Wikipedia:Reference desk/Archives/Mathematics/2011 June 29

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June 29

I don't believe in mathematics.

I think mathematics ceases to be true when you stop believing in it. Therefore, by any reasonable definition of truth (such as the correspondence definition), mathematics is false. Mathematics in fact, need not correspond to anything in the real world. We do not even have a guarantee that the real world exhibits logic, or only seems to. Moreover, mathematics is a simplification and abstraction: therefore, its only purpose can be decoration and embellishment: to take the bare reality, and distill a structure from it that is nowhere there. There is no circle: yet what is a circle, mathematically a locus of points? What are points. Mathematicians fantasies, full of sound and fury, and corresponding to nothing. I do not believe in mathematics. --188.29.241.38 (talk) 22:42, 29 June 2011 (UTC)

Not believing in mathematics means, at best, that you are uninformed. Of course you can believe that it does not reflect reality. That position is at least consistent. But then you must explain The Unreasonable Effectiveness of Mathematics in the Natural Sciences. --Stephan Schulz (talk) 22:51, 29 June 2011 (UTC)

Check, and mate. Where's the "like" button? — Fly by Night (talk) 23:02, 29 June 2011 (UTC)

At worst, is it a Tea thing? --188.28.169.51 (talk) 23:28, 29 June 2011 (UTC)

This page is supposed to be for asking questions. Michael Hardy (talk) 23:03, 29 June 2011 (UTC)

Okay. How can I succinctly disprove the proposition assumed by The Unreasonable Effectiveness of Mathematics in the Natural Sciences, viz. that mathematics is effective in the natural sciences? --188.28.169.51 (talk) 23:30, 29 June 2011 (UTC)

I guess the most appropriate and effective tool for that would be mathematics. Dmcq (talk) 23:58, 29 June 2011 (UTC)

• I think it's best that we leave this section as it stands, per don't feed the trolls. The maths reference desk is not a forum. It's a place where people ask mathematical questions, and where the reference desk regulars help to answer those questions with the use of Wikipedia articles. Coming to the maths reference desk and saying that you don't believe in mathematics is, besides deranged, an obvious attempt to insight conflict. You have come to the wrong place for that. — Fly by Night (talk) 00:02, 30 June 2011 (UTC)

Here is a list of irrefutable proofs that mathematics is false.

HTH. --COVIZAPIBETEFOKY (talk) 01:00, 30 June 2011 (UTC)

The poster has a point. If you e.g. believe in the Axiom of Choice, the continuum etc. etc. then you must live with the Banach–Tarski paradox Count Iblis (talk) 01:45, 30 June 2011 (UTC)

Once you strip away the "I don't believe" rhetoric, there are several interlinked questions here. Let's try to untangle them:

1. Is mathematics a practically effective model that allows us to predict and manipulate the physical world around us ? Undoubtedly, yes.
2. Is mathematics the most effective model of the physical world that we know of ? Again, yes.
3. Is mathematics the only way of interacting with the physical world ? No. Trial and error works well enough in some areas (home cooking, for example), but it is very inefficient.
4. Does every part of mathematics have some connection to the real world ? Not necessarily, although it is surprisingly difficult to name an area of mathematics that has absoutely no real world applications.
5. Can mathematics be effectively applied to all areas of human experience ? No (or, at least, not yet). Interactions between people, from individual relationships to global politics, do not seem to be very amenable to mathematical analysis.
6. Could there be a more effective way of modelling and manipulating the physical world than mathematics ? We don't know. Magic and crystal balls don't seem to work over here, but maybe in a galaxy far, far away things might be different.
7. Is the effectiveness of mathematics "unreasonable" ? That's a matter of opinion, and it depends on how you define "reasonable".
8. Does the effectiveness of mathematics reveal something deep about the physical world ? Or is it just an artefact of how we perceive the physical world ? Now that's a good question ... Gandalf61 (talk) 09:56, 30 June 2011 (UTC)

Regarding #5 - while mathematics is far from "solving" human interactions, game theory can give a lot of mileage in analyzing both interpersonal and international relationships. -- Meni Rosenfeld (talk) 11:08, 30 June 2011 (UTC)

1 + 1 = 2 is true at least until Hell freezes over - after that all bets are off. Whether you believe in it or not makes absolutely no difference to the truth of it. A statement that you don't believe in mathematics is effectively the same as declaring yourself an idiot and/or insane. Roger (talk) 11:08, 30 June 2011 (UTC)

Maybe Hell has frozen over. Has anyone been there lately? Can mathematics even prove it exists, or doesn't exist? -- Jack of Oz ^{[your turn]} 11:51, 30 June 2011 (UTC)

The existence of hell is a trivial corollary of a theorem by Euler. -- Meni Rosenfeld (talk) 13:06, 30 June 2011 (UTC)

Judging by his link, Roger (Dodger) apparently thinks the Universe is Hell. Now that's depressing. --Trovatore (talk) 17:21, 30 June 2011 (UTC)

Actually, what he wrote only presupposes that Hell is in the universe, and will be the last part of the universe to freeze over. Michael Hardy (talk) 05:48, 1 July 2011 (UTC)

That sort of takes me back. In high school I took a literature course in which we had a certain series of short stories in film form shown on television in the classroom. In one of the stories (which may have been by Updike but then again maybe not) a vicar is discoursing on Purgatory, and remarking that, for some subtle theological reason I probably didn't understand then and don't remember now, beings in Purgatory were physical beings, and therefore purgatory, unlike Heaven or Hell, had to be a place. But where? he wanted to know.

So if the vicar was right, the heat death of the Universe might freeze over Purgatory, but not Hell.

Does this story ring a bell with anyone? I'd kind of like to know the name of it. --Trovatore (talk) 06:51, 1 July 2011 (UTC)

Missing from this list: "Is mathematics 'true'"? The answer is "no". --188.29.128.61 (talk) 22:40, 30 June 2011 (UTC)

Saying that mathematics is "true" is like saying that soccer is true. Mathematics is an activity, not a set of truths. Looie496 (talk) 16:02, 30 June 2011 (UTC)

Mathematics is an activity aimed at discovering truths. (I was going to say "unlike soccer", but then again, who knows?) --Trovatore (talk) 17:23, 30 June 2011 (UTC)

Well, soccer certainly has no other discernible purpose, function or meaning. (God knows, I've looked long and hard, but not a sausage.) We already know, courtesy of Bill Shankly, that soccer is far more important than life or death. So, it's looking very much like its sole raison d'etre is to discover truths. Who knew? -- Jack of Oz ^{[your turn]} 08:59, 1 July 2011 (UTC)

OP, I have to agree with you there. I used to "believe" in math, but now I realized what you say is indeed true: it's just a fanatasy. All I do is write down meaningless symbols that's meant to represent some other worldly mental image. None of this stuff exist, it's all just random talk. Money is tight (talk) 15:05, 1 July 2011 (UTC)

Thank you (OP here), your response is helpful. However, it does not answer any of my questions (perhaps because I didn't raise any?) 87.194.221.239 (talk) 16:23, 1 July 2011 (UTC)

You're welcome. Since if maths is false then 0=1, not asking a question is the same as asking one - so no need for you to worry about that. Dmcq (talk) 19:21, 1 July 2011 (UTC)

I don't believe in uncountable quantitites, because you only have countably many descriptions to work with. You can define real numbers and integrate over the "uncountable reals", but all you are doing is appling some formal rules that all have a finite descriptions. Saying that the uncountable reals exist is like the Pope saying that God exists. Count Iblis (talk) 23:17, 1 July 2011 (UTC)

If you're going to take that tack, really you have only finitely many descriptions to work with. Arbitrarily large natural numbers are just as much an idealization as are completed infinities.

Moreover the hypothesis of their existence is falsifiable in Popper's sense, because they could imply an inconsistency, but have not yet been observed to do so. --Trovatore (talk) 23:19, 1 July 2011 (UTC)

That's okay, child: mathematics believes in you.