Comments on: An Economic Argument for a Mathematical Conclusion http://antimeta.wordpress.com/2008/04/27/an-economic-argument-for-a-mathematical-conclusion/ A general distrust of strong metaphysical claims in mathematics and philosophy. Tue, 14 Jul 2009 21:45:18 +0000 http://wordpress.com/ hourly 1 By: Theorems from Biology « Antimeta http://antimeta.wordpress.com/2008/04/27/an-economic-argument-for-a-mathematical-conclusion/#comment-2658 Theorems from Biology « Antimeta Wed, 16 Jul 2008 08:37:55 +0000 http://antimeta.wordpress.com/?p=169#comment-2658 [...] An Economic Argument for a Mathematical Conclusion [...] [...] An Economic Argument for a Mathematical Conclusion [...]

]]> By: Bryan http://antimeta.wordpress.com/2008/04/27/an-economic-argument-for-a-mathematical-conclusion/#comment-2628 Bryan Tue, 13 May 2008 23:44:45 +0000 http://antimeta.wordpress.com/?p=169#comment-2628 Very interesting. Both this and the physical argument you suggest in your<a href="http://yetanothersheep.blogspot.com/2008/05/on-reasonable-effectiveness-of.html#comment-2795096065596396830" rel="nofollow">reply to Michael</a> worry me a bit. Both arguments end in correct conclusions, and both arguments hide a lot of facts (empirical, mathematical) that might render one of their premises false. It's this possibility that we want to avoid. It's easy to generate wrong arguments for correct conclusions -- and such arguments are completely uninformative. What I would urge is plenty of caution with non-mathematical arguments for mathematical conclusions. I think that in many cases they <em>can</em> lead to new insight, and in some cases they do. But my suspicion is this: these non-mathematical tricks are instructive only insofar as they lead to <em>good</em> arguments. For a similar discussion: a <a href="http://soulphysics.blogspot.com/2008/05/4-line-proof-of-isoperimetric-theorem.html" rel="nofollow">"biological proof"</a> of the isoperimetric theorem in 3D. Very interesting. Both this and the physical argument you suggest in yourreply to Michael worry me a bit.

Both arguments end in correct conclusions, and both arguments hide a lot of facts (empirical, mathematical) that might render one of their premises false. It’s this possibility that we want to avoid. It’s easy to generate wrong arguments for correct conclusions — and such arguments are completely uninformative.

What I would urge is plenty of caution with non-mathematical arguments for mathematical conclusions. I think that in many cases they can lead to new insight, and in some cases they do. But my suspicion is this: these non-mathematical tricks are instructive only insofar as they lead to good arguments.

For a similar discussion: a “biological proof” of the isoperimetric theorem in 3D.

]]> By: Michael Greineckerer http://antimeta.wordpress.com/2008/04/27/an-economic-argument-for-a-mathematical-conclusion/#comment-2627 Michael Greineckerer Wed, 07 May 2008 15:32:46 +0000 http://antimeta.wordpress.com/?p=169#comment-2627 When you assume the existence of a present value, you are allready assuming that your series converges. Given that, there is a very easy way to find a expression for the infinite sum. The details are <a href="http://yetanothersheep.blogspot.com/2008/05/on-reasonable-effectiveness-of.html" rel="nofollow">here</a>. When you assume the existence of a present value, you are allready assuming that your series converges. Given that, there is a very easy way to find a expression for the infinite sum. The details are here.

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