If no friendly apocalypse arrives, the Universe might exist indefinitely which, Boddy and Carroll believe, is a bad thing because the Boltzmann Brains will be formed many times in this infinite future and such a cosmology automatically predicts that we should be Boltzmann brains, too.
I have explained several reasons why this is plainly nuts. Later, I saw a reaction by Jacques Distler titled "Zombies" where Distler says that it is plainly nuts, too.
In the discussion on that blog, Sean Carroll adds an irritated reaction without any substance. He just claims that his claims had been misinterpreted except that he doesn't offer a tiny glimpse of an inaccuracy in Jacques' interpretation of his and Boddy's paper. People like Carroll love to say the lie that their views have been misinterpreted which is almost the never case.
The main exchange in that discussion occurs between Mark Srednicki of Santa Barbara and Jacques Distler of Austin. In the blog post and the discussion, Jacques makes the same points as I did, using slightly different words:
- We have clear evidence that we are not Boltzmann brains because our observations are not chaotic and we may verify additional predictions that our observations are not chaotic, which rules out the Boltzmann Brain hypothesis at any confidence level we want. The confidence level grows very quickly; the \(p\)-value pretty much exponentially drops in time expressed in microseconds.
- This observation means that if we also assume a cosmology that does imply many Boltzmann brains, we may quickly determine that we are not "typical" among the conglomerates of matter locally identical to a brain. We may prove that the "typicality" assumption is just wrong.
- Assuming a cosmological model without many Boltzmann brains, we can't deduce anything new.
- Our observations implying that we are not Boltzmann brains can't allow us to favor Boltzmann-brain-free models and disfavor the Boltzmann-brain-containing models because both classes of models are compatible with our existence (assuming that they don't have some other, more serious bugs aside from the Boltzmann brains).
- It would be crazy if we could learn about our origins from the assumptions about the number of brains or people in the future because such an implication would be acausal. In the real world, the number of people or brains in the future is a consequence of the laws of physics combined with the initial conditions. You can't revert this causal relationship (even though Sean Carroll believes that there is a symmetry between the causes and their logical implications – he misunderstands the logical arrow of implications). The future is unknown, it will be whatever it will be (probabilistically calculable from the laws of physics and the initial conditions) and it is not teleologically constrained. If the mankind dies out soon, we (or our timing) may be close to generic; if it doesn't, we are among the early folks; the outcome is yet to be seen and it's nonsensical to suggest that we know the answer in advance. The only valid way to learn about the future (aside from waiting) is to predict i.e. to learn something about the present or past (the initial conditions) and about the laws of physics that will (probabilistically) determine the future. There is no valid statistical argument that would imply – while avoiding arguments based on the laws of physics entirely – that you can't have trillions of descendants in the future – just like there was no valid argument that a tiny seed of space at the beginning of the cosmic inflation couldn't expand to a huge space in the future (Sean Carroll arguably misunderstands this fact about inflation, too).
I thought that they were simply saying the same thing that I was saying for years, namely that the "typicality assumption" is unjustified by anything; we may scientifically prove that most of its particular realizations are false; and we shouldn't pretend that demonstrably false assumptions belong to the scientific axiomatic system.
Hartle and Srednicki said that theories make assumptions about "who we are" within a cosmological model and Carroll and similar folks were assuming that we have to be "generic" – they assume that some distribution about "who we are" among the candidates who could "be us", something they called the xerographic distribution, has to be uniform. However, we may also assume other xerographic distributions and the models that happen to predict Boltzmann brains are rehabilitated.
It seemed to me that they were saying the same thing. However, there was still an important part of their paper that was missing: a section explaining why the likes of Sean Carroll are idiots. Papers prepared for journals may be expected to avoid the word "idiots" although it's the most accurate description of what's going on in this case. However, I couldn't find any diplomatic equivalents of these assertions, either. So I wasn't sure whether this absence was due to some censorship and excessive politeness; or because of Hartle's and Srednicki's genuine confusion manifesting itself as an uncertainty about things that are completely certain.
At least in the case of Mark Srednicki, the answer turned out to be that the answer is "some genuine confusion". Srednicki really does propose that what I call the "basics of rational reasoning" represent just one possible scientific attitude among many. So Srednicki's views may be "more moderate" than Carroll's views but they're still crazy.
The first comment by Mark Srednicki more or less agreed with Jacques and mentioned the 2009 Hartle-Srednicki paper. Jacques Distler replied by his own comment that offered a clear Bayesian derivation of the fact that we're simply not Boltzmann brains. Srednicki added the first reply where the tension became manifest:
Jacques, I believe Sean would agree with everything you say. But you haven’t addressed the crucial next step in his argument: if we agree that we’re not Boltzmann brains (on the basis of the calculation that you just presented), can we tolerate a cosmology that nevertheless predicts the existence of a lot of Boltzmann brains (with precisely our data/memories as of right now)?Jacques replies and locates the sentence "we would have been equally likely" as what he considers to be the mistake in the would-be argument above (and so do I). The words "equally likely" mean the same thing as "having the same probability" so to use such a sentence, we need a definition of the probability and an argument that some probabilities are equal to each other.
Sean says no, those BBs can’t exist, because if they did, we would have been equally likely to have been any one of them, and then it’s overwhelmingly likely that we would no longer exist. But we do still exist. So we’re not BBs, and so therefore we must insist on a cosmology that prevents the existence of a lot of BBs anywhere in spacetime.
If we adopt the frequentist understanding of the probability, the probability that we are a Boltzmann brain would be defined as the percentage \(N_b/N\) where \(N\) is the total number of repetitions of the experiment (the whole life of the Universe) and \(N_b\) is the number of those repetitions in which we were Boltzmann brains. However, if we start a Universe from scratch, we can't identify who is "we" from a previous repetition of the Universe. The new Universe contains new objects and events. So unless we believe in reincarnation that maps the souls from the previous life of the Universe onto souls in a new life of the Universe ;-), the phrase "probability that we are a Boltzmann brain" is completely meaningless for a frequentist.
For a person who prefers the Bayesian understanding of the probability, the question about the "probability that we are Boltzmann brains" is potentially meaningful because the probability reflects his or her or its belief about his or her or its own identity. However, an essential part of the Bayesian probability is that it is being adjusted by the Bayesian inference using the evidence. Once we do so, we can quickly prove – even in a model which implies the existence of infinitely many Boltzmann brains – that the probability that we are Boltzmann brains is pretty much zero. So it is not equally high as the probability that we are a copy of the brain that evolved from a largely organized, well-behaved evolution process.
Again, for a frequentist without reincarnation, the phrase "equally likely" in that sentence is completely meaningless. For a Bayesian, it is potentially meaningful but easily demonstrable to be false. For a frequentist believing in reincarnation, the statement may be true but there is no evidence that our souls are "more identical" to some particular souls in other Universes than to others so all the conclusions derived from this reincarnation-dependent reasoning are bound to be unphysical, anyway. I am planning another blog post about reincarnation and after life in quantum gravity, by the way. ;-)
It's all very clear to us but Mark Srednicki remains ambiguous. First, he promotes the silly non-reasoning by some ad hominem comments:
Sean (and many other well known physicists, including Page, Linde, and Vilenkin) firmly believe that the only xerographic distribution that can be considered is a uniform one.That's great that they are well-known but if they're confused about the fact that we may prove that we are not Boltzmann brains, regardless of their predicted existence in some distant future, they're still nuts. This is a feature by which science differs e.g. from religion or politics. In religion, the truth may be determined by what the well-known people say. But in science, the relationship is directed in the opposite way: people are well-known and/or nuts and/or both according to how many important and/or new but correct things they may say about the Universe.
Srednicki decided that their understanding of the probability was Bayesian but he was instantly going to obscure this point, anyway:
You can think of it a Bayesian prior that gives the probability that “we” are any particular one of the copies. (For various reasons, Jim and I prefer not to call the xerographic distribution a prior, but that’s just semantics.)In 2009, I thought that their "xerographic distribution" was exactly the prior probability that we're here or there. But we're told that they had "various reasons" not to interpret the distribution as priors. I have no clue what the reasons could be if they were legitimate. In other words, I am confident that the reasons must be demagogic, silly, and irrational, and this subtle "semantics" is essential for Srednicki to maintain the irrational attitude to these questions as a possibility.
Well, let me tell you what are the "various reasons" why they try to avoid the word "prior" as a description of the xerographic distribution. The reason is that whenever you say "prior", everyone understands that it's just a "first guess" but the prior probabilities are quickly and gradually being updated and refined by Bayesian inference so that they become "posterior probabilities" whose values are almost always different from the prior probabilities. In particular, by the time we learn that a possibility is almost certainly true, its prior probability that could have been very small at the beginning (but it must have been nonzero, otherwise that would have prevented us from learning the truth) has grown to a large one, e.g. one close to 100%.
The reason why they don't like the word "prior" for these probabilities is that they never want to update them! They don't want to allow us (or anybody else) to offer proofs that we are not Boltzmann brains even if these brains may emerge in the future. They want to ban the Bayesian inference – they want to ban rational reasoning. But if they do so, they can't say that the words "equally likely" had a Bayesian interpretation. An inseparable component of the Bayesian reasoning is that the only probabilities we may talk about are prior and posterior probabilities and these probabilities should always been updated whenever we're finding new evidence! If you violate any of these basic rules, you are not a Bayesian. You are not doing any rational reasoning as understood by the Bayesian methodology.
Srednicki writes several paragraphs that claim that the rational reasoning is equally good as the irrational ones and summarizes them by this sentence:
My own personal philosophical belief (and Jim Hartle’s) is that we should not insist upon a uniform xerographic distribution.Holy crap. Rational reasoning in physics is not about "philosophical beliefs". If one can prove some proposition to be incorrect, you may take pounds of drugs to "philosophically believe it" but your philosophical beliefs are worthless crap, anyway. Science depends on the evidence. When it comes to some questions, the evidence is not available and the questions may remain undecided. But when it comes to very simple questions such as whether we are Boltzmann brains, we have tons of evidence to settle the question and the answer is simply No. If you prefer "philosophical beliefs" over rocksolid evidence, you are not acting as a scientist.
Jacques agreed with me and wrote the following reply to a sentence by Mark:
Srednicki: You can think of it a Bayesian prior that gives the probability that “we” are any particular one of the copies. (For various reasons, Jim and I prefer not to call the xerographic distribution a prior, but that’s just semantics.)Exactly. You're just not a Bayesian if you don't allow your probabilities (confidence in various propositions) to be updated if and when the evidence becomes available. More generally, you're not thinking rationally. You are being dogmatic in the same sense as the enforcement personnel in the Inquisition. This has nothing to do with science.
Distler: The whole point of the Bayesian theory is to provide a degree of robustness against badly-chosen priors. You’re not being Bayesian if you don’t avail yourself of Bayes’ Theorem!
Jacques repeats the calculation – an example of Bayesian inference – showing that we are not Boltzmann brains. So the conclusion is that this is not a matter of "philosophical beliefs", it's a question we may easily settle.
Srednicki replied again, claiming that he is a Bayesian because he has used the word "Bayesian". ;-) Was Stalin a democrat because he has used the word "democracy"? Srednicki reiterates his claim that the right and wrong answers are equally good:
Jim and I (and Sean!) are using Bayes’ Theorem. Bayes’ Theorem tells us that we should reject (with high confidence) the joint hypothesis of (1) a cosmological model that predicts lots of BBs, and (2) a uniform prior over the set of all identical copies of us (including the BBs). But Bayes’ Theorem does not tell us which part to reject, (1) or (2) (or both).Jacques (and I) are absolutely sure that (2) should be rejected because we may present – and Jacques has presented – a full proof that (2) is false. In this proof, it's clear what propositions are used as the input or the empirical evidence and they're taken into account exactly in the right way that the Bayesians call "rational reasoning".
You are absolutely sure that (2) should be rejected. Sean (and many others) are absolutely sure that (1) should be rejected.
The main point that Jim and I would like to make is that neither of you should be quite so sure, since there is no way to test anything except the combination of (1) and (2). (Except, of course, by trying to find other consequences, unrelated to BBs, of any competing cosmological models.)
The claim that (1) should be rejected – the claim that we must demand the Boltzmann brains to be absent in a viable cosmological model – is supported by no evidence whatsoever. There isn't any counterpart of Jacques' calculation of the probabilities that would imply such a conclusion. At most, Srednicki has offered the claim that the people saying that (1) should be rejected are well-known and can't be stupid. Except that they are stupid – or at least they are being stupid when they think about this question, so Mark is just adding another false proposition to his previous false propositions.
It's preposterous to suggest that Carroll's idiotic claims and Distler's calculation are "equally good".
At any rate, this exchange is an example of the fact that even in fundamental physics – at least its "cosmologically flavored" subdiscipline – the evidence and rational reasoning is sometimes being replaced by vague claims and additional unjustified, false claims that are only backed by the political power and references to the wrong people's being "well-known". This is not science, Mark.
And that's the memo.