Friday, 6 November 2020

On Fine-Tuning and the Multiverse

The Fine-Tuning Problem

I've been thinking a lot lately about the problem of fine-tuning and how it may or may not be resolved by appeal to a multiverse. This has been prompted by recent correspondence with the philosopher Philip Goff and by the book I am currently reading, The Beginning of Infinity by David Deutsch. I hope to get around to discussing Deutsch's ideas in future, but for now I'm focusing on an argument put forth by Roger White and endorsed by Goff.

The fine-tuning problem is just that the laws of physics describing the universe seem to be fine-tuned so as to allow life to exist. While trying not to be too parochial in our assumptions about what life requires to exist, at least in a universe even vaguely like ours, it seems reasonable to assume that it must at least have time and a stable environment in which to evolve, access to sources of energy and a varied assortment of building blocks from which to assemble itself.

But if the physical constants were slightly different, then perhaps stars, heavier elements or atoms could not have formed. Perhaps the universe would never have expanded from its initial hot, dense state, or would have recollapsed too quickly, or perhaps it would have expanded too quickly for particles to come together at all. When we say the universe appears to be fine-tuned, we are claiming that it appears to be delicately balanced so as to allow complex evolving self-replicators (i.e. life) to exist -- that almost any tweak we imagine to the constants or the laws of physics would result in a simpler, lifeless universe. This curious observation seems to demand an explanation.

Some other responses briefly considered and rejected

There are arguments about whether it is actually the case that the universe is fine-tuned. Some suggest that these claims are over-blown -- that life would find a way in most imaginable universes, or that this universe can hardly be said to be fine-tuned for life when most of it is lifeless. On the other hand, some suggest that it doesn't demand an explanation in any case, that there is nothing inherently special about a universe that supports life (the thought is that we only find it special because we are ourselves living things). Discussion of these options, as interesting as they might be, is outside the scope of this article. For now, let's assume that the universe is fine-tuned and that this demands an explanation.

So how to explain it? One possibility is that the laws of physics are somehow logically necessary for reasons not yet understood. If they are not contingent, then they would not require an explanation other than their logical necessity. This seems implausible to me, not only because I can't see why alternative laws of physics should be logically impossible, but also because it seems improbably coincidental that the only logically possible laws of physics should happen to be those that support life. All the same, if it could be shown that this were the only logically possible universe, I might grudgingly have to accept that this resolves the fine-tuning problem (albeit unsatisfyingly). But until that is actually proven, I think it's fair to regard this approach as highly dubious. Furthermore, I reject the idea that fine-tuning gives us independent reason to suspect that the laws of physics are logically necessary.

Another possibility is that the universe was designed by a god or some programmer running a universe simulation. Philip Goff has suggested that the universe might even have designed itself (the same video embedded above). Whatever the nature of the designer, this general design approach is worth discussing in more detail but it's not what I want to talk about here. I'm going to assume that it is false, because there seems to be a problem of infinite regress here. We would need to account for the origins and hence fine-tuning of the designer also. It also seems to fall afoul of Occam's razor, as the existence of a designer intelligent enough and powerful enough to design and create the universe is perhaps even more in need of an explanation than fine-tuning itself. More parsimonious explanations are available.

The physicist Lee Smolin has proposed that universes evolve according to an almost Darwinian process, selected for their ability to generate black holes. The formation of black holes, he proposes, may create new child universes with slight variations of the parent's laws of physics, such that universes which can create more child universes will have more descendants and so on, giving rise to a multiverse where most universes end up adapted for black holes. Meanwhile, he argues that the conditions for the formation of black holes happen to coincide with the conditions for life, such that most universes appear to be fine-tuned for life. The main problem with this approach, it seems to me, is how the whole thing got started. Without a whole lot of random variation in different versions of the laws of physics, it seems unlikely that a singular primordial universe would have had any successors. And starting with a whole lot of random variation is just the condition of having a multiverse with varying laws, which may be enough to explain fine-tuning all by itself (as we'll see). There's no need to assume that black holes can create new universes or inherit and mutate the laws of physics of their parents, so again Occam's razor is an issue.

The Anthropic Solution

My preferred solution appeals to the (weak) anthropic principle, which I have discussed before. It may so happen that there are many universes with many different versions of the laws of physics, and if this is the case then we should not be surprised to find ourselves in a universe with laws of physics which can support life. We could hardly have found ourselves in a universe with laws that cannot. This is certainly a good explanation for why our home planet is so uniquely well-suited for life, and it's natural to think it may explain the hospitality of the universe in the same way.

The only thing that stops this argument from being a clear winner is that we don't know that we really are in such a multiverse, though there may be independent reasons for believing so. First, the hypotheses of cosmic inflation and string theory taken together suggest that there may be many bubble universes with many different variations of the laws of physics. Second, I've argued elsewhere that the Mathematical Universe Hypothesis and its multiverse follows from the assumptions of naturalism, mathematical realism and computationalism (and argued in turn for each of these assumptions). But does fine-tuning itself give us reason to believe in a multiverse?

I had always assumed so, but I must say thanks to Philip Goff for alerting me to arguments to the contrary, specifically this paper by Roger White. I find the arguments therein to be interesting and tricky to disentangle, but ultimately unconvincing.

Roger White vs the Multiverse

The paper is well worth reading, and I'm not going to deal with every point therein, but in summary, I think the general problem with the arguments proposed by White is that they do not take the observer selection effect seriously enough. His various arguments and examples gloss over it in one way or another, usually by selecting the observer in some way in advance of or independently of the improbable event that is supposed to select the observer, when true observer selection effects require that the observer should only be identified by that improbable event.

White's formal argument

The first argument White aims to show that while a multiverse might well increase the chance of some life-supporting universe existing, it doesn't do anything to explain why our particular universe should be life-supporting.

White helpfully spells out his point with a formal theorem, which is correct as far as it goes but which mischaracterises the problem. The argument goes astray because White identifies our universe independently of its laws of physics. The way he conceives of the problem, it is as if we start with a bunch of placeholder universes with no laws of physics, and our universe identified as a specific one of these. We then imagine the universes being assigned laws of physics at random, and ask for the probability that our specific universe happens to be assigned life-supporting laws.

He's right that the multiverse doesn't help much with this scenario, but I think that's because White is making mistaken assumptions about the nature of identity. I've argued before that there is no such thing as essential identity in the case of persons, and I think the same is true for any object, including universes. Our universe is just that universe that has our physical laws (including initial conditions). The probability that our universe has these laws is therefore simply 1. The puzzling question is not what are the chances that our universe should have these laws, but instead why should any such fine-tuned universe exist?

White is well aware of this alternative interpretation of the problem, but he thinks that the confusion is the other way around, saying "the fact that our universe is life-permitting does not confirm the Multiple Universe hypothesis one iota. Perhaps the claim that it does results from a confusion between E [our universe is life-permitting] and E′ [some universe is life-permitting]".

To illustrate the problem, I can adapt White's argument to show that we should demand an explanation for why you were lucky enough to have been born as exceptionally intelligent as you are, given that you could have been a frog or a worm or a geranium. The number of relatively stupid living things is overwhelmingly vaster than the number of human beings, not to mention the number of human beings who take an interest in philosophical discussions like this.

(Note that I'm not looking for an explanation of how any fine-tuned minds could have arisen in the first place, so evolutionary biology is irrelevant. I'm taking it for granted that there exist a wide variety of minds of various different intelligences, just as in the multiverse scenario we take it for granted that there are a wide variety of different universes with various different capacities to support life.)

There's no doubt about it, your intelligence is incredibly fine-tuned. The probability of any arbitrarily chosen living thing being as smart as you is negligible, so we need an explanation!

The analogy to White's argument should be clear. I am making the mistake of identifying you with some placeholder for a living thing waiting to be assigned a mind, and then considering the probability that you will happen to be assigned a mind capable of following a philosophical argument. But taking the observer selection effect seriously means considering that frogs and worms and bacteria couldn't be reading this article, and reflecting on the nature of identity suggests that you are necessarily the living thing with your mind, and not a placeholder that once waited to be assigned one. The idea that you could have been a worm is nonsense, because if you were a worm you wouldn't be reading this and you wouldn't be you. As such it is not surprising at all that your mind is fine-tuned. It simply must be so. The idea that this universe could have had other laws of physics is also nonsense, as then it wouldn't have been this universe.

(On the other hand, the idea that the universe could have had other laws of physics is not nonsense, on the assumption that there is only one universe, and what we mean by "the universe" is "the universe that happens to exist" which is only contingently and not necessarily "our universe").

If it is true that the vast majority of minds are not fine-tuned, then you can infer from the fact that you have a fine-tuned mind that there are or have been lots of minds that aren't. This should be trivially obvious. Much the same reasoning can be employed to infer a multiverse from fine-tuning, at least in the absence of more parsimonious alternative explanations.

The remainder of the paper proceeds with a number of (dis)analogies making similar points.

The Sleeper and the Dice

Case B*: Jane knows that she is one of an unspecified number of sleepers each of which has a unique partner who will roll a pair of dice. Each sleeper will be woken if and only if her partner rolls a double six. Upon being woken, Jane infers that there are several sleepers and dice rollers.

Goff also discusses this idea in the video linked above with reference to a similar analogy where you will be killed if a particular monkey does not type a Shakespearean sentence within an hour. When you are not killed, Goff asks whether you have reason to believe that there were many people and monkeys in similar situations. This analogy is intended to be just the same as White's, only more colourful and intuitive. In this I think it succeeds, but I'll stick with White's framing as it's discussed in more depth in the linked paper and because the particular problems with it are instructive.

White claims that Jane's reasoning here is fallacious, and at first it seems so, even to me. But let's look more closely.

First, we note that White's usual problem arises again here, in that Jane has a specific identity before the experiment begins -- the identity of the observer is selected independently of the supposed observer selection effect. Let's leave that as it is, but there are some other problems with the analogy which might need some adjustment to make it more like the fine-tuning problem. Firstly, the chance of a double six is insufficiently improbable to push us very much to change our assumptions. Second, though he says "will be woken if and only if", he doesn't spell out what this means. If Jane is really never to wake again on the wrong dice roll, then he must mean we're murdering Jane. Otherwise, Jane would presumably wake up naturally at some point and observe that the dice roll had not come up favourably, and the fact that she is observing an improbable outcome could not be explained by the fact that she was observing it, because she could have observed otherwise. These issues are addressed in Goff's improved version of the analogy, where we have a very improbable event indeed and survival dependent on that event.

Let us therefore amend White's thought experiment as follows: let's say there are a thousand dice which must all come up sixes, and let's say that Jane would be murdered in her sleep otherwise. Under these circumstances, I claim that Jane might be forgiven for making some strange inferences on waking.

If I were Jane, and if I believed that the experiment had been carried out as described, then I would indeed infer that there were several sleepers. In particular, I might attribute my survival to the multiverse of quantum mechanics, and assume that countless of my doppelgangers had been murdered. Only on the many worlds interpretation (MWI) of quantum mechanics is my survival explicable (and indeed, guaranteed), on the reasonable assumption that the variance of quantum mechanics can influence dice rolls.

Despite the impossible odds, on the MWI I have nothing to be surprised about, because in helping myself to the multiverse of quantum mechanics, I negate the problem of identifying the observer in advance. Jane is no longer a unique individual identified in advance, but once more just once of a fungible class of initially identical Janes (for more on this, David Deutsch has an illuminating account of quantum fungibility in The Beginning of Infinity, where he discusses the MWI in terms of infinite initially identical universes which diverge rather than one initial universe which splits). I have no reason to be surprised that I have survived, because one of me was bound to and I as the observer of the survival am necessarily the one that happened to survive. The anthropic principle is therefore available to me to explain everything about my survival, at least from my perspective.

But perhaps this is cheating. Suppose I don't believe in parallel universes. We might first need to reduce the number of dice, because with a thousand dice survival becomes so improbable that I think any rational person would be forced to believe in parallel universes by the arguments above, or at least to doubt their own understanding of the experiment (or sanity!). So let's say there are 6 dice. The odds of winning are now 1 in 46,656, so unlikely enough to give us pause but not insuperable.

I think it will be useful to break Jane's observation into two surprising propositions in need of explanation.

  1. Someone has survived
  2. I have survived
Unintuitive as it may seem, I do actually think that proposition 1 justifies Jane's inference that there must have been very many participants in the experiment.

If we consider it first from a third-party point of view this is perhaps easier to see. First, we should rule out the possibility that we are only hearing of the experiment because of an improbable outcome. Otherwise, an improbable outcome is not so surprising, because the reference class we need to consider are all events which we might have learned of because of improbable outcomes. Hearing that someone has survived in these circumstances only allows us to conclude that there must be many opportunities for improbable outcomes of diverse events, and not that there must have been many sleepers. So we should stipulate that we are aware of and specially interested in this experiment in advance and that we expect to hear of the outcome. However, we have no idea in advance how many sleepers there are. In these circumstances, when we learn that there was at least one survivor, I think it correct to infer that there must have been thousands of potential participants. Otherwise it's too surprising that anybody survived.

The second proposition is more problematic. I agree with White that the multi-sleeper hypothesis does not help us here. The problem arises in part because of White's disanalogous move of selecting the observer in advance. Jane remembers and identifies with the Jane anticipating the experiment, who would reasonably have predicted that she would not survive. This prediction is defeated, so Jane is surprised. Her position is much like a lottery winner -- it is utterly unsurprising to any neutral third party that someone has won the lottery (assuming that lots of people enter), but utterly shocking to the winner herself. I think that's just too bad. There really is no good explanation that should satisfy Jane as to why she should turn out to be the winner, and her surprise is warranted.

And yet I maintain that a lottery winner should believe in the hypothesis that lots of people have bought a ticket just because she knows that somebody has won. Assuming that the numbers of people buying lottery tickets vary wildly from week to week, winners who guess that their week had many participants rather than few will usually be correct, because there are more such winners. On weeks where very few people bought lottery tickets, there will usually be no winners. On weeks with lots of competitors, there may be more than one winner.

I think the problem in explaining the second proposition is masking the import of the first for White and Goff, and I think this is the ultimate source of their mistake.

The rest of the paper continues in this vein, with similar reasoning leading to similar (in my view) incorrect conclusions. However there's one more analogy I think worth discussing.

The forest shooting

This is an analogy originally from John Leslie, where he discusses the idea that you are in a forest when without warning you find yourself being shot. You may either be alone in the forest or in a crowd, and for some reason (at least on White's version) you don't know which. This strains credulity, but let's go with it. Suppose you have two competing hypotheses to explain your shooting. Either a stray bullet from a hunter shot you by accident (this kind of thing being more likely to happen to somebody if there is a crowd), or an assassin was out to get you. What should you believe, and does your shooting give you reason to think you may be in a crowd?

In this case, the situation is altered because of the availability of the design (assassin) hypothesis in addition to the anthropic (crowd) hypothesis. It might indeed make more sense to believe that someone is out to get you, and not to believe that you are part of a crowd. Being part of a crowd explains proposition 1 (that somebody got shot), but it doesn't help with proposition 2 (that the person shot was you), while the assassin hypothesis explains both. The most rational hypothesis therefore is a matter of perspective. A neutral third party might be inclined to pick the crowd hypothesis, but from your unique perspective it might be more rational to pick the assassin hypothesis.

We can modify the lottery scenario similarly by introducing an analogous competing hypothesis. Perhaps your apparent lottery win can be explained by a mistake, hallucination, dream or psychosis. Depending on the odds of winning the lottery and how far you've gone to verify that the win is genuine, this might in fact be a better explanation, but only from the perspective of the winner herself. This echoes what I said about Jane's epistemic position when she has been the beneficiary of a thousand dice rolls all coming up six. In these extreme circumstances, she should not necessarily conclude that there have been many sleepers with distinct identities from herself. She should instead believe that she has been deceived, or that there is a quantum multiverse, or that God has intervened, or simply that she has lost her marbles.

Fortunately, we are not in this position with respect to fine-tuning, because there is no proposition 2 to consider. Our universe was not waiting around waiting to be assigned laws of physics and wondering what laws it would get. Our universe is instead properly defined as the universe with these laws of physics, and with these people in it trying to explain fine-tuning. In these circumstances, we need only consider proposition 1, why any universe at all is life-permitting. It makes no sense to ask why our universe (i.e. the universe with these laws of physics) should be the universe that got these laws of physics. Goff and White claim that it is intelligible to think that some other universe might have got these laws instead, and that people like us might then live in these other universes instead, but they wouldn't be us, because they wouldn't be in our universe. I think that's backwards. If this universe had not had these laws, then it wouldn't be this universe. If that other universe had these laws and had people in it identical to us, then that would be our universe and we would simply be those people. To believe otherwise is to believe that there is something to pick us out as distinct from people who are ex hypothesi identical to us. I just don't buy into that kind of essential identity.


I don't claim that fine-tuning by itself proves that there is a multiverse. There are a number of other possible explanations for and responses to the fine-tuning problem. These ideas should be judged and compared with each other and with the anthropic principle in terms of coherence, parsimony etc. I think the anthropic principle does rather well in this regard, your mileage may vary. Reasonable people can disagree on which answer works best.

But the idea that a multiverse does nothing at all to explain fine-tuning is a clear misake. 


  1. Hi DM,
    Good to see a post from you!

    Can't say I've ever found fine tuning arguments compelling, but my take on it lies among the options you excluded from the scope of the article. If, for the sake of argument, we accept that there actually is a fine tuning problem, then I agree a multiverse seems like one plausible solution, perhaps the best one.

    But I find the more narrow scientific reasons for each type of multiverse more compelling. A quilted multiverse is more likely if space is infinite. A bubble multiverse if eternal inflation is reality. (Hadn't heard before that string theory was necessary for eternal inflation. If so, to me, that weakens it.) And the MWI falls out of quantum mechanics if we dispense with the collapse postulate.

    Of course, all of this gets us to plausible, but not to true.

    1. Hi Mike,

      Thanks for dropping by, appreciate it!

      The focus in this article really is on rejecting Roger White's argument that it's a mistake to increase your credence in a multiverse because of fine-tuning -- that anthropic arguments are not only a poor explanation but no explanation at all. Sounds like you agree with me that his argument doesn't work.

      I don't think the quilted multiverse or MWI would necessarily help much with fine tuning, as typically each universe has the same laws of physics. You'd need either the MUH or the bubble universe where universes can have different laws of physics.

      You don't need string theory for eternal inflation, but string theory provides some of the motivation for supposing that each bubble might have different laws of physics. I gather there are something like 10^500 consistent versions of string theory, with no a priori way to choose between them, so some cosmologists imagine that each bubble universe in inflation get one of these assigned more or less randomly in the process of forming. Without string theory, the default assumption would probably be that the laws of physics are the same in each bubble.

    2. Hi DM,
      Thanks for the clarification on eternal inflation and string theory. Makes sense.