A relatively brief explanation of Boltzmann Brains

Eliezer Yudkowsky

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181 A relatively brief explanation of Boltzmann Brains

by Eliezer Yudkowsky

17th May 2026

5 min read

113

181

(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 makes it hard 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?"

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A relatively brief explanation of Boltzmann Brains

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[-]Mitchell_Porter5d362

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.

8EOC5d

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.

[-]orthonormal5d259

any account of mathematical realism / modal realism which does not try to explain why some universes or observer-moments have greater weight than others

"Try to explain" is too strong a requirement. It's OK to acknowledge in some contexts "I don't yet have a good candidate for how this part of the theory works". I believe you've called it "and here a miracle happens" when you describe things you are partially confused about.

E.g.

"God does not play dice with the universe, but I don't yet have a good hypothesis for how the results of QM come about in a deterministic universe." (Einstein being correct but not coming up with MWI)
"Consciousness and qualia must have a purely material explanation, but I don't yet have a good candidate for that explanation."
"There must be some weight on mathematical objects that causes the anthropic majority of observer-moments to exist inside larger regions of order, but I don't yet have a good candidate for an origin of such weights."

Boltzmann theories are falsified not because their proponents fail to fully specify them, but because they strongly make incredibly incorrect predictions. That's different from this.

P.S. I do have a candidate for a material e... (read more)

[-]Eliezer Yudkowsky5d103

Agreed. I will revise to "makes it hard to explain". The actual problem is that some such views seem to present significant barriers to somebody else coming up with an explanation, haven't even noticed that there's a problem, etc.

[-]Yitz5d245

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?

[-]ike5d123

The Solomonoff Induction universal prior solves it because it takes a lot more bits to "locate" a Boltzmann brain than a human in a well ordered Earth environment.

I was previously skeptical that SI actually produces different results than SIA and wrote about that in https://www.lesswrong.com/posts/Jqwb7vEqEFyC6sLLG/solomonoff-induction-and-sleeping-beauty but I've changed my mind. The argument there doesn't generalize to large numbers of observers. (I still believe my other arguments posted that year that "reality" is a meaningless concept, see https://www.lesswrong.com/posts/zm3Wgqfyf6E4tTkcG/the-short-case-for-verificationism and https://www.lesswrong.com/posts/PSichw8wqmbood6fj/this-territory-does-not-exist.)

The "locate" issue in SI solves both Boltzmann and the dust theory issues alluded to in OP - anything can implement any computation but you still need a computer program that outputs something and weird mappings will make that program longer.

You still have a puzzle about which language you use for the computer programs, and what exactly input and output mean, it doesn't solve everything but does dissolve much of the mystery.

2edge_retainer4d

This has always seemed very likely to me. It seems way easier to create a world governed by a few rules of physics that would incentivize perceptrons than randomly stumble into complicated perceptron architecture via random physics.

6StanislavKrym5d

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?)

8Ben5d

What is weird about this, is that in an eternal steady state universe the number of living observers in a given time period is much larger than the number of observers (including Boltzman brains) in a simialr slice of a universe approaching thermal equilibrium. So, depedning on how your Anthropic reasoning work, you could argue from the fact of your own existance that the universe must be steady state, regardless of any evidence otherwise. (This is kind of a tension inherent in all Anthropic arguments, I am more likely to 'be me' (as opposed to someone else, like a Boltzman brain) in a universe with fewer people, but most possible observers are in the crowded universes, so I am more likely to be in a crowded one. Similar logic, threading oppsosite conclusions.)

3Nick_Tarleton5d

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.)

5EOC5d

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.

1RHollerith5d

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".

0StanislavKrym5d

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".

7EOC5d

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.

2jmh4d

After a brief chat with one of the AI's I had the impression that the main value of the BB was more about model/theory evaluation. Basically a theory that predicts a lot of the phenomenon should be questioned and probably "back to the drawing board" case. A lot I don't follow here but seems like the post might be challenging that, or perhaps some more simplified applications of that view. But after the chats I actually wonder if that is the critical aspect rather than juts how we deal with infinities/really long time frames or how we think/define of equilibriums as the more critical areas of exploration.

[-]jdp5d*200

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 ru... (read more)

[-]DaemonicSigil5d124

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.)

4Nick_Tarleton4d

The probability of a thermal fluctuation is inversely related to its size, not its k-complexity. A universe-sized cloud of mass is less likely to congeal into any kind of order than a brain-sized cloud.

4quetzal_rainbow5d

It's not clear how to count "more often". If we are not in quantum multiverse, it's not clear how to compare two infinite number of observers with different frequencies on finite intervals. If we are in quantum multiverse and in thermal equilibrium, we have reached maximum number of branches, therefore we can't say that cellular-automata observers pick more measure than whole-assembled observers and then we are back to the issue of comparing two infinite numbers.

3Canaletto5d

Hmmmm. But this would say nothing about thermal bath type situations, where you can't make a seed, or at least, amount of concentrated resources for an expanding bubble type thing would be greater than for a brain.

[-]David Matolcsi5d140

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?"

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.

[-]Eliezer Yudkowsky5d2722

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.

[-]David Matolcsi5d12-3

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... (read more)

5Dweomite4d

What makes you think the explanation for why you won the lottery won't help you make useful predictions about what follow-up actions will fulfill your values? For example, if the explanation were something like "the lottery was rigged, and there's about to be a criminal investigation targeting you", that seems pretty relevant to your follow-up plans. Explanations of previously-mysterious phenomena are often useful in ways that are hard to foresee before you know the explanation. If you think that understanding "normal" things is typically useful, why single out this one specific thing to be incurious about?

2AprilSR5d

I think if I am not a Boltzmann-brain I do still want a mechanistic explanation of why not, even though my general decision-making process is robust to a scenario where non-Boltzmann brains are vanishingly rare.

2Aprillion5d

interesting point of view, somewhar different from my own (perhaps not much, perhaps uncanny valley close?) - having observed myself winning the "lottery" over and over and fucking over again, I have dropped the lottery hypothesis long time ago, it's not that I don't care about 99.9% of something, it's that the "wannabe mathematical thing" simply doesn't exist, "philosophical possibility" is an incoherent(ish) concept for me, I am incapable to engage with counterlogicals in any productive way and I am deeply fascinated that people seemingly derive spiritual meaning from what appears nerd leg shooting of course I am curious about mechanical explanations how this "lottery" was rigged / not a lottery at all, what is the principled way for it to not be a lottery (besides the unsatisfactory principle of induction by simple enumeration)

8TsviBT5d

(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

5Eliezer Yudkowsky5d

And then, on how my model of reality actually works, you wouldn't win the lottery. Do you think differently? [...] The map is not the territory. "Justifiable reason to believe something" is a map-thing that is not the same as "knowing why it happens" out in the territory. We have seen the universe be simple at us really really hard. We are justified in map-expecting our experiences to probably continue to be ordered. We don't know what territory lies behind it.

8TsviBT5d

(I timed out on fully thinking this through and better get back to work; I'll try to summarize, and leave a half-finished ramble below.) (I'll repeat that I barely hold the view represented here; to me it's a hypothesis / question. I assume you've heard this view before, but I'm just thinking it through. :) ) A supposed dissolution to the question [...] is something along the lines of: * All mathematical structure is real, and that's all that's real. * There are different regions / elements of Structure, such as minds, experiences, facts, or worlds. * Many creatures need various "weights" over Structure. * A creature has to divide its efforts, so it has to divide up a finite total weight of caring across Structure. * A creature wants to act differently depending on what its affectable surroundings are like, so it needs something like a probability distribution over "possible worlds" (mathematically coherent contexts of affectable surroundings). * There's no objective / intersubjective weight-of-existence to different regions of Structure. * More precisely, creatures would be far from fully agreeing on the sense in which comparatively tiny numbers of orderly experiences carry more weight-of-existence. * Probably a great "many" creatures would learn to / be born to distinguish map from territory, and to expect the territory to be simple. * Probably "weights over Structure" have to take on some sort of simplicity form, since any non-dogmatic weighting is some kind of simplicity weighting. * The reason it seems like orderly experiences carry more weight-of-existence is that when you try to model "what exists", you're implicitly calling on background presumptions such as "the world is orderly". * In other words, you're basically assuming that orderly experiences carry more weight-of-existence. * This assumption is partly borne out by experience. In other words, it's objective in the single-observer sense of "it's still there even if I bel

7Eliezer Yudkowsky5d

Why, because I don't expect to see that actually happen to me, of course! In a way that doesn't depend at all on which anticipation-dynamic I try to implement, even if I could modify my own source code. Beings that modify their own source code to expect to win the lottery are then promptly surprised by losing the lottery. Beings that modify their preferences to care much more about worlds in which they win the lottery, predominantly see themselves losing the lottery and ending up in the world they cared about less. If you decide to give up on anticipating that your vision stays ordered, it will nonetheless stay quite ordered. The dynamic by which we expect order is not an explanation for that order. "Reality is that which, when you stop believing in it, doesn't go away." Even if you were a kind of being that could stop believing in order, it still wouldn't go away. Of which I have also said: The art of shepherding is not about using pebbles to control sheep, but letting sheep control pebbles. Why not unwind our justification loop for expecting order? Why, because at the end of unwinding, we would still see order rather than chaos. You and I both know that's true. But why is it true? Not the map-why of how do we justify believing it; the territory-why of "How did it end up that way?"

1Q Home4d

I believe you should be able to make progress by writing out different map-level and territory-level things. Let me try: * 0) My prediction: I expect the universe to continue being ordered. * 1) In-map explanation for why I came to believe it: I use a simplicity prior to predict my observations and trust my memory. * 2) In-territory explanation for why my prediction succeeds: I'm a human (not a BB) in a simple universe. * The problem: I can't trust my memory and justify the simplicity prior. * 3) In-map justification for using the simplicity prior anyway: memory and simplicity aren't provably reliable, but I don't care about my life in case they are not reliable. * Potential crux A: (3) doesn't undermine the fact that I'm correct only because of (2), so changing what I care about doesn't change the outcome, yet it still counts as a justification of doing (1). If I cared about complex universes, I wouldn't be justified in doing (1). * 4) In-territory justification for using the simplicity prior anyway: I live in a multiverse where memory and simplicity aren't reliable in every universe, but I don't care about universes where they are not reliable. * 5) Another in-territory justification for using the simplicity prior: God or some power makes the simplicity prior true in the multiverse. * Potential crux B: some will say (4) is not an explanation because I have to explain "how you go from experience 1 in universe 1 to experience 2 in universe 1 instead of experience 2 in universe 2" or something; others will say it's all anthropic woo and any reasonable (5)-type theory is gonna be untestable by construction (until we die). * 6) A deeper in-territory explanations for why my prediction (0) succeeds: "God/power did it" (see 5), "I got lucky once to end up in an ordered universe" (see 4), "all experience histories created by the multiverse exist, therefore this experience history was fated to be experienced anyway" (see 4). Due to crux B, I assume the l

2EOC4d

Do you take the data in need of explanation to be a stream of orderly experiences, or one moment of orderly experience?

[-]Eliezer Yudkowsky4d128

One moment of orderly experience that includes remembering an ordered story of how it came to be.

1Q Home5d

Not all epistemological things can be justified (rejecting modest epistemology, simulation hypothesis, Pascal mugging, other weird anthropic scenairos). At least it's very unclear if they can be. So why should this one be justified? What kind of "Hilbert program" are you pursuing, how much do you want to justify in which foundation?

8EOC5d

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.

[-]avturchin5d112

For any BB there is another BB which constitutes what I will experience in the next moment t+1.
So BBs naturally form flux universe from dust theory and everything gets back to normal.

This also means that BB can't "die" or instantly dissolve – there is a form of big-world-immortality between BBs, especially if some longer-living similar brains exist somewhere.

Also, we can't judge from inside – am I living in extreme chaos or not, because thinking of BBs is not logical and they can have completely random thoughts. So maybe I observe complete chaos and still think that it os ordered.

5Oliver Sourbut5d

On the last - perhaps we need to ask whether 'this seems an orderly-enough universe' vs 'this sure is chaotic' is a more probable thought, conditioning on having any thoughts on the matter at all.

2avturchin5d

I think that in normal BBs they have equal chances. However, if we postulate that chains of similar BBs are possible, they will evolve into more stable states. relevant image: https://chatgpt.com/backend-api/estuary/content?id=file_00000000d35c71fdae277cb42b44cdcf&ts=494172&p=fs&cid=1&sig=ae767f2f792c2f370e84300dfdb5fb361b83af1b5266929320a3a97c11e49b78&v=0

2Oliver Sourbut5d

Either way (and even accounting for the Boltzmann immortality effect), I find it very hard to believe experiences like mine are remotely favoured by random fluctuations.

2jmh4d

Is this a modern extension of Boltzmann? I thought the standard view was these BB are very temporary and do "die" fairly quickly (though I suppose "quickly" could be a rather long time in human terms when thinking in infinite time). Edit: Perhaps that is answered in your other response but the link doesn't seem to work for me.

2avturchin4d

There is a great article "Law without law: from observer states to physics via algorithmic information theory" https://arxiv.org/abs/1712.01826 which explains how observer-moments can form chains. The idea of Boltzmann immortality was discussed here: https://www.researchgate.net/publication/308958767_Boltzmannian_Immortality Link was on a picture I generated but failed to embed. Here is another link on the same picture: https://ibb.co/fGCz0q1b

[-]Vanessa Kosoy3d90

I think that the solution to the puzzle of Boltzmann Brains will come out of the interpretation of quantum mechanics via the lens of Formal Computational Realism (FCR). On that view, the universe is sampling every possible quantum observable s.t. (i) the marginal distribution of each observable agrees with the Born rule (ii) the overall amount of computation made is minimal. (Tbc this is a very informal description of a rigorous mathematical framework.) For a time moment in an early history of the universe, if the observable you're sampling is related to ... (read more)

[-]DaemonicSigil2d110

This sounds very intriguing. Questions:

If we start from some fixed state, the distribution of fluctuates with time in a precise way, even if it approximates a Maxwell-Boltzmann distribution (because it arises from a pure quantum state that is just undergoing unitary evolution). Eg. after a Poincare recurrence time, the state has returned to its original value, and takes a non-equilibrium value. This would seem to imply that we must compute the full unitary evolution, even at late times, in order to get the correct fluctuations. Is this wrong?
Does this theory say that any other kinds of observers besides Boltzmann brains don't have subjective experiences? Can we engineer a scenario that creates such an observer (eg if we have an AI design that is very useful, but we don't know if it is conscious or not)?
Sampling from a thermal equilibrium distribution is not necessarily cheaper than time evolution. That kind of sampling is roughly speaking "in NP", while time evolution is just . How sure are we that thermal equilibrium sampling doesn't involve computations with subjective experience? Like, if the sampling process goes down certain very improbable paths, it's difficult to know

... (read more)

8Vanessa Kosoy2d

Quantum Poincare recurrences: Thank you so much for this question! It's silly of me that I haven't seriously thought about quantum Poincare recurrences in this context, but now that I did, I finally see a path towards formally testing the "no BB in FCR" claim. Explanation for readers who are following some of the formal details of FCR: Consider the same setting of Gergely's post that I linked, but instead of making time evolution stop after T steps, we can make it go on forever. The agent's memory tape is still of size T, so it will end up cycling through it and (reversibly) overriding it infinitely many times. My conjecture is that, in this new setting, we still have a version of Theorem 4.19 with a non-trivial lower bound. This would imply no BB in the traditional sense: despite the Poincaré recurrences, the agent does not experience all possible histories. Why would that be true? Because, if you measure the agent's memory time at a time in which its memory tape is full of "garbage", the results conveys only a little information about its policy, and its unlikely to make the agent "experience" too much in the formal sense defined by the bridge transform. Whereas if you measure the agent's memory at time in which the Poincare recurrence recently reset the tape, the "minimal computations" principle would make it likely for it see the same observations it saw during previous such cycles. Explanation for readers who are not following the formal details of FCR: The thing is, whether we "must" compute something or not is not a binary. Rather, the probability we compute something increases with the total variation distance between the distributions we need to distinguish. So, as long as different agent policies produce similar distributions, we only have a low probability of computing the policy (which in this framework is equivalent to the agent "experiencing" something). I think this also addresses your remark about "NP": it's likely easy to approximate the therm

2Vanessa Kosoy2d

Actually, I think things might be even better than this: in semiclassical quantum gravity in asymptotically de Sitter spacetime, your quantum state is necessarily mixed (due to tracing over things outside the cosmological horizon, which is how you get Unruh radiation). So, there are no quantum Poincare recurrences. If you plug a stationary mixed state into the FCR interpretation, all the observables become completely frozen in time. If you're just converging towards a stationary mixed state, I expect the observables to converge towards becoming frozen.

[-]JenniferRM4d96

Some reactions, from the end of the essay, and working (mostly) backwards...

the argument from "My experience does not look like a typical Boltzmann brain experience"... weighs against.. any account of mathematical realism / modal realism which makes it hard to explain why some universes or observer-moments have greater weight than others

The whole argument rests on naive/basic logic about complexity being expensive, and yet the actual Solomonoff Prior hasn't been mentioned?!?

"But we're not Boltzmann brains"... constitutes a strong-seeming anthropic objectio

... (read more)

[-]Eliezer Yudkowsky4d156

The whole argument rests on naive/basic logic about complexity being expensive, and yet the actual Solomonoff Prior hasn't been mentioned?!?

Why should mathematical realism obey the Solomonoff prior? There's a clear reason from epistemology why the map has to distribute its probability mass more and more sparsely over possible explanations of higher complexity, for in the limit there are countably infinitely many hypotheses of unbounded fine complexity. That's why, faced with a phenomenon that we think has only one true explanation, we follow Occam's Razor in our maps.

Why would a Solomonoff prior be out there in the territory? Who is in charge of distributing probability mass over mathematical structures with inhabitants? According to which possible measure of simplicity? What does it mean to pour realityfluid into a mathematical structure?

Mathematical realism answers none of this. To actually try to answer it is to try to come up with a metaphysics of realityfluid. This is beyond anything that Earth can publish in philosophy journals; you would have to look to online erotica for it.

7David Matolcsi4d

Can you share a brief description or a link to your favored metaphysics of reality-fluid? I haven't yet come across good write-ups on this topic.

5Garrett Baker3d

Eliezer is referring to The Erogamer (note: you do need to create an account to read this, since this is indeed online erotica), and his own collaborative online story planecrash.

6David Matolcsi3d

Ok, but are there specific chapters or pages he or others could link to? Linking to long novels is not very useful.

6Eliezer Yudkowsky3d

Erogamer "7.!", (Planecrash=) Project Lawful "the meeting of their minds", incredibly heavy spoilers on both though much more so Project Lawful.

1habryka3d

It's more useful than not linking to anything at all! And I read it mostly as a joke, so putting a burden of work on Eliezer feels a bit weird here. I do agree that a more direct link would still be useful, if any such exists.

6Lucius Bushnaq4d

You can get a Solomonoff prior by just taking the uniform prior over programs of length fed to a plain[1], monotone UTM and letting tend to infinity. No explicit simplicity weighting needed. The degeneracy of implementations for shorter programs sneaks an exponential weighting with minimum program length in automatically, without us needing to put one in by hand. So, any procedure that distributes reality fluid somewhat evenly over a program space like this ends up looking very Solomonoff-shaped. Of course that still doesn’t explain why the objects we are distributing reality fluid over should be programs for a monotone UTM instead of something else. 1. ^ So, not a prefix-free encoding.

[-]Eliezer Yudkowsky4d146

Well, yes. Any sane choice of UTM is famously pretty equivalent in terms of epistemology, if you're willing to presume that sanity. Eg, to end up thus convinced against all evidence that Guam is planning to invade the United States, you'd have to twist up the UTM to make it hugely costly to internally simulate other UTMs that would assign greater than negligible probability to "Guam is not planning to invade the United States". And even then, it washes out in the limit, etcetera.

But if we suppose it to be a prior metaphysical fact out there in the territory, you'd think the territory actually would have to fix some choice of UTM; the territory cannot just say, "Eh, they're pretty much equivalent" and leave itself uncertain, for all uncertainty exists in the map rather than the territory.

If the territory has picked any sane UTM, all sane UTMs will do well pretty well predicting it.

But how would the territory pick any UTM whatsoever to decide which universes got exactly how much reality-fluid?

2Lucius Bushnaq4d

I dunno. Maybe the mathematical realists would say that this is one of the very few things that actually are nailed down to one particular option in the laws of metaphysical reality, rather than all the mathematically self-consistent options getting a little bit of reality fluid? It seems sort of counter to the ethos of the whole endeavour as I understand it, but I don't really see any other way for them to do it. It seems to me like you've got to make some statements of the form "metareality is like this thing, not like this other thing" at some point, if you want to make meaningful statements about some sort of metareality at all. And any statement like that will presumably end up being expressible mathematically.

5Mitchell_Porter3d

Thank you for the exact references below. But it is not helpful to humanity for what is supposedly the most advanced thinking on such a subject to be buried in such a place. There is an opportunity for someone to make a post summarizing the "metaphysics of realityfluid" in each story, minus the story details.

4Richard_Kennaway4d

That came out of nowhere! Unless this is a specific reference to planecrash, which I have not read more than maybe half way through, so no spoilers please beyond the answer being just "yes, planecrash". Or is there a more general reason why studying the metaphysics of realityfluid leads in that direction?

3Eliezer Yudkowsky3d

It's just an empirical fact that all of the most advanced discussion and speculation about realityfluid has occurred in the context of online stories with at least some erotic component.

1EniScien4d

It is certainly not just plaincrash, there is at least also The Erogamer. If I needed to guess why, I would say that it is not about studying metaphysics per se, but about what people will be ready to give a try for reasoning about realityfluid metaphysics - same kind of people who will give a try writing about it inside of online erotica. Though I am actually even less sure why you can't publish about realityfluid metaphysics in journals.

2ike3d

I don't think it's necessary to have a "metaphysics of reality fluid." You can say that Solomonoff induction does a good job of making predictions, and then use it to conclude that you likely aren't a Boltzmann brain, that you have no particular reason to think the universe ends one day purely due to anthropic reasoning, etc. I lean towards realityfluid being meaningless, as do concepts like "exist", etc. "But why would the 'territory' act like SI?" This is of questionable meaning, and even if meaningful may be inherently unanswerable. As you note, any sane UTM ends up in the same place; you could have a single randomly picked UTM that worked, you could have a weighted distribution over UTMs that gives enough weight to the sane ones. We clearly don't have the kind of data that would let us discriminate between any of these possibilities. But it does seem pretty suggestive that the BB problem and related ones you mention like dust theory go away once you're working in SI. We can't perfectly ground SI but we can't perfectly ground anything else either. If we were going to do an observation tomorrow that would somehow settle the question of if the universe will go on indefinitely with many BBs or not, would you predict that the observation says No with overwhelming probability? I would not.

2jmh3d

Just a slight point, maybe, but should we be equating Boltzmann brains with simulation cases? They seem much different to me, even if some of the problems for the specific observer/entity are common to both. Curious about one other point as well. Could very much be my own ignorance and resulting confusion but it seems your position is that the math is real but we might not be. That seems to related to this AI answer to a prompt I made. Prompt With regards to Boltzmann Brains, did Boltzmann what is Boltzmann really assuming about the real universe and what it is made from -- is this just about some observing entity in a universe with the actual structure and masses (all the elements and physical laws we current assume exist) or some equilibrium disordered state (whatever level or disorder is thought to exist)? Part of the response included: "The concept of Cognitive Instability—why believing you are a Boltzmann Brain means you can't trust your own math." That seems to raise questions about how real one can assume their math is if one starts from the position of "I'm a BB." I am not entirely sure that is as reasonable for a simulation but that hangs on simulations and BBs being entirely different types of situations and settings.

4JenniferRM2d

The starting point for "absolutely raw empirical science" for me is "cogito ergo sum" and so on. This plus occams razor, plus lots of complex contents within my "thoughts and/or perceptions" drive me to a scientific theory about whether or not an external reality even exists, to plausibly account for the contents of my "thoughts and/or perception" with a theory of "a territory out there" seeming to exist that has a lot of coherent content (so much coherence! and so big! bigger than I can easily fit in my working memory at any given moment). In these thoughts, basic elements of math seem very very very solid, and (assuming other mathematicians really exist, and their claims about various math proofs are valid (which in many cases I haven't personally verified)) it does suggest to me that math is more likely to (1) not merely have a stable structure among the parts I can imagine or check for myself in reasonable time, but (2) it just keeps going out in a larger way that retains the character of being essentially eternally stable. So... it does seem to me to be a reasonable that I can be MORE certain that "math exists to be explored by any mind with this essentially eternal and stable character like this" than that, for example "I myself existed as I seem right now to remember myself to have exited 20 years ago". Then lots of other stuff (like the true admixture of quarks within protons (and the likely ontological usefulness of thinking in terms of protons that have 13% of a charm quark in them (even though I've never personally seen any of that, not checked the math for myself))) is something I personally have even lower credence in than "math" and "cogito". I'm not necessarily saying that you should copy me. More I'm trying to "honestly report in" as someone who has independently thought about this, and has tentative answers in a few places where other people seem to be reporting subjective confusion and I feel like I might be more justifiably confident (and may

2jmh2d

Thanks. If I think I'm a BB then I should not be very confident in 2+2=4 or that JenniferRM is connected to a human or even is an account on LW. All my memories and thinking (and quite likely any sensory input) is fake so disconnected from any external territory. If I assume I'm simulated then it's more complex. I don't think I am either, so I am quite comfortable with 2+2=4 and, since I think I can trust my senses, I can even verify that claim with my fingers and counting. These days I would have to question the JenniferRM is actually human and not some modern LLM that is fooling me a bit more. But, as you note, I do have some history to fall back on that precedes the more advanced LLM that can fool me and could be posting so still have a strong sense you're not one. But, yes, your point stands, I would trust the math more than the account. But that is possible, for me, just because I don't see myself as a BB or simulation. As for the "we", that was probably sloppy on my part. I tend to interpret claims of being a simulation to mean we're all in one, not that the speaker considers they are (or might be) one. I should change that view.

[-]Steffee4d30

To counter the idea of Boltzmann brains, isn't it enough to simply observe that order is self-replicating? Therefore ordered brains arising from order are vastly more likely than those arising from chaos.

[-]Stephen Fowler4d30

I wanted to give some literature links in case there was anyone who hadn't previously encountered the argument "if every physical object can with equal justice to be said to implement every computation."

My understanding is that you're describing the Simple Mapping Account of what makes something a computer. (As a side note: I'm not quite sure how much confidence I have that it is actually true, given that it is a completely unhelpful way to identify "computers" in any practical sense.)

I'd suggest a curious reader starts with Picinini's overview:

Picinini (2... (read more)

[-]simon5d3-2

Strong disagree with this post:

Even if you expect that most entities with your subjective instantaneous experience are Boltzmann brains, it does not follow that you should believe that you are a Boltzmann brain. Why? Because it is instrumentally irrational to believe that you are a Boltzmann brain.

If you are a Boltzmann brain, believing you are a Boltzmann brain doesn't do you any good, you dissolve anyway.

If you are not a Boltzmann brain, obviously believing you are a Boltzmann brain is counterproductive.

So, you should have beliefs weighted to the case ... (read more)

[-]Eliezer Yudkowsky5d104

Try deciding that it's useful to believe you'll win the lottery. You'll nonetheless not win the lottery! So what it is useful to believe cannot account for our experiences; and our experiences of an ordered universe continue to call out for an explanation even if you say that it's instrumentally useful to believe in an ordered universe. Of course in reality it's only useful to believe this if the universe actually is ordered.

I also note that if you're not familiar with the mores around here, we do not in general think it clever to violate the epistemic-instrumental firewall.

3simon5d

Eliezer, I did note that it's correct even from a correctness-maximization perspective to pre-commit to disbelieving in being a Boltzmann brain! I suggest thinking through it more carefully. By rejecting this, you are predictably making your beliefs less accurate conditional on Boltzmann brains existing.

3Eliezer Yudkowsky5d

You didn't say anything about "a correctness-maximization perspective" and those never have a need to "precommit" to anything, which is a decision-theory rather than epistemic concept.

3simon5d

Maybe not in so many words but I assumed it was clear in the footnote (which I have not edited). I do think an analogy with decision theory is valid though: two-boxer says: "I won't decide in advance not to pick both boxes, it's only 'rational' to decide in the moment, I don't care I'm predictably leaving out winnings ex ante" You might say: "I won't decide in advance not to believe I'm a Boltzmann brain, it's only 'rational' to decide in the moment, I don't care that I'm predictably sabotaging the accuracy of my future beliefs" Or if you don't agree with that... then what would your opinion be on that?

[-]Clobre5d32

I disagree with arguments of the form "My experience doesn't look like that of a Boltzmann brain, so I'm not a Boltzmann brain". If you were a Boltzmann brain, nothing you would think you know about physics or probability would actually be valid, nor would you have any capability to reason about the experience of a typical Boltzmann brain.

Perhaps the following definition can clarify the issue: say someone is "reasonable" if their experience correlates somehow with reality, and they have the ability to reason somewhat soundly (this concept was probably alre... (read more)

[-]Dagon5d3-1

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 i... (read more)

4JBlack5d

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.

2Nick_Tarleton4d

I can easily conceive of 'the experience I'm having now, except the left half of my visual field is noise'.

2Dagon3d

Sure, but that would be an ordered experience that you interpret as noise. You can't imagine what it'd be like for your neurons to fire randomly or for half of them to be disconnected. Heck, you probably don't even know what it's like to be a rock. Or a talking silicon rock.

2Shiva's Right Foot5d

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.

3Dagon5d

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.

[-]Ape in the coat3d20

I believe the same line of reasoning that I explore in Doomsday Argument and the False Dilemma of Anthropic Reasoning resolves this problem as well.

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.

This is true, conditionally on an assumption that my current observer moment is a random sample from all observer moments throughout time. But this do... (read more)

[-]Karl Krueger3d20

What happens to the Boltzmann-brain story if the smallest unit of thought takes too much processing time to fit into a quantum fluctuation?

[-]kman4d20

A bit off topic, but I have a question about anthropic reasoning that's been bugging me for a while: what do you make of us not finding ourselves in a glorious transhumanist future? (I know UDT says not to give up on this basis)

2Mitchell_Porter3d

Assuming the validity of the doomsday argument, it could imply that most post-singularity universe-conquering timelines are dominated by unconscious entities.

[-]pjohn4d*22

I do not think the fact that my experiences don't dissolve into chaos moment-by-moment is a good argument against my being a Boltzmann Brain. I fully understand that order-experiencing BBs must be uncountably more rare than chaos-experiencing BBs, but:

1) If the universe is infinite, all types of Boltzmann Brain must be infinite in number. Since humans are finite in number, being even the absolute-least-probable type of BB would thus still be infinitely more likely than being a human brain.

(I realise this requires some infinitie sets to be larger than other... (read more)

2CronoDAS3d

If the universe is infinite, what stops the number of humans from also being infinite? (If you flip a coin infinity times, every finite Heads/Tails sequence will eventually appear as many times as you want to look for it, even if you do see "HHT" more frequently than you see "HTHTHT".)

5Eliezer Yudkowsky3d

Well, yes, if you read the relatively more advanced works on anthropics, which universally take the form of online erotica, they will observe -- I think Erogamer does this as well as Project Lawful -- that probability stops working entirely if you claim that an "infinite" amount of stuff exists in the classic sense of infinity, just as much as if you claim that nothing exists. Everything that exists has to be a finite fraction of existence and you have to be able to take ratios between them. The ratios are the critical requisite for stuff to work. It doesn't matter if you say they exist infinitely, finitely, or zero, what matters is the ability to take ratios.

1pjohn3d

What stops the total number of humans from being infinite is the thermodynamic death of the universe. I'm not a cosmologist (so please do correct me if I'm mistaken here!) but I think the universe's lifespan can be divided up into epochs, and whilst Boltzmann Brains can exist within any epoch, humans can only exist in a limited few: too early and the universe is too violent and chaotic to support us (plus probably not all the elements we're made from have been produced yet); too late and there isn't sufficient negentropy left to support us. We're currently in the 'stellar' epoch - but I think we're already past the peak of stellar formation: the rate at which new stars are forming is slowing down. The 'black hole' epoch will come afterwards, once the stars have all burned themselves out and there's no fusible material left to form new ones, but that's probably fine: we can probably extract energy from black holes (and from whatever residual heat there remains in stellar remnants like brown dwarves etc.) But, after even that, there might be an infinitely long 'de Sitter' epoch, after the last black hole has evapourated into nothing, the last stellar remnant has fully cooled, and there are simply no remaining sources of free energy anywhere. Boltzmann Brains could exist within this epoch (they could coalesce spontaneously from the ever-present quantum vacuum fluctuations) but regular humans, even digitally simulated ones, could not.

2CronoDAS2d

The idea being that, since Earth is possible, a spacially infinite universe could have an infinite number of Earths with humans on them, even if the Boltzmann Brain epoch is longer than the stellar epoch. It's hard to compare infinities.

1pjohn2d

Partially agree. If the universe were both infinite in size and contained infinite negentropy (or, if you prefer, infinite matter and energy) then sure, I'd agree that there would likely be vastly more human brains than Boltzmann brains. However, if the universe were infinite in size but didn't contain an infinite amount of negentropy (for example, if the universe started with some fixed amount of negentropy -like all the matter and energy present at the Big Bang- and then became infinite in size by inflating for an infinite amount of time, but after the initial Big Bang no additional matter/energy was added) then I'd say the infinite size alone wouldn't be sufficient to make human brains more probable. I don't know enough about cosmology to know whether there's any sort of consensus on whether the amount of negentropy actually is finite or infinite. I was (as you probably deduced from my previous comment!) just assuming a universe that's infinite in size (both spatially and temporally) but not in negentropy (hence the maximum-entropy de Sitter 'heat death' epoch). [...] True, but that doesn't mean we can't make any comparisons between them! For example, I think we can say "If the universe is infinite in size and contains an infinite amount of negentropy/matter, then the "universe size" infinity must be a larger infinity than the "amount of matter" infinity, otherwise we would observe infinite density throughout the universe". There are purer examples: Cantor's infinite series maths, where by matching-up elements in sets you can compare not only the relative sizes of infinite sets but also the "size classes" of types of infinite set. So eg. you can compare the size of the set of positive even numbers (let's call that Set A) to the size of the set of positive integers (Set B) by saying "if we match up the 2 from Set A with the 2 from Set B, the 4 from Set A with the 4 from Set B, the 6 from Set A with the 6 from Set B, and so on all the way to infinity, we'd sti

2CronoDAS2d

"Cardinality" is the math term you're looking for.

[-]programjames5d2-5

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?

Solomonoff induction. How many bits does it take to describe an disorderly moment of conscious experience? There are >100 trillion synapses in the human brain; let's say around 1 Pb. Compare that to the bits needed to:

Start with a few axioms
Identify a planet with self-replicators
Describe the path of evolution to o

... (read more)

2Dweomite4d

I'm confused about why you think BBs should be complexity-penalized for the difficulty of specifying which of all hypothetically-possible BBs we're talking about, but you don't think Earth should be complexity-penalized for the difficulty of specifying which of all hypothetically-possible Earths we're talking about. I get that you can (we think) specify a recipe that eventually produces Earth, rather than explicitly specifying every detail of the current Earth. But presumably you could also specify a recipe that eventually produces a BB. And since the final result you are aiming with for the BB is much simpler than the final result you are aiming for with Earth, I would intuitively expect the recipe will also be simpler (in expectation).

1programjames4d

I don't think you should penalize Boltzmann brains or Earths (or sapient species) based on which particular one you are looking at. [...] I think the point of it being a Boltzmann brain is that there is no recipe. It's just a random fluctuation. If there were a recipe, there would be time-consistency and it wouldn't be a Boltzmann brain.

-2Dweomite4d

Any given configuration of the universe either eventually will produce a BB, or won't. Because BBs are much smaller than Earth, the number of configurations that eventually lead to BBs should be much larger than the number that eventually lead to Earths, and therefore the number of variables you need to control to ensure you eventually get a BB should (in expectation) be much smaller than the number of variables you need to control to ensure you eventually get an Earth. BBs are a larger target in possibility space, and therefore (in expectation) easier to hit.

0programjames4d

"eventually lead to a BB" is not the same as "locate a BB" you do not have a BB unless you can point to it

0Dweomite4d

How is that different from saying that you do not have an Earth unless you can point to it? If we require that you augment the recipe with some spacetime coordinates that tell you where in the resulting universe to look, why are those coordinates any longer for a BB than for an Earth?

3ike4d

To point to a BB that has the same experiences as a human, you need to go really far into the future. You essentially have to hardcode every bit of those experiences, none of it comes for free. For a human on Earth, you get the order somewhat cheaply. Compare two Earth humans, where one is like you, and the other introduces a bunch of ad-hoc changes. The changes reduce the amount of order in its experiences, which increases the complexity of the program. The fact that the experiences are less complex is what it means for them to be ordered. Now suppose you have a BB that "cheats" a bit by coding in some of the order to reduce complexity. Instead of hardcoding a memory of the sun rising every day or whatever, it codes it once and copies it, to save some bits. Well then the prediction it makes for the future is also ordered! In order to get a "pure" BB that produces total randomness for the future predictions, you need to hardcode all of the order in the past and not use it to cheapen your complexity.

-8programjames4d

1EniScien5d

It seems to miss the context of OP. Why isn't math full of universes which very fast dissolve into max entropy thermal baths which exist indefinitely, able to directly generate Boltzmann brains randomly, but unable to have evolution.

1ike5d

While I agree that SI dissolves the BB problem, this is overstated. When reasoning, you have direct access to far fewer than 1PB bits. You don't even have direct access to all your memories. You can locate someone that's indistinguishable from you by specifying orders of magnitude less information than 1PB.

-1programjames5d

I agree, a one-trillion parameter model (~4Tb) can probably simulate the brain well enough, and you might be able to squeeze out another order or two of magnitude. The brain only has a hundred billion neurons after all, and maybe the reason it needs many more synapses is because its clock speed is a hundred million times slower than a GPU. ETA: Also, only ~1% of human genes are coding, so you arguably only need 10 Mb for the evolved brain.

2ike5d

What it takes to simulate the brain is not really relevant here. What matters is how many bits you currently have access to. If something is not part of your direct consciousness, you don't need to specify it in the program. This includes memories you are not currently thinking about.

-1programjames5d

I think we're looking at this from two different directions. Mine is, once trained, how many bits are in the structure of the brain? Yours is, during training, how many bits does the brain absorb? The numbers should come out the same, but mine is easier to get a lower bound and yours is easier to get an upper bound with. You have to worry about issues like, "what about memory that isn't being accessed in this compute cycle?" while I made the assumption that every parameter is contributing 1 bit of information to the active computation. My assumption is actually too strong though. Mixture of experts poses a problem, but a bigger problem is that it actually takes many parameters per bit of information. Probably. I mean, you only need to add a few hundred bits to train MNIST to >95% accuracy, while it takes ~10k CNN parameters. (note: this is trained on a 300k ResNet, not a CNN).

[-][anonymous]5d20

To my knowledge, there are infinite expansion models that allow for the formation of a "relaxed" void where a fairly limited number of Boltzmann brains would ever form.

The recent discoveries about the nature of dark energy also seemingly suggest infinite expansion isn't going to happen, so that's another possible solution.

[-]Davey Morse10h1-9

I'm sitting in a sweetgreens in Manhattan as I type. From one vantage, one of the most orderly human spaces on the planet. The food bowls are in the same shape, assembled in a factory line, and transacted for touchless apple payment every 16 seconds.

And even so, most of the air molecules that surround me are, from most zoom scales, in totally random positions. Most electromagnetic radiation (outside of color) is totally crazy and chaotic and has no pattern to me. Rather than staying sitted where they are, the most orderly possibility, people are constantly coming in and out. Quarks are going bezerk.

From most vantages, Boltzman appears right: randomness prevails. From a special human vantage, one which looks for order, order seems to prevail.

Good order-finders are bound to find themselves, with pleasant shock, surrounded by order. Not only because it's a precondition (order finders can only exist in spaces that support them) but also because it's teleology (it's what they're looking for) That they find order has no bearing on whether the larger space is random.

[-]American Psychohistory2d10

Do we really know that Boltzmann brains outnumber observers living in solar systems that fluctuate into existence?

Sure, a solar system is a much larger fluctuation than a brain, but a brain requires a fluctuation to produce an extremely complex and unlikely combination of matter whereas a solar system is just a lot of hydrogen in one place. A solar system can also last for billions of years and evolve quadrillions of times more observers, each of whom will experience millions of times the number of observer moments as a lone brain before it decays back in... (read more)

[-]Ephraiem Sarabamoun3d12

I don't think the idea of boltzmann brains and the ideas of a thermalized universe are related. The argument that you offer does effectively refute the boltzman brain problem but does not argue against that our universe is moving towards thermal equilibrium.

This whole idea of "choas" hides a lot of baggage. For every physical system you must define the states of maximal entropy. Those states are only relevant given your system constraints. When people talk of "choas" or maximal entropy I always think that they are in the back of their mind thinking of a h... (read more)

[-]Ben Livengood3d10

Does the unification vs. duplication debate have anything to say about Boltzmann Brains? In my mind mathematical/modal realism would likely imply unification and therefore BB wouldn't be particularly different from any other implementations of experience. Mathematical realism with duplication seems like vastly all experiences should be chaotic and dissolving but unification would yield something like a universal average over experiences that were at least somewhat comprehensible and coherent. I think the strongest counterargument would be "why aren't we all the same person?

[-]nonarbitrarity4d10

I presented a version of this argument to Sean Carroll (prominent physicist/blogger) in his December 2022 AMA (for context, the past hypothesis is just the quantitative way to state the assumption that the universe began low entropy, thus throwing out all universes that emerged randomly from fluctuations and predict Boltzman brains):

Q: In the October AMA, you said there was “No experiment you can do” to prove the past hypothesis. However, it seems any universe where the laws of thermodynamics are true and the past hypothesis is false should makes some very... (read more)

[-]EniScien5d10

I think that a hint for solution may be that many sources of evidence we live in Big Universe imply that if any non tiny amount of universes ended up in Boltzmann generating states, then we will find ourselves as Boltzmann brains in a universe which allows them. So it should not just disprove all physical theories that end up in Boltzmann brains. There should be some factor which makes Boltzmann brains less likely than normal consciousnesses in all of universes, not just in result of physics of our universe.

Also I don't quite see how you would observe not ... (read more)

[-]DanArmak5d*1-2

There is another reason to rule out you being a Boltzmann brain. BBs cannot validly reason about anything, and this makes them not you. Admitting any nonzero probability of being a BB makes valid knowledge and reasoning impossible. (How can you know that you can validly reason? Well, what do you think happens if you assume that you can't?)

Slightly longer: if we admit some probability of being BBs, how can we bound that probability? This means assigning probabilities to different explanations of what we see. But an unknown proportion of reasoners-doing-the-... (read more)

2Dweomite4d

1. Doesn't this argument prove too much? Why doesn't similar reasoning rule out other mentally-impaired states like drunkenness, dreams, and brain injuries? In fact, why doesn't it rule out being a flawed human being, rather than an ideal reasoner? 2. Even if all your memories are false, couldn't you still reason validly about abstract concepts (like math) and hypothetical scenarios? This seems to show that BBs can do at least some valid reasoning. 3. Even if you might be in some state S that would totally prevent you from reasoning validly, if you conjectured you were in some state T that would permit you to reason validly, and your reasoning based on that conjecture leads to a contradiction, wouldn't that allow you to rule out state T without ruling out state S? This seems to show that you can do at least some useful reasoning without completely ruling out that you are in an impaired state.

0DanArmak4d

1. Some non-Boltzmann minds like most dreaming humans can't do any useful reasoning, but normal humans can. We know we can because we use it to succeed at life, and we know we are succeeding at life because we trust our senses. You have to ground your belief in reality in something; if you fully distrust your senses then, yes, you cannot reason about reality, just as a Boltzmann brain can't. And you can't reason about logic either, because we learn about logic using our physical senses. 2. You could not because your definitions of those concepts, and your understanding of the rules of reasoning, and your memory of starting a single-sentence-long proof or chain of thought by the time you're finishing it, would be as false as all your other memories. You can't reason about 2+2=5 if you don't know what + means. 3. Who is "you" in "if you conjectured"? You have to assume you're able to reason at all, before you can reason about state T. You, Dweomite, can make an argument about T, because you're not in an impaired state. A Boltzmann brain could not validly make the same argument, in the sense of arriving at a correct conclusion because the argument was correct. A Boltzmann brain which is considering your argument about T is equally likely to believe or disbelieve it, because it came into being thinking it just thought through it and either accepted or rejected it.

2CronoDAS3d

My dreaming brain isn't entirely incapable of useful reasoning - sometimes I can recognize that I am dreaming and choose whether or not to wake up, although during a dream I also tend not to be capable of doing coherent reasoning for more than a short period of time.

2DanArmak3d

I did say most dreaming humans. But the point isn't how well dreamers can reason, that's just an example and if it doesn't serve it's not essential. My argument was that imperfect reasoners can still be trusted because they can be evaluated empirically on their success, and their reasoning ability is caused by evolution and learning in an ordered environment; whereas Boltzmann brains are not grounded, and any correct reasoning they carry out will be an accident.

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