July 10, 2010

Time is the simplest (non-commutative) thing

One of the most elegant theorems of all times is 4-word: every finite field commutes (Wedderburn's little theorem). While having life-long interests in anagrams and questions about time, i never thought they were related. They are. Thanks to the conference: Un espace non-commutatif engendre son propre temps, by Alain Connes on 06 November 2007 in Metz, France (downloadable video, 220 Mb, flv format, since i failed in embedding it into the blog).

Alain Connes is both a tremendous mathematician and wonderful, passionate story-teller. A cryptic message by a friend's child:
Je suis Alençonnais, et non alsacien, si tu veux un conseil nana, rendez-vous au coin annales
and a story about book reading by japanese mathematician Minoru Tomita (and related results) lead us to a lesson on associativity and commutativity rules. Anagrams are possible only because written language is associative and non-commutative (no alternative!). Meaningful anagrams (such as seen in Remaniement) are seen as a commutative breach. What is important, says Alain Connes, is poetic spirit (not foreign to mathematics) and a clue on where you are heading (if you do not change direction, see Lao Tzu). Without too much mathematics, Connes conveys those insights (with Carlo Rovelli) that the sense of duration may well arises from the statistical state of a system, quite like temperature. A relic of the antic  3 K radiation of the Universe. Funny enough, both French and Italian languages have very close words for time (temps/tempo) and temperature (température/temperatura). Could they be physically closely related, as real and imaginery parts of a complex number? Do algebra have periods? Look at the audience questions at the end of the talk. See also: Alain Connes : une autre vision de l’espace.

Arte also proposes a series of questions to Carlo Rovelli, interestingly pertaining to the life of a physicist. Alain Connes book on Noncommutative Geometry is freely available in pdf. Clifford D. Simak (not the - associative - algebra) wrote one of the most poetic sci-fi book on time travel, Time is the simplest thing (Le pêcheur en langue française). M. Dhenin shares a series of radio broadcast in a Mindmap for time (in French).