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The Unreasonable Effectiveness of Mathematics

dartmouth.edu

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Re: The Unreasonable Effectiveness of Mathematics

#3

Post by Groxx »

Herring wrote: post #2

Next up: Unreasonable effectiveness of words in communication. We keep using the same words in different sentences, & they keep making sense.

To get a similar result, it'd be as if "Colorless green ideas sleep furiously" turned out to accurately describe ideas, without modifying the terms.

i.e., if it turns out ideas and "green" operate in the same locations in the brain, and if you exhibit anger + sleep patterns of thought while brainstorming.

Re: The Unreasonable Effectiveness of Mathematics

#4

Post by rayder »

The discussion of beauty in mathematics resonates deeply with me and I seem to always relate such discussions with music. As a musician turned math enthusiast, I think the thought processes involved in the creation of music parallel those involved in the creation of proofs quite nicely. My obsession with music seems to complement my obsession with mathematics on some level that I cannot quite define. As far as I know, there is not a distinctly important practical relationship between math and music (please correct me if I am wrong), but I still feel as though there is some connection. I do not know if this is a personal thing or not, but I cannot stop relating the two!

Re: The Unreasonable Effectiveness of Mathematics

#5

Post by ComputerGuru »

old proofs of theorems may become false proofs. The old proofs no longer cover the newly defined things. The miracle is that almost always the theorems are still true; it is merely a matter of fixing up the proofs. It is claimed that an ex-editor of Mathematical Reviews once said that over half of the new theorems published these days are essentially true though the published proofs are false.

I'm only around 55% of the way through (according to my scrollbar --- and thank you Readability!) but it's an incredibly interesting read. It's very lengthy, but I really advise taking the time to look it over. It really tickles those brain cells. Thus far, I'm not seeing anything "new" in this article, but seeing all these incredible things expressed and summarized up close is amazing.

Re: The Unreasonable Effectiveness of Mathematics

#6

Post by Herring »

Groxx wrote: post #3
Herring wrote: post #2

Next up: Unreasonable effectiveness of words in communication. We keep using the same words in different sentences, & they keep making sense.

To get a similar result, it'd be as if "Colorless green ideas sleep furiously" turned out to accurately describe ideas , without modifying the terms. i.e., if it turns out ideas and "green" operate in the same locations in the brain, and if you exhibit anger + sleep patterns of thought while brainstorming.

Hm, it's not productive to argue over analogies. They're just used to illustrate a point. I was saying math was explicitly designed to work & to be general. Likewise words were designed for communication (not just for describing the real world), & I'd say that sentence communicates your meaning very well.

eg later he says:

>"Is it not remarkable that 6 sheep plus 7 sheep make 13 sheep; that 6 stones plus 7 stones make 13 stones? Is it not a miracle that the universe is so constructed that such a simple abstraction as a number is possible? To me this is one of the strongest examples of the unreasonable effectiveness of mathematics. Indeed, l find it both strange and unexplainable. "

That makes absolutely no sense. You might as well wonder why the word "wheel" describes wheels. Or wonder why wheels exist. These are empirical facts.

Re: The Unreasonable Effectiveness of Mathematics

#7

Post by wazoox »

Groxx wrote: post #3
Herring wrote: post #2

Next up: Unreasonable effectiveness of words in communication. We keep using the same words in different sentences, & they keep making sense.

To get a similar result, it'd be as if "Colorless green ideas sleep furiously" turned out to accurately describe ideas , without modifying the terms. i.e., if it turns out ideas and "green" operate in the same locations in the brain, and if you exhibit anger + sleep patterns of thought while brainstorming.

Did you read Pinker, Chomsky or both ? :)

Re: The Unreasonable Effectiveness of Mathematics

#8

Post by wazoox »

Herring wrote: post #6
Groxx wrote: post #3

Earlier quoted context omitted.

To get a similar result, it'd be as if "Colorless green ideas sleep furiously" turned out to accurately describe ideas , without modifying the terms. i.e., if it turns out ideas and "green" operate in the same locations in the brain, and if you exhibit anger + sleep patterns of thought while brainstorming.

Hm, it's not productive to argue over analogies. They're just used to illustrate a point. I was saying math was explicitly designed to work & to be general. Likewise words were designed for communication (not just for describing the real world), & I'd say that sentence communicates your meaning very well. eg later he says: >" Is it not remarkable that 6 sheep plus 7 sheep make 13 sheep; that 6 stones plus 7 stones ma…

Mathematicians still are split into formalists, realists, intuitionists and logicists, debating around the nature of mathematical truth; i. e. does mathematical truth pre-exists (and is just "discovered") or is it a human invention? Good luck sorting this one out!
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