Out of curiosity, do you [Yudkowsky/other readers of this comment] have a metaphysics you think is likely correct and which dissolves the Boltzmann Brain problem?
There used to exist the Steady-state model. If it was true, then the problem would immediately dissolve because classical minds would emerge with a far, far bigger density than the paradox-inducing Boltzmann ones.
I think this misses out on two key points:
1) the standard anthropic-probability difficulty. We have no clue if "disordered experience" is even a thing, let alone how common it it. each of us knows exactly one experience, and there's no outside eye by which to compare them or choose among "possible" ones.
2) if you're hypothesizing the minimal Boltzmann-brain experience, it doesn't need an ordered universe. It just needs enough ordered spacetime for some 4-d bounding box to experience a MEMORY of what would be observed in an ordered universe.
(note: my intuition is that the universe is mostly real, and this isn't an instantaneous experience of remembering my life and having typed up to here. but I can't actually reason about it probabilistically, especially since I accept that probability is subjective - a measure of my ignorance).
1or any metaphysics which says you can't objectively answer the question "Which observer-moments exist or don't exist / have more weight to them than other observer-moments?"
Why can't I say that there is no objective answer to which observer-moments exist more, but that I subjectively care more about the observer-moments that happen in mathematically simple universes, in simple-to-describe locations, like Scott Garrabrant describes in Preferences without Existence?
In this ontology, "I expect that my brain won't dissolve into chaos in the next moment" translates to "I will continue preparing dinner instead of meditating on the meaning of mortality, because preparing dinner helps the versions of me who live in simple locations, and meditating on mortality helps the Boltzmann-brain versions of me who are about to die, and I subjectively care more about the versions of me living in simple locations".
With some added caveats on what exactly I care about (I hope to publish a sequence of this soon), I find this view more appealing than assuming the existence of a reality fluid that makes some moments objectively more real than others.
(Initially written for the LW Wiki, but then I realized it was looking more like a post instead.)
In 1895, the physicist Ignaz Robert Schütz, who worked as an assistant to the more eminent physicist Ludwig Boltzmann, wondered if our observed universe had simply assembled by a random fluctuation of order from a universe otherwise in thermal equilibrium. The idea was published by Boltzmann in 1896, properly credited to Schütz, and has been associated with Boltzmann ever since.
The obvious objection to this scenario is credited to Arthur Eddington in 1931: If all order is due to random fluctuations, comparatively small moments of order will exponentially-vastly outnumber even slightly larger fluctuations toward order, to say nothing of fluctuations the size of our entire observed universe! If this is where order comes from, we should find ourselves inside much smaller ordered systems.
Feynman similarly later observed: Even if we fill a box of gas with white and black atoms bouncing randomly, and after an exponentially vast amount of time the white and black atoms on one side randomly sort themselves into two neat sides separated by color, the other half of the box will still be in expectation randomized. If the Solar System had arisen by a fluctuation of order, in expectation the rest of the universe would be a random smear; even taking our own Solar System for granted, the appearance of the rest of the universe would be vastly-exponentially improbable.
The increased still-infinitesimal likelihood of "just one solar system fluctuates out of chaos", compared to "one Hubble-sized volume randomly fluctuates out of chaos", is vastly vastly greater than the ratio of a Hubble volume's size to a solar system's size. So if you pick a solar system that is part of a system that has randomly fluctuated out of chaos, the incredibly incredibly vast majority of solar systems like that find themselves alone in a larger bath of chaos.
Indeed, if a fluctuation out of chaos gives rise to a system containing something that can look around itself at all, by the far the most likely case is that it would be just a minimal brain that formed out of chaos, maybe for only a few moments before dissolving again. Any larger system would fluctuate out of chaos exponentially-vastly less often.
This, finally, reflects an anthropic challenge to any model of physics which predicts an eternal universe dissolving into thermal equilibrium and lasting literally forever -- or similarly, any sort of quantum continuum said to last for an eternity of equally-real distinct moments. "Boltzmann brains" assembled by random fluctuations would then vastly outnumber the sorts of brains that had found themselves in larger ordered worlds of thermal disequilibrium.
But if a supervast or infinite majority of observer-moments happen in Boltzmann brains, our own experience of reality seems miraculously ordered by comparison. Boltzmann brains that have briefly self-assembled do not on average find themselves with very ordered memories, nor seeing visual fields that are themselves highly structured and ordered. Boltzmann brains like this exist, but they are supervastly outnumbered by Boltzmann brains with more chaotic experiences, for the probably-few moments that they experience. Even among the infinitesimal fraction of Boltzmann brains that have a regular visual field, and see apparently ordered shapes on the left side of their visual field, a supervast majority of those would see chaos on the right side of their visual field.
Our current experience -- your own experience, at this very moment, of seeing ordered letters on a screen -- therefore seems to provide overwhelming anthropic evidence against any model of reality or physics which would imply that most brains are Boltzmann brains.
Any attempted objection to "the surprising overwhelming order of our present experience contradicts the theory that most experience is far more disordered" -- eg, "But I don't believe in anthropic reasoning, so there" -- makes the prediction that your experience will dissolve into chaos in the next moment. Assuming the Boltzmann scenario, even conditioned on your current experience being anomalously orderly, most orderly experiences like this dissolve into chaos within moments. So if your current experience does not dissolve into chaos within moments, you should regard the Boltzmann hypothesis as having made an extremely strong prediction which has now been falsified -- at least to the extent that you ever regard any physical theory as ever being falsifiable by your memories of what it predicted and your memories of what you observed.
Realistically, you expect your experience to not dissolve into chaos in the next instant. I think that given our incredibly ordered current experience and memories, to treat this as not just a coincidence of superexponentially tiny probability, seems to me wholly justified. If it is not coincidental, then indeed our currently orderly experience may continue to be orderly rather than dissolving back into chaos. We are then faced with the question of how and why reality works to make this not be the case. I find myself without the stamina to further dissect the one who now wisely smiles that this is just a pragmatic sort of useful assumption rather than a credible belief.
"But we're not Boltzmann brains" then constitutes a strong-seeming anthropic objection to any larger story about the universe which implies that most experience would reside in Boltzmann brains; for example, to any physical theory which implies that the universe would eventually turn into a thermal bath (which would then persist forever (through an infinite succession of distinct, equally-real moments and events)).
An analogous objection may be made to any larger metaphysical story which provides no basis on which to say that ordered experiences would outnumber disordered experiences; for example, a bare assertion that "All mathematical structures exist." If all mathematical structures exist, why do comparatively tiny numbers of orderly observer-moments seem to carry so much more weight-of-existence than the vastly more numerous horde of possible disorderly moments of conscious awareness?
Similarly if every physical object can with equal justice to be said to implement every computation. Then why would computations of orderly observer-moments outnumber computations of chaotic observer-moments?
So the argument from "My experience does not look like a typical Boltzmann brain experience" not only weighs against models of physics in which the universe ends up as a literally eternal sea of particles or quantum foam in thermal equilibrium, but also, any account of mathematical realism / modal realism which does not try to explain why some universes or observer-moments have greater weight than others; or any account of computationalism in which it is said to be ultimately subjective and arbitrary which objects implement which (conscious) computations; or any metaphysics which says you can't objectively answer the question "Which observer-moments exist or don't exist / have more weight to them than other observer-moments?"