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Some Musings on Mathematics

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Re: Some Musings on Mathematics

#41

Post by JadeNB »

MrManatee wrote: post #38
twelfthnight wrote: post #27

> Why do we care that there are only five Platonic Solids? The true answer is because there is an answer, and it would be intolerable not to know it I see a few holes with this argument: 1) Who is this "we"? I'm sure not all non-"non-mathematicians" agree with this sentiment. 2) If a mathematician is still looking for an answer to a question, they don't yet know if an answer exists or not (see: Godel, halting problem…

With regards to 2), there's a difference between trying to find an answer to a single yes/no question, and trying to find a general method for solving an infinite class of such questions. If a single yes/no question is clearly stated, then it does have an answer. This just a tautology - that's what it means to be clearly stated. For example, does there exist integers x, y, and z such that x^3 + y^3 + z^3 = 33? No one…

> If a single yes/no question is clearly stated, then it does have an answer.

Without having to reach for fancy counterexamples, how about the Empedoclean "Is the answer to this question 'no'?"?

Re: Some Musings on Mathematics

#42

Post by DougMerritt »

Mz wrote: post #40
DougMerritt wrote: post #33

Earlier quoted context omitted.

> Singling me out and talking down to me in public in no way improves your actual article. I think I see why you took it that way, but I am quite sure that that is not how Colin meant it, because I have seen him bend over backwards to educate, over the last decade or two. He said: > what it makes clear is that you never encountered any real pure math. That sounds bad to you at first blush, ok...but the thing is that…

I am sure there was no malice aforethought in his words. I also am well aware he is a real mathematician and serious educator. He spoke in his own defense very aptly. I am aware most people here will understand his side far better than mine and will generally be more sympathetic to him than to me. Let me suggest he understood my side far better than you did (and another who came to his defense, then deleted the remar…

Yeah, Colin is good that way. But:

> he understood my side far better than you did (and another who came to his defense, then deleted the remark) and his reply was far more respectful, diplomatic and appreciated.

Holy shit you are a rude fuck. I'm sorry I even tried to be understanding and explain to an aggressive tool like you.

> I'm sure you meant well and I appreciate the good intentions behind your words

I can't say the same for you. It's been a long time since I was so effectively "damned with faint praise".

Edit: regarding mathematics, you are anthropologically an outsider, but you're complaining because you might be looked down upon for that. Well you either join a community or remain an outsider, it's not complicated.

Re: Some Musings on Mathematics

#43

Post by conceit »

ColinWright wrote: post #9
conceit wrote: post #7

> The truth is far simpler. Mathematicians are solving puzzles, and some of those puzzles don't come from the real world at all, and can't be motivated in that way. Why is it that mathematicians are unable to see the recursion: Pure maths is maths applied to maths, so it is applied maths, nevermind how often this operation had to be repeated until the result would be substantiv?

There are two approaches to answering your question. Firstly, what makes you think that mathematicians are unaware of the trail back to "the real world"? Secondly, I'd be interested in knowing what you think this real world issue this problem might be descended from: Dissect a circle into congruent pieces, such that the centre point is contained in the interior of one of the pieces.

1. Because at least one claimed that there wasn't any such trail back.

2. The problem of not everyone having noticed yet how elated one is. \s

I think there is no positive solution to this geometric puzzle.

Re: Some Musings on Mathematics

#44

Post by ColinWright »

conceit wrote: post #43
ColinWright wrote: post #9

Earlier quoted context omitted.

There are two approaches to answering your question. Firstly, what makes you think that mathematicians are unaware of the trail back to "the real world"? Secondly, I'd be interested in knowing what you think this real world issue this problem might be descended from: Dissect a circle into congruent pieces, such that the centre point is contained in the interior of one of the pieces.

1. Because at least one claimed that there wasn't any such trail back. 2. The problem of not everyone having noticed yet how elated one is. \s I think there is no positive solution to this geometric puzzle.

Can you find a dissection where some pieces don't touch the center point?

Can you prove that it's impossible to have the center in the interior of a piece?

Re: Some Musings on Mathematics

#45

Post by conceit »

JadeNB wrote: post #41
MrManatee wrote: post #38

Earlier quoted context omitted.

With regards to 2), there's a difference between trying to find an answer to a single yes/no question, and trying to find a general method for solving an infinite class of such questions. If a single yes/no question is clearly stated, then it does have an answer. This just a tautology - that's what it means to be clearly stated. For example, does there exist integers x, y, and z such that x^3 + y^3 + z^3 = 33? No one…

> If a single yes/no question is clearly stated, then it does have an answer. Without having to reach for fancy counterexamples, how about the Empedoclean "Is the answer to this question 'no'?"?

Simple answer on the metalevel: It's not clearly stated, because it's self referential. It's not a question by the GP's standards.

Re: Some Musings on Mathematics

#46

Post by JadeNB »

conceit wrote: post #45
JadeNB wrote: post #41

Earlier quoted context omitted.

> If a single yes/no question is clearly stated, then it does have an answer. Without having to reach for fancy counterexamples, how about the Empedoclean "Is the answer to this question 'no'?"?

Simple answer on the metalevel: It's not clearly stated, because it's self referential. It's not a question by the GP's standards.

Well, to be sure, if the definition of 'clearly stated' is made to exclude counterexamples to the assertion, then there are no counterexamples. :-) I don't think many people would include 'not self referential' in the definition of 'clearly stated'; for example, "is this question more than eight words long?" is pretty clear.

Re: Some Musings on Mathematics

#47

Post by JadeNB »

conceit wrote: post #45
JadeNB wrote: post #41

Earlier quoted context omitted.

> If a single yes/no question is clearly stated, then it does have an answer. Without having to reach for fancy counterexamples, how about the Empedoclean "Is the answer to this question 'no'?"?

Simple answer on the metalevel: It's not clearly stated, because it's self referential. It's not a question by the GP's standards.

Also, it occurs to me that the self reference can be avoided by an epistemologically insignificant dodge: "Are you about to say 'no'?" (This dodge is, I admit, a little dodgy; it admits things like "I wasn't planning to" as a perfectly sound answer. However, I'm taking it as read that we understand all questions as yes / no questions.)

Re: Some Musings on Mathematics

#48

Post by MrManatee »

JadeNB wrote: post #46
conceit wrote: post #45

Earlier quoted context omitted.

Simple answer on the metalevel: It's not clearly stated, because it's self referential. It's not a question by the GP's standards.

Well, to be sure, if the definition of 'clearly stated' is made to exclude counterexamples to the assertion, then there are no counterexamples. :-) I don't think many people would include 'not self referential' in the definition of 'clearly stated'; for example, "is this question more than eight words long?" is pretty clear.

To put my words in context, I was thinking about mathematical questions, such as "does there exist a curve that goes through every point in a square?". Everyone has some kind of intuitive understanding of what's a "curve", but mathematicians need a precise definition in order to make this question clear enough for mathematical study. (There is such a curve: the Hilbert curve.)

It's not at all easy to recognize when a question is stated "clearly enough", and your questions provide an excellent example of this. The question "is this question more than eight words long?" refers to question itself (as a string), and in general, this kind of self-reference is perfectly harmless. The question "Is the answer to this question 'no'?" refers to its own answer, and this kind of self-reference is potentially problematic.

Re: Some Musings on Mathematics

#49

Post by conceit »

JadeNB wrote: post #47
conceit wrote: post #45

Earlier quoted context omitted.

Simple answer on the metalevel: It's not clearly stated, because it's self referential. It's not a question by the GP's standards.

Also, it occurs to me that the self reference can be avoided by an epistemologically insignificant dodge: "Are you about to say 'no'?" (This dodge is, I admit, a little dodgy; it admits things like "I wasn't planning to" as a perfectly sound answer. However, I'm taking it as read that we understand all questions as yes / no questions.)

Implicitly, the "no" references the answer to the question itself, hence it's still selfreferential.

In other words, the fallacy is to assume the following response was fixed to be an answer to the question. If I answered "no" it would be obvious that i wasn't planning to say "no" prior ("about") to the question. There is just no context in which the question would make sense the way you suggest. It's non-sense.

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