of light-years. The latest data, from the Wilkinson Microwave Anisotropy
Probe, comes down firmly on the side of the Greeks—as best we can de-
termine, the large-scale geometry of the universe is f lat, much as it ap-
peared to the Greeks even before it occurred to them that Earth itself
might actually be round.
NOTES
- R. Trudeau, The Non-Euclidean Revolution (Boston, Mass: Birkhauser, 1987),
p. 30. Items such as points and lines are called primitive terms. Euclid was say-
ing that points are the smallest objects that there are, and cannot be subdivided.
He also says such things as “a line is breadthless length,” but qualifies it with
the adjective “straight” as the situation dictates.
- Ibid., p. 40. I’m not enough of an expert to be sure that these statements are ab-
solute translations from Greek, but these are basically the ones everyone uses.
- Ibid., p. 43. You have to wonder why this particular version of the parallel postu-
late was chosen. It seems awfully awkward, and it was no wonder that substi-
tutes were sought. It’s usually easier to work with a simple characterization of a
concept than a more complicated one.
- Ibid., p. 128.
- D. Burton, The History of Mathematics (New York: McGraw-Hill, 1993), p. 544.
- Linus Pauling was once asked how he got so many good ideas. He replied to the
effect that he just got a lot of ideas and threw the bad ones away. I attempted to
do this, but ran into two obstacles—I didn’t have anywhere near the number of
ideas that Pauling had, and when I threw away the bad ones, not much was left.
There were a few, though.
- Tom Lehrer received a bachelor’s degree in mathematics from Harvard at age
eighteen, and a master’s degree one year later. Headed for a brilliant mathemati-
cal career, he was sidetracked by becoming one of the three greatest humorists
of the twentieth century, in my opinion (the other two being Ogden Nash and
P. G. Wodehouse). He was probably the first politically incorrect black humor-
ist—yes, before Lenny Bruce and Mort Sahl—and his songs are classics. There
will always be a soft spot in my heart for “Nikolai Ivanovich Lobachevsky,” “The
Old Dope Peddler,” and “The Hunting Song,” but the one most likely to incite a
riot is “I Wanna Go Back to Dixie.” Enjoy. Visit http:// members.aol.com/quentn-
cree/ lehrer/ lobachev .htm.
- Burton, History of Mathematics, p. 545.
9. Ibid., p. 548.
10 Ibid., p. 549.
- Ibid. pp. 549–50.
- Ibid. p. 554.
1 3. S e e h t t p : / / w w w - g r o u p s. d c s. s t - a n d. a c. u k / ~ h i s t o r y / B i o g r a p h i e s / B e l t r a m i. h t m l.
Never the Twain Shall Meet 113
