Book of the Universe - Revision history

Ingmardb at 22:36, 30 September 2023

2023-09-30T22:36:00Z

Ingmardb at 22:34, 30 September 2023

2023-09-30T22:34:44Z

Ingmardb at 22:34, 30 September 2023

2023-09-30T22:34:12Z

Ingmardb at 15:17, 27 September 2022

2022-09-27T15:17:29Z

Ingmardb at 13:52, 27 September 2022

2022-09-27T13:52:50Z

Ingmardb at 13:51, 27 September 2022

2022-09-27T13:51:33Z

Ingmardb at 13:50, 27 September 2022

2022-09-27T13:50:34Z

Ingmardb at 13:49, 27 September 2022

2022-09-27T13:49:18Z

Ingmardb at 13:47, 27 September 2022

2022-09-27T13:47:31Z

Show changes

Ingmardb at 13:43, 27 September 2022

2022-09-27T13:43:30Z

@@ Line 5: / Line 5: @@
 {| class="wikitable" style="background-color: #ffffff; width: 100%;"
 |style="padding: 20px;"|
-* Download: [[Media:The_Book_of_the_Universe_-_3.pdf | Asking "Why, why, why?" or the Tree of Science (v. 3)]]  [[File:Pdf3.gif]]
+* Download: [[Media:The_Book_of_the_Universe_-_3.pdf | The Book of the Universe (v. 3)]]  [[File:Pdf3.gif]]
 |}__NOTOC__

@@ Line 1: / Line 1: @@
 <div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;">
-<H1 style="margin-top: 0px;">Asking "Why, why, why?" or the Tree of Science</H1>
+<H1 style="margin-top: 0px;">The Book of the Universe</H1>
 <small>Ingmar de Boer, v. 3</small><br>
 {| class="wikitable" style="background-color: #ffffff; width: 100%;"
 |style="padding: 20px;"|
-* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or the Tree of Science (v. 3)]]  [[File:Pdf3.gif]]
+* Download: [[Media:The_Book_of_the_Universe_-_3.pdf | Asking "Why, why, why?" or the Tree of Science (v. 3)]]  [[File:Pdf3.gif]]
 |}__NOTOC__

@@ Line 1: / Line 1: @@
 <div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;">
-<H1 style="margin-top: 0px;">The Book of the Universe</H1>
+<H1 style="margin-top: 0px;">Asking "Why, why, why?" or the Tree of Science</H1>
 <small>Ingmar de Boer, v. 3</small><br>
 {| class="wikitable" style="background-color: #ffffff; width: 100%;"
 |style="padding: 20px;"|
-* Download: [[Media:The_Book_of_the_Universe_-_3.pdf | The Book of the Universe (v. 3)]]  [[File:Pdf3.gif]]
+* Download: [[Media:Tree_of_Science_-_3.pdf | Asking "Why, why, why?" or the Tree of Science (v. 3)]]  [[File:Pdf3.gif]]
 |}__NOTOC__

@@ Line 8: / Line 8: @@
 |}__NOTOC__
-<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)
+<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)
 <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>
-<h3>Language or Reality, but not Both</h3>
+<h3>Introduction</h3>
 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.
@@ Line 22: / Line 22: @@
 </ol>
-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.
+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.
 <h3>The Mathematical Universe</h3>
-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, this becomes unfalsifiable, introducing an even greater problem. Again, it cannot be both at the same time.
+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.
 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.
@@ Line 46: / Line 46: @@
 <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>
-The term does not do justice to the great philosopher, since we know 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, to the domain of reason.
+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.
 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.
@@ Line 54: / Line 54: @@
 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.
-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", but because in that case we cannot see it, it does not exist to us. In the words of Ludwig Wittgenstein's Tractatus:
+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:
 <ul><i>
 .113	Philosophy sets limits to the much disputed sphere of natural science.<br>
@@ Line 69: / Line 69: @@
 <h3>Conclusion</h3>
-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 diference 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. ●
+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. ●

@@ Line 1: / Line 1: @@
 <div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;">
 <H1 style="margin-top: 0px;">The Book of the Universe</H1>
 <small>Ingmar de Boer, v. 3</small><br>

@@ Line 1: / Line 1: @@
 <div style="width: 70%; padding: 20px; background-color: #f0f0f0; border: 1px solid #b0b0b0;">
 <H1 style="margin-top: 0px;">The Book of the Universe</H1>
 <br>
@@ Line 60: / Line 59: @@
 .113	Philosophy sets limits to the much disputed sphere of natural science.<br>
 .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>
-.115	It will signify what cannot be said, by presenting clearly what can be said. <br></i></ul>
+.115	It will signify what cannot be said, by presenting clearly what can be said. <br></i>
-<ul><i>4.113	Die Philosophie begrenzt das bestreitbare Gebiet der Naturwissenschaft. <br>
+<ul><i>
 .114	Sie soll das Denkbare abgrenzen und damit das Undenkbare. Sie soll das Undenkbare von innen durch das Denkbare begrenzen. <br>
-.115	Sie wird das Unsagbare bedeuten, indem sie das Sagbare klar darstellt.</i></ul>
+.115	Sie wird das Unsagbare bedeuten, indem sie das Sagbare klar darstellt.
 <h3>Conclusion</h3>
 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 diference 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. ●