by Allan Adler (copyright Allan Adler 2000)
The first meeting of Mathematical Culture took place on April 24, 2000 at Barnes and Noble's cafe on Campbell Lane in Bowling Green, KY. As it happens, it rained that night and that may be why no one showed up except me and the people who drove me there. They were nice enough to stay and participate and it turned out to be a good meeting.
We started by looking at a few of the one page poems and anecdotes at the end of the book. One of them was the poem Arithmetic by Carl Sandburg, which ends with the precious line:
"If you ask your mother for one fried egg for breakfast and she gives you two and you eat both of them, who is better in arithmetic, you or your mother?"
Another was the anecdote about Charles Babbage, a 19th century mathematician, who sent a letter to Tennyson complaining about the line of Tennyson's poem "The Vision of Sin" which reads:
"Every moment dies a man, every moment one is born."
Babbage complained that this implied that the world's population remains constant, whereas it is increasing, and urged that the second phrase be changed to "every moment 1 1/6 is born." In this respect, of course, Babbage was an ass for expecting poetry to do the job of a statistical abstract. But this also raises the question: what kind of mathematical accuracy should we expect from a short story that uses mathematics?
We were fortunate enough to have one person attending who had never seen a Moebius strip, so we made one and demonstrated its properties. Having done so, it became possible to explain the plot of the story "A.Botts and the Moebius strip". Apart from its merits as a piece of fiction, this story also uses mathematics honestly, in the sense that the only thing false about this story is the story itself: the author did not find it necessary also to deceive the reader about the relevant mathematics.
After explaining the Moebius strip, there was a digression in which I explained the Klein bottle and then introduced a way of thinking about Moebius strips, Klein bottles and doughnuts in terms of folding up a sheet of paper. This can be conveniently thought of in terms of a kind of video game. An illustration of this technique led to discussion of a method of making magic squares. By generalizing the technique to 3 dimensions, it became possible to show how to visualize the notion that the universe might be finite but unbounded and how to conceive of the expanding or contracting universe. This approach also makes it possible to visualize how it is that two apparently different stars might really be the same star. Actually, this topic is an active area of current research and an article on how to detect this possibility appeared in the Notices of the American Mathematical Society within the last year or so.
It was pleasant to discuss these more technical matters and, in a small group, it did no harm to the basic concept of Mathematical Culture, which is to focus on culture, not mathematics. It was also satisfying to be able to explain these advanced concepts so simply that a beginner could follow it. But if the group grows, I expect that more technical matters will be relegated to the puzzles group that I would like to form or, for really advanced topics, to the lecture series I plan to start.
The meeting lasted an hour and a half. That seems about the right length for a meeting.
To see the advertisement that was used for the first meeting, click on: