Gregory Chaitin is one of my preferred author and perhaps the best one, I read all his books, I read all his papers . He is the man who discover Ω , who discover the algorithmic randomness and I don’t believe in the existence of stochastic processes so I think the correct definition of random is the algorithmic randomness.
The objective of Chaitin is to prove that a random walk in the software space can increase the complexity . Trying to do this what he reach is a very interesting result.
I don’t agree with Chaitin in the starting point not in the conclusion.
To have an infinite increasing complexity evolving software we need the existence of
- a random stochastic source
- an oracle to solve the halting problem
The point 1 is a main problem , I think the universe is deterministic . It is very difficult to construct a stochastic universe that appear so deterministic. Why should we introduce a stochastic source where everything can be explained by deterministic systems? Without a stochastic source we can not define an “evolving program” , in this case the program will change following deterministic rules so the program never change what really change is its state. A program never change by definition.
Without a stochastic source we can not have a random walk in the software space , what we can do is to use an algorithmic random string S as a finite source of random data but in this case the random walk has a limit in the increasing of the complexity that an evolving software can reach.
If we have a stochastic random source the injection of the complexity from the random source to the evolving programs is not the most interesting part , we should move the attention to the stochastic random source with an infinite complexity , this strange object become really more interesting than the evolving programs .
Using the dictate of Occam’s razor isn’t it more simple to believe in a deterministic universe that follow deterministic rules and so using a finite algorithmic complexity the execution of such program express evolutionary characteristics without strange things like oracles and stochastic source?
Why the universe expose evolutionary behaviour? Can this evolutionary scenario be only a point of view of the behaviour of a deterministic program?
What Chaitin develop is an interesting tool to use with approximations , approximating our low knowledge of the deterministic behaviour of the evolutionary walk in the software space such that we can approximate it with a random walk, and other approximations like the oracle because I really don’t think this is the reality.
When Chaitin move to the field of biology I had a lot of doubts on the relevance of the results that was possible to reach but I am amazingly surprised by these results I trust the Chaitin development in this field will give me a lot of suprises.
I hope to give to the reader enough curiosity to read the new Proving Darwing book.