Chapter Eight – A Window on Infinity
Confession time. When I purchased my first copy of The Beginning of Infinity, it was because I’d decided I didn’t believe in infinity. I thought the book might give me some interesting insights. Instead, David Deutsch convinced me of essentially everything he argued, including that denying the existence of infinity is just a parochial error, the argument from incredulity.
The simple reasoning Deutsch uses to prove that infinity must exist is both beautiful and undeniable. Is there a largest natural number? If there is, then the rule about creating the next natural number simply by adding 1 to the previous number must stop applying somewhere. If there’s not, then infinity is real. It plays a role in our best explanations, and that’s the definition of reality. Arbitrarily creating rules to prevent infinity from existing creates very bad explanations.
The examples Deutsch gives of the implications of infinity are breathtaking, and the devastating effect that infinity has on the anthropic principle makes me rethink that whole subject. I’m not going to even try to do justice to the mind-blowing examples of infinity and its consequences here. You’ll have to read this chapter for yourself. Instead, I’m going to write about an insight that shook me even deeper than the idea of infinity.
I’d always had a nagging feeling that fine-tuning arguments about the universe are missing something basic. Deutsch showed me what that basic something is. The amazing thing about universal fine-tuning isn’t how unlikely the value of the cosmological constant or the mass of the electron are. Instead, the amazing thing is something more fundamental, the fact that we live in a universe where such things as the cosmological constant and the mass of the electron have any sort of logical meaning at all. This is what Deutsch points out:
“Three closely related ways in which the laws of physics seem fine-tuned are: they are all expressible in terms of a single, finite set of elementary operations; they share a single uniform distinction between finite and infinite operations; and their predictions can all be computed by a single, physical object, a universal classical computer . . .” (p 174)
I won’t pretend to understand everything he says here, and even less will I pretend to understand all the statements he makes in this chapter. For the first time (but not the last), Deutsch is stretching me beyond my current ability. I’ll study this chapter again, but for now what I take away is that, for some unexplained reason, we live in a universe that is explainable. And that, more than any of the fine-tuning coincidences, is amazing.
I should point out that this in no way should give hope to any supernatural answer to the question of fine-tuning, either the more ordinary sort of fine-tuning or this more fundamental fine-tuning. If there’s one take-away from Deutsch’s book that will be top of mind forever, it is that supernatural explanations are always bad explanations. Good, hard to vary explanations are out there. And problems are soluble.