How would Darwinism fare according to his attempt to define true randomness via algorithmic information theory?
Chaitin (right) found that concepts from computer programming worked well because, if the data is not random, the program should be smaller than the data:
Gregory Chaitin: I didn’t like that definition so I wanted a definition of lack of structure. You see, with the normal coin tosses, actually every possible finite sequence of heads and tails in a sense is equally random, because they were all generated by tossing a fair coin. But some of them, all heads has a lot of structure, all tails have a lot of structure, alternating heads and tails have a lot of structure. I was looking at something that ignored how the sequence is generated and just looked at it and said, is there structure here or isn’t there?
Now, the reason for doing this is because you can think of a physical theory to explain a phenomenon as a program — software that can calculate the predictions. If the program is short, then you have a very comprehensible theory and a lot of structure. But if the program is the same size in bits as the number of bits of experimental data, then that’s not much of an explanation. It’s not much of a theory because there always is a program the same size in bits as the bits of data.
Why? Because it just puts the data into the program directly and prints it out. That can always be done. But the smaller the program is, compared in size in bits to the number of bits of data that you’re trying to explain — and I’m talking about an explanation that gives no noise — it’s not a statistical theory. It has to give every bit of the data correctly. If that’s a small program, then you have a good theory. If you have two theories and one of them is a smaller program than the other, the smaller program is a better theory if the two of them calculate the exact sequence of your experimental data. It’s sort of a model of the scientific method.News, “Chaitin’s discovery of a way of describing true randomness” at Mind Matters News
Darwinism seems so full of exceptions now that it would be a very long program indeed.
Here are the stories, with links, to the earlier podcast discussion with Gregory Chaitin last week:
Gregory Chaitin’s “almost” meeting with Kurt Gödel. This hard-to-find anecdote gives some sense of the encouraging but eccentric math genius. Chaitin recalls, based on this and other episodes, “There was a surreal quality to Gödel and to communicating with Gödel.”
Gregory Chaitin on the great mathematicians, East and West: Himself a “game-changer” in mathematics, Chaitin muses on what made the great thinkers stand out. Chaitin discusses the almost supernatural awareness some mathematicians have had of the foundations of our shared reality in the mathematics of the universe.
How Kurt Gödel destroyed a popular form of atheism. We don’t hear much about logical positivism now but it was very fashionable in the early twentieth century. Gödel’s incompleteness theorems showed that we cannot devise a complete set of axioms that accounts for all of reality — bad news for positivist atheism.
You may also wish to read: Things exist that are unknowable: A tutorial on Chaitin’s number (Robert J. Marks)
Five surprising facts about famous scientists we bet you never knew: How about juggling, riding a unicycle, and playing bongo? Or catching criminals or cracking safes? Or believing devoutly in God… (Robert J. Marks)