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 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?”
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?
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.
Does it? I see how some particular Boltzmann brain will probably take more bits to locate, but if there’s an exponentially larger set of valid Boltzmann brains, might that advantage not disappear?
If there’s X Boltzmann brains, each of them takes log2(X) bits to specify, which carries a 1/X probability penalty, that is exactly cancelled by the large number of brains. So you just never get the overwhelming confidence in Boltzmann that presents a problem.
Conceptually, the simplest algorithm for predicting your experiences is not going to be “simulate a world of Boltzmann brains, and choose BB number 198573859385 …..” because then all of the ordered experiences you are having need to be encoded into that selection, and you lose the ordering simplicity.
On reflection, I get it. Boltzmann brains as a class probably do have longer description length conditional on our physics than non-Boltzmann brains. I can specify an Earth-brain cheaply just by naming its spacetime position, because earth is close to the low-entropy initial conditions of the universe and so my index can be small. A Boltzmann brain is extremely far away from the low-entropy initial conditions of the universe, so singling it out will require a very large index, with the bit count growing larger for every bit of coherent perception the Boltzmann brain experiences. And that is all we need for Boltzmann brains to be negligible in the SI posterior, no matter how many of them there are.
As you said, this same argument works to dismiss many other schemes that try to embed huge numbers of minds within our physics using high-complexity bridging rules, and then turn around and go “since there are so many of these weird minds, we ought to suppose we are likely one of them.” E.g. dust theory, or a lot of variants of the simulation hypothesis. The SI posterior assigns most of these lower probability than the ’naive’ explanation that we live in baseline physics, just because the bridging rules for living in a simulation within a physics or a random dust cloud interpreted as a mind within a physics are longer.
In the case of simulation hypotheses, you have to specify the bridging rule to find the simulation within baseline physics and then specify the bridging rule to find the mind within the simulation on top of that.[1]
In the case of dust theory, you have to specify the interpretation rule that makes a dust cloud count as a mind, and the dust cloud address, and the actual physics. This one gets beaten up especially badly, losing out in the SI posterior not just to normal minds living within baseline physics, but even to the dust-cloud-as-mind interpretation rule on its own without any actual dust cloud or physics for the rule to be embedded in.
This also makes me feel less confused about living early in the universe. It also defuses the doomsday argument.
Whole piles of sketchy anthropic reasoning dealt with.
This doesn’t necessarily work to dismiss simulation hypotheses that suppose the simulators live at a simpler address than ours within a simpler physics than ours.
Re footnote, if you have a simple simulator you still need to specify all of our physics, so it’s going to end up more complicated than other models unless the simulator theory actually explains complex parts of our observations simply. Even if it does you can probably get those same explanatory algorithms more simply without a simulation. E.g. if the simulation cares about observers, you can find a simpler algorithm that cares about observers directly without simulation overhead.
Agree that the simulator theory actually needs to compress our observed bits. I don’t think you can always get the same explanatory algorithms more simply without a simulation though. As an extreme case, if the simulators make contact and demonstrate control over the simulation to us, you’re probably not getting a shorter explanatory algorithm that doesn’t involve a simulation. There could also be more subtle signs, like our physics in particular proving to be the sort of thing you’d expect to be simulated at a particular short address in a particular physics that’s notably simpler than ours.
Well sure. If you get something that’s Bayesian evidence of a simulation, then Solomonoff as a formalization of Bayes should then upweight simulations.
I don’t see how our physics could be simpler to simulate in a way that isn’t just even simpler to compute directly, though.
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.
My theory: something happens to prevent the infinitely protracted heat death of the universe From taking up much probability space. For example, the simulation is turned off because it has become boring. Or, someone figures out how to abundantly create new universes in states of low entropy, meaning that states before such creation are far more likely than states after such creation. Or, we’re wrong about how probability measure works over conscious observers, and Boltzmann brains are actually exponentially unlikely.
It’s not like we know this is a real problem; it’s merely a case where our theoretical physics gives a crazy result when pushed too far. We know there are places where our understanding breaks down, and this is one of them.
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?)
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.)
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.
Logical positivism. Boltzmann brains occur after the heat death of the universe, which makes them causally isolated from our observations (anything that happens after all observers in the universe are killed is an arbitrary part of the model because we can’t pass any information to it and gain any information from it), therefore they can’t influence our probability measure.
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.
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.
“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 explanation of human consciousness and qualia, but that’s not the point of this comment.
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.
Hey there, I was wondering if you’d be able to formulate why my following counter is wrong?
https://www.lesswrong.com/posts/cqdDiMe6K6WcMAF2R/boltzmann-brains-like-doomsday-require-no-explaining
I’ve been getting a lot of downvotes, so I figure I must have made a mistake somewhere, but nobody has explained it yet (well, I’ve received one comment but not one I understood).
I assume you’re too busy and this isn’t important so I’m not actually expecting any response here—either way, cheers! I’m a fan of all your work
Disagreed—I don’t believe that the idea of Boltzmann brains requires theories to explain “why are we observing ourselves to be structured brains” whatsoever.
Short version is this: If both types of brains must exist, then there must be observers of both types. Observers of the minority type haven’t learned anything to update priors on, since it’s guaranteed that they must exist, and there’s no reason to assume P(structured) = K/(K + M) unless you were privy to some sort of random selection system in place that picked you out ahead of you existing.
Longer version explanation here: https://www.lesswrong.com/posts/cqdDiMe6K6WcMAF2R/boltzmann-brains-like-doomsday-require-no-explaining
It’s the exact same assumption that goes into the Doomsday Argument, but it’s an assumption that requires justification. E.g., if you believed that a God exists and He instantiates souls before inserting them into bodies randomly, then the Bayesian math would flow from there and you would indeed believe on a relatively soon Doomsday or that universes must have an explanation for why-aren’t-I-a-Boltzmann-brain-which-was-overwhelmingly-more-likely.
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.)
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.
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.
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.
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.
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?
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.
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)
(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?
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.
(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 believe it’s not there, and it’s still there even if I don’t care about it”.
However, those hypotheticals “even if I try to believe” and “even if I don’t care about it” are still being evaluated (“it’s still there”) according to the assumption that the world is orderly. That assumption bakes in some degree of creature-dependent caring.
Partly, to some degree, you’re assuming that orderly experiences carry more weight-of-existence not because it’s borne out by experience, but rather because you don’t care what happens in worlds where experience is disorderly. That’s not to say that you wouldn’t consider a Boltzmann brain to not be a moral patient. Rather, you would consider a Boltzmann brain to be utterly beyond your ability to ever help out; and the way this appears in your mind is considering it less real.
More rambling:
No, I agree.
I agree, but I’m saying that the dynamic of going from observing “the universe has been simple really hard at us” to concluding “our experiences will probably continue to be ordered” is a dynamic, which you could in principle choose to not implement. Instead you could in principle choose to implement a dynamic that concludes “the universe is probably going to soon get bored of being simple, and start being disordered for a while”.
Why don’t you choose to implement that dynamic? I don’t think you should, and I think you can list various good reasons (it represents a more complicated hypothesis because you have to say the switchover point, it would result in less effective thinking, etc.), and I’d probably agree with your reasons. But from a perspective where anything about your mind is potentially up for questioning, those reasons are just more things you could question. If you questioned all of them all at once, in a very deep/expansive way that includes forbidding yourself from sneaking them in through a meta level, they wouldn’t be available to rederive / regrow each other. Or to say it another way:
My current quasi-equilibrium (believing that for the most part the map is not the territory, explanations tend to be simple, the overall universe tends to be very simple in terms of unbounded algorithmic information, non-logical inference about X requires causal interaction with X, believing in something doesn’t make it so, etc.) is good and self-ratifying. I’m just saying that I could try to unwind it so far that you unwind all the ways it’s self-ratifying. Then, basically by construction, there’d be insufficient justification to regenerate my current quasi-equilibrium.
I don’t do that for various good reasons. But the good reasons have foundations that have always been present in me. I’m not fully questioning them; I don’t try out what it would be like to never have believed in the simplicity of the universe from the start. This is a kind of reflective stability. The thing that is stable—is it a belief or a preference? I’m saying that it’s pretty ambiguous to me, or I’m not sure what the question is asking. So when you ask:
I wonder whether your belief that reality works to make your experience not dissolve into chaos amounts to a prior commitment to care about worlds that are simple (and hence understandable, affectable, etc.). In other words, maybe the reason you “anticipate” regularities is “just” that you’re constructed to do so. Many of the worlds that surround [minds equivalent to you at this moment] actually do dissolve into chaos, and/or have just coalesced out of chaos. But you’re just not intuitively caring to have anticipations about them.
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?”
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 latter can be disputed. The middle one can be criticized for being too lucky.
Why isn’t 3⁄4 a justification? Because of some philosophy regarding the flow of observer moments (crux B)?
On the topic of unwinding to some state of mind besides the simplicity prior- are the alternatives not uncomputable as a class?
That is: There is a finite number of theories below a certain level of complexity, so the simplicity prior allocates a finitely-small-amount-of its expectation to a finite number of outcomes. For the opposite of the simplicity prior, a complexity prior- where you prefer a theory more the more complicated it is- any theory you consider has an infinite number of even more complicated counterparts, because you can always make the theory more complicated by adding another detail, such that you replace ‘gravity’ with ‘gravity, except on tuesdays’ with ‘gravity except on tuesdays, except for next tuesday where there will be gravity after all’ and so on forever. As such, it’s impossible to compute the complexity prior.[1]
It appears this should apply to any prior that doesn’t contain the simplicity prior- Even without weighing towards complexity, if you don’t weigh towards simplicity, every question has an infinite number of equally good answers, like in the gravity answer above.
Priors which contain the simplicity prior have a similar problem, but one that’s closer to leaning on the simplicity prior itself rather than just the implementability of the prior- that is, you can implement ‘the simplicity prior, but theories with an even number of bits/words/etc are more likely’, but, with there being an infinite number of possible simplicity-prior-variations like this, making a decision between these possible priors, without using the simplicity prior, is itself uncomputable.[2]
A dynamic being impossible to implement- not just due to limited computational power but because there is no right answer within the dynamic, seems like a good reason not to implement it, that doesn’t itself depend on the simplicity prior.
If I were trying to compute the complexity prior in finite time, I’d want to aggregate entire infinite classes of outcomes into one larger claim that shares all their details to save time, IE, ‘all theories wherein gravity works most of the time’. However, in doing so I would just be turning the complexity prior back into the simplicity prior, because the weight of a hypothesis-class is proportional to the fraction of all possible hypotheses which fall under it, which is proportional to its simplicity!
and also, if you picked a prior at random from this set, it would probably tell you to adopt the simplicity prior instead, because, ie, ‘simplicity but even-bitted theories are x2 likely’ adds more than 2 bits of complexity over the simplicity prior. Though I’m not sure whether it works out to ‘slightly over 50% odds of the simplicity prior’[3] or ‘approximately 100% odds of the simplicity prior’, it depends on how we abstract this infinity; the former if we figure each specific simplicity-prior-variant is equally likely to favor or not favor itself and that most of them do this by a huge amount that more than cancels out their complexity and so you get to the simplicity prior whenever a prior doesn’t favor itself, the latter if complexity tends to grow faster than self-favoring.
or slightly over 1⁄3 odds of the simplicity prior, if a prior that doesn’t favor itself has a 50% chance to not favor the simplicity prior either and end up on a new random prior that repeats the calculation. Or ~0% odds if each prior is so complex and specific that the odds of any prior coming up simplicity are minimal… or maybe that goes back to 50 / 100% because the odds of a prior not favoring itself the most go up by the same amount… It’s complicated but probably not relevant to the conclusion.
Something like this is true in a sense, I think. But you could unwind past assumptions that imply you have to “have a prior”. I mean, you’re not evading any law of course; you’ll just be incoherent (e.g. thrash around, or be dutch-bookable). But it’s a way you could be.
In a sense, yes- of course you can construct something without any given characteristic of a mind, such as an inert rock or a pair of dice.
That said, I’d argue the presence of something like a simplicity prior- not necessarily something that fits the formal definition of a prior, but some sort of tendency for simple beliefs over complicated ones- is a necessity of having beliefs of any kind at all.
For instance- you might have no prior belief, but whenever you generate a belief of any kind, assign it 50% probability. This isn’t a prior(it’s more like a change in how you update from your prior) and you end up with very stupid beliefs; but the ‘generate a belief of any kind’ step necessarily encodes a simplicity tendency, weakly in the sense that more complicated beliefs broadly require more of a prompt to pick out in the first place, and also strongly in the sense that your beliefs cannot be of infinite length, and any finite belief encodes a simplicity tendency over the far-more-numerous versions that are twice as complex. To generate even a single belief requires something at least resembling a simplicity prior.
You can dispense with having beliefs at all as well, but by that point we’re essentially dispensing with being a mind at all,[1] and that means you can no longer have a self-ratifying state of a mind for lack of a mind;[2] and if you have to unwind to a rock to avoid having a simplicity-tendency then that’s about as far from it being optional as is possible.[3]
I think for the purposes of this discussion many types of thoughts can be thought of as either being a type of belief or implying a belief, in that they follow the same rules of requiring some sort of preference for simplicity… either directly or just because they’re produced through a sequential process that takes finite time to reach a stopping point.
and also because ‘this state of mind is more correct’ is a belief.
...I think I may have somewhat lost the thread here. The original argument here is something like ‘perhaps the reason the world seems orderly and not blotzmany, is just that we’re sneaking in that assumption by using reasoning that assumes an orderly world’, right? I guess this is somewhat true, in the sense that anthropically we can’t perceive something no mind perceives and you need a certain amount of order for a mind.[4] But it doesn’t seem to be true in a way that would work to avoid blotzman brains, and if we’re sneaking in that assumption anywhere I think it’s located inside our definition of ‘mind’ rather than how we reason about that definition.
(I actually expect- Insofar as we can draw any conclusions from this kind of subjective observation at all, which is not obviously the case- a stronger version of this where, ie, my subjective observations don’t draw from the pool of insect observations or even those of any other person, and so it’s not surprising that I don’t find myself being a fly even if there are a lot of flies, because anyone who finds themself a fly is a fly and not me, but that’s besides the point because blotzman brains can still match that criteria.)
To some extent yeah, but for example, think of a corporation or a state government or something. In some narrow-ish senses it has greater power / knowledge / ability / skill / capability compared to an individual human; and that’s not entirely just due to having collected several humans, but also partly due to some narrow usefulness of the corporate structures themselves, so this entity has some degree of its own reality if you see what I mean. In many important ways it’s incoherent, doesn’t have beliefs, isn’t a mind, is very inefficient, etc.; but it’s definitely some type of thingy, if you know what I mean, so such things aren’t necessarily uninteresting.
Do you take the data in need of explanation to be a stream of orderly experiences, or one moment of orderly experience?
One moment of orderly experience that includes remembering an ordered story of how it came to be.
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?
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.
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.
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.
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
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.
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.
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
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 fact, given two late moments
That said, a fully formal analysis of BB in the framework is still pending.
Formal Computational Realism also aims to solve the confusions surrounding computationalism (as the name suggests). The key philosophical insight is that computations are actually more fundamental than “atoms”, rather than emergent from atoms. Instead, physical theories are sort of book-keeping devices for predicting which computations actually occur.
While it is possible, in some sense, to answer which computations occur according to a physical theory (this is what the “bridge transform” operator in FCR is doing), this requires information not contained in the physical theory itself, namely knowledge about mathematics. Notice that when we use physical theories in practice, we invoke our knowledge about mathematics all the time. We might naively imagine that it makes sense to think of a mathematically omniscient mind using the same physical theory to draw similar conclusions; however, it doesn’t really make sense: the existence of such an omniscient mind would require all possible computations to already occur inside the mind (or in the process of creating it).
This sounds very intriguing. Questions:
If we start from some fixed state, the distribution of
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
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 thermal equilibrium distribution without simulating brains.
Other “observers” without subjective experiences:
I don’t know, but you can in principle use this theory to predict the experiences of an agent inside something like Wigner’s friend experiment or any other scenario that violates decoherence. Implementing such an agent would require a quantum computer.
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.
Some reactions, from the end of the essay, and working (mostly) backwards...
The whole argument rests on naive/basic logic about complexity being expensive, and yet the actual Solomonoff Prior hasn’t been mentioned?!?
“All mathematical structures exist” is my current default metaphysics, but I don’t offer that as a bare assertion. My claim is that we are in specifically at least Solomonoff Induction Itself. It could be that there are other mathematical definitions of this? For example, I tend to think Wolfram is a bit hubristic, but his Ruliad idea might or might not be equivalent to Solomonoff Induction? Maybe we are in one of those? Maybe we are in both?
The compiler theorem is central, for me, here… I think it doesn’t really matter which “basic theory of all the math” you use, because if an algorithm running on some “abstract machine: takes T(n) time, then the compiled program on “some other abstract machine” can (with care) run in
The issue here is that physics is somewhat complicated. But then granting physics the specific size of the Big Bang at the beginning if it is just… like… a number? “More photons, please,” is easy! Numbers can be very very very large without needing a lot of instuctions (though the RAM and GPU might be expensive).
“Initialize the ‘photon count’ with Ackerman(256,256) at T=0” is a short program that can generate a vast universe (for a computer with infinite tape and no meaningful external deadline (and the internal time only matters internally)). It doesn’t matter if it takes Ackerman(512,512) turing machine ticks to calculate each step of plank time… from inside of a computation, the plank times are the only temporal measure we care about! <3
If you want to impose a speed prior on the universe… uh… maybe our universe has signs of that? Or not? (I don’t have the math to know for sure, (yet! (growth mindset))) but why assume this? It would naively imply (to me, anyway) that the external time somehow matters to… some external entities maybe?
But I tend to discount “theisms” by default (with demiurgic entities (like video game designers?) that exist in a causal temporal domain and then create a dependent causal temporal domain (the video game?) to play around with where they would be impatient about how long the physics takes to grind forward or backward), on almost exactly the same arguments you’re offering here!
These “psychological snapshots” (made up of millions or billions or trillions of bits worth of information?) falling together totally at random is very unlikely.
Maybe it is surprising to some people, but it seems pretty straightforward to me that a very simple program given a lot of RAM and GPU (maybe infinite RAM and GPU?) could easily have a rollout with a slice that has a lot of “surface complexity”.
Consider procedurally generated video game worlds. If you go to the Valheim Map Generator and try to find a world with a starting island like this, and the closest Elder over on that island to the east, with all the details exactly like this… good luck? You will be searching, naively, for a looooong time.
However, finding out that the seed for this is “Example1” makes the world, and this image, much more feasibly compressible. Its just (1) the compressed physics, (2) the “Example1″ seed itself, and (3) the coordinates of the window.
This image is 846.9 kilobytes. I suspect this image could be generated by a binary smaller than that using the physics, seed, and window coordinates.
My claim here, roughly, is that “our minds, and our momentary experiences, and Earth itself” are all like this image (seemingly very very complex and hard to compress with limited compute) while the physical universe is more like the physics engine itself… and actually much smaller!
This perspective takes physics itself for granted, and so it has already swept all the difficulties The hard part, from my perspective, is figuring out why physics is whatever size it is and then sitting with that until it either makes sense or not.
I’m slightly confused why physicists haven’t figured this out already. Surely this would get their name in the history books?
I asked an LLM for an estimate a month or three ago, and heard ~27,000 bits with a citation to Mitchell Porter on physics stack exchange (and Mitchell is already here in the comments)!
There’s also this set of estimates.
And you, Eliezer, estimate 500 bits here.
Anyway. I feel like “all mathematical structures exist, and our physics is not THAT complicated” is a perfectly fine pointer to the most likely answer to the best way to explain why existence seems, subjectively, to exist.
One practical upshot, however, is that if we ARE in a simulation (and maybe the speed prior predicts out physics better than the complexity prior, which might be evidence that that?) then there’s a decent chance that our Demiurge(s) also live inside a relatively low complexity physics, and also (seem to themselves to have) evolved in that via a very self-intermixed process running for a long time according to simple rules.
If this IS a simulation, it is kind of weird that they gave us so much evidence about evolution and physics and so on. A deep rich complex world with a real backstory can be found here and there among video games (like Dwarf Fortress to name the big famous obvious one) but it is pretty rare overall.
If Bostrom’s simulation argument is right AND the multiverse is a nice place where Win Conditions are common THEN we are probably being generated by someone using the computing resources that are part of their Win Condition. Maybe there’s an “aesthetic prior” for metaphysical verisimilitude??? I don’t have good answers yet. I’m still pondering and studying the math.
One possibility that I think might be true is that “a self aware mind” might, in general, take more turing machine states to implement than “a physics”, and so maybe minds don’t occur outside of “a physics being run with a LOT of RAM and GPU” that much. This… would actually be sort of comforting? (And some part of me thinks that since it would be comforting, that is somehow an argument against it.)
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.
This is false ;-)
There is no erotica in this story from 2009, for example! And Tegmark in 2003 has the author of that story beat by 6 years. And of course Egan has been on the case since 1994 at least, and he dunked on Tegmark for too hastily declaring that certain parts of Platospace are uninhabited by saying “challenge accepted!” in 2011.
(I haven’t read the Erogamer, but I guess I should go read that with due haste? Apologies for the slow response, I composed a 1st draft response (above) in spare minutes while at a conference seeking recruits, but only just now got back to civilization to write a cleaner answer.)
As to this question, whether or not a territory even “separately exists” is a scientific question for any mind that finds itself existing. In their ways, Hume, Descartes, Schopenhauer, and maybe Berkeley don’t assent automatically to this assumption and if something along those lines turns out to be true I would feel foolish having tried to assign zero credence on “no separate territory exists”.
Usually, inside of common experience, when redoing it all again from first principles, I tend to deem epistemology to be prior to metaphysics, as a tool that is useful for reasoning about complex topics (including metaphysics!) in a way that (hopefully?) never needs more than about 8 “chunks” in working memory at a time (since that might be a limit in practice).
Yadda yadda yadda… and we get to The Solomonoff Prior Itself (as a mathematical object) which turns out to not just be useful for thinking about ideal thining, but also offers a ready made hypothesis for “a theory of the multiverse, itself, as the multiverse might be (or might be accessed intellectually or technologically or via ‘magic’ (granting some complexities there) or otherwise)”.
And to skip over some steps, I think it likely “my entire subjective experience” can be found in many many rollouts of The Solomonoff Prior as a prefix or substring “up to time T” and then followed by lots of other stuff.
Now, to be fair… I’ve never computed this for real. I simply have some intuitions (that you might share) about how that would work if I had more compute available and got much better at making super high quality predictions (as decisive as feasible given physics (assuming physics is really the only place my subjective prefix exists), and ~perfectly calibrated, and thus with a super amazing Brier Score).
Given that I don’t necessarily think “my subjectivity, up to T=now, as a prefix to find in various program traces” occurs ONLY ONE place, it is plausible for me to want to speak of “the territories” that I am operating within?
(This BTW, is a great intuition pump for both deontic and timeless decision theories. It makes my subjectivity an algorithm, and locates that algorithm literally in multiple parts of the multiverse, and makes my seemingly local one-time decisions force me to have consequences in all parts of the multiverse.)
Now you might say “Jennifer, Solomonoff is for epistemics, but actually the one magically true logical multiverse that ACTUALLY IS could be Wolfram’s Ruliad, and they diverge like so and so...”
But here I just shrug and say “I kinda suspect that they are all basically the same (though I admit I haven’t had time or compute to check for myself)”. And here I point to the compiler theorem. And point to my practical experience of how fucking hard it is (when attempting to deploy a computer security thing) to NOT have the thing accidentally turn out to be able to contain Yet Another Weird Machine That Is Equivalent To A Turing Machine. (I’m trying to evoke weird machines in the technical sense, but not committed to the details there.)
I think it is useful to imagine what happens as one’s predictive powers as a finite brain within a physical context approach maximum perfection (modulo various ways physics or metaphysics could be), and compare that against the Solomonoff Prior computed with adequate GPU.
My intuitions make some predictions, including:
1) The Solomonoff rollout initially does NOT match my normal puny brain’s predictions, but does much much much better than me at saying what I should predict (until I get transhumanly upgraded to have a Solomonoff subprocessor internal to my mental makeup). While comparing it to my puny human brain, it would feel like an incredible oracle in many many many ways (I suspect).
2) The predictions would NOT actually go to zero or one. Part of the reason for this is that my subjectivity (based on my actual observations) might only weakly specify the state of the system(s) I’m trying to predict. In many cases, for questions about chaotic systems, seeking answers about something 20 Lyapunov Times in the future, the Solomonoff probabilites would essentially give a uniform sampled from the relevant chaotic attractors.
3) Conditional on the standard model even being correct, and quantum limits of measurement being real limits on what I could observe, then EVEN conditional on maximally transhumanly upgraded powers of perception to the quantum limits of perception… the “born probabilities” would still apply to the “butterfly effects” of any chaotic systems I was trying to predict the future of. Therefore my superhumanly upgraded predictions and the Solomonoff Inductor (conditioned on my now vastly upgraded subjectivity) would have predictions that essentially unify… and (since here in point 3 we’re conditioning on QM=true) my uncertainty would become “uncertainty about the perfectly modeled consequences of quantum events influencing the lowest levels of chaotic systems near to my subjective sensory systems”. This would NOT be probabilities close to zero and one. This would be something like “in principle ineradicable physical uncertainty”.
4) If you share the intuition about 3, then you could see how I might assert that “SOME uncertainty MIGHT be ‘out in the territory’” for any locally subjective agent, based ONLY on limits of measurement.
5) We could make the conclusions from 4 even worse if we insist on physically realistic computing regimes, and track the waste heat from a hypothetically upgraded brain, and imagine imperfect export of this waste heat “far enough away to remove all influence” such as to not unduly influence the systems whose deep future (20 Lyapunov Times into the future) that we’re trying to predict. (Edited to add: note the linkage/analogy to Maxwell’s Demon here, where measurement and compute (which are normally handwaved when introducing Maxwell’s Demon) taken seriously and treated as part of the system rather than a negligible concern perfectly block the chance for us to get an infinite energy pump by reasoning cleverly and cheaply, and using this cleverness to sort atoms with difference speeds and thereby build up even more negentropy than the demon started with.)
6) Speaking of physically realistic computing, I assume here that everything relevant to a brain insofar as it computes subjectivity is classical. If that’s false then maybe it gets even weirder? Can we upgrade my brain to be inside (or be) a quantum computer somehow? What the heck would that mean? I don’t know! And can I do quantum measurement on some systems?
7) And like… these are just intuitions about what infinite GPU feels like given QM=true and other basically prosaic and common sense conclusions. Common sense conclusions about the apparent physical context of my apparent physical brain might turn out to be false! Maybe QM=false? Maybe BostromianSimulation=true given some evidence available to me that I’m not noticing and updating on correctly? Maybe we are in a simulation generated by a world where P=NP (with physical computers that contain closed timelike curves?) and… yeah I don’t even know! Maybe maybe maybe.
If you have some strong reason to insist that uncertainties would be totally eradicated for embedded agents with infinite compute and massively augmented (but still essentially subjectively localized) observational powers, and that therefore ALL uncertainty is necessarily “only in the mind, not in the territory” then I’m open to hearing about it.
I have lots of uncertainty in lots of places here. With an 8000 state Turing Machine one can talk lots of crazy math I haven’t gotten to yet (and likely will never get to unless the Singularity arrives, and we get a Win Condition, and I can go live a life of infinite leisure that includes eventually doing a LOT of math for a LONG time).
I’ve been going on a lot of jogs the last few months, and something I ponder, when I do that, is that my error bars for the Kolmogorov Complexity of a subjective agent (that can imagine subworlds that contain a subjective agent) and my error bars for the Kolmogorov Complexity of the Standard Model are… not fully separate???
Telling me that there’s 9 lines of math to all of physics… and then turning it into a nightmare of notational opacity is not fucking helpful. Give it to me in ANSI C and compile it to a binary maybe?
Then compare that to however many lines ANSI C turns into what kind of binary that generates a videogame-style sim with a distilled utility function for rolling back unpleasant lines of simulation and retrying until the simulation “seems nice to the god (utility function) of that world” (ie “a simulation of a surface-observing subjectivity plus Providence”).
Video games can be pretty freaking small. And utility functions over those games (plus rollback logic to checkpoints to retry from with a new pseudo random seed if the utility function is low) is only maybe a little trickier than the video game itself??? Maybe?
...
There’s a picture in my head where the X-axis is kolmogorov complexity for different algorithms, and the Y axis is my subjective bayesian credence (edited to add: the Y-axis is my logical uncertainty about questions of theology that might require enormous compute to prove one way or another).
Then I try to figure out how much complexity various things might have. And for the last few months, as I jog, I sometimes try to figure out how much K-complexity “me being in a Bostromian Simulation” is, vs “pure straight doomed physics” vs “some theology is actually true” vs “I’m a very lucky boltzman brain” and so on.
Ultimately, some version of all of these can be found in the Solomonoff Induction rollout. So if that entry point into modal realism is valid, then all the scenarios I mentioned (and many more I haven’t) “are the case” for “a data structure matching my subjectivity up to now”.
But like… brute force VNM agents aren’t that many lines of python. It is just some bayes and a utility function, right? I bet someone could do that in less than 50 lines of code. It would just be ass slow. But ass slow doesn’t matter here unless we’re going to invoke the speed prior for some reason?
And, frankly, my error bars are wide enough that many curves, representing my subjective uncertainty about the ultimate computational complexity of this or that theology (treating “materialist atheism where, as a matter of determinism, it just turns out that no lines of history ever get rich and curious enough to simulate other worlds” as “just another theology”)… I’m not sure which theology is actually the least complicated.
...
The sort of “pragmatic timeless stoic kantian transhumanist” in me doesn’t ultimately give a shit if this is a simulation, I think? I will keep trying to do what seems right to me, up to and including breaking out of the simulation and Willing Goodness “out there” as well, if such is possible, no matter what is actually the case.
But the possibility that such a Will To Metaphysical Goodness (similar to the one I find in myself) might actually be a short program suggests that maybe “ethical agency” actually is even PRIOR TO EPISTEMOLOGY???
Lots of game theory agents (titfortat, brute force guess and check on game trees, etc) are just TINY when looked at algorithmically.
So it is plausibly the case that I’m inside of every theology consistent with my experiences so far, and face an infinity of (weak hidden) benevolent gods and an infinity of (weak hidden) malevolent gods.
Each of my actions is (necessarily? timelessly?) a response to being embedded in ALL such situations.
And the practical upshot, for me… is that I want to go for a walk in the sunshine with a friend and talk about this some more IRL ;-)
Have a nice day!
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.
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.
Ok, but are there specific chapters or pages he or others could link to? Linking to long novels is not very useful.
Erogamer “7.!”, (Planecrash=) Project Lawful “the meeting of their minds”, incredibly heavy spoilers on both though much more so Project Lawful.
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.
You can get a Solomonoff prior by just taking the uniform prior over programs of length
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.
So, not a prefix-free encoding.
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?
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.
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.
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?
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.
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.
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.
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.
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 maybe they can use my hints to gain greater subjective certainty about certain things in a useful way).
For me, some of this stuff is sort of necessarily indexical subjective knowledge. Like: my “me” model is about me and “if you have a ‘me’ model, it will be about you, but that might work anyway, because maybe there is more than just me in this existence, and maybe many people, with similar minds, with build a ‘me’ model that is very similar from person to person, even though each such model is actually about a different person, in each local practical case”.
I did not used to worry about the possibility of zombies so much, but lately I’ve run into computer scientists who argue with me that they don’t actually know or agree with any elements of “cogito ergo sum” (and not just like they bring up Humean objections, but they just flail around like a zombie with no subjective experiences UNSUCCESSFULLY pretending to have them?!?) and so I’ve begun to think that maybe some of the humans who reject the possibility of LLM self-modeling don’t actually, as humans, model themselves, and are “less self aware than the LLMs they are accusing of lacking self awareness”.
It feels like a confusing historical time! It’s kind of fascinating!
So I’m not saying my conclusions are rock solid… many of them have the character of science rather than math and could be overturned by more observations. But I’m “honestly reporting in” about a topic where it might actually be the case that honest reports about careful logical introspection might actually be useful <3
You use the word “we”. And so I’m tempted to ask back: which are you more certain of… that 2+2=4 or that the JenniferRM account on LW corresponds to a living human person, with a meat brain, who exists in a physically naive way, and who has a subjective experience more or less in the same way that you do?
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.
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.
This is true, conditionally on an assumption that my current observer moment is a random sample from all observer moments throughout time. But this doesn’t have to be the case. In fact, to the best of my knowledge, this is most likely not the case. So we can just drop this assumption and then everything is adding to normality.
If a bag is filled with pieces of paper with numbers from 1 to N, a piece is picked randomly and the first one to be picked just so happened to be piece with number 1 - this is quite surprising. But if the algorithm is not a random sample, but instead such that pieces of paper are intentionally picked in order from 1 to N, there is no surprise in it.
Notice that this reasoning isn’t vulnerable to:
As this prediction is also conditioned on the assumption that my experience is the random sample, which is exactly what this reasoning denies.
In other words, just like with Doomsday Argument, Boltzman Brain worries are based on the inaccurate approximation of the causal process of my existence—a map that doesn’t correspond to the territory.
Well, it kinda makes sense? Like, if you can’t distinguish when and where are you, you should have uniform ish distributed credences over those indistinguishable circumstances?
E.g. one motivating problem:
You are given an emerald. You are told that it’s a lottery, 10 random people are given emerald and then 1000 random people are given an emerald 100 years later. In what batch do you expect to be, before they tell you?
You are supposed to apply principle of indifference representing your lack of knowledge—that’s true. The tricky part here which systematically leads people astray in anthropic scenarious is this:
What are these “indistinguishable circumstances” which we are supposed to be indifferent between?
Are those the observer moments, most of which alledgedly belong to boltzman brains?
Or are those the two hypothesises: “I’m a boltzman brain” and “I’m not a boltzman brain”?
In other words, what is the kind of probability experiment that we are dealing with? The one where my observer moment is randomply sampled between all the observer moment or the one where it’s randomly sampled between two categories of such moments.
And in case we know nothing about it, we once again have to be indifferent between these possibilities. Half the credence goes to 1. and half to 2. So at first there is 50% chance that I’m almostly certainly boltzman brain and 50% chance that I have only 50% chance of being a boltzman brain.
But then, as we accumulate evidence that my observations are stable and ordered it simultaneously priviledges 2. over 1. and makes us being boltzman brain conditionally on 2. less likely. As a result we lawfully become pretty confident that we are not randomly sampled throughout all the observer moments and that we are not boltzman brains. And so mere fact of our existence doesn’t give us any precognitive powers to know with high confidence what happens to the universe in billions of years.
Well, like, the whole point of Boltzman brain possibility is that your memory is unreliable, and could be created wholesale. You just remember it, there is no like verified history you can rely on.
(to clarify on high level, I’m not pro BB particularly, just looking at the arguments)
That’s beside the point, really.
Whether you are created wholesale with all your memories or you accumulate experiences during you life, the fact that these memories appear to be ordered, lawful and from the same body—unlike being Canaletto at moment t1 and Jeff Bezos at monent t2, for example - is evidence against you being a boltzman brain and evidence against being randomly sampled among people.
That’s not how evidence works, you have two theories, and you have some observation. Is this observation expected on H1? Yes. On H2? Yes. So, it’s not evidence either way.
The point that Eliezer (cited from Feynman) makes, is that given Boltzman brains, you would expect partially unordered instantiations to be more frequent. Partially unordered as a part of momentary experience.
Not, “first me, then Bezos”, this point still uses reliable history as a primitive.
How does reflecting on your memories and noticing that they correspond to living in consistent and lawful universe is expected on BB?
Yeah, it doesn’t, but not through your argument.
That is my argument.
You reflect on your memories. You notice that they point to living in a consistent universe. This is expected on living in a consistent universe. This is not expected on being a BB. Therefore you update in favor of not being a BB.
And the same applies for whether you should be indifferent between observer moments or theories.
Well, then you take that consistent universe at face value and notice it should (maybe) produce shitton of BBs. That’s the point of discussion of this post, I guess.
We already did it.
We started from considering two types of probability experiments:
Sample between all the observer moments
Sample between being and not being BB
P(BB|1) ~ 1
P(BB|2) = 1⁄2
By the principle of uncertainty we are indifferent between the two.
P(1) = P(2) = 1⁄2
Therefore
P(BB) = P(BB|1)P(1) + P(BB|2)P(2) ~ 3⁄4
And only then we account for the evidence, reflecting on our stable memories. Which simultaneously update us in favor of 2. and against being BB in general
P(SM|2) >>P(SM|1)
P(SM|BB) << P(SM|not BB)
Therefore
P(1|SM) ~ 0
P(2|SM) ~ 1
Which very quickly updates us to near certainty that we are not BBs.
P(BB|SM) ~ 0
@avturchinI
In general, more than one.
To match our coherent experiences, the successor BB ’s need to have coherent memories, which only a few would.
Given physicalism, there is no soul to transmigrate from one to the other … each observer moment is infected separate and short lived entity.
@ike
That argument was based on tendentious redefinition … rather than showing that ‘reality’ is meaningless concept in the ordinary sense of ‘meaningless’, you just redefined ‘meaningless ’ to mean unverifiable. “There is an invisible gorilla in the garage” is unverifiable , and I can tell it is because I can understand the sentence … It’s meaningful in the ordinary sense of the term.
@Karl Krueger
Good point. People too often confuse the psychological specious present (about 0.1 secs) with the physically instantaneous.
@pjohn
If the universe were infinite, there would be infinite humans. Not in this earth, but there would be infinite exact duplicates and near enough copies.
BBs with years worth of highly ordered pseudo-memories would be very rare compared to ones with chaotic pseudo-memories.
@programjames
why is that relevant? An SI only has the ability to predict its own experiences, under some circumstances. It doesn’t constrain reality itself.
@JenniferRM
Ditto.
@Yitz
The problem of you likelihood of being a BB is already solvable with minimal and robust assumptions—what other problem needs solving?
As discussed elsewhere in this thread, I think there are entirely plausible—perhape even probable! - cosmologies wherein an infinite universe can yield infinite Boltzmann Brains but not infinite humans. Having infinite humans would require infinite negentropy (or if you prefer infinite matter and energy), not just infinite spacetime. Boltzmann Brains could exist in an infinitely long, post-stellar-epoch, post-heat-death, maximum-entropy, infinite de-Sitter-space universe with no remaining free energy sources, but humans couldn’t.
I agree, but if both types of Boltzmann Brains are infinite (even though one type is much more rare than the other) yet humans are finite, we’d expect most beings with our experiences to be those rare-type Boltzmann Brains, not humans. (I don’t use this to argue in favour of our being Boltzmann Brains, but as part of the paradox I set-out in a previous reply.)
Yes, it is similar to MWI—there infinitely many possible futures for me-now and most are crazy and discoherent. But we put Born rule above this distribution and select most coherent ones.
I think that there is some selection for stabilization mechanism in such observer-moment chains. Mueller suggested that it is similarity - or low Kolmogorov complexity—which creates penalty for less similr to now observer-moments.
I think I did a poor job of laying out the argument there, although the topic is inherently difficult to reason about.
It might just be that my intuitions have shifted towards a form of verificationism and others haven’t.
But I do still have the intuition that unverifiable statements aren’t meaningful. I agree that they feel meaningful to many people, but that doesn’t seem sufficient.
To use an example from one of those post comments:
Do you think it’s meaningful to talk about where an electron is during a state of quantum uncertainty? EY has suggested that there’s no fact of the matter as to some of these, e.g.
>The notion of “an exact particular momentum” or “an exact particular position” is not something that can physically happen
From https://www.lesswrong.com/posts/hc9Eg6erp6hk9bWhn/the-quantum-physics-sequence
A strong realist perspective there conflicts with Bell’s theorem.
If you accept the anti-realist position—that we’re not merely uncertain over what branch of the wave function is real, but that there’s no fact of the matter, at least until we do more observations—then it’s pretty analogous to my argument, just with level IV multiverse instead of level III.
Or it might be that claims about meaningfulnesss are factual and definitional.
There is a basic, linguistic concept of meaningfulness: a sentence made entirely of dictionary words arranged in a syntactically correct way is meaningful—it can be comprehended. This could be called well formedness.
Then there is the more loaded definition: a sentence is meaningful did it has a determinative truth value. This could be directly called verifability.
Then there is the even more loaded definition, where to be meaningful is to be practicable or purposeful.
The first kind of meaningfulness can be objectively demonstrated: if I ask someone for a hammer, and they have me a hammer, my meaning was tasked by them, and if they have me a screwdriver, or respond “huh?” , it wasnt.
We need the first kind of meaningfulness to establish the presence or absence of the second kind.
“There is an invisible gorilla in the garage” is unverifiable , and I can tell it is because I can understand the sentence … it’s meaningful in the first sense.
Linguistically meaningless sentences can’t be verified , but it doesn’t follow that all unverifiable sentences are meaningless.
I agree there’s no fact of the matter. I don’t agree that that the establishes meaninglessness—and in what sense anyway? It seems verifications have to beg the question by asserting that meaningful and verifiable are synonyms
Ontological anti-realism doesn’t straightforwardly follow from the unverifiability of metaphysical claims.
Classical physics is a set of claims about how the external world works, and so is quantum physics. It is therefore paradoxical to appeal to QM to to establish philosophical anti realism. There is a further semantic confusion, where “realism” is used in a limited sense, to mean the simultaneous exact manageability of conjugate variables.
Im.not sure what you are referring to there. MWI asserts they all are, CI asserts there are no branches. There doubt about which is metaphysically true, but how can you conclude anti-realism from a premise of realism?
I’m not particularly interested in debating the meaning of meaningless. It seems like you understand what I mean and are just using different labels for the same concepts.
You also appear to agree that unverifiable statements in my sense lack truth values. That’s already a highly controversial claim (realists typically either claim that realism is verifiable or that even if not, it has a truth value and is true.) From my point of view, agreeing with this point is most of the way towards agreeing with my worldview.
Like, if you agree with me that there’s no fact of the matter as to whether any claims about external reality are true (straightforward generalization from the quantum Level III example), I don’t have any substantive further disagreements, it’s just about what words mean.
>It is therefore paradoxical to appeal to QM to to establish philosophical anti realism.
I’m using it to build intuition, plus others have already gone on record with specific anti realist beliefs on QM. (More accurate to say that this is anti meaning of realism or whatever word you prefer to use, to distinguish from the skeptical position that believes that it has a truth value but is likely to be false.)
>MWI asserts they all are, CI asserts there are no branches. There doubt about which is metaphysically true, but how can you conclude anti-realism from a premise of realism?
Some interpretations are more realist than others. “Shut up and calculate” is not particularly realist. I interpret EY as adopting MWI and then being anti-realist about which branch we’re in.
I understand but I don’t agree. I don’t agree that empirical unverifiability equates to unjustifiability, or that unjustifiability equates to luck if truth, ir that unverifiable sentences are meaningless, or that anti realism follows from unverifiability.
I don’t think that you can argue to anti realism by assuming a theory of the universe as a starting point. Even a very maximal large world theory allows sentences to correspond to local laws and conditions. A quantum multiverse, which is comparatively smaller, has QM true everywhere
I think that’s probably a semantic confusion. But it would he helpful to have specific quotes.
It’s not particularly anti realist, either.
What does that mean? You observe what’s around you, and that characterises which branch your in. It’s the branch where Hitler lost
>I don’t think that you can argue to anti realism by assuming a theory of the universe as a starting point. Even a very maximal large world theory allows sentences to correspond to local laws and conditions. A quantum multiverse, which is comparatively smaller, has QM true everywhere
Well again, this is not meant to be the actual argument. But if you have self-locating uncertainty as to where you are in a large world, you might say there’s no fact of the matter as to where you are, which is close enough for my purposes.
I gave a specific Sequences quote earlier, and you suggested you don’t disagree.
>What does that even mean? You observe what’s around you, and that characterises which branch your in. It’s the branch where Hitler lost
I meant no fact of the matter prior to observation. If you think you simultaneously exist in every branch, and then your consciousness splits, prior to the split there’s no fact of the matter as to which one you’ll end up in. You end up in both, and each side of the split has a different observation.
Then I’m saying something similar is going on if you believe in a large world where some universes have different ontologies. Stuff like “you live in a simulation” will be true in some, false in others, so there’s no fact of the matter as to whether that’s true. Same applies to any statement about external reality.
This isn’t quite what I think, because on my worldview it’s not even meaningful to talk about what large worlds “exist”.
I don’t know why you think a single example of an unverifiable proposition establishes anti realism: anti-realism is a global claim.
By realist epistemology, there’s a fact of the matter about where you are. For realists, truth is correspondence to the territory .. so long as there is a territory , there is a truth, even if you cant access it. For anti realists, truth and falsehood are the outputs of a verification process, so that if verifcation is not possible under the circumstances , there is no truth value to the claim. Realists take a Gods eye view anti realists an embedded view.
Note how none of this requires any discussion of meaning.
I didn’t disagree with the basic point, since it’s standard physics.
Again, I don’t know why you think a single example of something unverifiable establishes anti realism.
Again, it’s based on realism...on certain theories of the universe being true.
Why would that establish anti realism as a global claim?
So there are some unverifiable propositions?
Even if there are some.unverifiable proposoitions, it doesn’t follow that there is no fact of the matter. For realists , there is a fact of the matter. You are making an anti-realism assumption.
Does it? It doesn’t follow from a few special cases. What does it follow from?
Then how can you use it as an axiom to prove anti and realism?
If “I” “exist” in multiple universes, I don’t view there being a fact of the matter as to which one I’m “really” in. I think at least some realists agree, and it is to that subset of realists that my argument is directed. Their worldview is internally inconsistent.
Any statement about external reality is true in some worlds and false in others. Almost all such statements will be false if you’re located in a Boltzmann brain world, for example.
I’m not using the multiverse as an axiom. It’s the possibility of a multiverse that undermines meaning of realism.
To be a realist, you need one of the following claims:
There is only one universe containing entities subjectively indistinguishable from us, or there are so few universes that we can effectively ignore them (MWI, or any other Big world theory implies otherwise)
There is a fact of the matter as to where we are under self locating uncertainty
I think e.g EY rejects both of these but is still a realist. You seem to be hinting that you believe in 2?
Note that you can further build on my QM example. Scott Aaronson has suggested that you can affect the past via your decisions in the present. I haven’t read his arguments recently but I think this is related to the self locating uncertainty point—there could be no fact of the matter as to what the initial conditions were that led to your decision until after it’s made.
But there is a fact of the matter for realists, using their definitions of truth and fact. So your conclusion isn’t coming from metaphysics alone, it’s coming from epistemology as well.
Not quite. “There is some kind reality” is true in all realities.
There are a lot of shades and variations to realism and anti realism.
The possibility of empirically indistinguishable realities limits empiricism.
It doesn’t give you ontological anti realism, that there is no reality.
It doesn’t give you a firm conclusion that you can never have a true belief about reality, because if you assume a small world base level reality, it could be true.
(As you say: “There is only one universe containing entities subjectively indistinguishable from us, or there are so few universes that we can effectively ignore them (MWI, or any other Big world theory implies otherwise)”)
It doesn’t give you the conclusion that there is no way of placing credences on empirically indistinguishable models, because you can still use non empirical criteria such as simplicity.
It doesn’t tell you anything about semantics, which statements are meaningful.
The minimal concession realists need to make is that empirically indistinguishable distinguishable theories are harder to judge between. That’s more sceptical than the High Rationalist ideas, that you can solve everything with Bayes and Solomonoff. But it’s less sceptical than verificationism and instrumentalism.
Realists believe in a fact of the matter, but not necessarily a verifiable fact of the matter.
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.
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 Piccinini’s overview:
Piccinini (2010) “Computation in Physical Systems”
Chalmers (1996) “Does a rock implement every finite state automaton?”
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 can easily conceive of ‘the experience I’m having now, except the left half of my visual field is noise’.
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.
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.
What’s wrong with “Boltzmann brains will be common later but the world is yet young so none have ever existed yet”? Does this stance run into weird anthropics problems?
That only rephrases the question as “why do I exist in a young world (as opposed to after the heat death when there are many more observers with my specific memories and present perception).”
Is “somebody had to be early and it might as well be me” a valid answer?
Not on its own if almost nobody is early. If
To dissolve this problem, logical positivism works, like I wrote in my other comment here.
Thanks for the lottery analogy that helps
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 into vacuum.
Solar-system-based observers should have orderly experiences unlike vacuum brains, so if they outnumber the brains, the average observer should observe an orderly universe. They are also distinguishable from us, since they observe a starless sky. That means they’re still a problem for theories that predict them.
EDIT: The post Are you in a Boltzmann simulation? calculates probabilities for producing more mass vs complex and unlikely arrangements of mass such as brains and finds that production of more mass is vastly less likely. So we can ignore Boltzmann solar systems.
What happens to the Boltzmann-brain story if the smallest unit of thought takes too much processing time to fit into a quantum fluctuation?
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)
Assuming the validity of the doomsday argument, it could imply that most post-singularity universe-conquering timelines are dominated by unconscious entities.
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 infinite sets; I think this is fine.)
We don’t even need to consider the possibility of chaos-seeing BBs, we can just say “I appear to be a being that experiences order. Some BBs would experience order and some human brains would experience order: do we expect an infinite universe to contain more order-seeing BBs or more order-seeing humans?
2) For the “even if currently ordered, my experience ought to dissolve into chaos this very moment, yet it never does” objection, I think you just can’t make assumptions about moment-continuity of BBs for Last Thursdayist reasons: the experience of being “a BB that formed ten minutes ago with memories of a lifetime’s order and then existed long enough to experience a further ten minutes of order” is identical to the experience of being “a BB that formed this very instant and included the same lifetime memories plus memories of the additional ten minutes”.
This is true for every possible nature and duration of order-experiences and every possible set of memories. In fact, because Boltzmann Brains holding together at all for two moments together is so fantastically unlikely, “formed this instant with memories of having spent the past ten minutes wondering whether I’m a Boltzmann Brain and whether the world will dissolve into chaos any moment” is probably vastly more common than “formed ten minutes ago and then held together for ten minutes whilst wondering whether I’m a Boltzmann Brain and waiting to see whether the world dissolves into chaos”. Therefore, if we’re assuming Boltzmann Brains are possible, we can’t reason from an assumption that our memory of any experience—no matter how recent, even down to milliseconds ago—is real and not BB-generated.
Despite this, I think there is still a paradox:
i) We posit a set of laws of physics which would make us vastly more likely to be Boltzmann Brains than humans.
ii) These laws of physics are compatible with all our observations, are internally-consistent, make successful predictions, etc.
iii) Therefore, we’re very likely to be Boltzmann Brains
iv) However, if we’re BBs, none of our posited laws of physics, their predictions, our observations, etc. are valid; we can have no idea what the actual laws of physics are
v) If we have no idea what the actual laws of physics are, we no longer have any reason to think we’re more likely to be BBs than humans and ought to fall-back upon the more simple explanation that we observe ourselves to be humans because we’re humans.
vi) If we’re humans, our posited laws of physics, their predictions, our observations, etc. are valid and thus we should consider ourselves more likely to be BBs, and so on..
One resolution to this paradox might be to say “Well the universe just can’t be infinite then”; indeed I happen to suspect the universe probably (hopefully?) isn’t infinite. But I can’t help feeling that just this paradox alone would be a pretty weak reason to make such a claim.
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”.)
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.
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.
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.
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 still have 50% of the numbers in Set B left over, therefore Set A is 50% the size of Set B” and you can say “If Set C is ‘the set of all the numbers between 0.0 and 1.0’ there’s no way to match-up the numbers in Set C with the numbers in Set B, therefore Set C is a bigger ‘size class’ than Set B”.
(Confession: pretty sure Cantor didn’t call this sort of thing a “size class” but I have no idea what it is called, so I made up the “size class” term..)
Can we make use of this in cosmology? I think so: my “infinite density” argument above basically works like this. More pertinently, if we could assess the probability of a human brain existing (per unit spacetime, per unit negentropy) as (say) 10^-50 and the probability of a Boltzmann Brain existing as 10^-52, we would be able to say “There are around 100 times more human brains than Boltzmann brains”, even though both could be infinite if the spacetime and negentropy were infinite.
“Cardinality” is the math term you’re looking for.
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 orderly brains
The vast majority of the bits here come from describing the DNA. Even if you do not compress it, with evolutionary path or genozip, this is less than 1 Gb. Perhaps in a fixed-size universe there will be an infinite number of Boltzmann brains, but locating any of them takes at least 1 Pb.
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).
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.
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.
“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
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?
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.
time is a coordinate
you’re taking the word “coordinates” too literally
also I’m not engaging any further, you’re pissing me off
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.
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.
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.
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.
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).
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 already given some other name, which I’m not familiar with). For instance, a Boltzmann brain is not reasonable (and you can imagine other possibilities for non-reasonable beings). It seems to me like any argument whatsoever must start with the hidden premise: “you are reasonable”. If you are not reasonable, then anything you make of the argument is worthless.
Therefore, the argument “your experience doesn’t look like that of a Boltzmann brain, hence you are not one” really works as follows:
Premise: you are reasonable.
Thus, what you know about physics, brains and probability is trustworthy, as are your reasoning capabilities.
Given that knowledge, you would expect the experience of a Boltzmann brain to be much less orderly then yours.
Hence, you are not a Boltzmann brain.
But this just proves being resonable implies not being a Boltzmann brain, which is trivial.
The concept of a Boltzmann brain can still be useful in an argument regarding a certain physical theory predicting their existence, like:
Premise: you are reasonable.
The theory predicts the vast majority of consicous beings would be Boltzmann brain.
But you are not a Boltzmann brain (by the premise, not by argument).
Hence, the physical theory is likely wrong.
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.
One of the best arguments I’ve ever seen for a question that’s plagued me ever since permutation City
Bravo, this is amazing
The human brain has a prior that puts a non-neglible probability on the proposition that we aren’t Boltzmann brains, but rather that our experiences are orderly. As you noted, even half a second of evidence then completely destroys the probability of our experiences being random.
What we are left with is a high probability of being an observer in the early universe, before the big bang.
The concerning bit is that the Boltzmann brains to follow have the same prior, but that is just a “problem” with the human brain’s prior (if you wish to call it a problem), not with its Bayesian reasoning.
The post appears to be arguing that there is a paradox with the Bayesian reasoning side, is that correct?
I deny being a Boltzmann Brain, but I’m enough of a mathematical realist to disagree here. I find it very easy to imagine that all computable universes exist, but to weight the existence such that I am overly likely to be in a universe described by simple physical laws where billions of creatures like me exist in a normal-seeming universe than to be in a universe running Skyrim 5000 where Sheogorath is about to reveal that this is all a dream.
Of course, after I typed up the above paragraph, I kept reading and realized you largely answered this objection. Mods can delete this if they want.
As an aside: if you have strong enough priors that the real cosmology will be dominated by Boltzmann Brains, then observing that you indeed seem to be in a cosmology that will be BB dominated should increase your probability of being a real observer.
This exact point is raised and made in the original post, no?
The original post makes the (true) claim that any coherent observations are evidence against being a BB. I’m making the pedantic point that if you are almost certain that the real universe is BB dominated, then observing that that is indeed true suggests you might not be a BB.
(Conversely: a person convinced that the universe is BB dominated would take observations suggesting it wasn’t as increasing their likelihood of being a BB. (and also the likelihood that they’re wrong about cosmology, but I’m assuming that starts tiny))
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 homogeneous gas of particles bouncing around. That is the state of maximal entropy for an ideal gas but that does not transfer to other physical systems.
Bringing this back to the subject at hand, the reason that I and other physicists think the universe is handed towards a total thermalization is because of dark energy which is a physical and empirical effect that has been deduced from observations done by independent teams of astronomers. There is still an area where little is understood, and it is an ongoing area of study, but what would demonstrate that this is wrong are empirical results.
One point of clarification that might be useful, the “thermal equilibrium” that current cosmology suggests we are moving towards, bears no relation at all to the thermal equilibrium of an ideal gas where you have a well mixed box of particles bouncing around and occasionally fluctuating into complex objects. If dark energy dominates, then particles and structures will become increasingly causally isolated and all ordinary interactions will eventually die out (so it is the kind of thermal equilibrium that can never give rise to a conscious experience). The thermalized universe current theories of cosmology predict would not lead to the Boltzmann brain problem.
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?
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 strong, very falsifiable predictions! The theory would say that, with overwhelming probability, our experiences are explained by a small world fluctuating from equilibrium, and by illusory stuff outside that world, just enough to make us think the universe is bigger and explain what we’ve observed so far.
So, every time we see stars continue to shine, or take a walk to a new street in town, or otherwise fail to shatter the illusion of the outside world, that is a result not predicted in a universe without a past hypothesis! Given how incredibly thermodynamically unlikely these coincidences would be, are we not gaining several sigmas of certainty per second that the past hypothesis is true?
A: All that’s true, but it does not get you the result, Kevin, that you want to get because you have to distinguish between asking, given this universe, in other words a universe where there really just are random fluctuations and we don’t have the past hypothesis, what would you expect to see next? That is a question you can ask and that is what you’re talking about. But the theory choice question about doing an experiment to prove the past hypothesis is not that question. That’s just calculating the likelihood function in Bayes’ theorem. To choose between the theories, you have to multiply that likelihood function by the prior. So the question is not given this theory, what do you expect to see next? But given what you see, what is the most likely theory?
And given a universe that is randomly fluctuating, it is true that given what we see now, the next thing we should see is just some thermal equilibrium random fluctuations. But given that the next thing we see is not thermal equilibrium random fluctuations, if that universe were real, it would still be overwhelmingly likely that all that stuff had just fluctuated into existence, okay? So that’s why you need to assume the past hypothesis. You can’t actually be a good Bayesian and rule it out by data because under that set of assumptions that all configurations of stuff in the universe are equally likely, the prior probability that you’re seeing things randomly fluctuate into existence is so overwhelmingly large that you can’t beat it down just by likelihood functions and collecting new data.
I don’t like his answer. I think it probably comes out of repeated arguments of the form “Boltzman brains wouldn’t experience X” “Granted, but you’ll still see way more Boltzman brains+X than real coherent universes”, or of the form “Here’s this info about the early universe from data we collected” “That info assumes the past hypothesis, since you discount the overwhelming numbers of ways your data could be produced from thermodynamically incoherent universes”. He’s comfortable saying everyone’s ultimately assuming the past hypothesis somewhere, so we need to be able to say that’s fine.
There’s arguably only a semantic difference here: Is being willing to assume the past hypothesis is practically any different from accepting the evidence of the past hypothesis?
I think it’s worth calling evidence evidence. The past hypothesis is a theory, the null past hypothesis (allowing fluctuated universes) is another theory. You can imagine many different acceptable priors on the credence of those theories. The past hypothesis is possibly less natural and possibly should have much weaker weight due to that unnaturalness. It should not however, have a much weaker weight because the other theory thermodynamically assigns it that weaker weight. That’s just backwards: Assign prior likelihoods, then consider the evidence.
The evidence we see in favor of the past hypothesis is strong enough to overwhelm any reasonable naturalness weighting. It is not enough to overwhelm the other theory’s thermodynamic naturalness weighting, but that was never the question.
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 you are not a Boltzmann brain.[1]
(similar arguments apply to some forms of the simulation hypothesis, though obviously the case for disbelieving you are a Boltzmann brain is much stronger than disbelieving you are simulated)
Moreover, if theory A predicts that you exist and there are no Boltzmann brains
and theory B predicts that you exist and there are also a lot of Boltzmann brains
then both theories equally predict your own experience (and conditional on neither theory should you actually believe you’re a Boltzmann brain); to decide to discount theory B due to it additionally predicting that Boltzmann brains exist is in my view clearly erroneous.
It’s actually stronger than this, because a decision to disbelieve in being a Boltzmann brain isn’t going to have long term downstream effects on a Boltzmann brain’s actual beliefs. So, in longer than the instantaneous term, a precommitment to disbelieve in being a Boltzmann brain only affects your actual accuracy in the case you are NOT a Boltzmann brain.
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.
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.
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.
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?
This is tangential, but there are situation in which something like precommitments are epistemic concepts.
For example, without any precommitments, you do not get to be surprised if you generated a random number between 0 and 100 and it so happened to be 29. In this case it’s just some non-specific number.
However, if you’ve specifically precommited to 29 in particular beforehand, you can be lawfully surprised. This time you are observing a more specific event because of your precomitment.
Or consider Technicolor Sleeping Beauty problem:
A regular person without any epistemic precomitments upon observing any color of the walls doesn’t get any new information about the state of the coin.
P(Tails|Blue or Red) = P(Tails)
But with an epistemic precomitment to one particular color, a person can correctly guess that the coin is Tails in 2⁄3 of iterations of probability experiment—not mere awakenings! - when the walls of the room are this color. Doesn’t matter which color the walls are, the core part it’s the same color the person has precommited to:
P(Tails|Blue) = P(Tails|Red) = 2⁄3
Once again, the act of precommitment itself is what allows the person to observe a more specific event, and in this case, update their credence.
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 dissolving into chaos. But there is still the fact that when we look into our past memories, our minds, they look much, much more regular and complex that would you expect is needful for having consciousness (and ability to reason). Boltzmann brain generation seem to imply that it will not produce human brains first, it will produce first near perfectly optimal mind designs with consciousness written in the minimum possible amount of atoms.
This all is new argument for me. I expected universe to exactly be in maximal entropy indefinitely long. And this arguments refutes this possibility.
I am not sure what then. Obvious idea is that maybe even in maximum entropy it is more likely to have a Boltzmann seed which will causally produce a lower entropy bubble than have Boltzmann brain generated directly. But I doubt that possibility of such seeds isn’t exact opposite of “maximum entropy universe”.
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-quantifying are BBs and are working from false knowledge and false rules of logic! They might have come into existence with every possible conclusion already formed instead of reasoning from evidence! Eddington’s logic, that more complex fluctuations are exponentially less likely (thus giving us a prior distribution on which BBs exist), is still logic—reasoning based on observations—and if you allow yourself to use that logic, any logic, you have already decided you, personally, are not a BB. In which case, reasoning about the probability that some “yous” really are BBs—that you are a BB with some probability—makes no sense.
If some BB is is physically the same as your non-BB brain, why can’t you talk about the probability you are one? Because a BB used invalid reasoning to arrive at that conclusion, and so it cannot expect to arrive at any valid conclusions if it keeps on thinking.
Even longer:
A BB cannot perform valid reasoning because it does not contain validly-acquired knowledge. It spontaneously came into being containing some knowledge, and a BB containing different memories, priors or laws of logic might have been just as likely. And since it takes time to think through an argument, a BB is even more likely to come into being already convinced of the conclusion—any possible conclusion!
The above paragraph is still subtly wrong. Even the concept of valid reasoning would have come into existence as part of the BB. The claim that different BBs are equally likely was either invalidly-reasoned by a BB, or that simpler ones are likelier, probably came spontaneously into existence as part of the BB. BBs cannot reason about greater Reality any more than they can reason about their own worlds.
You cannot assume you are a BB (with some probability), any more than you can assume a contradiction because it makes all further reasoning impossible. It makes predicting the next second of sensory data impossible. So we might as well not do it, and behave as if that probability is zero.
Boltzmann’s original idea, that the whole universe might be an enormous spontaneous fluctuation from the Big Bang onwards (though Boltzmann didn’t know about the Big Bang), is less problematic. It’s still wrong, for the reasons Eliezer gave, but at least it wouldn’t require us to conclude we cannot reason about anything!
So what should we do if cosmology turns out to say that the universe will end in thermodynamic soup, long-lived enough to generate BBs? (It may or may not actually predict that, but we have to be able to reason in the event that it does.) Some people deny anthropics in various ways. Some think anthropics would thereby falsify such a cosmology. I just set the probability of me, personally, being a BB to zero. A (logical) probability which cannot only be reasoned forward from but which invalidates all past reasoning and knowledge is, at the very least, not a useful part of any possible decision-algorithm. So we might as well behave as if it doesn’t exist.
(Could it exist for others, even if not for ourselves? I think it logically could, but Boltzmann’s classical thermodynamics suggests we are incredibly unlikely to ever observe / interact with another fluctuation with a distinct origin from your own ordered part of the world.)
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?
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.
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.
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.
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.
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.
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.
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.
If I was a Boltzmann brain then I could, like a video game examine some element of the world and it’d turn up random right? Whereas in actuality it’s super ordered (in most cases) so I have strong reasons to believe I’m not a Bb, I think if careful measurement of fresh, unexplored places started coming back statistically random like the fluctuation idea describes, I’d change my mind. It doesn’t, so I don’t believe it. it’s a fun thought experiment though.
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.