Welcome to this week’s installment of the From Eternity to Here book club. This is a fun but crucial part of the book: Chapter Ten, “Recurrent Nightmares.”

Excerpt:

Fortunately, we (and Boltzmann) only need a judicious medium-strength version of the anthropic principle. Namely, imagine that the real universe is much bigger (in space, or in time, or both) than the part we directly observe. And imagine further that different parts of this bigger universe exist in very different conditions. Perhaps the density of matter is different, or even something as dramatic as different local laws of physics. We can label each distinct region a “universe,” and the whole collection is the “multiverse.” The different universes within the multiverse may or may not be physically connected; for our present purposes it doesn’t matter. Finally, imagine that some of these different regions are hospitable to the existence of life, and some are not. (That part is inevitably a bit fuzzy, given how little we know about “life” in a wider context.) Then—and this part is pretty much unimpeachable—we will always find ourselves existing in one of the parts of the universe where life is allowed to exist, and not in the other parts. That sounds completely empty, but it’s not. It represents a selection effect that distorts our view of the universe as a whole—we don’t see the entire thing, we only see one of the parts, and that part might not be representative. Boltzmann appeals to exactly this logic.

After the amusing diversions of the last chapter, here we resume again the main thread of argument. In Chapter Eight we talked a bit about the “reversibility objection” of Lohschmidt to Boltzmann’s attempts to derive the Second Law from kinetic theory in the 1870’s; now we pick up the historical thread in the 1890’s, when a similar controversy broke out over Zermelo’s “recurrence objection.” The underlying ideas are similar, but people have become a bit more sophisticated over the ensuing 20 years, and the arguments have become a bit more pointed. More importantly, they are still haunting us today.

One of the fun things about this chapter is the extent to which it is driven by direct quotations from great thinkers — Boltzmann, of course, but also Poincare, Nietzsche, Lucretius, Eddington, Feynman. That’s because the arguments they were making seem perfectly relevant to our present concerns, which isn’t always the case. Boltzmann tried very hard to defend his derivation of the Second Law, but by now it had sunk in that some additional ingredient was going to be needed — here we’re calling it the Past Hypothesis, but certainly you need something. He was driven to float the idea that the universe we see around us (which, to him, would have been our galaxy) was not representative of the wider whole, but was simply a local fluctuation away from equilibrium. It’s very educational to learn that ideas like “the multiverse” and “the anthropic principle” aren’t recent inventions of a new generation of postmodern physicists, but in fact have been part of respectable scientific discourse for over a century.

It’s in this chapter that we get to bring up the haunting idea of Boltzmann Brains — observers that fluctuate randomly out of thermal equilibrium, rather than arising naturally in the course of a gradual increase of entropy over billions of years. I tried my best to explain how such monstrosities would be the correct prediction of a model of an eternal universe with thermal fluctuations, but certainly are not observers like ourselves, which lets us conclude that that’s not the kind of world we live in. Hopefully the arguments made sense. One question people often ask is “how do we know we’re not Boltzmann Brains?” The realistic answer is that we can never prove that we’re not; but there is no reliable chain of argument that could ever convince us that we are, so the only sensible way to act is as if we are not. That’s the kind of radical foundational uncertainty that has been with us since Descartes, but most of us manage to get through the day without being overwhelmed by existential anxiety.