There seems also to be a conveniently available 1998 version[1] which, unlike the version linked in the OP, contains still-working links to several additional chapters.[2-6]
I don't know how the content compares to Chaitin's books, including The Unknowable (1999).[7]
> So I like to apologize in an aggressive way about my field. I like to say that my field has no applications, that the most interesting thing about the field of program-size complexity is that it has no applications, that it proves that it cannot be applied! Because you can't calculate the size of the smallest program. But that's what's fascinating about it, because it reveals limits to what we can know. That's why program-size complexity has epistemological significance.
The key idea I get from this field is that mathematics and rational thought can create logical systems more complex than what it can deterministically study.
Thus, any scholar of any theoretical discipline should be warned that the very activity of expanding its field generates unknowable entities faster than it uncovers certain knowledge.
I love the way this is written to be as simple and understandable as possible. Too bad more writing in mathematics and science is not approached this way.
It turns out that a number being odd is almost inevitable. How do we know that? Well, take a look at this sequence:
1 2 3 5 4 7 9 11 13 6 ...
As you can see, there's a lot of odd numbers between every even number, and the fraction of even numbers falls and falls as you keep going. Therefore, virtually every number is odd...
I don't know how the content compares to Chaitin's books, including The Unknowable (1999).[7]
[1] https://jillian.rootaction.net/~jillian/science/chaitin/www....
[2] https://jillian.rootaction.net/~jillian/science/chaitin/www....
[3] https://jillian.rootaction.net/~jillian/science/chaitin/www....
[4] https://jillian.rootaction.net/~jillian/science/chaitin/www....
[5] https://jillian.rootaction.net/~jillian/science/chaitin/www....
[6] https://jillian.rootaction.net/~jillian/science/chaitin/www....
[7] https://link.springer.com/book/9789814021722