Saturday, September 19, 2009

Group-theoretical confusion, rhyming words and non-rhyming names

The words rage and age definitely rhyme. The pairs rhymetime and grouploop are spelled differently, but still do rhyme. We expect rhyming words in songs and rhymes. Sometimes, however, the fact that words do not rhyme at line's end is intended. The following song, that captures a panic during an epoch of exciting discoveries in group theory [1], is a case in point:
The floodgates were opened! New groups were the rage!
(And twelve or more sprouted, to greet the new age.)
By Janko and Conway and Fischer and Held
Mc Laughlin, Suzuki, and Higman, and Sims.

No doubt you noted the last lines don't rhyme.
Well, that is, quite simply, a sign of the time.
There's chaos, not order, among simple groups;
And maybe we'd better go back to the loops.

The panic of the 1960s and 1970s is over, unless you fear the Monster. Now finite simple groups are classified (completely?) and group theorists have their Atlas of Finite Groups, also known as Atlas of Symmetry (a “Rosetta Stone of science”), where groups are mapped out by beginning with A5 and finishing with M, the Monster that might as well been called the Friendly Giant or the Fischer-Griess group (see page 336 in [1]).
The names of mathematicians, mentioned in the above song, refer to Zvonimir Janko, John Horton Conway, Bernd Fischer, Dieter Held, Jack McLaughlin, Michio Suzuki, Graham Donald Higman, and Charles Sims.

Keywords: rhyme, mathematicians, symmetry, history of group theory, classification of finite simple groups

[1] Marcus du Sautoy: Symmetry. A Journey into the Patterns of Nature. First Harper Perennial Edition, Harper Collins Publishers, New York, 2009; page 306.

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