The Mathematics of Emergence and Flocking
author:
Stephen Smale,
Department of Mathematics, University of California
Description
Stephen J. Smale, a professor emeritus of mathematics at the University of California, Berkeley, who has contributed to a broad range of mathematical fields, has been named a recipient of the 2007 Wolf Foundation Prize in Mathematics, one of an array of prestigious prizes awarded yearly by the Israeli foundation.
Though retired from UC Berkeley since 1994, Smale continues to explore new fields, such as learning theory - the mathematical description of nerve connections in the brain that give rise to intelligence and learning; flocking, the tendency of group behavior to look coordinated, as with a flock of birds or a school of fish; and the mathematics of data mining. (UC Newsroom, University of Califonia, 2007-01- 19)
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| Slides | |
| 0:00 | Emergence |
| 4:44 | Example - primitive language - part 1 |
| 8:08 | Example - primitive language - part 2 |
| 12:52 | Flocking - part 1 |
| 13:26 | Mechanisms |
| 14:41 | Flocking - part 1 |
| 22:05 | Flocking - part 2 |
| 24:37 | Flocking - part 3 |
| 29:02 | Flocking - part 4 |
| 30:08 | Flocking - part 5 |
| 31:51 | Flocking - part 7 |
| 36:03 | From flocking to the general emergance problem |
| 37:19 | The price adjustment problem |
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assuming the participants (e.g., birds) to be significantly influenced by all other participants is needlessly complicated and, imo, implausible. more credible would be a model which incorporated screening effects, whereby the behaviour of near(est) neighbour(s) would be determinative. this presupposes much less demanding cognitive processing, whether we are dealing with bird brains, or wall street analysts. in the limit, each participant is effectively influenced solely by his nearest neighbour, and we get an ising like model. perhaps there are even pendants to the concepts of temperature and entropy, so that we would see a second order phase transition to a flocked phase. anyway, the attempt would be bound to be amusing...