Thursday, September 6, 2007

Anti-Quinean Hoaxers?

This NYT article quotes a letter in which Quine tells his friend’s kid about an arithmetic trick.

It is interesting to hear about the private life of the great man, but I think the comment section is even more interesting: rather than proving to themselves via normal elementary school math why the trick *must* work for all positive integers many posters seem to just try a bunch of cases. e.g. “The algorithm does not work for 29 x 31.” “In fact, it does not work for the number 29 at all. Why is that?” Then, sometimes they forget to take into account the first column (which causes trouble only when the first number you are trying to multiply is odd) so these cases seem to ‘falsify’ the claim, from which they conclude that the algorithm has “holes”. They even guess (apparently purely inductively) what the holes might be e.g. ‘all pairs of numbers starting with 29’. Other responders disagree by going through their observations of the particular instance in question. Then the same thing happens with another pair of numbers!

Is this just a case of decaffeinated blog posting or a bit of sly performance art which envisages what the state of mathematics would be like if we *did* form and revise mathematical beliefs in the same way as other more traditionally empirical parts of our web of belief?

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