The Problem with Multiverses

In The Multiverse & You (& You & You & You…), Sam Harris talks about multiverses with Max 'Mad Max' Tegmark.  Sadly, Harris didn't take the opportunity to ask Tegmark about his foundation, Foundational Questions Institute (FQXi), being funded by Templeton.  To be fair, the FQXi website has a page on their finance arrangements which make huge efforts to distance the Institute from their financiers.  Even so, they are playing with Templeton money which is always disappointing when proper science is involved.

But this is about multiverses.  In their discussion Harris and Tegmark (although possibly more so Harris) make much about the idea that if there is a multiverse, noting that they only got to Level 2 Multiverses, then there will be an infinite number of Harrises and Tegmarks doing slightly different versions of the podcast.  At one point the googolplex is mentioned, a number which although not infinite is officially considered to be very big - 10 to the power of 10¹⁰⁰.  Apparently, someone worked out that the number of possible arrangements of the original particles in the universe is in the order of a googolplex.  Not quite infinity but, you know, a lot.  The idea is that out of those arrangements, even if a relatively small fraction of them would result in us, that would still be a lot of arrangements with beings indistinguishable from us in them.

Take that one step further and say there is the possibility that there were more or fewer particles in the initial arrangement of the universe, then you get a huge number of googolplexes of possibilities.  Within that suite of possibilities, there would again be a lot of arrangements with beings indistinguishable from us in them. Then there's the possibility of duplication - which brings us to the possibility of an infinite number of replications of us in existence.  There might not only be an infinite number of universes which are very, very similar to our own, but also an infinite number of universes (albeit a "smaller infinity") that are exactly the same.

So, it's true enough that, if Tegmark is correct about multiverses, that there are an infinite number of Tegmarks and Harrises who has a discussion that was turned into a podcast.  And it's true that there is an infinite number of Tegmarks and Harrises who had very similar, but slightly different, discussions that either did or didn't get turned into a podcast.  And it's true that this infinity of variations might include discussions in which Harris suddenly began talking in Hungarian.

What concerns me, however, is that either by accident or design, the presentation of multiverses was staggeringly arrogant.  They failed to mention that there was an infinite number of universes in which their discussion didn't take place even within the infinite number of universes which contain a Max Tegmark and a Sam Harris.  It's a bit like a series of matryoshka dolls, each of which is infinite in size but, because the rubberiness of infinity, can be ranked:

The infinite number of universes in which the Harris-Tegmark discussion happened precisely as it did in ours which is a subset of:

The infinite number of universes in which the Harris-Tegmark discussion took place which is a subset of:

The infinite number of universes in which Harris and Tegmark met each other which is a subset of:

The infinite number of universes in which both Harris and Tegmark exist which is a subset of:

The infinite number of universes in which humans exist which is a subset of:

The infinite number of universes in which intelligent life is possible which is a subset of:

The infinite number of universes in which there is something rather than nothing:

The infinite number of possible universes.

Tegmark himself points out that human endeavours have been plagued by a sense of arrogance – this, our village, is the only village.  No?  But this land is the only land.  No?  But this continent is the only continent.  No? But this planet is the only planet.  No?  But this solar system is the only solar system.  No?  But this galaxy is the only galaxy.  No?  Well, the universe that we can see is certainly the only universe.  Perhaps we’ll soon be trying on “this is the only multiverse” for size.

The arrogance is inherent in the contemplation of what we are doing (right now) and the imagining of what would be changed if things were very slightly different, as if our activities were some sort of focal point for the universe.

But I think it gets a bit worse, as least in so far as the discussion that Harris and Tegmark actually did have, in our universe.  They were discussing how there could arguably be an infinite number of universes such that anything that is possible does actually happen.  Think about that for a moment.  Anything that is possible happens in some universe or another.  Really?

Is there a universe in which an analogue of me (clearly not actually me, because I live in this universe, but a version of me that would think precisely the same as me except that this other version …) buys a lottery ticket every week and wins the jackpot every time?  This is very highly unlikely, to be sure, but it's not strictly impossible.  Oh Grand Pixie, why oh why am I not that version of me?

It gets worse.  Harris and Tegmark touch on how the brain (and the suite of the processes within the brain) interacts with the outside world, implying that the common ground is mathematics.  My concern isn't so much with that, but with the concept that there are things go on inside our brains that are interpreted as interactions with an external world that really aren't.  Usually these are minor hiccups and most of us resolve them and carry on.  Some however are constantly plagued by voices in their heads and other delusions.  It's highly unlikely that we could all be affected by chemical states in our neurology that results in coherent voices that all tell us that a god is real.  But it's not strictly impossible.  And it's not strictly impossible that cloud formations could take on the appearance of an old man in the sky (or an old woman in slightly less politically incorrect alternate universes).

What I'm suggesting here is that, at least in the rather light touch on multiverses discussed by Harris and Tegmark, the odds are that in some universe there will be all the evidence that anyone could ever need to prove the existence of a god.  The vast majority of prayers would be answered in such a universe (merely on the basis of coincidence, but the supplicants don't know that).  Everyone would get visitations from what appear to be divine agents (or rather have internally generated experiences of such visitations, purely due to random chemical reactions in their brains).

Remember that we are talking about infinity here, not just a very big number.  Even if the likelihood of an apparently god-infested universe is infinitesimally remote, if there is an infinite number of universes, then there is at least one universe like that, and possibly even an infinite number of them.

Would Harris and Tegmark agree with this, as a possibility?

Either way, it seems that multiverse predictions do tell us something about the likelihood of there being a god.

Consider the difference between 1) a great being which exists and for whose existence there is clear evidence and 2) another great being for which there is no compelling evidence of its existence.  Which is the greatest?  Unless hiddenness is defined as a strength (which seems unlikely since we are repeatedly told that the god of the theists wants to have a relationship with us), the evidence based god is superior.  Some theists will argue that it's not possible to have evidence of their god.  But what multiverse theory seems to be telling us is that it actually is possible to have overwhelming evidence of a god, even their specific god, and that that applies even if such a god does not exist.  But clearly you and I don't live in a universe in which there is overwhelming evidence of anything of the sort.

On the contrary, we live in one of the universes in which it is not only possible but entirely reasonable to reject the notion of a god.  The question therefore is this: How do theists who buy into multiverses and subscribe to some sort of mandatory divine hiddenness get around this issue?

Unbelievable! It's Max Andrews!

In his Unbelievable discussion, Max Andrews stated that he has noted in himself, when shaping apologetic arguments, the tendency to beg the question of god.  You may recall that begging the question is, at base, a fallacy of circular reasoning, even though the circularity might be subtle.  It appears that he and I might have some alignment here in that I have noticed, on the part of apologists, the exact same tendency.  That said, while I agree that many arguments for god presume god, or something attributed to god, I would not, however, have necessarily included fine-tuning based arguments in the list.

These are the apologetic arguments that, off the top of my head, include some element of begging the question:

Moral Argument

Ontological Argument

Argument from First Cause

Argument from Resurrection

Argument from Revelation

Argument via Inference to Best Explanation

A good example of the sort of apologetic question begging involved appears in this video by Dave S at theglobalatheism, which concludes that the ontological argument proves no more than that if god exists, then god exists (which is the law of identity: if X, then X, or X=X).

Another video by Dave S, on the argument from resurrection, also hints at begging the question, pointing out that to get a high-ish likelihood that god exists (Pr≈0.5) you need to assume that claims that god raised people from the dead were true.  Think about this for a moment.  If you assume, up front, that claims that your god raised people from the dead are true, this necessitates the assumption that your god actually exists.  You should find this a little odd, because it would mean that, rather than adding support to the notion that the apologist's god exists, the resurrection argument reduces the likelihood of that god's existence.  This seems odd to me.

Anyway, what about the fine-tuning argument.  Does this include an element of begging the question?

Perhaps there is.  The fine-tuning argument first suggests that the universe is fine-tuned (arguing the reality of fine-tuning is a speciality of Andrews' partner in the discussion, Luke Barnes).  But that's insufficient to show god.  To show god, the apologist has to go one step further and argue that nothing else explains fine-tuning other than their god.

This is where a question can be comprehensively begged, on two levels.

Firstly, there is the definition of "god".  As indicated above, it can be argued that the ontological argument can fail based on the fact that it tries to define a god into existence.  The fine-tuning argument fails on the same grounds, because of begging the question.  The apologist pressing this argument is effectively trying to define their god into existence via the claim that their god can do anything that is necessary to prove that existence.  Their god can make a universe that looks like ours and seems incredibly unlikely, but you can bet your bottom dollar that if it ever starts to look like the universe is incredibly likely, the same apologist will argue that their god can make an incredibly likely universe as well.  Or an eternally inflating multiverse.  Or a quantum multiverse.  Therefore, their argument collapses into "if our universe were created by the sort of being that can make universes of the sort that we live in, then our universe was created by the sort of being that can make universes of the sort that we live in, let's call it god".

Secondly, there is the sheer unlikeliness of our universe versus typicality.  In this argument, there is no assumption of a god followed by a conclusion of a god, it's more an assumption of atypicality followed by a conclusion of atypicality which feeds into a "this is so surprising, therefore god" argument.  Ignoring for a moment the fact that multiverse theory arises totally independently of counter-apologetics, if we were to posit a multiverse to solve the unlikeliness of our universe, the counter-counter-apologists then rush in to say that, if there were many different kinds of universes in this multiverse, then our type of universe would be atypical - and, therefore, we have an obligation to explain why we are in this atypical universe.

This atypicality is often expressed in terms of a Boltzmann multiverse, the sort that fails on the basis of Boltzmann brains.  In a Boltzmann multiverse, each universe is a fluctuation of order in a vast, enduring region of comprehensive disorder.  In such a regime, small regions of order would be far more likely than regions like our observable universe and we would indeed be unusual.  However, all this does is put a kibosh on a Boltzmann multiverse.  But no-one is seriously positing a Boltzmann multiverse (I will do so semi-seriously in a later article though).

Nevertheless, when people regurgitate WLC's argument against the multiverse (including people like Barnes) they assume a Boltzmann multiverse and conclude that a multiverse is impossible.  Thus they are arguing that an impossible form of multiverse is impossible, which is trivially true.

The other element of the argument is based on the assumption that we must be typical.  This seems similar to the argument that leads to (counter-apologetically derived) multiverses, but there is a subtle but important difference between very highly unlikely and very highly atypical.  When you bring the multiverse to bear on the problem, the likelihood of a very highly unlikely universe existing increases, towards 100% as N (the number of universes) approaches infinity.  At the same time, as N approaches infinity, the number of atypical universes increases, the number of distinct chances of being atypical increases.

Think of it in terms of jellybeans with the probabilities being indicative, rather than rigorous.  If one in every 100 jellybeans was atypical, then with a sample of 100 jellybeans, you would expect on average that one would be atypical and there would be only chance to be atypical.  If there were 10,000 jellybeans, then we'd expect there to be 100 chances to be atypical.  Agreed, there would still be a lot more typical jellybeans than atypical ones, but the increased number of atypical jellybeans would increase commensurate with sample size.  If we introduced a filter that only permits a certain shape of atypical jellybean to pass through, and used a very large, approaching infinite sample size, then so long as the shape is possible, then we should not be surprised to see one.

This is the situation that we find ourselves in.  We are in a universe which, although atypical, must be the way it is for us to find ourselves in it - because it's precisely the sort of universe in which we could develop as persistent intelligent life (rather than Boltzmann brains).

In other words, our atypicality is very much the point, rather than being a failure of the multiverse to explain our fortuitous existence.

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Curiously enough, Dave S includes, as further reading for the resurrection video, which was posted a year ago, both my Sweet Probability and Max Andrews' dissertation on Bayes Theorem and the resurrection.  Some nice recognition there for both of us, even though I at least hadn't noticed it.

The Four Mechanisms of the Ignopalypse

Max Andrews is a philosopher who started out with a Bachelor of Science in Religion (that's actually a real thing!) from the Liberty University in Virginia, which claims to the be the largest Christian university.  He went on to get a Masters of Arts in Philosophy, also from Liberty University for which, of course, he wrote a thesis.  The contents of his thesis have reappear in various guises, for example as articles on his blog and embedded in his (two?) public debates.  (As noted in The King of Spades and the Strong Anthropic Principle, Max Andrews has changed his position a little in recent times, so even he may no longer concur with what I refer to below.) 

I've been reading through his thesis and have come across (once again) his "four mechanisms" (here's a shorter document which refers to them - you could even listen to his lecture which mentions the mechanisms, if the link had worked).  What Andrews argues is that there are four mechanisms that are necessary for an inflationary multiverse to produce a life-generating universe:

A mechanism that supplies the energy needed form bubble universes

A mechanism that forms bubbles

A mechanism that converts energy of the inflation field (by which he seems to mean inflaton field) to "normal mass/energy" (by which he means not Dark Mass and not Dark Energy)

A mechanism that leads to variation in the fundamental constants between universes

Oh boy.

This is not an original Andrews argument.  It's an argument that was raised by Robin Collins in The Teleological Argument, an essay that appeared in The Blackwell Companion to Natural Theology which was edited by our old friend William Lane Craig (and J.P. Moreland).  This is a go-to book for wannabe apologists and quite possibly ought to be one for wannabe anti-apologists, since it collects together the best of the current defences of theism - on the grounds that we should always try to interact with the best form of any argument we might want to argue against.  Unfortunately, the book costs in the order of $200, so I'm just going to work from Collins' own preliminary version of his essay.

Robin Collins quotes the Shaw Prize winning cosmologist, John A. Peacock, when he formulates the four mechanisms, although it does seem that he's only using Peacock's words with respect to the inflaton field related to the first mechanism, specifically the following words: "the vacuum acts as a reservoir of unlimited energy, which can supply as much as is required to inflate a given region to any required size at constant energy density".  In Collins' view, the inflaton field has to "conspire" with Einstein's equations in order to form and populate bubble universes.  There's no indication that he has cosmological support for this notion.

Andrews, however, quotes Collins and another couple of chaps, Axel de la Maccora and Boris E. Meierovich.  To the former he attributes the following notion:

If inflation is not complete or efficient then the remaining energy density within the bubble must be fine-tuned to give the correct value distribution.

And to the latter:

Attempts to circumvent fine-tuning concerning the inflation field have focused primarily on describing what occurs posterior to the moment of bubble inflation.

With respect to de la Maccora's attribution, it is true that Maccora said something very similar in the referenced paper, but look at the context taken from the abstract (my emphasis):

If the inflaton decay is not complete or sufficient then the remaining energy density of the inflaton after reheating must be fine tuned to give the correct amount of Dark Matter. An essential feature here, is that Dark Matter-Inflaton particle is produced at low energies without fine tuning or new parameters.

de la Maccora immediately follows the referenced sentence with a clear indication that fine-tuning is not required, a conclusion that can be comprehended if one reads the actual text of the paper.  For example:

However in our scheme the regeneration of φ takes place naturally without fine tuning and, once the field φ becomes nonrelativistic, when its mass m_o > T, φ will decouple since n_φ is exponentially suppressed.

and

The aim of this section is to show how a single scalar field φ can account for inflation at early times and as Dark Matter at a late time, without any fine tuning of the parameters.

In other words, this is cherry picking of an astounding quality.

As for Boris Meierovich, I have tried to find a sentence or a paragraph from which the notion attributed to him could be extracted, with no success.  Perhaps someone with more time or sharper eyes can find it, but I note that even if this were to happen, this is just another example of cherry picking.  Meierovich's paper also speaks against fine-tuning:

The parametric freedom of the theory allows to forget the troubles of fine tuning. In the most interesting cases the analytical solutions of the Einstein’s equations are found.

and

The equations (31,49) with the boundary conditions (50) are easily integrated numerically. The regular solutions are free from fine tuning. Moreover, the existing parametric freedom results in a great variety of possible configurations.

Absolutely staggering.

But there's more …

Let's go back to Collins' four mechanisms (via Andrews).  The first mechanism needed to supply the energy to form the bubble universes, according to Andrews, is the fine-tuning of the "inflation" field.  Someone more sceptical than I might suspect at this juncture that Andrews is deliberately equivocating over the term "inflation field".  No educated person really doubts that inflation is an excellent solution to a number of problems with standard cosmology (although there are other solutions put forward by respected cosmologist that don't rely on inflation).  What we don't really understand at this point in time is what the mechanism behind inflation would be.  But there are speculative theories.  The inflaton is associated with one of those.  To put this theory into perspective, if you google "inflaton" and look really carefully, you'll see that there are only about 530 mentions of inflaton on the internet (none of which are Andrews, because he consistently misrepresents it as an "inflation field" and many are repeats so that unique mentions probably amount to no more than 160 - at least one of which was due to a typo).

Collins and Andrews really should be more forthcoming about how speculative the theories that they are hanging their arguments on are.

So, if current theories about inflationary multiverses are correct and if the inflaton theory is correct and the two qualified people quoted by Andrews in support of his argument are wrong about the substance of their papers (but not that which was cherry picked from those papers), then maybe we would be in a position to suggest that multiverses are fine-tuned.  But even then, the claim that this is indicative of a volitional agent's design is no more than a brash appeal to ignorance - "we can't think of any other reason for this, therefore goddunnit".

Another Chance of Design - Response to Travis R

There's been a short exchange in the comments following Chance or Design:

measureoffaith - FYI, the objections you list here appear to have been sourced from WLC rather than Robin Collins, and the accompanying reference to Penrose is on pages 762-765 of TRtR (The Road to Reality).

neopolitan - Thanks, I've updated accordingly. I don't think that pages 762-765 say what you want them to say. Penrose is arguing against the anthropic principle. Towards the end of an earlier section, "28.6 The anthropic principle", he writes (having linked the strong anthropic principle with a creationist god hypothesis):

"My own position is to be extremely cautious about the use of the anthropic principle, most particularly the strong one. My impression is that the strong anthropic principle is often used as a kind of ‘cop-out’, when genuine theoretical considerations have seemed to reach their limit. I have not infrequently heard theorists resort to saying something like: ‘the values of the unknown constant parameters in my theory will be ultimately determined by the anthropic principle’. Of course it might indeed ultimately turn out that there is simply no mathematical way of fixing certain parameters in the ‘true theory’, and that the choice of these parameters is indeed such that the universe in which we find ourselves must be so as to allow sentient life. But I have to confess that I do not much like that idea!"

Note that he moves from having particular issue with the strong anthropic principle to just referring to it as the anthropic principle. Thus, when he's protesting strongly against the anthropic principle in a later section, he is most particularly protesting against the strong anthropic principle, and thus against your god. Given the context, it's a little disengenuous to call upon Penrose in support of your case.

I see no strong objection in Penrose's book against multiverses. Even when we limit ourselves to the very specific thing that WLC could be thought of as honestly referring to - the extravagance associated with having such a large, long-lived universe when perhaps we need a much small(er) region of order, no more than one galaxy, with the current laws in place only for as long as required for humans to evolve - we see that Penrose is arguing that for the purpose indicated (creating us, apparently) there would have been 10^10^123 more options that were significantly less extravagant. This is a strong argument against god, not a strong argument against multiverses. If anything, it implies that if there are multiverses (and thus more likelihood of the initial conditions from which intelligent life might spring) then the argument against god only increases.

measureoffaith (writing as Travis R): You assume too much. I don't "want" Penrose's argument to say anything in particular, nor am I making a case for any particular view. I was simply skeptical of the story put forth in your original version and so wanted to inform you of the correct sources after locating them for myself. Perhaps I should have been more explicit - it is WLC, not me, who refers to pages 762-765 of Penrose'sTRtR in the context of the quote. So the point was that your remarks about WLC presumably (and amusingly) referring to pg 784 is a strawman and is probably best exorcised from the post. As far as I can tell, WLC accurately characterizes the cited argument from Penrose, though he simultaneously fails to acknowledge the accompanying implications for theism that you outlined.

You are right, Travis, I assumed too much and misspoke (or miswrote).  I perhaps should have written " I don't think that pages 762-765 say what WLC wants them to say" or " I don't think that pages 762-765 say what John Piippo wants them to say" or " I don't think that pages 762-765 say what the theist might want them to say".  Probably, however, I should have just stuck with the facts and avoided speculation as to what other people want.

My point was that John Piippo was presenting arguments against the multiverse and had quoted WLC who made reference to Penrose.  And in the Penrose book, the word multiverse is only used once, on page 784, after which he uses the term "omnium".

It is true that WLC, as you linked, was referring to a different section of Penrose's book.  The questions then are whether WLC was "accurately characterising" Penrose's argument - and whether John Piippo was accurately reporting WLC's case.  WLC seems to have used Penrose repeatedly, in his book On Guard, on the page you linked and also at his Defenders podcast.  Here's what WLC had to say in the last of these:

Moreover, thirdly, the Many Worlds Hypothesis faces what may be a truly devastating objection. Do you remember when we talked about the thermodynamic properties of the universe, we discussed Boltzmann’s Many Worlds Hypothesis? You will remember that the Austrian physicist Ludwig Boltzmann tried to explain away the current disequilibrium of the universe by a kind of Many Worlds Hypothesis. He said that the universe as a whole really is in a state of equilibrium but there are just little pockets of disequilibrium throughout the universe, and these are different worlds. He called them “worlds” and we are one of these little pockets. We are one of these worlds. You will recall what sank Boltzmann’s hypothesis was that if our world is just a random member of a World Ensemble like this, then it’s vastly more probable that we should be observing a much smaller region of order than the vast universe that we do. In order for us to exist, all you would need would be a small fluctuation from equilibrium, say, enough to produce our solar system and not an entire universe which exists in such a state. It turns out that a parallel problem faces the Many Worlds Hypothesis as an explanation of cosmic fine-tuning.

The Oxford University physicist Roger Penrose has pressed this objection with great force. Penrose points out that the odds of our universe’s initial low entropy condition existing by chance alone are somewhere on the order of one chance out of 10^10(123). A truly incomprehensible number. By contrast the odds of our solar system’s forming by just a random collision of particles, Penrose calculates to be about one chance out of 10¹⁰⁽⁶⁰⁾. A number which is so tiny in comparison to 10^10(123) that Penrose calls this number “utter chicken feed” in comparison with 10^10(123). What that implies is that it is far more likely, incomprehensibly more likely, that we should be observing an orderly universe no larger than our solar system, since a world like that would be unfathomably more probable than a finely tuned universe like ours.

To me, this is not an "accurate characterisation" of what Penrose had to say.  Craig was very clearly implying that Penrose was pressing an objection to the "Many Worlds Hypothesis as an explanation of cosmic fine-tuning".  It's very difficult to interpret what was written here differently. 

Now, Penrose did write:

Much more problematic are versions of the strong anthropic principle, according to which we try to extend the anthropic argument to determine actual constants of nature (such as the ratio of the mass of the electron to that of the proton, or the value of the fine structure constant §26.9, §31.1). Some people might regard the strong anthropic principle as leading us to a belief in a ‘Divine Purpose’, whereby the Creator of the universe made sure that the fundamental physical constants were pre-ordained so as to have specific values that enable sentient life to be possible. On the other hand we may think of the strong principle as being an extension of the weak one where we broaden our questions of ‘where’ and ‘when’, so that they apply not just to a single spacetime, but to the whole ensemble of possible spacetimes (Fig. 28.13b).27 Different members of the ensemble might be expected to possess different values for the basic physical constants. The where/when question now also involves a choice of universe within the ensemble, so again we must find ourselves in a universe which permits sentience to come about.

Penrose is not necessarily talking about a multiverse here, but of an ensemble of "alternative universes", which involves a range of possible universes - not necessarily a range of instantiated universes.  The difference here is subtle.

Put roughly, we arrive at the idea of a multiverse via three possible paths, none of which involve thinking about a god: there is something like string theory in which each universe is a different solution to the equations, none of which has a higher likelihood than any other; there is the patchwork greater universe, in which for one reason or another, the laws of physics and the fundamental constants vary from region to region (eternal inflationary theory fits in here); and, some sort of cyclical or branching multiverse, like Penrose's CCC or a mother-daughter relationship between universes mediated by black holes, in which the constants are randomised in each cycle or branch.

The ensemble of worlds idea is a little different, especially as it pertains to the strong anthropic principle.  The basic idea is that not only is it a truism that we live in a universe in which life of our sort is possible, but also that sort of universe must also be possible - our sort of universe is a necessary member of any set of possible universes, by virtue of the fact that at least one example of our sort of universe exists.  If you come up with a theory that expressly prohibits a universe of the sort we live in, then your theory is wrong.

Just in case it is not entirely clear, the difference between the multiverse and the world ensemble is the direction from which the idea is approached.  As I wrote in Chance or Design, consideration of fine-tuning resolves down to chance or design.  If you find design to be unpalatable, then you are left with the question of how it could be that a universe so (apparently) unlikely as ours should exist.  A potential solution hangs on the notion that our universe, however unlikely, is still possible (and necessarily so, since it is existent).  This is the point at which you might posit a world ensemble, an array of possible universes, all slightly different and numerous enough to drive the posterior likelihood of our sort of universe towards unity … Pr(our sort of universe|world ensemble) -> 1.

What you can't do, legitimately, is suggest that there is a world ensemble purely on the basis of finding design unpalatable.  What you can do, legitimately, is look around and see whether there is any good reason for thinking a world ensemble exists.  It is at this point that you might meet up with multiverse theories coming in from another direction.  Some theists might not believe that multiverse theories arose independently of apologetics, but there are some who are becoming aware that this is in fact the case.

Another approach is Bayesian in nature (the equation above should have given this away).  We are considering a posterior, P(U|WE) which is given by the prior P(U) multiplied by the likelihood P(WE|U) divided by the marginal likelihood P(WE).  If we were to erase all knowledge of there being any universe in existence, what is the (marginal) likelihood of a world ensemble?  I'd suggest that this would approach zero, since the absence of any universe doesn't move us anywhere close to thinking there should be many of them (that are possible).  Therefore, we have a very low number, according to fine-tuners, for P(U) divided by a very low number.  This is rather arbitrary, but we could say that it's close to zero - especially if we were to stipulate that this world ensemble should be very highly populated given that the more highly populated it is, the lower P(WE) would be.

So, P(U)/P(WE) ≈ 1 and therefore P(U|WE) ≈ P(WE|U).  We need to consider how likely a world ensemble is, given the existence of our universe.  We could consider this in terms of how likely it would be that there is no world ensemble, given the existence of our universe - in other words, how likely would it be that, if there were only one universe, this would be the universe that came into existence?  If you say "very unlikely", then you are saying that a world ensemble, given the existence of our universe, is "very likely".  Once we've accepted that a world ensemble is highly likely, we need only to work out how populous this world ensemble would be.  With nothing else to guide us, we find ourselves being driven towards an infinite number of universes - because there is one population size for the world ensemble to the left of three and an infinite number of sizes to the right, so it's more likely to be a population size to the right of three.  Keep going (forever) and you'd eventually arrive at the conclusion that infinity is the most likely size.

I'm aware that this argument is a little dodgy, but fortunately, we don't need to rely on Bayesian skulduggery nowadays because we have pretty clear indications that the multiverse is an actual thing.

Anyway, it is very clear that, in pages 762-765, Penrose was forcefully dealing with a theistic version of the strong anthropic principle because he kept mentioning a Creator.  WLC cannot be thought of as "accurately characterising" Penrose's position when he fails to mention that.

Chance or Design?

In Barnes' Objections to Fine-Tuning, I concluded that there are only two fundamental responses to claims fine-tuning, that fine-tuning (and/or the appearance of fine-tuning) is due to chance or that fine-tuning (and/or the appearance of fine-tuning) is due to design, since the other options inevitably collapse down to chance or design.

We should perhaps revisit Barnes' "11 objections" in light of this:

Chance: It’s just a coincidence

Chance (overlaid by an appeal to ignorance): We’ve only observed one universe, and it’s got life. So as far as we know, the probability that a universe will support life is one out of one!

Chance/Design: However the universe was configured, evolution would have eventually found a way

Chance/Design (with another appeal to ignorance): There could be other forms of life

Chance/Design: It’s impossible for life to observe a universe not fine-tuned for life

Chance/Design: Maybe there are deeper laws; the universe must be this way, even though it looks like it could be other ways

Chance: Maybe there are bajillions of universes, and we happen to be in one of the few that supports life

Design: Maybe a physics student in another universe created our universe in an attempt to design a universe that would evolve intelligent life

Chance: This universe with intelligent life is just as unlikely as any other universe, so what’s the big deal?

Chance: The universe doesn’t look like it was designed for life, but rather for empty space or maybe black holes

Design: Fine-tuning shows there must be an intelligent designer beyond physical reality that tuned the universe so it would produce intelligent life

I have left a few of them as undetermined, Chance/Design because, at the end of the day, these "objections" don't really distinguish between the two fundamental options.  For example, while "(no matter how) the universe was configured, evolution would have eventually found a way" implies an end goal (intelligent life) that evolution is "trying" to achieve, there's nothing inherent to the argument that prefers (cosmic) evolution being designed to find intelligent life over (cosmic) evolution simply stumbling upon it.  The latter sort of relies on our knowledge that intelligent life is - at the very least - possible in one possible sort of universe, even if it may be improbable and the implication is that, given enough time and/or space, (cosmic) evolution would therefore eventually lead to intelligent life.

The main problem, the problem that theists want us all to come unstuck over, is that the fine-tuning of our universe for intelligent life does appear to be highly improbable.  We are supposed to throw up our hands and say "It's so unlikely that this should have happened by chance, so it must have happened by design.  Therefore, god."

It's for this reason that the multiverse is disliked by some theists, the multiverse short-circuits the theistic fine-tuning argument, because if there are an infinite (or sufficiently large) number of universes, with random tunings, then it becomes a lot more likely that some of them will be tuned sufficiently well for intelligent life.  If there are universes without end, a potential infinity of them, and it is possible that a universe may be tuned for intelligent life (which we know to be so), then it becomes statistically certain that there will be universes in which intelligent life arises - so such a universe existing becomes unsurprising and its existence cannot be counted as evidence for design.

Note that a universe with intelligent life is not evidence against design in and of itself but, given a claim with respect to a particular type of designer, a particular type of universe can be evidence against that designer (hence the problem of evil and the existence of vagueists, theists who strip away anything and everything associated with their god that might permit it to be falsified).

Barnes' list does have a multiverse related "objection" to fine-tuning: "Maybe there are bajillions of universes, and we happen to be in one of the few that supports life".  This is a somewhat flippant way to describe the multiverse, but they seem to be Luke Muehlhauser's words, not Luke Barnes'.  In the Pale Blue Dot podcast that Barnes appeared on, he confirms that we don't necessarily need an infinite number of universes, merely "enough" to make the supporting of life, somewhere - in one of those universes, likely.

This is part wriggle and part lure.  It seems reasonable to answer the argument that this universe is highly unlikely with one that, while not certain, nevertheless is likely.  However, the theists have a philosophical argument to the effect that their god is not only likely, but necessary.  In their minds, it doesn't matter if our universe is likely on a naturalistic assumption, given the multiverse - because they have the universe being the necessary product of a necessary being.  (It doesn't seem to matter to them that their necessity arguments have holes in them large enough to fit a few multiverses - they still have an argument.)  The lure involves encouraging those thinking about multiverses to satisfy themselves with a less than infinite number of universes (even a less than ridiculously huge, but not infinite, number of universes).  It's more of a rhetorical trick than anything else since the equations will tell us how many universes fall out of a multiverse theory, not any desire to explain fine-tuning.

Rather strangely, when discussing the multiverse with Muehlhauser, Barnes doesn't start with any of the scientific theoretical models that lead to a multiverse, like Guth's eternally inflationary multiverse, or string theory.  No, he starts with a couple of philosophical multiverse - although he does express bafflement at them.  Perhaps, we could think he's just dispensing with the nonsense first.  But no.

Directly after mentioning (and mischaracterising) eternal inflation, he leaps into typicality and Boltzmann brains.  Now I know that some well-educated, apparently sane and respected people do apparently take Boltzmann brains seriously, but I don't.  Briefly, the idea is that random fluctuations in thermal equilibriums, given enough time and space, will sometimes create a "brain", which I interpret to be little more than a nexus of something or other that is (or becomes) conscious, but is not necessarily encased in walnut like globs of flesh.  These could fluctuate into existence with a complete history in place and, albeit briefly, it would be impossible to distinguish between the existential experience of these Boltzmann brains, and that of our brains.

Furthermore, the argument goes, these fluctuations would be far more common (due to entropy considerations) than instances in which brains like ours evolve out of some primordial soup over a period of three to four billion years.  So, if this were true, the fact (if it indeed is a fact) that we humans have the nature that we have rather than being Boltzmann brains would be very unlikely.  We'd be very untypical of intelligent beings in general, since most of them would be fluctuations that dissipate soon after coming into existence.

I think this is a nonsense argument for the basically the same reason that, although it is theoretically possible in quantum physics for someone to spontaneously teleport from one spot to another, spontaneous quantum teleportation of humans will never happen.  The fluctuation required for an intelligence (even one as humble as my own) to come into existence and have pre-loaded experience is extremely specific - it's very highly ordered, which means that it's very low entropy (it's also very "surprising" but more of that in a later post).  I would consider the fluctuation of this intelligence into existence, pre-packaged with experience and awareness, without the slow grind of evolution behind it to be sufficiently astonishing as to be miraculous.

What I observe, as inherent to the Boltzmann brain argument, is an effect that I'd like to term "inconsistent poverty of imagination".  The theist is willing, when confronted with the idea of a multiverse, to imagine all sorts of nonsense and then place what we know to exist (intelligence based on evolution from very humble beginnings) on a par with the nonsense that they just thought up (intelligence based on thermodynamic fluctuations in some high entropy region of a universe or multiverse), but when asked to imagine alternatives to their god, all that imagination suddenly dries up and they can't think of a thing.

There are also rhetorical games played with infinities.  If there are an infinite number of universes, then anything that can happen will happen, and if something can (and does) happen, it will happen an infinite number of times.  This means that if Boltzmann brains are possible and they can fluctuate into existence, then they will do so an infinite number of times (but not necessarily everywhere, all the time).  Similarly, if intelligence as a consequence of cosmic and biological evolution is possible, then it will happen and it will happen an infinite number of times.  The argument is that Boltzmann brains would occur in high entropy universes (which may be thought of as being common and plentiful, and thus unsurprising) while the evolutions (cosmic and biological) that led to us could only happen in low entropy universes (which may be thought of as being rare and unlikely, and thus surprising).  We then arrive back at a sort of geocentricity-like situation, while our planet is not the centre of the universe, our universe is of a very special type rather than being typical.  From this it is argued that Boltzmann brains (as temporary denizens of the far more common high entropy universes) are more typical than we are, so we should be surprised at not being a Boltzmann brain in a different type of universe.

I disagree.

We have at least one more thing to consider, our persistence.  If we considered only one aspect of ourselves in isolation, that we are conscious and aware, then sure we might be surprised that we are not a Boltzmann brain.  But we are also persistent, we don't dissipate.  And Boltzmann brains will dissipate because, by nature, they are fluctuations in high entropy, thermally flat universes.  They represent a region of low entropy and very argument that leads to them assumes the second law of thermodynamics, that entropy increases.  The Boltzmann brain would necessarily decay, about as quickly as it came into existence, and return to equilibrium.  Absent magic, the Boltzmann brain could not choose to persist, or to replicate itself.

In other words, we are not just a thing (intelligence), we are thing of a particular type (persistent intelligence, noting that a host of other adjectives could be involved).  If I were to say that I am human, and consider only that, then I should be surprised if I was neither Asian nor African (who together make up more than three quarters of the world's population).  But if I were to note that I also have a genetic abnormality (say mutation to the melanocortin-1 receptor on chromosome 16), then I should not be at all surprised if I had pasty white skin, bright red hair, a vile temper and lived in Auchtermuchty (in Fife, Scotland not that far from Ladybank, which sounds like a euphemism - also not that far from St Andrews, ancestral home of "sweary rambling with sticks" (also known as golf)).

Being a persistent intelligence, it should come as no surprise that I am not a Boltzmann brain and for that reason, I think this rather stupid objection to multiverses fails.  (It also fails because, if Boltzmann brains are a problem, they are also a problem for monoverses.)

So, are there any meaningful objections to the multiverse other than Boltzmann brains?  Well, there are three objections from Robin Collins WLC, as summarised here by John Piippo:

For in order to be scientifically credible, some plausible mechanism must be suggested for generating the many worlds. But if the many worlds hypothesis is to be successful in attributing fine-tuning to chance alone, then the mechanism that generates the many worlds had better not be fine-tuned itself. For if it is, then the problem arises all over again: How do you explain the fine-tuning of the multiverse?

(The BGV theorem) requires that even a multiverse of bubble universes must have a beginning. In that case the mechanism that generates the bubble universes has been chugging away for only a finite amount of time. So by now, there may well be only a finite number of bubbles in the world ensemble, which may not be enough to guarantee the appearance of a finely tuned universe by chance alone. There's no evidence that the sort of world ensemble required by the many worlds hypothesis actually exists.

If our world is just a random member of a world ensemble, then it's vastly more probable that we should be observing a much smaller region of order. It turns out that a parallel problem faces the many worlds hypothesis as an explanation of fine-tuning. [Oxford physicist] Roger Penrose has pressed this objection forcefully.

The first objection, re fine-tuning of the multiverse, is merely a caution that a theoretical multiverse, presented as an objection to god as designer, cannot be fine-tuned.  Okay, thanks for that.  It's not really an objection to the multiverse per se and there's no indication that I am aware of that any of the theoretical multiverse necessitate fine-tuning.

The key element in the second objection is that there is no evidence for a multiverse, but thing is that there is evidence, certainly evidence for a multiverse generating process (watch George Efstathiou's comments, indicating that Planck data constitutes evidence in support of eternal inflation).  Even if there were no scientific evidence at all in support of a multiverse, this would not mean that the multiverse would be less supported than the god did it theory.  And with the multiverse theory, there are things that theoreticians can look out for because the theory is testable.

The third argument is actually associated with the Boltzmann brain argument (order and entropy are inextricably linked concepts).  Again, the argument is based on selected aspects of our existence and when we consider the totality of our existence, then we should not be surprised that we live in the sort of universe that we live in since it's clearly a possible universe and it's just the sort of universe that permits intelligence like ours to develop.  This objection seems to miss the point rather spectacularly.

A quite amusing aspect to Collins'  WLC's third objection is the reference to Roger Penrose (note that I changed the link to something more relevant than the Amazon page for The Road to Reality: A Complete Guide to the Laws of the Universe).  In the book that Piippo links to, Penrose mentions the word multiverse on only one page.  According to the index this was on page 783, but I could not find it on that page.  This review indicates that it might be on page 784 (which is not part of the Google Books review).  And the mention of multiverse is only to say that Penrose prefers the word "omnium" to "multiverse", a strange position to take if you are arguing forcefully against the fundamental concept (confirmed).  Additionally, Penrose's conformal cyclical cosmology is a temporal form of a multiverse, with our universe being reset and recycled ad infinitum (and Penrose claimed that circular patterns in the CMB data from WMAP were suggestive of earlier universe, some might claim that they are suggestive of young bubble universes bumping into each other or side-effects of inflation, while others might suggest that some people are just seeing what they want to see).

<edit> The blogger measureoffaith (see comments below) suggests that Penrose forcefully makes the case that multiverses face the same problem with fine-tuning that our universe does in sub-chapter 28.7 The Big Bang’s special nature: an anthropic key?  It would appear, however, that this section must be read very optimistically by a theist, especially when Penrose's conclusion mirrors mine - that it comes down to either design or chance, that god did it or there's some mathematical/scientific reason why the universe is the way it is, and that it's worthwhile investigating the latter.

Robin Collins also presents some objections to the multiverse, in this document.  His objections relate to the nature of a "many-universes generator".  I wrote about these objections in "The Four Mechanisms of the Ignopalypse", but I am holding off on publishing it (or was at time of writing, if you are reading this later).  It should be up later in the year.  For the moment, suffice it to say that I don't find Collins' objections to be meaningful or substantive. <end edit>

If there are any meaningful and substantive objections to multiverse theory, I would be keen to hear of them but so far there seems to be little more than a chorus of appeals to incredulity.

In conclusion, the fine-tuning of the universe can really only be explained by chance or design, since all other objections resolve down to one or the other.  I'm not overly fussed by the nature of the designer, since I don't consider a designer to be the correct answer anyway (for other reasons, quite separate from the theoretical impossibility of design).  That said, given the nature of the design argument, nothing we ever come across will be sufficient to eliminate design as a theoretical possibility - since a designer could have created the universe with the intention to make it totally indistinguishable from a universe that came into existence by chance.  All that we have is a counter to the argument that a designer must exist because there is no other alternative.  We do have an alternative, in the form of a multiverse.

Something that is worth considering, particularly if you are a pro-fine-tuning, anti-multiverse theist, is that science is inching closer and closer to proving that the multiverse is reality, rather than just hypothesis.  If you have nailed your colours to the notion that fine-tuning is a knock-down argument for god because you think that the multiverse might not exist, it is high time that you reconsider your position. (Much as Jeff Zweerink has - listen to the second impressive moment.)

The Eternally Inflated (Multiverse and WLC)

Skydive Phil has released a new video in his "Before the Big Bang" series, Eternal Inflation and the Multiverse.  In this video he interviews Alan Guth of BGV fame (there are also interviews with Anthony Aguirre, Yasunori Nomura and George Efstathiou).

The reason that Guth is of much interest to me is that he was one of the three who collaborated on the Borde-Guth-Vilenkin theorem (BGV) which WLC invariably refers to in support of his Argument from First Cause.

In order to recap, I will quote Alexander Vilenkin (who is quoting WLC, before taking issue with WLC's first premise):

The cosmological argument for the existence of God consists of two parts. The first is straightforward:

·       everything that begins to exist has a cause;

·       the universe began to exist;

·       therefore, the universe has a cause.

The second part affirms that the cause must be God.

The BGV is used, by William Lane Craig, as evidence in support of the second premise - the idea that the universe began to exist.  The problem, however, is that WLC explicitly assumes that the universe (all that for which we have evidence of existence) was brought into being, from nothing, by a spaceless, timeless, immensely powerful mind which he identifies as his god.

However, the beginning of our universe does not preclude the existence of something else prior to our universe, something that is not a mind, but instead is a multiverse - an eternal inflation that spawns universes such as ours.  In doing so, Guth not only describes a mechanism by which our universe could begin without an intention directed cause, but also explains how our universe could be both contingent and as fine-tuned as it appears to be.  (It's complicated, so I suggest that you look at the video to get the gist of it.  I wrote a comment to the video that contains a link to Alan Guth's written explanation as to how inflation works which might be of assistance.)

Now, the power of WLC's argument, such as it is, is rooted in ignorance.  We can't think of any other mechanism by which the universe might have begun, therefore it must be caused (which Vilenkin disputes) and therefore it must have a causal mechanism and the only possible causal mechanism we can think of is a god.

What is on show in the video is that the ignorance on which the argument rests is illusory.  As a species at least, even if not as individuals, we can think of other mechanism by which our universe may have begun (Vilenkin's uncaused universe) and, in any case, we can think of other possible causal mechanisms (pocket universes from the decay of eternal scalar field inflation).

---

There are, of course, potential objections with the eternal inflation multiverse.  Most obviously is the fact that it is, in a sense, not really a multiverse at all.  The process results in one vast but nevertheless connected region of space-time, with the overwhelming majority of it in a state of inflation.  This is not a major issue, however, since this would just mean that we are talking about a Tegmarkian Level II Multiverse in which there is an effectively infinite universe populated with an infinite array of pocket universes so the argument that it's "not really a multiverse" is merely betraying a misunderstanding about what constitutes a multiverse.

Another possible route that an apologist might take is to suggest that while the infinite array of pocket universes explains the apparent fine-tuning of our universe, some fine-tuning of the multiverse would still be required to permit our type of universe to fall within the range of possible universes.  This would be justified if the range of possible values for physical constants in a pocket universe are limited to small variations from the values of physical constants in the precursor universe (from which inflation commenced).

This however ignores a feature of quantum mechanics on which much of this rests.  If there is any set of values of physical constants that is possible then this corresponds to a non-zero probability of that set being instantiated, no matter what the original set of values of physical constants looked like in the precursor universe.  And with an infinite number of pocket universes being spawned by that precursor universe, the likelihood of a universe with a set of values of physical constants like ours is unity - meaning that it is a necessary consequence.  (Note that this strikes at the heart of WLC's trilemma: physical necessity, chance or design.)

And even if it were true that the set of values of physical constants that characterise our universe were not reachable from a possible set in a possible precursor universe, then all this means is that our universe did not derive from one of those types of precursor universe.  We need to step back and think about how the initial precursor universe would have arisen, which means that we turn to Vilenkin:

Quantum tunneling can create a universe 'from nothing' [because] in quantum mechanics things that are classically forbidden by energy barriers can happen by tunneling through energy barriers. So a universe of zero size — that is, no universe at all — can originate spontaneously by 'tunneling through' an energy barrier and then expanding by inflation.

If that can happen naturally once, in other words if it is at all possible, then we have no reason to think that such quantum tunnelling is limited to happening only once (as might be the case with a supernatural origin of the universe).  Therefore, quantum tunnelling like this could potentially happen an infinite number of times.  As a consequence, we could have not only an infinite number of pocket universes in our multiverse, being spawned by inflation that was initiated in the original precursor universe but also an infinite number of original precursor universes being created by quantum tunnelling processes.  Each of these precursor universes would assume a set of values of physical constants that falls within the possible range, including sets that allow the set in our universe to be instantiated.

If this is the case, then the apologist could still claim that her god is the author of quantum mechanics and this hugely wasteful process, generating an infinite number of precursor universes each of which generates an infinite number of pocket universes, is all part of the plan to create humanity.

She then runs, however, into the bunny problem.

WLC argues that if there is a possible world in which rabbits suffer unremittingly, then it follows that there is no maximally great being - that there is no god.  But if god is a quantum engineer and has created this infinity of infinities, then a world in which cute fluffy creatures suffer unremittingly is not only possible, it must actually exist.

We can easily imagine scenarios in which rabbit analogues suffer without end - even on this planet in the future: a plague wipes out all other creatures including pests as well as predators, a couple of small genetic changes lead to the immunity of rabbits to all fatal viruses and bacterial infections and another to prevent the deterioration of telomeres beyond a certain point so that death due to old age is prevented but the ageing and deterioration of bones, ligaments and so on still goes on.  Imagine the life of a rabbit (or any sufficiently cute animal) under these conditions, barring accident or starvation, it will live forever, crippled and in pain and constantly hungry because rabbit numbers will rise and fall with the availability of food - there will never be enough to support an increasing population of creatures that pretty much do not die unless they starve to death.

So, I accept that this might be unlikely.  But impossible?  No, I don't think so.  The question then is how many variations of this universe do we need for the likelihood of this scenario to be quite high?  The actual number doesn't really matter because, in a universe created by a god as quantum engineer, we would have an infinite number of them, making the likelihood is unity.  Following WLC's own argumentation, we find that a maximally great being does not and cannot exist.

The apologist must therefore back away from the multiverse, away from the evidence, and rely ever more heavily on argumentation from (false) ignorance.