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The Unreasonable Effectiveness of Mathematics

dartmouth.edu

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Re: The Unreasonable Effectiveness of Mathematics

#31

Post by Herring »

wazoox wrote: post #14
Herring wrote: post #11

Earlier quoted context omitted.

Well that's what comes of not taking a scientific approach with hypotheses. The invention of math is out there for anyone to see.

Interesting. So are you so down-to-earth that you consider philosophical speculation on the nature of mathematics (or anything else, I suppose) to be nonsensical?

Don't make this about me. Read the history of math & tell me what conclusion you come to when you see people making algorithms, essentially, for dealing with natural processes.

Re: The Unreasonable Effectiveness of Mathematics

#33

Post by 10ren »

I think our sense of geometry comes from hunting (not body decoration).

It's a little bit like mathematicians invent little "chains of reasoning" rather than "mathematics", and that these chains are interesting and useful; even if their original assumptions turns out to be incorrect, the reasoning is still valid. In the marketplace/ecosystem of mathematics, people then choose the ones that they find most useful and/or interesting.

I love the thought that when we meet aliens, they have utterly different mathematics from us, so it reveals how parochial our particular toolbox is. This has actually happened, in a sense, with Chinese mathematics. Apparently, their approach to "proof" was algorithmic rather than declarative - not just a different toolbox, but a different kind of toolbox.

Re: The Unreasonable Effectiveness of Mathematics

#34

Post by ComputerGuru »

jonsen wrote: post #28
ComputerGuru wrote: post #5

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…

(Safari Reader doesn't show the full article)

File it as a bug. It's in the menu and only a click away.

Re: The Unreasonable Effectiveness of Mathematics

#35

Post by ComputerGuru »

dspeyer wrote: post #23

So after all that verbiage, he concludes: Some math was designed to be useful. Science is by definition those practical problems to which math can be applied. He still doesn't know. Very disappointing.

Sometimes it's important to realize just how little we know and clearly define it. Knowing that you don't know, knowing why you should, and understanding the inherent difficulties standing in the way of an explanation is 99% of getting there.

Re: The Unreasonable Effectiveness of Mathematics

#36

Post by calibraxis »

asdflkj wrote: post #29
calcnerd256 wrote: post #27

Earlier quoted context omitted.

Mathematics is not a product of the mind any more than physics is. All theorems are true (or, more precisely, all theorems follow from their axioms), even the ones we haven't discovered yet. That a mind can choose an axiomatic system to explore does not mean the relationships between those axioms and their theorems are created by that mind.

Mathematics and physics are products of the mind, obviously. Mathematicians and physicists do their work by using their minds. They don't channel some divine truth--they merely filter what their mind makes through certain criteria. I don't understand this common tendency, exemplified by your comment, to shift attention away from how mind makes things, to the criteria according to which we filter them before we call t…

On philosophy of mathematics, have you checked out Reuben Hersh? Or Lakatos? They're much more interesting to me than the usual platonism/formalism.

I'm guessing platonism/formalism were popular in arguing against other ways of understanding the world, like folk science, authoritarianism and mysticism. (I'm not equating the last three.) Maybe also as a foundation myth for professional mathematics.

Re: The Unreasonable Effectiveness of Mathematics

#38

Post by zeynel1 »

" 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."

this is confusing because what he is talking about is -counting- not mathematics -mathematics- is an academic field that may include -counting- as one of its areas of study -but- it is confusing to reduce mathematics to counting

Re: The Unreasonable Effectiveness of Mathematics

#39

Post by calcnerd256 »

asdflkj wrote: post #29
calcnerd256 wrote: post #27

Earlier quoted context omitted.

Mathematics is not a product of the mind any more than physics is. All theorems are true (or, more precisely, all theorems follow from their axioms), even the ones we haven't discovered yet. That a mind can choose an axiomatic system to explore does not mean the relationships between those axioms and their theorems are created by that mind.

Mathematics and physics are products of the mind, obviously. Mathematicians and physicists do their work by using their minds. They don't channel some divine truth--they merely filter what their mind makes through certain criteria. I don't understand this common tendency, exemplified by your comment, to shift attention away from how mind makes things, to the criteria according to which we filter them before we call t…

I'm not talking about how we build them. I'm talking about what they are, and what they are is as they would be whether they were built by humans or computers or nature. That the theorems follow from their axioms is not a human invention, nor could it be. There is a difference between discovering something and inventing it. Man could not invent mathematics any more than man could invent electricity. When I say physics exists, I mean that the physical world exists and follows rules. If we discover those rules, it does not mean we have invented them.

Re: The Unreasonable Effectiveness of Mathematics

#40

Post by wazoox »

Herring wrote: post #31
wazoox wrote: post #14

Earlier quoted context omitted.

Interesting. So are you so down-to-earth that you consider philosophical speculation on the nature of mathematics (or anything else, I suppose) to be nonsensical?

Don't make this about me. Read the history of math & tell me what conclusion you come to when you see people making algorithms, essentially, for dealing with natural processes.

Of course, as long as you stay in the realm of measurable things. However, we still need to explain how and why the perfect abstract mathematical objects are of any use in the real world (as opposed to other abstract objects such as patonician ideas, or more commonly gods).
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