Comments on: The Cutest Fallacy In The World http://crookedtimber.org/2009/04/02/the-cutest-fallacy-in-the-world/ Out of the crooked timber of humanity, no straight thing was ever made Sat, 21 Nov 2009 15:07:19 -0800 http://wordpress.org/?v=2.8.6 hourly 1 By: Frank http://crookedtimber.org/2009/04/02/the-cutest-fallacy-in-the-world/comment-page-2/#comment-271609 Frank Sun, 05 Apr 2009 20:36:10 +0000 http://crookedtimber.org/?p=10372#comment-271609 I think you have all missed the point: a very intellegent young lady was taking the piss. Bless her. I think you have all missed the point: a very intellegent young lady was taking the piss.
Bless her.

]]> By: Tangurena http://crookedtimber.org/2009/04/02/the-cutest-fallacy-in-the-world/comment-page-2/#comment-271589 Tangurena Sun, 05 Apr 2009 14:06:23 +0000 http://crookedtimber.org/?p=10372#comment-271589 Well, I could easily think of multiplying matrices being non-commutative, but salient's comment got me wondering <em>just how much</em> of those old math classes I was forgetting. Well, I could easily think of multiplying matrices being non-commutative, but salient’s comment got me wondering just how much of those old math classes I was forgetting.

]]> By: Matt Heath http://crookedtimber.org/2009/04/02/the-cutest-fallacy-in-the-world/comment-page-2/#comment-271583 Matt Heath Sun, 05 Apr 2009 11:01:24 +0000 http://crookedtimber.org/?p=10372#comment-271583 James @76: That's only a special case of what she was asked though. The question is adding two (possibly different) odd numbers <blockquote cite="Tangurena">Are there any groups where addition is not commutative? I can’t think of any.</blockquote>This is kind of a question about language rather than mathematics. There are plenty of groups where the operation is non-commutative (the group of symmetries of a equilateral triangle, say) but it wouldn't be usual to refer to the operation as "addition" in these cases (whereas you might in an arbitrary commutative group). This probably isn't very relevant to primary school arithmetic, though. James @76: That’s only a special case of what she was asked though. The question is adding two (possibly different) odd numbers
Are there any groups where addition is not commutative? I can’t think of any.
This is kind of a question about language rather than mathematics. There are plenty of groups where the operation is non-commutative (the group of symmetries of a equilateral triangle, say) but it wouldn’t be usual to refer to the operation as “addition” in these cases (whereas you might in an arbitrary commutative group). This probably isn’t very relevant to primary school arithmetic, though.

]]> By: Tangurena http://crookedtimber.org/2009/04/02/the-cutest-fallacy-in-the-world/comment-page-2/#comment-271575 Tangurena Sun, 05 Apr 2009 04:52:18 +0000 http://crookedtimber.org/?p=10372#comment-271575 <em>Even that requires exploring whether addition is commutative, of course.</em> <em>Are</em> there any groups where addition is not commutative? I can't think of any. Even that requires exploring whether addition is commutative, of course.

Are there any groups where addition is not commutative? I can’t think of any.

]]> By: JoB http://crookedtimber.org/2009/04/02/the-cutest-fallacy-in-the-world/comment-page-2/#comment-271501 JoB Sat, 04 Apr 2009 10:54:06 +0000 http://crookedtimber.org/?p=10372#comment-271501 James, yes, that's actually easier, still Einstein at that age but if you add 2 odd numbers then divide by two you get the add number you started with ... It is beyond me why the hell anybody would like to prove this with advanced formalisms. James, yes, that’s actually easier, still Einstein at that age but if you add 2 odd numbers then divide by two you get the add number you started with … It is beyond me why the hell anybody would like to prove this with advanced formalisms.

]]> By: James http://crookedtimber.org/2009/04/02/the-cutest-fallacy-in-the-world/comment-page-2/#comment-271486 James Sat, 04 Apr 2009 03:57:34 +0000 http://crookedtimber.org/?p=10372#comment-271486 When first learning even and odd, I was taught that even numbers are numbers that are divisible by two. If she had been told that, then it wouldn't be out of the ordinary for her to reason that any number added to itself would produce an even number, no matter if it were an odd or even to begin with. When first learning even and odd, I was taught that even numbers are numbers that are divisible by two. If she had been told that, then it wouldn’t be out of the ordinary for her to reason that any number added to itself would produce an even number, no matter if it were an odd or even to begin with.

]]> By: Michael Drake http://crookedtimber.org/2009/04/02/the-cutest-fallacy-in-the-world/comment-page-2/#comment-271478 Michael Drake Sat, 04 Apr 2009 01:46:56 +0000 http://crookedtimber.org/?p=10372#comment-271478 (BTW, this is why we need socialized epistemology.) (BTW, this is why we need socialized epistemology.)

]]> By: Michael Drake http://crookedtimber.org/2009/04/02/the-cutest-fallacy-in-the-world/comment-page-2/#comment-271476 Michael Drake Sat, 04 Apr 2009 01:46:04 +0000 http://crookedtimber.org/?p=10372#comment-271476 Well, you have to know these things when you're a Mom, you know. Well, you have to know these things when you’re a Mom, you know.

]]> By: Mom http://crookedtimber.org/2009/04/02/the-cutest-fallacy-in-the-world/comment-page-2/#comment-271469 Mom Fri, 03 Apr 2009 23:46:23 +0000 http://crookedtimber.org/?p=10372#comment-271469 Looks right to me. Looks right to me.

]]> By: Anthony http://crookedtimber.org/2009/04/02/the-cutest-fallacy-in-the-world/comment-page-2/#comment-271462 Anthony Fri, 03 Apr 2009 22:47:31 +0000 http://crookedtimber.org/?p=10372#comment-271462 Eszter - in my high school precalculus class, the rule was we could use on an exam (or homework) anything which we'd had in class or shown on the exam. One exam was after we'd learned the definition of a derivative, but not any of the really useful formulae for derivatives of various functions. The exam was a bunch of "find the derivative of this polynomial function", with the intent of doing it the hard way - going through the polynomial and using the definition of derivative. For problem 1, I worked out the formula for the general case of the derivative of mx^n, and then solved the remaining problems by plugging them into the formula. Teacher was not amused, but did give me full marks. Eszter – in my high school precalculus class, the rule was we could use on an exam (or homework) anything which we’d had in class or shown on the exam. One exam was after we’d learned the definition of a derivative, but not any of the really useful formulae for derivatives of various functions. The exam was a bunch of “find the derivative of this polynomial function”, with the intent of doing it the hard way – going through the polynomial and using the definition of derivative. For problem 1, I worked out the formula for the general case of the derivative of mx^n, and then solved the remaining problems by plugging them into the formula. Teacher was not amused, but did give me full marks.

]]> By: Curtis http://crookedtimber.org/2009/04/02/the-cutest-fallacy-in-the-world/comment-page-2/#comment-271448 Curtis Fri, 03 Apr 2009 19:15:48 +0000 http://crookedtimber.org/?p=10372#comment-271448 Even number can be written as 2k where k is any integer 2(1) = 2, 2(2)=4, 2(3) = 6 Odd can then be written as one more then an even so 2k+1, 2+1 = 3, 4+1 = 5, 6+1 = 7 (2k+1) + (2k+1) = 4k+2 = 2(2k+1) 2k+1 is an integer so 2(2k+1) must be even Even number can be written as 2k where k is any integer 2(1) = 2, 2(2)=4, 2(3) = 6
Odd can then be written as one more then an even so 2k+1, 2+1 = 3, 4+1 = 5, 6+1 = 7

(2k+1) + (2k+1) = 4k+2 = 2(2k+1)

2k+1 is an integer so 2(2k+1) must be even

]]> By: Calum http://crookedtimber.org/2009/04/02/the-cutest-fallacy-in-the-world/comment-page-2/#comment-271446 Calum Fri, 03 Apr 2009 18:43:50 +0000 http://crookedtimber.org/?p=10372#comment-271446 Can also be proven by modular arithmetic or induction. But c'mon that's asking a lot from a six-year old or however old she is. Can also be proven by modular arithmetic or induction. But c’mon that’s asking a lot from a six-year old or however old she is.

]]> By: go4broke http://crookedtimber.org/2009/04/02/the-cutest-fallacy-in-the-world/comment-page-2/#comment-271441 go4broke Fri, 03 Apr 2009 17:31:58 +0000 http://crookedtimber.org/?p=10372#comment-271441 I think the point was not whether you could prove this true. The point was how this was a logical fallacy for an argument. Namely the "proof" for the little girl is an appeal to authority. One of the fundamental flaws in logic that from a very early age we teach our children to do even though its wrong. Sadly even people well versed in mathematics fail to understand logic when it is applied to language :P That's why its titled Fallacy and not can you prove this with math. I'm just amazed that there are 65 posts here and not a one realized what it was about. I think the point was not whether you could prove this true. The point was how this was a logical fallacy for an argument. Namely the “proof” for the little girl is an appeal to authority. One of the fundamental flaws in logic that from a very early age we teach our children to do even though its wrong. Sadly even people well versed in mathematics fail to understand logic when it is applied to language :P

That’s why its titled Fallacy and not can you prove this with math.

I’m just amazed that there are 65 posts here and not a one realized what it was about.

]]> By: Sock Puppet of the Great Satan http://crookedtimber.org/2009/04/02/the-cutest-fallacy-in-the-world/comment-page-2/#comment-271429 Sock Puppet of the Great Satan Fri, 03 Apr 2009 15:19:08 +0000 http://crookedtimber.org/?p=10372#comment-271429 "Belle says that P So, P." I hope that Belle's Husband uses the same logical analytic framework. “Belle says that P
So, P.”

I hope that Belle’s Husband uses the same logical analytic framework.

]]> By: armand http://crookedtimber.org/2009/04/02/the-cutest-fallacy-in-the-world/comment-page-2/#comment-271426 armand Fri, 03 Apr 2009 14:13:40 +0000 http://crookedtimber.org/?p=10372#comment-271426 No, it's definitely a Miata. Or maybe a Del Sol... not sure. No, it’s definitely a Miata. Or maybe a Del Sol… not sure.

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