- #71
disregardthat
Science Advisor
- 1,866
- 34
Mathematics is not "arbitrary noodling", it is more correctly described as "how to calculate", and calculation must accede to formal rules. There is no such thing as an informal calculation. Mathematics is surely and as you certainly will agree arbitrary in the sense that we can freely choose what to calculate, but what we want to calculate is however often not arbitrary. It's a simple point really, but not relevant to the status of mathematics itself.
(How does it make sense to be intrinsically arbitrary? It seems quite meaningless to me.)
Mathematics is not at any rate modeling, and must not be confused with the physical model in which it is utilized. We can set up a mathematical framework for a model, but the conclusions about reality will never be mathematical. The problem is that people have too many conceptions about what mathematics is, as if it somehow transcends its usage to a language of something abstract or even a language about reality itself. It does not however describe anything in the ordinary sense of the word describe. The description, or representation, is an interpretation depending on context, and is very much arbitrary, but not mathematical.
(R^2, the real plane, is used for limitless representations, but as a mathematical object it has no particular connection to either of these things)
What a mathematician may have in favor in this issue is that he can see the possibilities, and not get too entrenched in some particular usage of mathematics only to be tricked into believing that there is a deep connection to be found (as if mathematical statements about R^3 somehow were statements about space).
The main issue here is that the questions themselves are wrong. If it still makes sense to ask whether reality itself is mathematical (or as I translate your wording: territory) one has to backtrack ones thoughts about what mathematics actually is, and not confuse oneself into believing its various usages are part of it as a concept.
Don't think of intuition or visual imagination of mathematics as in any sort of conflict with the formalities of mathematics. The reality of the issue is that our intuition is exactly intuition of the mechanics of the mathematical rules. Much like intuition in chess. Reading your last post, I would like to give the following example: Does chess-players frown upon having a vivid imagery of what e.g. their following moves should be? No. (does it conflict with the rule-governed aspect of chess?)
(How does it make sense to be intrinsically arbitrary? It seems quite meaningless to me.)
Mathematics is not at any rate modeling, and must not be confused with the physical model in which it is utilized. We can set up a mathematical framework for a model, but the conclusions about reality will never be mathematical. The problem is that people have too many conceptions about what mathematics is, as if it somehow transcends its usage to a language of something abstract or even a language about reality itself. It does not however describe anything in the ordinary sense of the word describe. The description, or representation, is an interpretation depending on context, and is very much arbitrary, but not mathematical.
(R^2, the real plane, is used for limitless representations, but as a mathematical object it has no particular connection to either of these things)
What a mathematician may have in favor in this issue is that he can see the possibilities, and not get too entrenched in some particular usage of mathematics only to be tricked into believing that there is a deep connection to be found (as if mathematical statements about R^3 somehow were statements about space).
The main issue here is that the questions themselves are wrong. If it still makes sense to ask whether reality itself is mathematical (or as I translate your wording: territory) one has to backtrack ones thoughts about what mathematics actually is, and not confuse oneself into believing its various usages are part of it as a concept.
Don't think of intuition or visual imagination of mathematics as in any sort of conflict with the formalities of mathematics. The reality of the issue is that our intuition is exactly intuition of the mechanics of the mathematical rules. Much like intuition in chess. Reading your last post, I would like to give the following example: Does chess-players frown upon having a vivid imagery of what e.g. their following moves should be? No. (does it conflict with the rule-governed aspect of chess?)
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