Watching this interview/presentation by Phil Goff on Cameron Bertuzzi’s “Capturing Christianity” channel about the multiverse and the fine tuning argument.

Phil does note at the start of this that he is presenting this for the first time, in preparation to include it in the book. So this critique is offered constructively, in the hopes that whatever winds up in his book is of much higher quality.

Dr. Goff is a an Associate Professor at Durham University whose research focuses on philosophy of mind and consciousness. He is probably familiar to most as a high profile promoter of Panpsychism. Here he is discussing some rather abstract physics and cosmology with an irritatingly photogenic Christian apologist.

The focus of his presentation was on a single Intuition Pump which is meant as an analogy to the multiverse hypothesis as it applies to the fine tuning argument.

The Intuition Pump – Jane’s Origin Story

We are presented with a woman, Jane, who learns that her mother’s pregnancy was the result of IVF which was done by a Doctor. So far so good.

At some point the Doctor confesses something unusual. At the time of her mother’s treatment, he was mentally unstable. He decided that before carrying out the procedure, he would roll two dice. If he rolled two sixes (a probability of one in thirty six), then he would carry out the procedure. Otherwise, he would do something to spoil it effectively preventing Jane’s mother from becoming pregnant and therefore preventing Jane from existing.

We are further told he did this only once, at the depths of his breakdown, and swore to never do it again. Guaranteeing that we can’t do any statistical analysis from the other times it happens.

The question, which comes somewhat out of left field, is whether Jane would have evidence for arguing that there must have been many such Doctors also at the lab rolling dice, so that the law of large numbers would increase the probability that someone rolled double sixes would approach 1 and so Jane could be born.

I believe I have faithfully represented the scenario. So you may want to take a moment to let the feeling of wtf set in.

Understanding it requires a bit of a physics update that Dr. Goff brushed past.

The Original Problem

The physics of every day life are very well understood and our understanding is compiled into something called “The Standard Model”. This model is mathematical and calculations require the inclusion of certain numbers (say a measure of the gravitational force between two 1kg blocks of lead) that are not known a priori but are derived from experiments. Occasionally one of those parameters is found to not be fundamental, but derivable from simpler principles of the theory. But many of those numbers are, as far as physicists are concerned, brute facts about the universe. And from their bare appearance in the the theory, it’s not possible to state that they must be this way, and prompts the curious to wonder whether they can be changed and what the world would look like if they were different.

But staying with the physics, it turns out that you only get the kind of universe we are familiar and comfortable with if those numbers stay more or less exactly as they are. Different numbers means not just a different universe, but a completely unrecognizable universe. No planets, no stars, no atoms, no people. Then becomes a philosophical/theological question as to why we have these numbers not others.

The Unexpected Bit

It turned out that physicists who had no interest in philosophical or theological concerns stumbled on some startling conclusions. In the largest theories that look at the history of the universe as a whole, they include something called Inflation which accounts well for several improbable features of the observed universe. Unfortunately, the theory is a bit ambiguous as to how you “turn inflation off” and it’s possible this process just produces universe after universe, all of which exist as causally disconnected bubbles.

In theories of the very small, it becomes possible to take the same theory but rearrange the pieces to get different observable universes.

So at present, our understanding of nature contains the not yet disproven (and possibly undisprovable) possibility that there are just whole bunches of other universes.

This, by the way is not as unsettling as it sounds. The authors of the bible imagined a single planet beneath a firmament of little white dots painted on the ceiling. We then understood that we were in a solar system of many planets orbiting the sun. We then discovered that we were one of hundreds of billions of solar systems orbiting the centre of the galaxy. We then discovered we were one galaxy among hundreds of billions. We then discovered that a consequence of inflation that our patch of the universe should be a few billion billion times greater than that, even though we are causally disconnected by the finite speed of light. So to discover we are one bubble universe among many wouldn’t go against the grain of history at all.

The Objection

There is a quasi-moral assumption in modern theology that the universe that we observe is the universe that ought to be. We were supposed to be here. It’s part of a plan. We imagine ourselves in a movie where the screenwriter is contractually obligated to produce a happy ending. A universe that fails to produce us is a failed universe and can’t exist. That grounds a very deep seated intuition. If the universe looks the way it was when it could have looked another way, someone must have wanted it that way. And once you have that intuition, pretty much the only being to play the part of someone is god.

The objection stated mathematically is that if we just let the constants of the universe float randomly. The odds against our particular universe are staggering (as in all of the matter in the universe could not provide enough paper to write all the zeroes in the number we’re talking about.) As we will see, the objection basically boils down to a feeling: That’s so improbable, clearly the existence of a god is more likely than that!

An Aside

It’s not relevant to this discussion, but it’s worth noting that physicists don’t like the multiverse hypothesis. Scientists don’t like armchair discussions. They want to design experiments to test who’s right and who’s wrong. The idea of universes that are causally disconnected from ours, and therefore beyond the reach of experiments really rubs them the wrong way. They find them aesthetically displeasing probably more than a theist does. So physicists were dragged into this situation more or less against their will. They have created at least three different sources for multiverses:

1. Eternal Inflation
2. The String Theory Landscape
3. The Many Worlds Interpretation of Quantum Mechanics

As much as anyone – theist or not – wants to view the multiverse as preposterous, whether or not our universe is actually preposterous is not up to our sense of aesthetics.

Let’s Keep Pumping

Returning to Jane and her rather unusual circumstance, let’s see what intuitions can be pumped. Cameron pressed Dr. Goff on the reliability of the Doctor’s testimony. We are told to assume this is given.

Unfortunately, if the Doctor’s testimony is presumed reliable, this is not a probability question. It is an elementary logic problem. Modus Tollens to be precise:

1. If (not double sixes), not Jane
2. Jane
3. Therefore double sixes.

Dr. Goff attempts to frame this is a question for Bayes Theorem. However he never makes his calculation explicit. So let’s do that. Let J be the event Jane exists, and D be the event the Doctor is telling the truth. Then a direct statement of Bayes’ Theorem would be:

We are trying to ascertain whether the Doctor is telling the truth given that we know Jane exists. Examining the formula with order of operations in mind, it splits into three sections. One on top, two added together on the bottom. Unfortunately, we are explicitly granted the reliability of the Doctor in the question, so the bottom right segment is zero. So the top and the bottom are the same number. A number divided by itself is 1, and we reproduce the simple result of Modus Tollens with probability 100%.

If the doctor is reliable, this an entirely useless intuition pump because the probability of rolling two sixes doesn’t factor into it. What you would really hope to do is open the doors to an unreliable doctor so that we are forced to consider alternate hypotheses.

The Barnes & Noble Fallacy

Dr. Goff commits what we can call the Barnes & Noble Fallacy. Some experts in a technical field do complicated research and publish their findings in inaccessible obscure scientific journals. Then a scientist, or sufficiently enterprising science journalist, attempts to distill the research into an accessible form and produces a popular book on the subject that winds up on the shelves of a Barnes & Noble. A non expert in that field reads the accessible distilled version with its summaries, helpful analogies and friendly every day language. (We all learned in 2012 that the Higgs field was like driving a car in a puddle of molasses.) That non-expert (in our case a philosopher or apologist) now takes the friendly every day language and transports it into the little syllogisms and apply some good old fashioned common sense, and assume the conclusions of those syllogisms are reliable without having to go check with anyone in that field to see whether or not they understood properly.

Dr. Goff uses the Open Barnes & Noble Fallacy where he admits that he doesn’t really understand the math and the physics he’s discussing, but then proceeds to discuss them with full confidence anyway.

So What If…

If the Doctor is unreliable, now this opens the floodgates to all of the alternative possibilities. Without feeling the need to be exhaustive, let’s list a few:

1. Jane was the result of regular sexual intercourse between her parents and the Doctor’s role was irrelevant
2. The Doctor made the whole thing up and there never were any dice
3. The Doctor was telling the truth, but some other person in the lab double checked his work and fixed whatever the problem was so the Doctor’s dice were irrelevant.

If you think of that list, you’re left scratching your head where the hypothesis of a large number of doctors all rolling dice fits into this. The short answer is, it doesn’t. One of the immediate logical consequences of Bayes’ Theorem is that when you hear hoofbeats, think horses, not Zebras. Tackle your hypotheses in descending order of prior probability.

Unfortunately, the Doctor’s story is so implausible on its face that a mere one-in-thirty-six probability of rolling two sixes is actually a huge number. (A quick bit of googling reveals there are thousands of IVC clinics in the world and millions of children born through IVF, so by the time you factor that in, the 1/36 will be a drop in a bucket of improbability.)

The other thing that is obvious is that Dr. Goff simply isn’t comfortable with probability. These are concepts that come out in a first year university class but are nonetheless counterintuitive. How you define the problem radically changes the outcome. Set up a lottery with certain characteristics. What is the probability that I win the lottery? What is the probability that someone wins the lottery? How long would I have to play the lottery before I could expect* to win? Those questions are of varying difficulty and the person creating that assignment has to carefully provide specific information to ensure that it has an answer. (And teachers who don’t do a good job of this know that they will have students lined up around the block begging for extra marks after the fact.)

* “Expect” is a technical term in statistics with precise definition.

Fixing the Analogy

Unfortunately, the intuition pump is useless because the most important number in the calculation (what is the probability do you assign to the doctor’s account being reliable) is inestimable because the circumstances described are so absurd. I tried to come up with two that fare a little better. First I tried to focus just on the improbable event, using only everyday occurrences of probability we might be able to tackle.

Jane finds a lottery ticket and turns it in. She is congratulated and given ten million dollars. Is it reasonable for Jane to infer that many such lottery tickets are sold?

Here, our intuition tells us that the answer is yes. But that’s because we know lotteries work in real life and that ten million dollars is coming from somewhere, namely the large N of people who bought tickets.

Unfortunately, it’s not fair, since our understanding of lotteries is equivalent to granting the existence of the multiverse. So how about this?

Jane’s friend gives her a sealed envelope and is told to take it to a particular address and turn it in to the people who work there. When she arrives, she is congratulated and handed ten million dollars. If we are not allowed to ask about the nature of the building she went to is it reasonable for us to infer that this envelope contained a (wining) lottery ticket?

This captures everything because we are now agnostic as to the existence of the lottery ticket. Instead we are left to investigate the only ambiguous thing in the problem: Who exactly is this friend? (How much do we know both about these laws of quantum physics and this god-person?) We can imagine that Jane and her entire social circle are working class living paycheque to paycheque. Then the probability of this being a lottery ticket is rather high. We can also imagine Jane as being quite wealthy, perhaps having just sold the original Van Gough that belonged to her family at auction.

Unfortunately the philosopher has now been sidelined. We have produced an empirical problem and have to go out into the world, possibly accompanied by an economist or six, to start asking at a given time:

1. How many lotteries are out there and what are their payout probabilities?
2. How many ~$10Million transactions are taking place?

This is the multiverse problem.

Where F is the event that the universe is our particular Finely tuned one, and M is the event that our universe is part of a Multiverse.

Notice the top and the lower left quantities of the fraction are the same. And we are all agreed that they represent a small number. The question is what to do with that lower right quantity. The not-M is meant to encompass all the alternative hypotheses which include both theistic and non-multiverse-non-theistic explanations for the fine tuning. Those might include the simulation hypothesis, cyclic cosmologies or deist gods.

This is the sleight of hand: In order to reach a conclusion about whether or not the multiverse is likely, you have to include in the probability of not-M, your estimation of the likelihood that god exists. That means you have to make explicit how likely you think your particular brand of theism. If you try and reach an answer without explicitly statin the missing probability, this is commonly called The Prosecutor’s Fallacy. It’s generally the assumption (which is generally false) that conditional probabilities commute. That P(F|M) and P(M|F) can be assumed to be roughly the same number, so we don’t have to work out the other probabilities in the question and we don’t have to do the full Bayesian calculation.

Dr. Goff wants to sweep this under the table. He does this with Jane by sloppy wording. We must accept the Doctor’s account as reliable, while considering alternatives. Which doesn’t make any sense, and makes it hard to get a grip on the question when you’re not told what assumptions in the scenario you’re allowed to question.

He also commits another minor Barnes & Noble Fallacy. Cosmologists describe the “Measure Problem“. Essentially, when you’re talking about varying constants of nature, creating new universes, it hasn’t been established that you can meaningfully discuss “probability” across those universes. So you can say that the probability of the constants of nature being what we observe is Small. But we aren’t entirely ready to commit to that being a statement that’s allowed. This is analogous to the statement in the cosmological argument that “The universe began to exist.” If you’re talking about an earliest moment in time, it’s not guaranteed that sentence is intelligible in that context. But it’s just assumed that those words automatically carry their intuitive meaning into this context without issue.

That error can be allowed temporarily. We can assume a fortiori that a multiverse and theism are an exhaustive set of explanations. And we can grant the smallness of P(F|M). In that case, we can also argue a fortiori that P(F|not-M) is 1 so that number disappears from the formula. (Essentially God’s nature demands that he create not just a universe, but this universe.) The question has reduced to the prior probability that Theism is true. If that probability is large relative to P(F|M), then the multiverse doesn’t seem likely. If that number is small relative to P(F|M) then the multiverse becomes likely.

The good news is that’s a discussion that can be had. The bad news is it’s no longer a question about the multiverse. Your prior belief about the existence of God, basically caries directly through the computation. If you’ve lived your life accepting the existence of the Christian God as true, you won’t find anything here to change your mind.

However, if you are skeptical of the arguments and evidence for God’s existence, as a great many are, now you have to have a deep think. We know Quantum Fields exist. We know they have the property that if left alone for long enough they will do counter-intuitive things that were possible, but so improbable, we mentally classified them as “impossible.” You compare the unlikely behaviour of things known to exist, with the predicted behaviour of a being that hasn’t been demonstrated to exist.

Dr. Goff admits her has done this calculation but doesn’t follow through. He has essentially treated Christian Theism as a scientific hypothesis and falsified it. (He says this is because of the problem of evil.) So the explanation in (Not-M) must be something other than the Christian God. If you take the a fortiori example from above, a falsified Christian Theism makes P(not-M) zero and the probability of the multiverse 100%. Not the desired outcome.

What is then required is to investigate all the alternatives beyond the Multiverse and Straightfroward Christian Theism. Unfortunately, he doesn’t at this stage spend any time on the alternatives so that we could tease out the relevant probabilities and actually do the calculation.

The moral of the story seems to be Garbage In, Garbage Out. If you get philosophers and apologists together to try and figure out math and physics problems, they don’t tell you anything you didn’t already know.

Ultimately he made a point that no one would disagree with. Fine tuning is not evidence for the multiverse. The theories of physics that spit out multiverses as possible consequences are the evidence for the multiverse. Ultimately, explaining the fine tuning is not a necessary condition for disproving the existence of God. In the same way that when you have a murder victim, you don’t need to find the actual murderer to show that they probably weren’t stabbed by a unicorn. God was plenty disprovable before we invented String Theory.

So he’s spending a lot of mental energy failing to make a point that he didn’t need to make anyway.