Circle - Revision history

Ingmardb at 02:56, 24 December 2022

2022-12-24T02:56:44Z

Ingmardb at 12:37, 21 December 2022

2022-12-21T12:37:09Z

Ingmardb at 12:36, 21 December 2022

2022-12-21T12:36:47Z

Ingmardb at 12:36, 21 December 2022

2022-12-21T12:36:15Z

Ingmardb at 09:50, 18 December 2022

2022-12-18T09:50:49Z

Ingmardb at 09:49, 18 December 2022

2022-12-18T09:49:32Z

Ingmardb at 09:48, 18 December 2022

2022-12-18T09:48:56Z

Ingmardb at 09:48, 18 December 2022

2022-12-18T09:48:03Z

Ingmardb at 09:42, 18 December 2022

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Ingmardb at 09:37, 18 December 2022

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 '''The Language of Mathematics'''
-All natural languages, also those which are historically unrelated, are all structured similarly in their deepest layers. In language we can see a reflection of how humans have modelled the world around them in the course of some thousands of years of their evolution. Languages are completely subject to their purpose, that is describing the specific surroundings of a social group. We can find however, only relations between observables in the outside world if we can describe them to ourselves in some form of language, explicitly or implicitly. Language and mind are in this sense not completely separate entities. We encode a model of these relations in the brain, if it were only to have the ability to reproduce them when asked, in the form of natural or mathematical language, for example when we are writing an article on it, or describing it to those who are interested. During the course of its evolution, the language of mathematics has become closely related to the way structures are stored in the brain. If, for the sake of the argument, we would go one step further, and equate mathematics with neural structures, it would be inappropriate to be surprised that the language we have used to store something in the brain, is able to effectively describe that same thing. Differently phrased: it was encoded in the brain in such a way that it can be accurately decoded, so we should not be too surprised if accurately decoding is indeed possible. We could call it an example of "circular" reasoning.
+All natural languages, also those which are historically unrelated, are structured similarly in their deepest layers. In language we can see a reflection of how humans have modelled the world around them in the course of some thousands of years of their evolution. Languages are completely subject to their purpose, that is describing the specific surroundings of a social group. We can find however, only relations between observables in the outside world if we can describe them to ourselves in some form of language, explicitly or implicitly. Language and mind are in this sense not completely separate entities. We encode a model of these relations in the brain, if it were only to have the ability to reproduce them when asked, in the form of natural or mathematical language, for example when we are writing an article on it, or describing it to those who are interested. During the course of its evolution, the language of mathematics has become closely related to the way structures are stored in the brain. If, for the sake of the argument, we would go one step further, and equate mathematics with neural structures, it would be inappropriate to be surprised that the language we have used to store something in the brain, is able to effectively describe that same thing. Differently phrased: it was encoded in the brain in such a way that it can be accurately decoded, so we should not be too surprised if accurately decoding is indeed possible. We could call it an example of "circular" reasoning.
 '''Effectiveness Because of Natural Law, not Because of Language'''

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 * Download: [[Media:Wigner_-_The_Unreasonable_Effectiveness_of_Mathematics.pdf ‎| Eugene Wigner: The Unreasonable Effectiveness of Mathematics]]  [[File:Pdf3.gif]]
 |}
 __NOTOC__
 <i>It is certainly true that in nature nothing miraculous exists, but in order to distinguish things we understand in terms of their causes from those of which the causes are unknown to us, we rightly call these miracles, not because they actually are, but because they so present themselves to us. </i>[tr. IdB]

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 __NOTOC__
-<ul>
 <i>It is certainly true that in nature nothing miraculous exists, but in order to distinguish things we understand in terms of their causes from those of which the causes are unknown to us, we rightly call these miracles, not because they actually are, but because they so present themselves to us. </i>[tr. IdB]
 <br><br>
 <ul><i>Tis wel waer datter inde Natuer niet wonderlick en is, nochtan tot onderſcheyt der dinghen die wy duer de oirſaken verſstaen, vande ghene welcker redenen ons onbetekent ſijn, ſoo gheuen wy deſe met recht de naem van wonder, niet dat ſijt eyghentlick ſijn, maer om dattet hem voor ons alſoo ghelaet. </i> [Simon Stevin, Beghinselen der weeghconst, Leyden, 1586]</ul>
 <br>

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 '''Effectiveness of Language in General'''
-[[File: Wonder_en_is_gheen_wonder.png|right|200px]]The languages we humans use to communicate with each other, we call them natural languages, are all very effective means to describe the world around us. In some areas some languages may be more effective than others, but generally speaking it does not matter that much if we describe a certain situation, say, in Chinese or in English. For instance, there is never any doubt if Chinese children would be able to learn the same things and learn them as efficiently as English children, as a result of the capabilities of the language they have been growing up with. It may be our command of a language, our observations, our reasoning and many other things standing in our way when we describe the world, but, generally speaking, what is hindering us is not the language in which we try to describe things. We could say: "the world looks the same in any natural language." Vice versa, we could say that languages are apparently of an elastic nature, where "one language can fit all." The language is more effective if we can accurately encode and decode a larger part of our world with a more concise sentence and smaller vocabulary. This has something to do with the development of language itself, for example with the possibility of natural languages to form completely new sentences with a relatively small vocabulary, because of various grammatical mechanisms. Languages have evolved to very flexible tools, having solved for example in many different ways major syntactic problems. Ineffective mechanisms have died out in natural language, or have never come into being. In that respect, again, mathematics not very different from natural language. The fact that we can describe the results of our experiments in mathematical or other terms is not at all miraculous: it is precisely what languages are good at.
+The languages we humans use to communicate with each other, we call them natural languages, are all very effective means to describe the world around us. In some areas some languages may be more effective than others, but generally speaking it does not matter that much if we describe a certain situation, say, in Chinese or in English. For instance, there is never any doubt if Chinese children would be able to learn the same things and learn them as efficiently as English children, as a result of the capabilities of the language they have been growing up with. It may be our command of a language, our observations, our reasoning and many other things standing in our way when we describe the world, but, generally speaking, what is hindering us is not the language in which we try to describe things. We could say: "the world looks the same in any natural language." Vice versa, we could say that languages are apparently of an elastic nature, where "one language can fit all." The language is more effective if we can accurately encode and decode a larger part of our world with a more concise sentence and smaller vocabulary. This has something to do with the development of language itself, for example with the possibility of natural languages to form completely new sentences with a relatively small vocabulary, because of various grammatical mechanisms. Languages have evolved to very flexible tools, having solved for example in many different ways major syntactic problems. Ineffective mechanisms have died out in natural language, or have never come into being. In that respect, again, mathematics not very different from natural language. The fact that we can describe the results of our experiments in mathematical or other terms is not at all miraculous: it is precisely what languages are good at.
 '''The Language of Mathematics'''

@@ Line 32: / Line 32: @@
 '''Effectiveness of Language in General'''
-The languages we humans use to communicate with each other, we call them natural languages, are all very effective means to describe the world around us. In some areas some languages may be more effective than others, but generally speaking it does not matter that much if we describe a certain situation, say, in Chinese or in English. For instance, there is never any doubt if Chinese children would be able to learn the same things and learn them as efficiently as English children, as a result of the capabilities of the language they have been growing up with. It may be our command of a language, our observations, our reasoning and many other things standing in our way when we describe the world, but, generally speaking, what is hindering us is not the language in which we try to describe things. We could say: "the world looks the same in any natural language." Vice versa, we could say that languages are apparently of an elastic nature, where "one language can fit all." The language is more effective if we can accurately encode and decode a larger part of our world with a more concise sentence and smaller vocabulary. This has something to do with the development of language itself, for example with the possibility of natural languages to form completely new sentences with a relatively small vocabulary, because of various grammatical mechanisms. Languages have evolved to very flexible tools, having solved for example in many different ways major syntactic problems. Ineffective mechanisms have died out in natural language, or have never come into being. In that respect, again, mathematics not very different from natural language. The fact that we can describe the results of our experiments in mathematical or other terms is not at all miraculous: it is precisely what languages are good at.[[File: Wonder_en_is_gheen_wonder.png|right|200px]]
+[[File: Wonder_en_is_gheen_wonder.png|right|200px]]The languages we humans use to communicate with each other, we call them natural languages, are all very effective means to describe the world around us. In some areas some languages may be more effective than others, but generally speaking it does not matter that much if we describe a certain situation, say, in Chinese or in English. For instance, there is never any doubt if Chinese children would be able to learn the same things and learn them as efficiently as English children, as a result of the capabilities of the language they have been growing up with. It may be our command of a language, our observations, our reasoning and many other things standing in our way when we describe the world, but, generally speaking, what is hindering us is not the language in which we try to describe things. We could say: "the world looks the same in any natural language." Vice versa, we could say that languages are apparently of an elastic nature, where "one language can fit all." The language is more effective if we can accurately encode and decode a larger part of our world with a more concise sentence and smaller vocabulary. This has something to do with the development of language itself, for example with the possibility of natural languages to form completely new sentences with a relatively small vocabulary, because of various grammatical mechanisms. Languages have evolved to very flexible tools, having solved for example in many different ways major syntactic problems. Ineffective mechanisms have died out in natural language, or have never come into being. In that respect, again, mathematics not very different from natural language. The fact that we can describe the results of our experiments in mathematical or other terms is not at all miraculous: it is precisely what languages are good at.
 '''The Language of Mathematics'''