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Posts Tagged ‘math nerd’

Due to the advertising overload that is Valentine’s day, most men (including the writers of this fine blog) spend the day thinking about woman/women (depending on marital status).

Under the circumstances, I thought this was the right time to advertise the ‘flaw of averages.’ It’s a really simple idea, but one that needs to be taught in every business school. Very simply, if you’re planning for some uncertain eventuality- the plan that works well against the average eventuality probably doesn’t work very well on average.

So, in particular gentlemen, please don’t plan to snag these women:

It probably won’t work out well on average…

HT: the Face of Tomorrow via the now annoyingly redone Gawker site that is Gizmodo.

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Zermelo Frankel Humor

Math as we understand it is straightforward, incontrovertible, and unarguably true. It appears a far cry from the inconsistencies of the real world and/or the chosen professions of these bloggers, which lie somewhere in the union of economics, finance and policy. Not even the pure sciences (did I hear a Higgs Boson) appear quite as prisitine.

Deep within the bowels of pure math, in courses reserved for the ritual acolytes (read: graduate students), there exist some troubling details. In particular it suggests that the seemingly ‘harmless’ axiom:

  • (Axiom of Choice): Given any collection of non-empty sets, the Cartesian product is not empty.

plus the standard axioms of set theory (it’s already strange enough that this isn’t a standard axiom) implies this seemingly crazy result:

  • (Banach-Tarski, in English): You can take a ball of volume 1 and cut it into a few pieces, and then recombine those pieces into 2 balls of volume 1.

The deep machinations that resulted into the truthiness of this result I once knew but have now forgotten. However, jokes on the Banach Tarski result remain my favorite brand of math humor. My two favorites are reproduced below:

  1. Q: What’s a mathematician’s favorite anagram of Banach Tarski? A: Banach Tarski Banach Tarski.
  2. The Banach Tarski paradox was originally discovered by King Solomon, but his gruesome attempts to apply it set back Set Theory by millenia.[via the ever delightful webcomic xkcd]

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