Friday, January 25, 2008

Causes of importance

Couple of weeks ago as part of our regular discussions Suzan and I were discussing about ones importance in society and service to humanity. She was saying that all kinds of work are equally important and that it's unfair to down weigh a particular type of work as easy and boring. Just recently Scott posted trying to show how it's meaningless to argue about one field of science being more fundamental (and hence superior). Whether something is important is not, makes only sense in the context of time and majority as per our current understanding of Nature. For eg. we need large number of particles acting at a micro-scale for the second law of thermodynamics to hold on the macro-scale and usually a theorem has to be checked over and over again independently for its correctness.

Monte Carlo methods are usually used for simulations of complex probability distributions without closed forms. Using such methods random samples are drawn from probability distributions to represent the distributions. Drawing random samples implies that all samples are equally likely according to the distribution. But the main problem is that it is seldom possible to draw samples from the complex distributions (partly because they don't have closed forms). Hence the samples are drawn from a heuristic approximation and then given importance weights according to a likelihood function. Metropolis-Hastings is a very famous algorithm for such simulations. If the distribution is dynamic then the simulation is called filtering and particle filtering is a very common tool. Essentially all such techniques depend on the Bayes rule. But that's not my point. For successful simulation of a distribution the crucial design aspects are the proposal and the likelihood functions. These functions can be chosen arbitrarily and usually domain specific knowledge is heavily needed. If they are designed properly then over a period of time the samples start behaving random with equal importance weights, meaning representing the true distribution.

If humans are supposed to represent uniformly drawn particles of the distribution of life energy then all humans will have equal chance of survival. But because of complex correlations and interdependences such uniform sampling is not possible and hence we have to design proper proposal and likelihood functions to give appropriate importance weights so that over time the chances of survival become uniform. We can already start seeing some of such changes based on today's ages of expectancy through out the world. Hence it is important to have such importances to different types of work like giving more importance to let's say medical work compared to the work that can be automated effectively. Thus it is not only not unfair to undermine some kind of work but in fact recommended for greater good. Once the humans reach certain peaks in the distribution then they would have similar weights as is the case for physicists vs. mathematicians vs. computer scientists vs. biologists and so on.

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