Sunday, July 06, 2008

Need for change

Most of us agree that change is important yet hard. All of us can understand the benefits of change but the reason it seems hard is partly not having an "causal understanding" of why it is important. In this post I try to analyze why change is necessary for our survival. For that first I generalize the perspective of change to be more than just variance in temporal dimension of life. This means change characterizes any variance in the needs in any of our effective neighborhood. For e.g. it could be variance in the tastes of your roommates or variance in the goals of your friends etc. Having this generalized perspective, as I will try to argue, helps to see that variance in temporal dimension is not much harder than issues like tolerances etc. and that variance is essential.

Let's see why we need variance in the first place. There is high correlation between the composition of various chemicals in the body to the personalities and behaviors we manifest. Nature which has limited resources. For life to be persistent it is important that life can sustain on variety of resources so that Nature can efficiently "refill the resources". Based on the refilling abilities of Nature our bodies evolved to incorporate variance in the needs. We are not that variant in terms of needs for oxygen for e.g. since Nature seems to be very efficient in that resource regeneration. Hence the variance in our needs can be roughly traced to the variance in the availability of resources in our Natural neighborhood. Since Nature cannot handle all (varied) needs of all the life in a global way efficiently it decentralizes need fulfilling activities into the life forms itself. In other words the body chemical compositions are evolved in such a way as to locally have a cycle of supply and demand: starting from the most obvious examples, some are male, some are female, some have strong feelings about environment, some have strong feelings about high energy colliders creating black holes (see here), some are interested in making money, some are interested in education, some are spiritual, some are materialistic, some are good in theory, some are good in practice etc. etc. So to summarize we can think of local variances in needs is an efficient design of Nature for long-term sustenance of life. Something like: For a rope to be strong the individual fibers and yards and then strands have to be intertwined with friction among them. One other important thing with variance is that variance has to be "normal" locally so as to have the benefit of decentralization otherwise it would demand redundant effort. For e.g. if the friction between the fibers or yarns or strands is too high the rope might self-destruct under it's own friction without additional effort.

Now since the cycles of supply and demand usually are formed locally we might get stuck at local optima (which would be evident by diminishing returns in the cluster etc.). Change in temporal dimension would shuffle around the neighborhoods and gives us a chance to get out those local optima and form new cycles. Eventually we hope to find global optimum configuration. But as it is well known such optimization problems though can be "solved" require exponential amount of time in principle. So enjoy the journey and don't be scared to enter new cycles. It also helps to keep in mind an important property of stochastic optimization methods that not every move is better than the previous move which precisely is its strength. Of course blind (ignorant) change is not great since there are lot of probabilities (based on evidences, priors and likelihoods) you could compute to figure out the types of changes (moves) to reduce the mixing time.

I would ask the readers to pay attention to the words "efficient" and "local" as they carry the central message. Of course what all I discussed above (or in general in this blog) is not always new but is based on original thought. Lot of economists study such behaviors professionally and it would greatly help design your lives better by reading papers in such fields (I don't though): that's why the mathematicians who study and contribute to understanding such patterns are eligible Nobel prizes.

No comments: