| This humorous short story about a brawl in a pub of mathematicians appeared in the November 2005 issue of Math Horizons magazine. There is quite a bit of "mathematical name-dropping" in the form of quick one-liners (e.g. "Below a sign that reads 'Mobius Strip" lies something all scratched up on one side. A jug that will never again hold anything inside it is by a placard that reads 'Klein Bottle'.") But, the main mathematical content of the story concerns the conflict between what characterizes a "small" subset of the reals. On the one hand, there are those who argue that any countable subset is small and on the other are those who think that it must have "measure zero". Both may sound sensible at first, but both also produce a supposedly "small" set that doesn't seem quite so small. Sure, it makes sense to say that the integers form a "small" subset of the reals because they are countable...but so are the rationals. And how can the rationals be considered a small subset when they are dense? Similarly, the integers have measure zero and so would appear to be small by the other definition as well...but the Cantor set is an example of a measure zero set that is uncountable. How can it be considered small when it is in one-one correspondence with the real numbers?
It is interesting to see these ideas in the form of a story. Unfortunately, they are not presented in a way that will inform those who are not already familiar with the concepts. Those with the necessary background in topology and analysis will find the story entertaining, but for everyone else this is a long-winded joke whose punchline must be explained.
| Contributed by
Bob Vallin
In defense of my story, Gangs of New Math, the mathematics of measure, denseness, and
what defines a small set (there are four conditions to be met) were all in the original version. It
was sliced by the editors to fit the space.
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BTW In case anyone doesn't "get" the title, check out both The Gangs of New York and the new math. |
