Thursday, October 01, 2015

Against the "Still Here" Reply to the Boltzmann Brains Problem

I find the Boltzmann Brain skeptical scenario interesting. I've discussed it in past posts, as well as in this paper, which I'll be presenting in Chapel Hill on Saturday.

A Boltzmann Brain, or "freak observer" is a hypothetical self-aware entity that arises from a low-likelihood fluctuation in a disorganized system. Suddenly, from a chaos of gasses, say, 10^27 atoms just happen to converge in exactly the right way to form a human brain thinking to itself, "I wonder if I'm a Boltzmann Brain". Extremely unlikely. But, on many physical theories, not entirely impossible. Given infinite time, perhaps inevitable! Some cosmological theories seem to imply that Boltzmann Brains vastly outnumber ordinary observers.

This invites the question, might I be a Boltzmann brain?

The idea started getting attention in the physics community in the late 2000s. One early response, which seems to me superficially appealing but not to withstand scrutiny, is what I'll call the Still Here response. Here's how J. Richard Gott III put it in 2008:

How do I know that I am an ordinary observer, rather than just a BB [Boltzmann Brain] with the same experiences up to now? Here is how: I will wait 10 seconds and see if I am still here. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ... Yes I am still here. If I were a random BB with all the perceptions I had had up to the point where I said "I will wait 10 seconds and see if I am still here," which the Copernican Principle would require -- as I should not be special among those BB's -- then I would not be answering that next question or lasting those 10 extra seconds.

There's also a version of the Still Here response in Max Tegmark's influential 2014 book:

Before you get too worried about the ontological status of your body, here's a simple test you can do to determine whether you're a Boltzmann brain. Pause. Introspect. Examine your memories. In the Boltzmann-brain scenario, it's indeed more likely that any particular memories that you have are false rather than real. However, for every set of false memories that could pass as having been real, very similar sets of memories with a few random crazy bits tossed in (say, you remembering Beethoven's Fifth Symphony sounding like pure static) are vastly more likely, because there are vastly more disembodied brains with such memories. This is because there are vastly more ways of getting things almost right than of getting them exactly right. Which means that if you really are a Boltzmann brain who at first thinks you're not, then when you start jogging your memory, you should discover more and more utter absurdities. And after that you'll feel your reality dissolving, as your constituent particles drift back into the cold and almost empty space from which they came.

In other words, if you're still reading this, you're not a Boltzmann brain (p. 307-308)

I see two problems with the Still Here response.

First, we can reset the clock. While after ten seconds I could ask the question "am I a Boltzmann Brain who has already lasted ten seconds?", that question is not the sharpest form of the skeptical worry. A sharper question would be this, "Am I a Boltzmann Brain who came into existence just now with a false memory of having counted out ten seconds?" In other words, there seems to be nothing that prevents the Boltzmann Brain skeptic from restarting the clock at will. Similarly, a Boltzmann Brain might come into existence thinking that it had just finished introspecting its memories Tegmark-style, having found them coherent. That's the possibility that the Boltzmann Brain skeptic will be worried about, after having completed (or seeming to have completed) Tegmark's test. The Still Here response begs the question, or argues in a circle, by assuming that we can have veridical memories of implementing such tests over the course of tens of seconds; but it is exactly the veridicality of such memories, even over short durations, that the Boltzmann Brain hypothesis calls into doubt.

Second, this response ignores the base rate of Boltzmann Brains. It's widely assumed that if there are Boltzmann Brains, they might be vastly more numerous than normally embodied observers. For example, a universe might produce a finite number of normal observers and then settle into an infinitely enduring high entropy state that gives rise, at extremely long intervals, to an infinite number of Boltzmann Brains. Since infinitude is hard to deal with, let's hypothesize a cosmos with a googolplex (10^(10^100)) of Boltzmann Brains for every normal observer. Given some sort of indifference principle, the Boltzmann Brain argument goes, I should initially assign a 1-in-a-googolplex chance to being a normal observer instead of a Boltzmann Brain. Not good. But now, what are the odds that a Boltzmann Brain can hold it together for ten seconds without lapsing into incoherence? Tiny! Let's assume one in a googol (10^100). The exact number doesn't matter. Setting aside worries about resetting the clock, let's assume that I now find that I have indeed endured coherently for ten seconds. What should be my new odds that I am a Boltzmann brain? Much lower than 1-in-a-googolplex. Yay! Only about a googolth of a googolplex! Let's see, how much is that? Instead of a ten followed by a googol of zeroes, it's only ten followed by a googol-minus-100 zeros. So... still virtual certainty that I am a Boltzmann Brain.

So how should we respond to the Boltzmann Brain hypothesis, then? Sean Carroll has a two-pronged answer that I think makes a lot of sense.

First, one can consider whether physical theories can be independently justified which imply a low ratio of Boltzmann Brains to normal observers. Boddy, Carroll, and Pollack 2015 offer such a theory. If it turns out that the best physical theories imply that there are zero or very few Boltzmann Brains, then we lose some of our grounds for worry.

Second, one can point to the cognitive instability of the Boltzmann Brain hypothesis (Carroll 2010, p. 223, drawing on earlier work by David Albert). Here's how I'd put it: To the extent I think it likely that I am a Boltzmann Brain, I think it likely that evidence I have in favor of that hypothesis is delusional -- which should undercut my credence in that evidence and thus my credence in the hypothesis itself. If I think it 99% likely that I'm a Boltzmann Brain, for example, then I should think it 99% likely that my evidence in favor of the Boltzmann Brain hypothesis is in fact bogus evidence -- false memories, not reflecting real evidence from the world outside -- and that should in turn reduce my credence in the Boltzmann Brain hypothesis.

An interesting feature of Carroll's responses, which distinguishes them from the Still Here response, is this: Carroll's responses appear to be compatible with still assigning a small but non-trivial subjective probability to being a Boltzmann Brain. Maybe the best cosmological theory turns out not to allow for (many) Boltzmann Brains. But we shouldn't have 100% confidence in any such theory -- certainly not at this point in the history of cosmological science -- and if there are still some contender cosmologies that allow for many Boltzmann Brains, we (you? I?) might want to assign a small probability to being a Boltzmann Brain, in view the acknowledged possibility that the cosmos might, though unlikely, have a non-trivial ratio of Boltzmann Brains to normal observers. And although a greater than 50% credence in the Boltzmann Brain hypothesis seems cognitively unstable in Carroll's sense, it's not clear that, say, an approximately 0.1% credence in the Boltzmann Brain hypothesis would be similarly unstable, since in that case one still might have quite a high degree of confidence in the physical theories that lead one to speculate about the small-but-not-minuscule possibility of being a Boltzmann Brain.

[image source]


Dave Baker said...

Good post. It's surprising that so many people are tempted by something like Tegmark's response, which just amounts to ignoring the real problem.

I'm concerned that the first Carroll et al response (the de Sitter vacuum one) requires assuming that the cosmological constant won't take on different values in different branches of the quantum state (adopting the Everett approach for the sake of argument).

If the CC does happen to take on different values in different branches--which I think is supposed to be likely according to string cosmology ideas floating around these days--then you will have *some* parts of the state that don't behave like de Sitter space and so are hospitable to Boltzmann brains. Then, presumably, the infinitely many BBs in these branches will dwarf the number of "regular brains" in the de Sitter branches and the problem will return in a slightly different form.

In other words, this solution only works if there is a sufficiently high cosmological constant *everywhere in the multiverse,* but my sense is that current theory suggests that's unlikely. Although the relevant theory is very speculative, and maybe this sort of problem gives us a strong reason to reject it.

Eric Schwitzgebel said...

Right -- I meant to support Carroll's general approach of finding independently justified physical theory that reduces the likelihood of BBs. I don't necessarily support that particular instantiation of the theory, partly because evaluating Boddy et al 2015 goes beyond my expertise. In general, though, I think one of the attractions of multiverse theory is that it helps solve the fine-tuning problem, which it only does if possibly-fine-tuned features (like the cosmological constant) are allowed to vary between universes.

Dave Baker said...

Exactly. Then if it turns out that the BB problem is a worse problem than fine-tuning, we may need to decide that the best theory involves accepting a truly fine-tuned cosmological constant, since an anthropic explanation of the CC's value will necessarily lead to the BB problem.

dshiller said...

Consider the following argument:

1. If I were a conscious observer in a universe infested with BBs, I would (almost certainly) currently be experiencing static rather than coherent thoughts.

2. I am not currently experiencing static rather than coherent thoughts.

3. Therefore, I am (almost certainly) not in a universe infested with BBs.

This seems to be in the spirit of the "still here" reply. It doesn't give us a reason to think we're not BBs if BBs do actually exist. But it gives us some justification in believing that we're not BBs because none exist. What do you think?

dshiller said...

Consider the following argument:

1. If I were a conscious observer in a universe infested with BBs, I would (almost certainly) currently be experiencing static rather than coherent thoughts.

2. I am not currently experiencing static rather than coherent thoughts.

3. Therefore, I am (almost certainly) not in a universe infested with BBs.

This seems to be in the spirit of the "still here" reply. It doesn't give us a reason to think we're not BBs if BBs do actually exist. But it gives us some justification in believing that we're not BBs because none exist. What do you think?

Arnold said...

Is freak observer and ordinary observer description of Observing or of Observation..
Is the logic to simple..States of Being exist without time because of Observation...
...or observers of all kinds have a place, not for how long but for how come...
Verticallity is limited to this Dimension when without Observation as a Constant...

chinaphil said...

This is catnip to me, being all about the numbers. I think one of the problems of both the Boltzmann brain scenario and Nick Bostrom's argument that we're probably sims is that they ignore the number of additional contingencies in between the existence of an intelligent life form which is in fact a sim/BB, and the chances of *me* being a sim/BB (and apparently surrounded by others who are?). I think that gap adds considerably to the probability issues that a sim/BB argument faces

Eric Schwitzgebel said...

dshiller: I think that version is still subject to the base rate objection, though -- no? Compare: 1000 people are flown to New York to be members of an audience from which there is already only one pre-determined winner. I'm in the audience. I think: If I were not the winner, I'd almost certainly not be here (I'd be among the millions of non-winners at home), therefore I am very likely the winner.

If there are a million BBs with coherent thoughts for every one normal observer, I still have to basically win the lottery to be the non-BB, if we accept the basic setup of the BB argument. It doesn't matter how many other non-coherent BB's there also are.

dshiller said...

I do agree that I shouldn't count myself the winner in that case. That case seems analogous to the case where I know there are lots of BBs. I think the argument I proposed only works as an argument against the hypothesis that we live in a world with lots of BBs. It can't show that I should think that I am not a BB even if there are many. Nevertheless, if it does work, it has the potential to be vastly more powerful evidence against the existence of BBs than anything we could get from physics experiments in favor of the existence of BBs.

Try out this analogy. Suppose that there are two theological possibilities:

Good God Small World – Everyone has a happy life and there are very few people.

Bad God Big World – There is a vast number of people who have a miserable life and a tiny fraction of that who have happy lives, but the total number of happy people outnumbers the total number in Good God Small World.

And suppose that you know one and only one thing: you have a happy life. Isn't that a powerful reason to favor Good God Small World?

Callan S. said...

The Boltzmann thing seems to include inexplicably dissapearing shortly after as well? Not sure why that's added in?

Anyway, will we get onto us being a Boltzmann phenomina, if only many times derivative of the original 'spontationus' manifestation?

I mean life, at some simple level, fell together at some point. Many derivitives latter, here we are.

So in a way we're (including the animals, insects, microbes...) all Boltzmann beings, aren't we?

David Duffy said...

introduces the "still here" argument, along with the idea that new solar systems and new universes are also as "likely" as Boltzmann Brains - each giving rise to comparable numbers of "ordinary" observers. His discussion of observing BBs (skepticism about other minds - it is more likely to observe the appearance of a BB than an actual BB) is just as entertaining.

Eric Schwitzgebel said...

Sorry for the slow replies, folks! I was away at a conference in North Carolina -- giving a paper with a Boltzmann Brain component in it, as a matter of fact.

dshiller: Very interesting case! It reminds me of the Doomsday Argument also. Probably you know that one? If you take as an assumption, "I'm probably a fairly typical observer", you can sometimes get some weird results (as in the Doomsday case). A lot hinges on what the reference class of "typical observers" is, as what qualifies as atypical. (On the latter, one is not shocked that one's license plate is 3XNY352, even though no one else has that plate, while one might be shocked to randomly receive plate 0OOO000, though the odds are the same.) I could imagine the proper application to the Small World case depending a lot on the details of the case and how exactly one applies the principle.

Callan: But we come from a very low entropy Bang, not a (random) fluctuation from a high entropy state -- that's the crucial difference!

David: Yes, it does seem right that one is more likely to observe the appearance of a BB than an actual BB. The rate at which new universes come into existence vs. new BBs is crucial to the final ratio of BBs vs. normals, if we are allowed to consider beings in all universes and not just our own (as I guess I'd be inclined to think, for this type of argument). If things are infinite, then evaluating that ratio turns out to be pretty tricky!

Callan S. said...

Not sure if I replied already, but I don't understand, Eric? It's random in either case - whats different between one random and another?