Monday, March 16, 2015

Manichean Mathematics

In overwrought politics and religion, it is commonplace to demonize some of one’s foes.  Thus, for Christians, the Antichrist;  for Muslims, the comparable Dajjâl.   On the cover of the current Time, Hilary Clinton appears with a pair of horns.  So it goes.

Although disputes exist (both personal and professional) within the ranks of mathematicians, you really don’t find that sort of thing, so far as I know.   About as far as it goes  is witty dismissals of some subdiscipline;  as, Cantor’s innovations in the transfinite, which some dismissed as “more theology than mathematics” -- theology, though, not diabolism.  Or Category Theory as “the higher macramé” (as wits had it back when I was in college.  Since then, the Category approach has knit -- or rather knotted, to continue the metaphor -- some quite interesting structures, that seem to hold.)

So it was with some surprise that I ran across this passage:

Euclid has been the evil genius … for the history of mathematics.
-- Imre Lakatos, Proofs and Refutations (1976), p. 140

(Having just the other day watched the old Fritz Lang film, “The Testament of Dr Mabuse”, this phrase delivered a particular chill.) 

In the course of his book, Lakatos does permit himself some unkind or dismissive digs at certain mathematicians, historians of the field, or styles of mathematizing, but this formulation seemed extreme.  Yet as the author’s footnote immediately reveals, it is taken straight from so sober a source as R. B. Braithwaite, who (in 1953) called Euclid the “evil genius of philosophy of science”  -- though, to be sure, the “good genius of mathematics" itself.   (One pictures twin miniature Euclids, one red with a tail, one white with wings, perched on Donald Duck’s shoulders and whispering conflicting counsels.)


This mild and forgettable aside  yet brought back memories of Berkeley days, when some of my friends were refugees from the group then known as the National Caucus of Labor Committees, a sect around the guru Lynn Marcus (later known as Lyndon Larouche).   That formation made diabolization a positive organizing principle of their style of thought.   What made it all so fascinating to follow, was trying to guess whom they would seize on to demonize: Zbigniew Brzezinski, all right, but -- the Queen of England?  (And that, lastingly.  Never was a doily of an old lady more improbably cast.)   And then things got really interesting when the dichotomization was extended to figures from intellectual history.   As, Plato they liked (yay, Plato);  but he appeared ever in a duality, contrasting with “the evil Aristotle”.
The NCLC even extended this perspective to mathematics, their particular hero being Riemann (again, hoorah hoorah).   Whom they chose as the anti-Riemann  I forget, but anyhow it was impressive that a group that was vying for converts in an arena crowded with such aggressively ignorant rival leftist sects (for the NCLC was formally of the Left at that time)  as the Weathermen, various Maoist groups, the "Symbionese" 'Liberation' '''Army''', the Black Panthers and so forth,  had even heard of such figures as Riemann, and deemed them of world-historical importance.
(Note:  It is by way of arcane allusion to that episode, that I titled my ongoing feuilleton of dark doings among the Illuminati, the Riemann Conspiracy.  Something like three people will get the joke.)

Is .... this .... the face of Evil ??


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