So I finally picked up a copy of Probability Theory: The Logic of Science, by E.T. Jaynes. It’s pretty intimidating and technical, but I was surprised how much prose there is, which makes it surprisingly palatable. We should recommend this more here on Less Wrong.
Just remember that Jaynes was not a mathematician and many of his claims about pure mathematics (as opposed to computations and their applications) in the book are wrong. Especially, infinity is not mysterious.
It should be obvious that infinity (like all things) is not inherently mysterious, and equally obvious that it’s mysterious (if not unknown) to most people.
Infinity is mysterious was intended as a paraphrase of Jaynes’ chapter on “paradoxes” of probability theory, and I intended mysterious precisely in the sense of inherently mysterious. As far as I know, Jaynes didn’t use the word mysterious himself. But he certainly claims that rules of reasoning about infinity (which he conveniently ignores) are not to be trusted and that they lead to paradoxes.
So I finally picked up a copy of Probability Theory: The Logic of Science, by E.T. Jaynes. It’s pretty intimidating and technical, but I was surprised how much prose there is, which makes it surprisingly palatable. We should recommend this more here on Less Wrong.
Just remember that Jaynes was not a mathematician and many of his claims about pure mathematics (as opposed to computations and their applications) in the book are wrong. Especially, infinity is not mysterious.
It should be obvious that infinity (like all things) is not inherently mysterious, and equally obvious that it’s mysterious (if not unknown) to most people.
Infinity is mysterious was intended as a paraphrase of Jaynes’ chapter on “paradoxes” of probability theory, and I intended mysterious precisely in the sense of inherently mysterious. As far as I know, Jaynes didn’t use the word mysterious himself. But he certainly claims that rules of reasoning about infinity (which he conveniently ignores) are not to be trusted and that they lead to paradoxes.