Monday, December 29, 2003

Most of my mathematics degree classes in Portugal in the early 70s focused on conceptual structure rather than computation. For most of my professors, the style of Bourbaki was the apex of mathematical discourse, including Dieudonné's Foundations of Modern Analysis, which rejected lowly intuition: This has also as a consequence the necessity of a strict adherence to axiomatic methods, with no appeal whatsoever to “geometric intuition,“ at least in the formal proofs; a necessity which we have emphasized by deliberately abstaining from introducing any diagram in the book. I learned abstract algebra, analysis, topology, differential geometry, probability that way. My only computational escape was programming, totally outside class, which my favorite professor dismissed as “keyboarding.” Applied mathematics was ignored or ridiculed. I wonder how much of this came from a cultural parallelism between mathematical abstraction and the artistic and architectonic abstractions of modernism. Many Portuguese intellectuals of the time saw modernism as the apex of culture, partly because Salazar's dictatorship was esthetically reactionary, making modern tastes in art a mild and less dangerous manifestation of political dissent. Anyway, it took me a while to shake off a snobbish disdain of "concrete" and "applied" in mathematics. I'm thinking about this now because I keep needing "concrete" and "applied" more and more, and sometimes I wish I had learned it earlier. In theoretical computer science, there's a vaguely parallel gap between "euro theory" and "american theory." Could it have something to do with the different histories of modern culture in the two continents, and the different roles of intellectuals? 9:53:06 PM

After finding topographic inaccuracies in Crowded with Genius, I recalled my irritation and disappointment some 25 years ago when I got to the Lisbon episodes of Mann's The Confessions of Felix Krull, Confidence Man. Not only was its Lisbon a cartoon, but attempts at reproducing Portuguese speech and forms of address were embarrassingly wrong, for instance the use of the Castilian "Don" instead of the Portuguese "Senhor" in polite address to a man. However, I don't read German, this was in an English translation. Where were the inaccuracies? In the original, which was incomplete at Mann's death and therefore likely unrevised; in the translation; or in my recollections from so long ago? Regardless of the origin, I never fully recovered that glow of admiration for Mann acquired reading The Magic Mountain and Joseph and His Brothers. Of course, it could be that if I were to reread those books today, after experiencing alpine regions and Israel, I would find other reasons for irritation. 10:15:55 AM

Alain de Botton: A Danger of travel is that we see things at the wrong time, before we have had a chance to build up the necessary receptivity and when new information is therefore useless and fugitive as necklace beads without a connecting chain. Same with reading. Convention or school demand that we read certain books way before we had recognized the questions that those books work to answer. This is true even for scientific books. In college, I paid little attention to statistics and completely bypassed combinatorics. Now, they matter for the questions that interest me much more than the algebra and topology I cared about most back then. 9:52:35 AM