Unexpectedly, it turned out that this year, I gave twice an introductive mini-course on logarithmic Sobolev inequalities, for distinct audiences, at Institut Henri Poincaré, in April, and at École normale supérieure, in December. Here are the short notes : PDF.
There is something fun about it. I like very much to connect logarithmic Sobolev inequalities to the work of Boltzmann. This is not what I have learned, since my teachers Dominique Bakry, Michel Ledoux, and Laurent Saloff-Coste were not particularly versed in or attracted by Physics. Meanwhile, Cédric Villani, who knows very well Boltzmann, is a limited probabilist. Personally, I like very much the Physics of Boltzmann, however, I am not excited and seduced by the technical mathematics that have been constructed around his evolution equation. I have discovered that many of the mathematicians specialists of this equation are not even aware of what is really a Boltzmann-Gibbs measure. All these facts are striking effects of hyperspecialization in science. A somewhat similar phenomenon can be observed for the Schrödinger equation, which has a deep probabilistic and physical content, but which is studied by several high profile mathematicians from the mathematical analysis perspective, with often a very limited culture in probability and even in Physics. All this should be seen as a motivation to give more introductory talks, across fields, to reduce the effects of hyperspecialization. At least this is what I try to do !
In a way culture is the result of curiosity and memorization. A limited culture comes from a limited curiosity and/or memorization. Curiosity is instinctual, takes time, requires effort, and implies a sort of intellectual appetite for danger, since it could force to revisit some foundational certainties. Also it is often replaced by a sort of contempt, hiding an intellectual laziness. These mechanisms can operate at various scales/scopes, with various intensities, and vary over time.
Even if it can help, a pluridisciplinary culture is neither necessary nor sufficient for being deep and creative, it is something else. Curiosity can be even defocussing, time consuming, and counterproductive in the short-term. This plays into the game of hyperspecialization, which is essentially the result of a sort of short-term utilitarianism, something unconscious which is implicitly encouraged by the selective educational and academic systems. However, an advantage of culture is that it always helps to be a better teacher and guide for young people.
Leave a Comment