Friday, June 22, 2012

Pseudorandom Numbers and Pseudoreal Theories.

There was something that was very interesting I wanted to record. I was thinking about the nature of science blah, blah that I used to think often when walking to work down the streets of Manhattan. It is about randomness that we have in this world and the probabilistic methods to explain it.

John von Neumann cautioned us, "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin." True randomness is determined by nature however generation of random numbers is too important to be left to chance. All the randomness that we produce are truly pseudorandom but they are quite powerful in answering many questions.

Similarly, when we use mathematical methods to explain nature (especially probabilistic methods, like the quantum mechanics formulation in terms of L2 theory), we are using a deterministic framework to explain randomness. Probability has a strong axiomatic and hence deterministic basis (remember Kolmogorov's axiomatic construction of probability space). Therefore, any explanation of physical phenomena through probabilistic methods is only pseudoreal. In other words, true explanation to any physical phenomena should be based on axioms that are truly "random" in nature. Having said this, pseudoreal theories are just as powerful as pseudorandom numbers in explaining this world.

Einstein was right after all when he said "God does not play dice".