In a previous post I looked at Boddy and Carroll’s controversial claim that a cosmological model which predicts Boltzmann Brains is problematic. In essence, they claim that if a theory predicts the existence of many observers whose subjective experience is identical to yours, but which is based on random thermal fluctuations, then the theory is `cognitively unstable’ because (1) the laws of physics indicate there is a good chance you are one of those observers, but if you are, then (2) you can’t trust your reasons for believing those same laws that led you to that conclusion, because they appeared in your brain by random chance!
Personally, I am suspicious that there might be some kind of hidden flaw in this rather mind-bendy argument. So far, critics have argued that Carroll’s assertion of (1) is far from obvious, and that alternative assumptions exist that do not lead to a problem. However, apart from Mark Srednicki, everyone seems to think that their own choice of starting assumption is obviously correct. For my part, I really do not think that the question `could I have been born as somebody else?’ has an obvious answer that can be derived in the absence of philosophical considerations. It is one thing to ask, `would this ball fall to the ground if I dropped it?’ and quite another thing to ask `if my parents had conceived me one day earlier, would I be the same person’? One question is quite easily defined and answered by known science, the other not so much. Luckily, there is a man called Nick Bostrom who is much smarter than you and me and has spent much more time thinking about such things. Below is my own take on his take on the problem.
The Bearded Man Paradox
Imagine you have two competing theories of the universe. In both theories, the universe consists of three cells, walled off from each other. In each cell there materializes a bearded man, whose beard is either black or white. In this first theory, called TB, two men have black beards and one has a white beard. In the second theory, TW, two men have white beards and only one has a black beard. Now, suppose you have materialized as a black-bearded man in a cell. Given your subjective experience of having a black beard, which theory is more likely to be true?
Intuitively, we would tend to think this supports theory TB, which allows for more black-bearded observers. But this intuition rests on an assumption: namely, that we might have materialized as a white-bearded man. But to allow for this possibility means that we are including in our reference-class (i.e. the set of people that we might have been) some observers whose subjective experience is different than ours, namely, we are allowing that we might have had the experience of having a white beard, even though we in fact have a black one. We could instead argue that, since there exists at least one black-bearded man in both models, the knowledge that we have a black beard simply tells us that we exist within the relevant subset of observers in either model that have black beards. Indeed, if it was a given that we were always going to be one of the black-bearded observers in the model, then the fact of having a black beard tells us nothing about which model is the correct one! Just like in the Adam & Eve problem, it is an issue of assigning your`soul’ to possible bodies, which is indeed dependent on philosophical assumptions.
Bostrom argues that we should allow our reference class to include observers with slightly different subjective experiences. To Bostrom, for a black-bearded man to believe that he always had to have a black beard in any possible universe is absurd. However, even if you are not willing to go as far as that, you must wonder how exactly an observer’s experiences should match yours before you are willing to concede that you `might have been’ that observer. What if, instead of beards, the observers were identical except that one of them happened to get an itch on his elbow at a particular moment in time, whereas the others got an itch on their noses? How similar must your possible incarnations be, in order for you to consider them possible experiences for yourself?
Bostrom saves the day
Unlike Carroll, Bostrom considers the `problem’ of Boltzmann Brains to be the fact that they might lead us to reason `incorrectly’ in cases like the bearded men problem. But Bostrom’s judgement of `incorrect reasoning’ rests only on his intuitive feeling that the observation of our subjective experiences (like not being a Boltzmann Brain) should allow us to prefer models in which there are more observers having this property than not. This intuition is expressly not shared by Jacques Distler (nor, presumably, by Motl). Distler sees no reason to look for a model free from Boltzmann Brains, so long as the present model predicts the existence of at least one real Jacques Distler who is not a Boltzmann Brain. Since he had to end up as the real Jacques Distler in either scenario, the fact that he is himself and not a Boltzmann Brain gives him no further information to choose between models.
But if we agree with Bostrom for the moment, then we can rescue Boddy and Carroll: for then there is a perfectly good reason to prefer a BB-free model over one that contains BB’s, based just on probabilities, without needing to invoke `cognitive instability’. To reason correctly, Bostrom says we should include in our reference class of observers those whose subjective experience might have been slightly different to our actual experience (eg. that we might have had a white beard, even though we have a black one). But in the present case, this means including BBs whose fake past experiences might deviate somewhat from our actually observed experiences. If the deviations were consistent with the overall laws of physics observed in our experiences, this would not matter; but since Boltzmann Brain memories are random fluctuations, the overwhelming majority of BBs experiences are not exactly like ours, but are completely whacked-out and crazy. If you allow that you might have been one of the conscious BB’s with a completely scrambled-up subjective experience, then the fact that your life is remarkably ordered and consistent with the laws of physics is far better explained by a model that is completely free from BB’s than by a model that contains legions of BB’s. Thus, it appears Bostrom’s philosophical argument lends support to Boddy and Carroll’s conclusion, but by using an alternative argument to the possibly suspect notion of cognitive stability. Since I share Bostrom’s philosophical sentiment on this matter, I also agree with Carroll’s conclusion: a model without BB’s is better than a model with BB’s (provided one does not have to include any nasty ad-hoc elements to get rid of them). From this point of view, Boddy and Carroll’s work is well-motivated after all.
In fact, I’m even going to go out on a limb here and say that this work sets a precedent for using a philosophical argument as a constructive tool for building theoretical models. This is certainly not a new idea, but physicists nowadays seem to dismiss philosophy too quickly; they have forgotten how to make philosophy work for them in doing real physics. I hope the Boddy and Carroll paper encourages more physicists to look to philosophy for inspiration in the fine art of theory-building.