Wednesday, September 06, 2006

Man, Machine and Math

Scientists and artists are both fascinated by one thing: Nature. Artists are more obsessed with causality while the former are with results. Both scientific and artistic efforts try to use rationality but under different bounds and are important. Working in bounded rationality is something that is hard to be avoided in this finitistic world. The most profound questions in science happen to be those that question causality like the quest for Unified Field Theory by physicists, quest for proof of P?=NP by mathematicians. Artificial Intelligence is one of the most coveted dreams of man that if realized has unparalleled consequences on machines. An artist can dream of a machine pursuing its dreams like in A.I. by Speilberg. A scientist can dream of finding proofs for most intriguing theorems automatically.

What is the main problem in realizing such dream machines or dream theories like unified theory? It's their complexity. Efficient representation of ideas is very essential in making them useful. Math is a popular tool that allows us to make judgements about different representations, to apply the ideas to a large scale avoiding manual errors, to give new insights which are elusive without it. There are many wonderous things in Nature that are not mathematical (or atleast not mathematized yet) like humans, plants, viruses etc. (BTW the P vs. NP question precisely asks whether humans can be completely efficiently mathematized in terms of their mathematical ability).

Most people agree that to understand a phenomenon completely one must be able to look inside the process. But when we start looking inside our own processes we start being spiritual. For example in one way or the other we try to reason out some important events based on karma philosophy. Though there is no consensus mostly because of non-verifiability scientifically, we eventually settle down for it. If someday we can formalize karma using math, which would certainly be extremely sophisticated and need lot more evolution, we could have unified field theory, more predictability of events in life etc. But then again we need room for growth even then. We don't have to worry unless we overturn the existing logical system.

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