamental problems.<br />
<br />
In a sense, we could even consider mathematics the only way to describe the stable connections between quantities, that we call laws of nature. Without language or modelling tools, we cannot describe nature. This means that we can only discover the laws of nature if they satisfy certain conditions. That is one aspect of why it seems that mathematics is a surprisingly appropriate language to describe nature. We can only perceive that reality which is "mathematical", because we see our way of understanding things reflected in everything we perceive. We could not perceive nature if it was "unmathematical", and it could not exist to us. In the words of Ludwig Wittgenstein's Tractatus:<br />
<ul><i><br />
4.113 Philosophy sets limits to the much disputed sphere of natural science.<br><br />
4.114 It must set limits to what can be thought; and, in doing so, to what cannot be thought. It must set limits to what cannot be thought by working outwards through what can be thought.<br><br />
4.115 It will signify what cannot be said, by presenting clearly what can be said. <br></i> <br />
<br />
<ul><i><br />
4.113 Die Philosophie begrenzt das bestreitbare Gebiet der Naturwissenschaft. <br><br />
4.114 Sie soll das Denkbare abgrenzen und damit das Undenkbare. Sie soll das Undenkbare von innen durch das Denkbare begrenzen. <br><br />
4.115 Sie wird das Unsagbare bedeuten, indem sie das Sagbare klar darstellt.<br />
</i></ul><br />
</ul><br />
<br />
<h3>Conclusion</h3><br />
<br />
The universe is physical, and our mind is perhaps "mathematical". The physical universe is made up of physical structures which may be described using mathematical structures. If we think that there is a way for our subjective consciousness to be one with objective reality, as is in a sense presupposed yoga philosophy and other forms of mysticism, then we might have to dramatically change our ideas about the external world. Perhaps Tegmark moves very subtly into that direction in his book, but before embracing those or similar ideas, it remains important that the difference between the internal and external world is respected, or at least taken into consideration, in order to be philosophically correct, which is of course in turn physically correct. ●</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Book_of_the_Universe&diff=1260Book of the Universe2023-09-30T22:34:44Z<p>Ingmardb: </p>
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<H1 style="margin-top: 0px;">The Book of the Universe</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
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<i>Philosophy is written in this grand book, which is continually open before our eyes (I call it the Universe) but cannot be understood, if one does not first learn to understand the language, and knows the signs, in which it is written. It is written in the language of mathematics, and the signs are triangles, circles, and other geometrical figures, without which means it is humanly impossible to understand one word of it; without these, one is wandering through a dark labyrinth in vain.</i> (Galileo Galilei, in Il Saggiatore, p. 285 in the 1623 ed., Engl. IdB)<br />
<br />
<ul><i>La Filoſofia è ſcritta in queſto grandiſſimo libro, che continuamente ci ſta aperto innanzi agli occhi (io dico l’ Univerſo) ma non ſi può intendere, ſe prima non s'impara a intender la lingua, e conoſcer i caratteri, ne' quali è ſcritto. Egli è ſcritto in lingua matematica, e i caratteri ſon triangoli, cerchi, ed altre figure Geometriche, ſenza i quali mezzi è impoſſibile intenderne umanamente parola; ſenza queſti è un aggirarſi vanamente per un oſcuro laberinto.</i></ul><br />
<br />
<h3>Introduction</h3><br />
<br />
In his 1623 work Il Saggiatore (The Assayer), Galilei responds to various points of critique on his earlier work. The cited fragment is considered an important statement in the history of science, since it is thought to be the first time in history when the universe is seen as essentially "mathematical". Let us sum up the picture Galilei has painted for us.<br />
<br />
<ol><br />
<li>The universe is compared metaphorically to a book in which philosophy is encoded.<br />
<li>The book can only be understood knowing its language, that of mathematics.<br />
<li>The signs of the language are geometrical figures.<br />
</ol><br />
<br />
Due to this metaphore, this fragment seems to reflect at the same time two different opinions about mathematics, the first being the idea that mathematics is a language, and the second that mathematics is inherently part of reality itself. Further, we could argue that if mathematics is a language, it cannot be an inherent part of nature, since language originates in the human mind. It is part of culture instead of nature, and it depends entirely on collective agreements. It is therefore not part of "the world outside". Language is not discovered, but invented, or perhaps defined. Vice versa, if mathematics is embedded in reality, it cannot be a language, since in that case it originates in the outside world, and is discovered, instead of invented by man.<br />
<br />
<h3>The Mathematical Universe</h3><br />
<br />
In his 2014 work Our Mathematical Universe, as well as the 2007 article The Mathematical Universe, the sympathetic Max Tegmark is putting forward the same idea as Galilei. His theory is presented as the mathematical universe hypothesis (MUH), stating in brief, that "our external physical reality is a mathematical structure". (see p. 207 of the book) The problem here, is that the term "mathematical" is used loosely (and not metaphorically), not only as the language of mathematics, as the scientific area of research, but also as the order, the regularities found in nature. Structures in reality are strictly speaking not mathematical but physical structures, and the scientific discipline which studies them is called physics. For example, Tegmark speaks of symmetry as a mathematical property (p. 265), and of course in everyday speech we would call it that, but strictly speaking it is not a property of mathematics, but of physics. According to Tegmark, the definition of mathematics should be taken "broad enough" to encompass the whole of physical reality. (p. 271) He then goes even a step further when he says that everything which exists in mathematics should also exist in reality. This seems easily to be falsified by creating a mathematical fantasy which does not correspond to anything in any reality. However, if we predefine any mathematical reality as ontological reality, it becomes unfalsifiable, introducing an even greater problem. Again, it cannot be both at the same time.<br />
<br />
To support his argument he defines a hypothesis, the external reality hypothesis (ERH), which is "accepted by most but not all physicists". This is of course not completely true, if it were only because no physicist had heard of this hypothesis before Tegmark defined it himself. Further, it seems strange that "most but not all physicists" would "accept" a hypothesis without any proof: hypotheses are not things to be accepted, but things to be proven or disproven. Obviously this is again a loose way of formulating.<br />
<br />
In mainstream western philosophy there has been an ancient debate about the existence or non-existence of external reality. In physics however, the existence of external reality is not generally put up for discussion. One reason for this is, not that physicists are accepting a hypothesis without proof, but that physicists usually leave this kind of problems to philosophers, and that philosophy's judgement on the "mind-only" world is not very favourable. Solipsism, as it is called there, is often seen as an untenable or particularly unproductive worldview, and for that reason it does not attract a lot of interest from philosophers today. <br />
<br />
Another reason for not doubting external reality in physics, is related to the essence of natural science itself. The larger problem which is the reason of existence of natural sciences is that external reality is only known to us by the grace of the senses, and not by mathematical discovery or imagination. This is why we have to measure things in the external world and design experiments to discover relations between what we have measured. These relations are strictly speaking, again, not mathematical but physical, however there is perhaps a case to be made for calling these both mathematical and physical. Summarising: if the universe was really "mathematical", there would not have existed any form of natural science, neither would there have been any need for it.<br />
<br />
<h3>The World Described by a Subset of Possible Descriptions</h3><br />
<br />
Let us return to the point of view that mathematics would be a language. What can be said in most languages is much more than what we can perceive, or vice versa: reality corresponds to only a subset of what we can describe. For example, we can state that Edward is the son of Henry and Jane as well as of Albert and Victoria, but it is clear that if we are speaking of the same Edward, this cannot be true. Nevertheless, as a sentence there is nothing wrong with it. The language of mathematics is in that respect not different from natural languages, as it is also able to describe much more than what could exist in reality. <br />
<br />
A telling example in natural science is the mathematical invention of complex numbers. In technical applications complex numbers seem to function well, and they are even very important in many areas of physics and engineering, but we do not have any idea what they refer to in reality. A "physicalist" would perhaps argue that as long as we are not able to investigate their reality by means of the methods of natural science, they cannot be real. They do exist in mathematics but do not have any counterpart in reality. For this reason physicists have investigated if the use complex numbers (or at least their imaginary parts) might be eliminated from physics.<br />
<br />
<h3>Platonism in Mathematics</h3><br />
<br />
Following the 1934 lecture by Paul Bernays Sur le platonisme dans les mathematiques, the term Platonism is used (in a strict or less strict sense) in western philosophy to indicate the idea that mathematical entities exist in reality. In fact, in the English version of the article produced from the lecture text, Bernays formulates it as follows:<br />
<br />
<ul><i>[...] the tendency of which we are speaking consists in viewing the objects as cut off from all links with the reflecting subject. Since this tendency asserted itself especially in the philosophy of Plato, allow me to call it "platonism".</i></ul><br />
<br />
The term does not do justice to the great philosopher, since his thoughts about mathematics were probably almost the exact opposite of what Bernays is suggesting here. According to the actual Platonists, mathematics belonged primarily to the "world of ideas", which is not an objective world which is "cut off from the reflecting subject". Around 2000 years later, Immanuel Kant also interpreted this the same way: in chapter I.2.1.2.3 of his Kritik der Reinen Vernunft, he associates the world of ideas, the noumenal, with the domain of reason. <br />
<br />
On the other hand, we know the discoveries of mathematics are not only subjective in nature. Mathematics is not based on introspection in the sense that its discoveries are only of value to the person who observes them in his own subjective inner world. This duality between "inner" knowledge and objectivity makes the status of mathematics as a science hard to understand, at least at first glance. We may think that the progression of neuroscience can shed definitive light on this.<br />
<br />
<h3>The Structure of Reality</h3><br />
<br />
Perhaps things will become clearer if we investigate the role of mathematics in more detail here. Despite Galilei's sincere argument, actual triangles or circles are not found in nature. The language of geometry, of triangles and circles—or anything else we have learnt for that matter—may serve as a tool to model natural phenomena, but they cannot be building blocks of the phenomenal world, since they do not exist in that world. If one considers triangles and circles to be parts of a language, of geometry, and not of reality, then mathematics should also be considered to be a type of language, or perhaps a set of modelling tools, but not the structure of reality. The structure of the universe is therefore not "mathematical". Mathematics is a way for us to perceive, analyse, or define the structure of reality. Certainly, we should not be calling something mathematics/mathematical from now on, which has been called physics/physical for centuries, and think that that in itself will solve any fundamental problems.<br />
<br />
In a sense, we could even consider mathematics the only way to describe the stable connections between quantities, that we call laws of nature. Without language or modelling tools, we cannot describe nature. This means that we can only discover the laws of nature if they satisfy certain conditions. That is one aspect of why it seems that mathematics is a surprisingly appropriate language to describe nature. We can only perceive that reality which is "mathematical", because we see our way of understanding things reflected in everything we perceive. We could not perceive nature if it was "unmathematical", and it could not exist to us. In the words of Ludwig Wittgenstein's Tractatus:<br />
<ul><i><br />
4.113 Philosophy sets limits to the much disputed sphere of natural science.<br><br />
4.114 It must set limits to what can be thought; and, in doing so, to what cannot be thought. It must set limits to what cannot be thought by working outwards through what can be thought.<br><br />
4.115 It will signify what cannot be said, by presenting clearly what can be said. <br></i> <br />
<br />
<ul><i><br />
4.113 Die Philosophie begrenzt das bestreitbare Gebiet der Naturwissenschaft. <br><br />
4.114 Sie soll das Denkbare abgrenzen und damit das Undenkbare. Sie soll das Undenkbare von innen durch das Denkbare begrenzen. <br><br />
4.115 Sie wird das Unsagbare bedeuten, indem sie das Sagbare klar darstellt.<br />
</i></ul><br />
</ul><br />
<br />
<h3>Conclusion</h3><br />
<br />
The universe is physical, and our mind is perhaps "mathematical". The physical universe is made up of physical structures which may be described using mathematical structures. If we think that there is a way for our subjective consciousness to be one with objective reality, as is in a sense presupposed yoga philosophy and other forms of mysticism, then we might have to dramatically change our ideas about the external world. Perhaps Tegmark moves very subtly into that direction in his book, but before embracing those or similar ideas, it remains important that the difference between the internal and external world is respected, or at least taken into consideration, in order to be philosophically correct, which is of course in turn physically correct. ●</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=Book_of_the_Universe&diff=1259Book of the Universe2023-09-30T22:34:12Z<p>Ingmardb: </p>
<hr />
<div><div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;"><br />
<H1 style="margin-top: 0px;">Asking "Why, why, why?" or the Tree of Science</H1><br />
<small>Ingmar de Boer, v. 3</small><br><br />
<br />
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<br />
<i>Philosophy is written in this grand book, which is continually open before our eyes (I call it the Universe) but cannot be understood, if one does not first learn to understand the language, and knows the signs, in which it is written. It is written in the language of mathematics, and the signs are triangles, circles, and other geometrical figures, without which means it is humanly impossible to understand one word of it; without these, one is wandering through a dark labyrinth in vain.</i> (Galileo Galilei, in Il Saggiatore, p. 285 in the 1623 ed., Engl. IdB)<br />
<br />
<ul><i>La Filoſofia è ſcritta in queſto grandiſſimo libro, che continuamente ci ſta aperto innanzi agli occhi (io dico l’ Univerſo) ma non ſi può intendere, ſe prima non s'impara a intender la lingua, e conoſcer i caratteri, ne' quali è ſcritto. Egli è ſcritto in lingua matematica, e i caratteri ſon triangoli, cerchi, ed altre figure Geometriche, ſenza i quali mezzi è impoſſibile intenderne umanamente parola; ſenza queſti è un aggirarſi vanamente per un oſcuro laberinto.</i></ul><br />
<br />
<h3>Introduction</h3><br />
<br />
In his 1623 work Il Saggiatore (The Assayer), Galilei responds to various points of critique on his earlier work. The cited fragment is considered an important statement in the history of science, since it is thought to be the first time in history when the universe is seen as essentially "mathematical". Let us sum up the picture Galilei has painted for us.<br />
<br />
<ol><br />
<li>The universe is compared metaphorically to a book in which philosophy is encoded.<br />
<li>The book can only be understood knowing its language, that of mathematics.<br />
<li>The signs of the language are geometrical figures.<br />
</ol><br />
<br />
Due to this metaphore, this fragment seems to reflect at the same time two different opinions about mathematics, the first being the idea that mathematics is a language, and the second that mathematics is inherently part of reality itself. Further, we could argue that if mathematics is a language, it cannot be an inherent part of nature, since language originates in the human mind. It is part of culture instead of nature, and it depends entirely on collective agreements. It is therefore not part of "the world outside". Language is not discovered, but invented, or perhaps defined. Vice versa, if mathematics is embedded in reality, it cannot be a language, since in that case it originates in the outside world, and is discovered, instead of invented by man.<br />
<br />
<h3>The Mathematical Universe</h3><br />
<br />
In his 2014 work Our Mathematical Universe, as well as the 2007 article The Mathematical Universe, the sympathetic Max Tegmark is putting forward the same idea as Galilei. His theory is presented as the mathematical universe hypothesis (MUH), stating in brief, that "our external physical reality is a mathematical structure". (see p. 207 of the book) The problem here, is that the term "mathematical" is used loosely (and not metaphorically), not only as the language of mathematics, as the scientific area of research, but also as the order, the regularities found in nature. Structures in reality are strictly speaking not mathematical but physical structures, and the scientific discipline which studies them is called physics. For example, Tegmark speaks of symmetry as a mathematical property (p. 265), and of course in everyday speech we would call it that, but strictly speaking it is not a property of mathematics, but of physics. According to Tegmark, the definition of mathematics should be taken "broad enough" to encompass the whole of physical reality. (p. 271) He then goes even a step further when he says that everything which exists in mathematics should also exist in reality. This seems easily to be falsified by creating a mathematical fantasy which does not correspond to anything in any reality. However, if we predefine any mathematical reality as ontological reality, it becomes unfalsifiable, introducing an even greater problem. Again, it cannot be both at the same time.<br />
<br />
To support his argument he defines a hypothesis, the external reality hypothesis (ERH), which is "accepted by most but not all physicists". This is of course not completely true, if it were only because no physicist had heard of this hypothesis before Tegmark defined it himself. Further, it seems strange that "most but not all physicists" would "accept" a hypothesis without any proof: hypotheses are not things to be accepted, but things to be proven or disproven. Obviously this is again a loose way of formulating.<br />
<br />
In mainstream western philosophy there has been an ancient debate about the existence or non-existence of external reality. In physics however, the existence of external reality is not generally put up for discussion. One reason for this is, not that physicists are accepting a hypothesis without proof, but that physicists usually leave this kind of problems to philosophers, and that philosophy's judgement on the "mind-only" world is not very favourable. Solipsism, as it is called there, is often seen as an untenable or particularly unproductive worldview, and for that reason it does not attract a lot of interest from philosophers today. <br />
<br />
Another reason for not doubting external reality in physics, is related to the essence of natural science itself. The larger problem which is the reason of existence of natural sciences is that external reality is only known to us by the grace of the senses, and not by mathematical discovery or imagination. This is why we have to measure things in the external world and design experiments to discover relations between what we have measured. These relations are strictly speaking, again, not mathematical but physical, however there is perhaps a case to be made for calling these both mathematical and physical. Summarising: if the universe was really "mathematical", there would not have existed any form of natural science, neither would there have been any need for it.<br />
<br />
<h3>The World Described by a Subset of Possible Descriptions</h3><br />
<br />
Let us return to the point of view that mathematics would be a language. What can be said in most languages is much more than what we can perceive, or vice versa: reality corresponds to only a subset of what we can describe. For example, we can state that Edward is the son of Henry and Jane as well as of Albert and Victoria, but it is clear that if we are speaking of the same Edward, this cannot be true. Nevertheless, as a sentence there is nothing wrong with it. The language of mathematics is in that respect not different from natural languages, as it is also able to describe much more than what could exist in reality. <br />
<br />
A telling example in natural science is the mathematical invention of complex numbers. In technical applications complex numbers seem to function well, and they are even very important in many areas of physics and engineering, but we do not have any idea what they refer to in reality. A "physicalist" would perhaps argue that as long as we are not able to investigate their reality by means of the methods of natural science, they cannot be real. They do exist in mathematics but do not have any counterpart in reality. For this reason physicists have investigated if the use complex numbers (or at least their imaginary parts) might be eliminated from physics.<br />
<br />
<h3>Platonism in Mathematics</h3><br />
<br />
Following the 1934 lecture by Paul Bernays Sur le platonisme dans les mathematiques, the term Platonism is used (in a strict or less strict sense) in western philosophy to indicate the idea that mathematical entities exist in reality. In fact, in the English version of the article produced from the lecture text, Bernays formulates it as follows:<br />
<br />
<ul><i>[...] the tendency of which we are speaking consists in viewing the objects as cut off from all links with the reflecting subject. Since this tendency asserted itself especially in the philosophy of Plato, allow me to call it "platonism".</i></ul><br />
<br />
The term does not do justice to the great philosopher, since his thoughts about mathematics were probably almost the exact opposite of what Bernays is suggesting here. According to the actual Platonists, mathematics belonged primarily to the "world of ideas", which is not an objective world which is "cut off from the reflecting subject". Around 2000 years later, Immanuel Kant also interpreted this the same way: in chapter I.2.1.2.3 of his Kritik der Reinen Vernunft, he associates the world of ideas, the noumenal, with the domain of reason. <br />
<br />
On the other hand, we know the discoveries of mathematics are not only subjective in nature. Mathematics is not based on introspection in the sense that its discoveries are only of value to the person who observes them in his own subjective inner world. This duality between "inner" knowledge and objectivity makes the status of mathematics as a science hard to understand, at least at first glance. We may think that the progression of neuroscience can shed definitive light on this.<br />
<br />
<h3>The Structure of Reality</h3><br />
<br />
Perhaps things will become clearer if we investigate the role of mathematics in more detail here. Despite Galilei's sincere argument, actual triangles or circles are not found in nature. The language of geometry, of triangles and circles—or anything else we have learnt for that matter—may serve as a tool to model natural phenomena, but they cannot be building blocks of the phenomenal world, since they do not exist in that world. If one considers triangles and circles to be parts of a language, of geometry, and not of reality, then mathematics should also be considered to be a type of language, or perhaps a set of modelling tools, but not the structure of reality. The structure of the universe is therefore not "mathematical". Mathematics is a way for us to perceive, analyse, or define the structure of reality. Certainly, we should not be calling something mathematics/mathematical from now on, which has been called physics/physical for centuries, and think that that in itself will solve any fundamental problems.<br />
<br />
In a sense, we could even consider mathematics the only way to describe the stable connections between quantities, that we call laws of nature. Without language or modelling tools, we cannot describe nature. This means that we can only discover the laws of nature if they satisfy certain conditions. That is one aspect of why it seems that mathematics is a surprisingly appropriate language to describe nature. We can only perceive that reality which is "mathematical", because we see our way of understanding things reflected in everything we perceive. We could not perceive nature if it was "unmathematical", and it could not exist to us. In the words of Ludwig Wittgenstein's Tractatus:<br />
<ul><i><br />
4.113 Philosophy sets limits to the much disputed sphere of natural science.<br><br />
4.114 It must set limits to what can be thought; and, in doing so, to what cannot be thought. It must set limits to what cannot be thought by working outwards through what can be thought.<br><br />
4.115 It will signify what cannot be said, by presenting clearly what can be said. <br></i> <br />
<br />
<ul><i><br />
4.113 Die Philosophie begrenzt das bestreitbare Gebiet der Naturwissenschaft. <br><br />
4.114 Sie soll das Denkbare abgrenzen und damit das Undenkbare. Sie soll das Undenkbare von innen durch das Denkbare begrenzen. <br><br />
4.115 Sie wird das Unsagbare bedeuten, indem sie das Sagbare klar darstellt.<br />
</i></ul><br />
</ul><br />
<br />
<h3>Conclusion</h3><br />
<br />
The universe is physical, and our mind is perhaps "mathematical". The physical universe is made up of physical structures which may be described using mathematical structures. If we think that there is a way for our subjective consciousness to be one with objective reality, as is in a sense presupposed yoga philosophy and other forms of mysticism, then we might have to dramatically change our ideas about the external world. Perhaps Tegmark moves very subtly into that direction in his book, but before embracing those or similar ideas, it remains important that the difference between the internal and external world is respected, or at least taken into consideration, in order to be philosophically correct, which is of course in turn physically correct. ●</div>Ingmardbhttp://www.ingmardeboer.nl/index.php?title=File:Tree_of_Science_-_3.pdf&diff=1258File:Tree of Science - 3.pdf2023-09-30T22:33:43Z<p>Ingmardb: </p>
<hr />
<div></div>Ingmardb