Thursday, April 28, 2005

472: Predicting with unpredictability : Nature

Predicting with unpredictability : Nature:

When the temporal evolution of a system cannot be studied by traditional means, random numbers can be used to generate an 'alternative' evolution. Starting with a possible configuration, small, random changes are introduced to generate a new arrangement: whenever this is more stable than the previous one, it replaces it, usually until the most stable configuration is reached. Randomness cannot tell us where the system likes to go, but allows the next best thing: exploration of the space of the configurations while avoiding any bias that might exclude the region of the possible solution. If we are able to guess the probability distribution of the configurations, then instead of conducting a uniform random search we can perform an 'importance' sampling, focusing our search on where the solution is more likely to be found.

Optimization problems are often solved using stochastic algorithms that mimic biological evolution. Although it may sound vaguely unpleasant, we come from a random search. In nature, new genetic variants are introduced through random changes (mutations) in the genetic pool while additional variability is provided by the random mixing of parent genes (by recombination). Randomness allows organisms to explore new 'designs' which the environment checks for fitness, selecting those most suited to survival. But the optimal solution is not found once and for ever. A continually changing environment means evolution is an on-going process; it does not produce the 'perfect' organism, but rather a dynamic balance of myriad organisms within an ecosystem.

Generating true randomness is a challenging task. Early attempts at stochastic simulation produced samples through processes such as dice tosses or card draws. These phenomena in principle obey newtonian mechanics, but in practice evolve unpredictably owing to their chaotic dynamics. Computers have made it much easier to produce large numbers of samples. They cannot, however, generate true random numbers.

That's in the midst of a paper talking about the development of random number generators. Math and physics rely on evolutionary biology!