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The Unreasonable Effectiveness of Mathematics

dartmouth.edu

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Re: The Unreasonable Effectiveness of Mathematics

#11

Post by Herring »

wazoox wrote: post #8
Herring wrote: post #6

Earlier quoted context omitted.

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!

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

Re: The Unreasonable Effectiveness of Mathematics

#12

Post by Arun2009 »

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…

> Is it not remarkable that 6 sheep plus 7 sheep make 13 sheep; that 6 stones plus 7 stones make 13 stones?

Personally, I find it rather remarkable that a pattern observed from pebbles, sheep or apples (i.e., 6 + 7 = 13) should hold for any set of discrete objects anywhere in the universe. It could well have been that, say, 1 apple + 1 apple = 2.5 apples, but 1 kitten + 1 kitten = 1.5 kittens.

Re: The Unreasonable Effectiveness of Mathematics

#13

Post by michael_dorfman »

Arun2009 wrote: post #12
Herring wrote: post #6

Earlier quoted context omitted.

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…

> Is it not remarkable that 6 sheep plus 7 sheep make 13 sheep; that 6 stones plus 7 stones make 13 stones? Personally, I find it rather remarkable that a pattern observed from pebbles, sheep or apples (i.e., 6 + 7 = 13) should hold for any set of discrete objects anywhere in the universe. It could well have been that, say, 1 apple + 1 apple = 2.5 apples, but 1 kitten + 1 kitten = 1.5 kittens.

Not really, because having one something plus one something equal two somethings is pretty much the definition of discrete object.

Re: The Unreasonable Effectiveness of Mathematics

#14

Post by wazoox »

Herring wrote: post #11
wazoox wrote: post #8

Earlier quoted context omitted.

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!

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?

Re: The Unreasonable Effectiveness of Mathematics

#16

Post by nandemo »

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…

It's right there on the top: "It is evident from the title that this is a philosophical discussion". In case you aren't interested in philosophy, I don't see why bother reading the article and commenting on it -- unless perhaps you want to say something against doing any philosophy in the first place.

But if you are interested in philosophy, then you should know that the philosopher often starts by wondering about something that most sane people take for granted. Case in point, some people do wonder why the word "wheel" describes wheels. There are tons of papers and books about philosophy of language.

Others ask why wheels exist, what is a wheel, or whether do they really exist at all. You can only be sure that the existence of wheels is an "empirical fact" after you have examined these questions. After all, "empirical fact" is a philosophical term.

Incidentally, "6 sheep + 7 sheep = 13 sheep" is not an empirical fact.

Re: The Unreasonable Effectiveness of Mathematics

#19

Post by carterschonwald »

sb wrote: post #18
pmichaud wrote: post #15

This guy could easily cut 50% of his words and lose no meaning. He needs an editor.

Richard Hamming needs an editor -- that's a good one... PS: http://en.wikipedia.org/wiki/Richard_Hamming

for those who haven't read it, the transcript of his "you and your research" talk is worth repeatedly reading.

Re: The Unreasonable Effectiveness of Mathematics

#20

Post by tome »

michael_dorfman wrote: post #13
Arun2009 wrote: post #12

Earlier quoted context omitted.

> Is it not remarkable that 6 sheep plus 7 sheep make 13 sheep; that 6 stones plus 7 stones make 13 stones? Personally, I find it rather remarkable that a pattern observed from pebbles, sheep or apples (i.e., 6 + 7 = 13) should hold for any set of discrete objects anywhere in the universe. It could well have been that, say, 1 apple + 1 apple = 2.5 apples, but 1 kitten + 1 kitten = 1.5 kittens.

Not really, because having one something plus one something equal two somethings is pretty much the definition of discrete object.

Yes, I agree and think this is a very smart observation. It doesn't hold for jugs of water, say, if you're allowed to pour water between the jugs.
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