A lot of those worlds will be ones in which we are “freak observers”: coincidentally arising computations that resemble our coherent experience, with our perception of the external world of humans and Earth, but that fall apart immediately. Boltzmann brains are one type of freak observer - but there are others, like e.g. a storm in the night sky coincidentally implementing the right computation for just a moment.
This isn't necessarily true. If "experience" is inherently extended in time, if there's no such thing as an instantaneous experience — if the briefest event that looks like a coherent experience is too long in time to fit in "just a moment" — then "freak observers" such as Boltzmann brains would not exist, which means I'm not one.
It doesn't depend on your viewpoint on that particular question - there are also freak observers that, by sheer coincidence, are coherent for more than one moment.
[Epistemic status: weird philosophy]
Here’s a simple argument:
How do we know what exists?
Well, we don’t - not for certain. Many different possible worlds are consistent with our observations.
A lot of those worlds will be ones in which we are “freak observers”: coincidentally arising computations that resemble our coherent experience, with our perception of the external world of humans and Earth, but that fall apart immediately. Boltzmann brains are one type of freak observer - but there are others, like e.g. a storm in the night sky coincidentally implementing the right computation for just a moment.
No matter what our larger epistemological and metaphysical framework is (e.g. how much we apply Occam’s razor, like the simplicity prior in UDASSA), it seems like our probability of being a freak observer should be nonzero.[1][2]We can’t definitively rule it out.
But freak observers can’t just happen in our universe - they can happen in many possible universes. The condition for it is probably that the universe has a lot of “stuff” / moving components in it so that we, from our perspective, can’t rule out there being some subcomputation with sufficient structure[3] to manifest our experience. So this rules out tiny pocket universes[4] or large but extremely simple ones, but leaves almost all others possible.
So for each of these universes, our probability of it being the “true reality”, and us actually being a freak observer in it is nonzero. And this can never be otherwise - it will always seem at least possible to us that we just arose spontaneously in one of these freak-observer-compatible universes, and that the world we think is real actually isn’t.
So insofar as we think we can have some effect on these universes even as freak observers (e.g. if we use evidential and/or logical counterfactuals), we will take them into account in our decisionmaking.
So, in practice, we will always act as if these universes are real (to some nonzero extent).
Therefore, we de facto believe that they exist.
Tegmark 3.5
This argument works on some pretty basic assumptions:
In fact, it seems like you should care a nonzero amount about almost every freak-observer-compatible universe - since, unless it’s extremely small, there will be some chance of other freak observers than you in there, including versions of yourself and all your loved ones.
All of this is also what makes this argument still apply if you prefer deriving probabilities from preferences in the first place - a “caring measure” approach, the main alternative to a simplicity prior (like Wei Dai here, the ADT paper, the insight here that you can interchange probability and utility, discussion here, and David Matolcsi’s OSAC).
This is then also a slightly “softer”, more “permissive” notion of existence - e.g. it includes universes that would be logically incoherent or impossible from an omniscient perspective, but which we can’t rule out from our limited, completely a priori perspective.[5]
Generally, I think a useful analogy for this kind of “extreme a priori” philosophy (à la Kant or Descartes) are the extreme hot conditions right after the Big Bang, when the four fundamental forces may still have been stuck together as one, and discrete protons and neutrons had not yet constituted themselves out of the quark-gluon plasma soup. Similarly, in the fitful, grasping ignorance of a priori philosophy, the epistemic, ontic, and axiological blur into each other. (see, for example, Wei Dai’s very clarifying What Are Probabilities, Anyway?)[6]
So this set[7] of freak-observer-compatible universes seems important, and I want to coin a term for it. (Note that it’s not the universes which actually have freak observers in them, but those which, from our limited perspective, could.)
Max Tegmark famously talked about levels of multiverses that increase in size, with level III being the quantum multiverse from the many-worlds interpretation of quantum mechanics, and level IV being the proposal that all mathematical structures (or in a later version, all computable structures) exist.
The set of freak-observer-compatible structures/universes sits between those, so let’s call it Tegmark 3.5.
Tegmark tried to specify a measure over Tegmark IV. I won’t be doing that. Instead, I'll follow Tegmark's example in level II (where the cosmological measure problem was already an established difficulty), and leave the measure question open (since it’s an already established problem too). Tegmark 3.5 is just the minimal claim of nonzero existence of all freak-observer-compatible universes.
So my claim in this post is that basically everybody’s metaphysics should at least go as far as Tegmark 3.5, because of the simple argument above.
That’s the unavoidable baseline soup that we wade in - everything is at least a tiny tiny bit real, due to fundamental philosophical constraints. We get our full measure from elsewhere, just like normal, from purely epistemic or axiological tools like Bayesian updating, simplicity priors or caring measures (or some future conceptual advances). Those can impose some discipline and make us concentrate our probability mass and focus, but can never quite return us to a naive vision of a tight, unitary reality.
Addendum: Metaphysics-first decision theory
Why does this matter?
This is a very simple argument that will be obvious to many people familiar with the Tegmark / Schmidhuber / everything-list / UDASSA lineage. But I think its power often gets minimized in that context because the possibility of us being a freak observer is a problem there. (When it comes to epistemology and the problem of induction, it makes it much trickier to rigorously justify our perception of what the world is like).
But in the decision-theoretic context, it’s actually a huge asset! As I wrote in my last post, LessWrong-style decision theory requires metaphysics. But luckily, as I’ve argued here, some wild metaphysics actually just seem true! This makes things much easier (at least for a certain kind of person, haha).
Let’s take a blackmail scenario:
Now we are perfectly able to justify the Functional Decision Theory (FDT) / Updateless Decision Theory (UDT) recommendation of not paying:
(this will get a little bit complicated, buckle up)
Tegmark 3.5 includes the universes in which this happens basically how I am perceiving it - but it also includes all the others, in which I am a freak observer whose perceptions are wrong. For example, it also includes universes extremely similar to the one that I am perceiving - except that my current experience of being blackmailed is actually a freak observer somewhere else in it. So this pushes me, to some extent, towards not paying - since in these similar universes, even as a freak observer, I can make it with my choice that Omega predicts that I wouldn’t pay up, and doesn’t blackmail me in the first place. Then the versions of myself on those universes’ Earths, with real futures, will save 100$.
Note that I don’t have any weight on me being those non-blackmail versions of myself - since the observer-moment that I am (of being blackmailed) never happens on those Earths. So this does require caring about other versions of myself (not being “indexically selfish”). “My” (strictly speaking) experience will instead immediately disintegrate in those non-blackmail-universes, and continue in the blackmail-universes where my embarrassing secret gets revealed when I refuse to pay. (And to be clear, even then, I don’t stop believing in the existence of the non-blackmail-universes. It’s still in Tegmark 3.5, I’m now potentially a different freak observer there.)
How big this push towards not paying actually is completely depends on the measure (which is why FDT proponents often don’t like to frame things this way - if you assign very low measure to the non-blackmail-universes you will recover “normal decision theory” and pay). But we can at least see that FDT/UDT’s reasoning definitely does go through in principle. There’s nothing crazy about the metaphysics required - it just works.
In fact, if I want to recover FDT/UDT's recommendation, I only need to postulate that the prior measure of the non-blackmail-universes is not too much lower than the prior measure of the blackmail-universes (which is plausible on many intuitive implementations of both a simplicity prior and a caring measure). Then I don’t pay[8], because that would make my epistemic tools lower the measure of the blackmail-universes drastically (since Omega almost certainly would have predicted that and wouldn’t blackmail me, i.e. the blackmail-universes get much less likely). So the non-blackmail-universes then have much more measure than the blackmail-universes, which increases my utility by a lot.
This might seem like a really strange way to reach the conclusion that you shouldn’t pay, but I think it’s the minimal one that actually fully works![9][10][11]Many people try to justify it with nontrivial metaphysical reasoning about how everything existing is the simplest hypothesis or about how there’s no coherent distinction between “existing” and “possible but not existing”, but that’s not actually strictly necessary. We can deduce a lot of what we need a priori, from the possibility of being a freak observer.[12]
As I argued in my last post, it can get confusing when people center decision-theoretic intuitions in these issues, and this is probably partly a historical thing. (e.g. “updatelessness” is a somewhat confusing term for what is often de facto a metaphysical stance, unless you know the historical context).
So I want to coin a term for this alternative way of approaching things, of locating the crux in the measure: metaphysics-first decision theory. I think more people should frame the topic in this way.
Thanks to David Matolcsi and Quinurum for comments on a draft.
It may even be quite high.
This is eliding the possibility of a continuous space of universes, where a universe could be in the support but have zero measure. I don’t think I know of a live proposal like that though, since the set of programs is countable - e.g. UDASSA assigns nonzero measure to everything computable.
In the Mathematical Universe Hypothesis, there’s continuums of mathematical objects (e.g. versions of our universe with real numbers as fundamental constants), but Tegmark abandoned it (for the Computable Universe Hypothesis) precisely because of this problem, that you can’t define a measure over it.
And even if there is a continuous space, your perception is probably only able to restrict yourself as being in some subset of it (e.g. the error bars in our estimates of the fundamental constants of the standard model), which can have nonzero measure.
Including deep counterfactual structure like in Chalmers’ Counterfactual State Automaton approach - I’m not making a triviality / relabelling / dust theory / “a rock implements every computation” argument here.
(except the ones with just us in it)
This is also what solves the problem of logical updatelessness - that you need to act like impossible realities are real to get the desired answer on e.g. logical counterfactual mugging. I say more about how I make this work in footnote 10.
There’s also an active inference-style intuition that the epistemic and the axiological are deeply wedded in terms of how intelligence/agency works, and maybe even introspectively the same sensation (i.e. we might be able to use the intuition even in a priori reasoning).
I’m not trying to say that this is the rigorous mathetical notion of a set - I just don’t know of an easier word to use.
Ignoring effects in other universes, which are smaller since this exact computation doesn’t get predicted anywhere else. (Although not necessarily smaller in aggregate - this is where it gets complicated/weird and maybe everything is dominated by acausal effects. But we don’t have to think about this for these illustrative purposes).
One thing to note here is that it seems like universes which allow normal observers probably almost always have enough “stuff” to also allow freak observers (with some nonzero probability from our perspective). This is important because this reasoning doesn’t work in universes that are somehow known to definitely not have freak observers.
A quick aside on how this deals with logical updatelessness (or at least, more overt instances of it): In logical counterfactual mugging (counterfactual mugging where the “coin” is the parity of the 1000th digit of Pi), we would reason like “I may be a freak observer who has a wrong belief about the result of this computation, since I can’t hold it in my head all at the same time - so the universe where the parity is opposite and Omega would give the other version of me money if I paid up here still seems possible and is in Tegmark 3.5”.
I think this kind of radical skepticism about logical beliefs is appropriate when we are already talking about possibly being freak observers. But you’re still free to treat these cases differently (especially if the computation is small, or you’re a much smarter agent who can hold a lot in their head at once), and assign less measure to the alternate universes in these cases than in the “empirically updateless” cases. This is another way in which this framing is very flexible, and can accommodate different intuitions without destroying our entire framework for thinking about reality each time (because it’s based on very few assumptions).
(Logical updatelessness is not a niche concern because e.g. normal blackmail in a deterministic universe where you know the initial conditions is also technically a logical updatelessness issue. Generally, if you buy that everything is a computation, any empirical update has a logical update alongside it.)
Finally, I want to address a general category of objection that I think is quite powerful: Sean Carroll’s “cognitive instability”. Originally proposed in the context of Boltzmann brains, it says that reasoning like “Our theories of physics imply an astronomical number of Boltzmann brains that have my experience - therefore, I probably am one” doesn’t make sense, because the conclusion contradicts the means you used to reach it (belief in a reality of a human community of physicists that have learned how the universe works). There’s a kind of looping behavior: “oh, I’m probably a Boltzmann brain. So my perceptions are wrong. Oh, but then I have no reason to think I’m a Boltzmann brain. So I can believe my perceptions again. Oh, but then I’m a Boltzmann brain.” And so on.
I think this correctly identifies an important concern, but Carroll uses it as a reason to dismiss cosmological models where Boltzmann brains dominate, when he should’ve instead taken it as a sign that his fundamental metaphysics/anthropics/epistemology need work, because this looping should never be able to happen in the first place (even if you entertain crazy hypotheses). It shouldn’t be possible that you update on evidence to believe something inconsistent with the evidence.
The issue is that you should’ve never had certainty that your perception of the universe is correct in the first place. You should have figured out how to deal with the fundamental soup of uncertainty long ago. Boltzmann brains just forced you to finally confront what you’ve been sweeping under the rug.
(Cognitive instability also prevents you from using Boltzmann brains and generally freak observers in Tegmark levels one through three (which are: infinitely large unobservable universe, eternal inflation bubbles, many-worlds interpretation of quantum mechanics) to justify logical updatelessness in the same way I did in footnote 10. And we would also probably want decision theory to work in a fully deterministic universe where we know the initial conditions, where all updatelessness would be logical updatelessness (about what the computation of the universe results in). So we do need to go as far as I do in this post to fully justify LessWrong-style decision theory, in my opinion).
Anyway, the reason I bring this up is that you could advance a similar charge against…
I do think the cognitive instability concern (or let’s maybe call it something more accurate like “the self-contradiction check on metaphysical overconfidence”) matters for evaluating measures and metaphysical reasoning in general. For example, it might apply less to arguments that route through being in a simulation than ones that route through being a freak observer, and therefore license us to be more confident in them. It’s interesting and maybe underrated.
And note that Tegmark 3.5 is very large, and we get basically everything out of Tegmark 4 that we might need. I considered calling it Tegmark 3.9 but thought it was not as memetic.