Monday, May 28, 2012

Khan Academy's "brain teaser" about how to defeat an alien abduction attack: the power of one person, but can he act on his own?


The Khan Academy has a 17-minute “Alien Abduction Brain Teaser” video that offers an interesting example of mathematical induction.

Salman likes to do these lessons himself, drawing sketches on a virtual blackboard, producing inexpensive animation that requires no film editing before publication on YouTube.  His voice always sounds comforting.  He would be a good classroom math teacher if he wanted to be.

In this problem, ten people have been abducted, and each represents the welfare of one-tenth of the world’s population. The aliens put a hat, either blue or purple,  on the back scalp of each person, who can see those in front but not behind. The people (as in the IFC film “Exam”) have 24 hours to come up with a strategy.  Each person, in reverse order, will be asked the color of his hat. If he guesses right, he and his people are saved, from being converted to mushroom or fungus farms. (This sounds like a notorious Bible story, doesn’t it.)  There is a way, involving counts of even or odd occurrences of a color, to answer in such a way that all people but the rear person can survive.  The rear person is exposed to a possible Isaac-like “sacrifice”.

The puzzle would work, of course, for any finite number of people. 

Why is this important to me?  “Mathematical induction” (here combined with a little number theory) is certainly an important way to prove many mathematical propositions.  More nebulous is inductive reasoning, and statistical prediction, and settings of the “scientific method”.   (I suspect Khan has videos on these.)
In my own life, in a few areas (“self-broadcast” and personal relationships), I certainly have experienced a dose of having to listen, sometimes after the fact, of what people “want” from me, and thing is morally “right” for me.  Some of this has to do with my own dependence on “fantasy” and interest in self-broadcast without the expected willingness to accept intimate or personal contact with other people on their terms rather than mine – before being noticed globally.  I can extrapolate the “moral principles” involved, but then I start noticing that people want contradictory results.  Even so, “induction” from the possible color of my own “hat” can cover a lot of moral territory.

There are ways to complicate the experiment.  Imagine that all the abductees are young men, and are each expected to step into or dive into separate swimming eddies, some of which contain chemical depilatories.  Afterwards, they can’t see themselves or those behind, but can still see those in front.  (Believe it or not, a health club in Dallas had an “accident” like this with its whirlpool in the 1980s.) 


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