A relatively brief explanation of Boltzmann Brains
(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?”
As far as I know, Boltzmann brains became an issue in contemporary cosmology after a 2002 paper by Susskind, Kleban, and Dyson, “Disturbing Implications of a Cosmological Constant”. in which they specifically focus on Boltzmann brains in eternal De Sitter space, which is what you get if you assume that dark energy is constant and perpetual.
One thing that has changed since those days, is that the very existence of eternal De Sitter space in string theory or quantum gravity is in doubt, thanks to the “swampland” program which tries to identify worlds that aren’t possible. It’s controversial because the conception of the string “landscape” of possible worlds, that many people including Susskind promulgated in the 2000s, is heavily populated with De Sitter vacua. However, these were made using supergravity approximations and destabilizing mechanisms from full string theory have since been discovered.
So it may be that at the level of physical theory, the Boltzmann brain may disappear as an issue when counting cosmological observers, because De Sitter space simply doesn’t last long enough before decaying into flat space. Whether it is still an issue at Tegmark level 4, I couldn’t say, the structure of possibility there is too unclear to me.
There is also some debate over whether eternal de Sitter space would even exhibit the right kind of fluctuations to support Boltzmann Brains at all. See Boddy, Carroll & Pollack (2014) for a standard argument.
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?
This paper (2015) argues that the idea of quantum fluctuations without an observer/measuring apparatus to decohere the wavefunction is confused, and therefore (I didn’t fully understand this part), depending on unknown details of physics/cosmology, even thermal fluctuations (what the OP discusses) in an old universe that give rise to Boltzmann brains might not be a thing. (ETA: this sounds like it overlaps with Mitchell Porter’s top-level comment that “[maybe] De Sitter space simply doesn’t last long enough before decaying into flat space.”)
(That doesn’t help with the problems with the mathematical multiverse, or which computations a physical system implements.)
Ah I just left basically the same pointer haha.
Though I think the Boddy-Carroll-Pollack argument is separate from the swampland argument that Mitchell Porter is referencing. The swampland argument is saying that long-lived de Sitter space might not be possible at all in quantum gravity, whereas the Boddy-Carroll-Pollack argument is saying that long-lived de Sitter space might not give rise to Boltzmann Brains at all.
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. This could imply that the real physics (not even metaphysics!) also somehow dissolves the issue, but we have yet to understand the mechanism (a false vacuum decay which stops the universe from expanding and creates matter in sufficient quantities to make classical brains likely to emerge instead of the Boltzmann one?)
By “the BB problem”, you might mean the problem of how to know whether you are a BB, but the OP explains how, and I can’t imagine what else you might mean by “the BB problem”.
The wiki page had Yudkowsky describe the problem as follows:
Yudkowsky’s paradox
Suppose your model of physics says that the universe will eventually dissolve into a sea of particles in thermal equilibrium, and these particles will then exist indefinitely.
Then an exponentially vast supermajority of all observer-moments in this universe take place inside brains that momentarily assemble themselves from the sea of entropy by random fluctuations, and probably dissolve a moment later. These are “Boltzmann brains”.
The vast supermajority of Boltzmann brains have relatively disordered experiences; they momentarily see chaos before dissolving again.
So your own, far more ordered and orderly experience in this very moment weighs heavily against the hypothesis “I am a Boltzmann brain”. Inder most systems of anthropic reasoning this weighs heavily against the possibility “a supervast majority of all moments of consciousness are vastly less orderly than my own”.
To be clear, it’s not “Yudkowsky’s paradox” as Yudkowsky is explaining a standard and known problem in cosmology here.
Admittedly, many cosmologists are not super careful when reasoning about Boltzmann Brains and they also disagree about what exactly is the problem they pose (e.g., see this dialectic between Carroll (2017) and Elga (2025) about whether belief in Boltzmann Brains leads to “cognitive instability”). But the core phenomenon of Boltzmann Brains and that they seem like bad news for many cosmological models is well-understood.
I feel like a much simpler objection to the Boltzmann Brain is that to the extent the big bang is a miracle where something arises from nothing a much greater proportion of experiential observers should be downstream of “Boltzmann” cellular automatons than Boltzmann brains because the k-complexity of the cellular automaton is lower than the complexity of a Boltzmann brain and therefore much more likely to arise by chance.
Basically an instance of the standard model should arise by chance more often than an instance of any given observer with a complex life history and each instance of the standard model should produce many more observers with more observer moments on average than Boltzmann brain causalities do. Though obviously this is subject to how rare you think it is for life to arise in an instance of the standard model.
“But doesn’t all of this occur inside an instance of the standard model regardless?”
Sure. What I really mean is that a low structure cloud of mass that eventually congeals into order is actually an easier state to reach than a Boltzmann brain so most observers states should be downstream of a large low k-complexity (i.e. a prng) seed state that has consistent rules applied to it over an extremely specific high k-complexity seed state (i.e. a fully formed observer), especially since the former can create more observers which last longer on average.
This is of course closely related to the notion that you should not observe a well ordered life history if you are a Boltzmann brain, so I obviously agree with you.
Kolmogorov complexity is not quite the right metric to use, because it doesn’t count the memory usage of the program, just the length of its source code. But the actual cost that’s used to figure out how improbable some configuration is is different. It equals the total number of bits that have to be flipped a certain way, including both the program, the memory it needs to do its job, and any bits that are erased. (The program has to be reversible, so if it has to erase bits, we interpret this as writing those bits to memory that is then not used for anything else.)
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.
If you cared a lot about universes where you won the lottery, would you expect to win the lottery?
The correct answer is: No. Your preferences don’t control what you see, so they don’t explain what you see, so actually seeing a simple universe calls out for an explanation that is not preference.
I currently think I don’t actually need to explain what I see. What is the advantage of explaing it? Under normal circumstances, it’s useful to explain why I see e.g. the washing machine not working, because that gives me useful predictions about how the washing machine will behave in the future, and knowing that is useful for fulfiling my values.
But if I have a preference like “life only has meaning if I win the lottery”, then I think it’s not action-relevant to find an explanation if I see myself winning. The day before the lottery, I was already only making follow-up plans for what to do if I win—that’s the only case where life has meaning. And it was not part of the plan to do an investigation of why I won the lottery—why would I want to waste my time on that? So when I actually win, I in fact don’t investigate it further.
To be clear, I think that caring a lot about universes where you win the lottery, at the expense of other universes, is a very sillly moral belief. If someone held this belief, I would tell them to meditate a little and play with a toddler and imagine if they would really care less about her if she was living in a universe where they don’t win the lottery. But if they come back saying that they genuinely only care about lottery-winning universes, then I can’t argue with their utility function.
I think having at least 0.1% of my caring allocated to short description-length space-time points is not that crazy of a moral belief. And once I have that, it’s reasonable to have a policy like “if I see an ordered world, I will act as if I was not a Boltzmann-brain, because these ordered situations are important for the 0.1% of my values, but are vanishingly rare and unimportant from the perspective of the 99.9%”.
I now see an ordered world, so in accordance with this policy, I act as if I was not a Boltzmann-brain. Acting as if I was not a Boltzmann-brain includes not looking for mechanistic explanations for why I’m not one, so I don’t do that.
(This is speculative and not a battle-hardened opinion)
One could respond: The thing you want an explanation for, the thing which you have anticipations about, isn’t existence in its entirety. It’s differences between relevant ways that existence could be, and how you participate in existence, i.e. “what world you turn out to be in” or what you expect to see or how you think you can affect the world.
This sets up a dichotomy:
Things that you could reasonably think you might possibly be able to change, or anything contingently related to those things (e.g. a cause or effect of some of those things). These are things about which you have separate beliefs and preferences, because you want to track targets and realities separately in order to find more successful actions.
Things that you know, to the very core of your being, baked in from the start, that you couldn’t ever possibly change or that you won’t even consider as possibilities.
(Ok fine it’s not a dichotomy yet, I didn’t work it out, but maybe you can see what I’m trying to get at.)
For example, you wrote about “where recursive justification hits bottom”, and the loop of a simplicity prior justifying itself through the meta level: I believe in some kind of simplicity prior because it’s a simple hypothesis that such a prior will keep on being true and useful, given that it has been true and useful constantly up until now. Why not truly question the simplicity prior so hard that you stop evaluating its possible alternatives by the meta-level judgements of the simplicity prior itself? Seems a bit like a preference, in the sense that there might be a self-ratifying alternative state of mind, but you don’t like it / wouldn’t choose it. (The fact that it would be much less effective is something you only induce based on the simplicity prior!) The preference and the belief are kinda created in motion as already always mushed together, if you see what I mean.
The lottery is something you view as being under your control. If it was baked in, by evolution say, to only care about worlds where you win the lottery, then you really might be expecting to win the lottery. (Is there a toy model of this from the shutdown button indifference work?)
Maybe no one views Boltzmann brains as moral patients who we’d possibly be able to help?
For me at least, this picture just doesn’t capture the phenomenon at hand.
The data I have are certain first-personal facts of the form “there is a stream of experience playing before me, and the contents of this stream exhibit certain features and regularities”, and I am trying to explain why I am experiencing this particular inner movie in my head rather than some other inner movie. (If you want to dispense with talk of continuity over time and subjective anticipation, then replace all talk of “stream of experience”/”inner movie” with “snapshot of experience”/”inner photo”.)
“You in fact subjectively care more about certain experiences” does not seem like the right kind of answer to the question of “why these/this experience?”, in the same way that “you in fact subjectively care more about ordered universes” does not seem like the right kind of answer to the problem of induction.
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).
The vastly more likely bounding boxes enclosing an experience-having entity are microscopically tiny and as disordered as possible while remaining consistent with the condition that it has an experience-having entity in it.
Although we don’t know what sort of constraints the “experience-having entity” condition imposes, it doesn’t seem likely that it so massively favours ordered experiences over disordered ones, to the extent that it can overwhelm the superexponential penalty on order in a system near maximum entropy.
I have mildly disordered experiences on some mind-altering drugs (or at least memory of it) and I’ve seen some strong evidence that other beings have internal experiences (like you possibly), some of which seem to be disordered in more severe ways than what I have experienced and for longer duration.
The issue is that the larger the box the less likely to occur in random fluctuations. Extremely exponentially so.
Right. The minimal experience is probably a kilogram of matter for a few seconds. The extreme conception of a Boltzmann Brain is Solipsism x simulation-argument without the actual simulators. There is no “reality”, all of your consistent memories are an accident that lasts just long enough to register the experience.
You haven’t actually experienced anything in real-time—it’s all just an instantaneous memory.