Eric Holloway: … randomness is unprovable, which was proven by three different computer scientists: Ray Solomonoff, Andrey Kolmogorov and Gregory Chaitin. The only thing we can know is that something is not random. Hence, we can never know that something originated from randomness.
Chaitin reflects on the fact that if he had to do practical work 60 years ago, there wouldn’t be practical research today based on the Omega number. But that raises a question: If materialism were true, why does theoretical stuff matter so much?
Chaitin: The normal view if you dabble in metaphysics is that the universe is made from mathematics. That’s a Pythagorean idea, that God is a mathematician. And I prefer to say God is a … a computer programmer or a programmer.
Creativity is what we don’t know. Once it is reduced to a formula a computer can use, it is not creative any more, by definition.
Robert J. Marks sometimes uses the paradox of the smallest “uninteresting” number to illustrate proof by contradiction — that is, by creating paradoxes
Chaitin: I have a pessimistic vision which I hope is completely wrong, that the bureaucracies are like a cancer — the ones that control research and funding for research and counting how much you’ve been publishing. I’ve noticed that at universities, for example, the administrative personnel are gradually taking all the best buildings and expanding. So I think that the bureaucracy and the rules and regulations increases to the point that it sinks the society.
Decades ago, Gregory Chaitin reminds us, mathematicians were not forced by the rules of the academic establishment to keep producing papers, so they could write key books.
Chaitin, best known for Chaitin’s unknowable number: “Some mathematics, I think, is definitely invented, not discovered. That tends to be trivial mathematics … But other mathematics does seem to be discovered. That’s when you find some really deep, fundamental mathematical idea, and there it really looks inevitable. “
More scandalous still, Gödel was not a Darwinist: “I believe that mechanism in biology is a prejudice of our time which will be disproved.”
Chaitin offers some thoughts on Georg Cantor and Srinivasa Ramanujan as well, both of whom thought that their math discoveries were divinely inspired.