Boltzmann’s Brain explained

I'd blogged earlier on a Cosmic Variance article about emergent brains in the eternal soup of a senescent universe, but I didn't know the original context of the Boltzmann Brain idea. Another CV article today pointed me to one from last year that filled in the gaps. The Boltzmann Brain comes from a 2004 paper by Albrecht and Sorbo, and it was described in CV last year:

Boltzmann’s Anthropic Brain | Cosmic Variance

...Let’s posit that the universe is typically in thermal equilibrium, with occasional fluctuations down to low-entropy states, and that we live in the midst of one of those fluctuations because that’s the only place hospitable to life. What follows?

The most basic problem has been colorfully labeled “Boltzmann’s Brain” by Albrecht and Sorbo. Remember that the low-entropy fluctuations we are talking about are incredibly rare, and the lower the entropy goes, the rarer they are...
...So if we are explaining our low-entropy universe by appealing to the anthropic criterion that it must be possible for intelligent life to exist, quite a strong prediction follows: we should find ourselves in the minimum possible entropy fluctuation consistent with life’s existence.

And that minimum fluctuation would be “Boltzmann’s Brain.” Out of the background thermal equilibrium, a fluctuation randomly appears that collects some degrees of freedom into the form of a conscious brain, with just enough sensory apparatus to look around and say “Hey! I exist!”, before dissolving back into the equilibrated ooze.

You might object that such a fluctuation is very rare, and indeed it is. But so would be a fluctuation into our whole universe — in fact, quite a bit more rare. The momentary decrease in entropy required to produce such a brain is fantastically less than that required to make our whole universe. Within the infinite ensemble envisioned by Boltzmann, the overwhelming majority of brains will find themselves disembodied and alone, not happily ensconsed in a warm and welcoming universe filled with other souls. (You know, like ours.)

This is the general thrust of argument with which many anthropic claims run into trouble. Our observed universe has something like a hundred billion galaxies with something like a hundred billion stars each. That’s an extremely expansive and profligate universe, if its features are constrained solely by the demand that we exist. Very roughly speaking, anthropic arguments would be more persuasive if our universe was minimally constructed to allow for our existence; e.g. if the vacuum energy were small enough to allow for a single galaxy to arise out of a really rare density fluctuation. Instead we have a hundred billion such galaxies, not to count all of those outside our Hubble radius — an embarassment of riches, really....

Of course there's no end to the anthropic principle, which I tend to think of as an extreme application of Bayes theorem. We can be anthropic ad absurbum, and say that since we live in a rich universe we must exist in a really, really, really big and really, really, rare entropic excursion event.

Or maybe we're a dream of a more modest excursion, which is, after all, more likely.

Hmph. Cosmology is becoming about as satisfying as quantum mechanics.