A couple weeks ago I wrote about the logical implications of the multiverse as a potential solution to the so-called fine-tuning problem. I was responding to a paper discussed by a philosopher  (Goff) claiming that the multiverse hypothesis is not a valid argument but rather based on a logical fallacy, the inverse gambler’s fallacy. I won’t repeat the entire discussion here, just read the original article. I am writing this follow up because the original article garnered a great deal of discussion. I also presented the issue on the SGU, triggering a flood of e-mail responses. Clearly I need to take another bite at this apple.

I do think the discussions have clarified my thinking, although they have not changed my position. I am still willing to change – statistics can be very counterintuitive and can hinge on seemingly unimportant details. The Monty Hall problem is a classic example, which some call a “statistical illusion”. One where I was tripped up previously deals with gambling, this time the regular gambler’s fallacy. A number of sources will claim that casinos win largely because players go bust, and end their betting as a loser, but the house never busts. So there is an “absorption wall” at one end, but not the other. Players can keep playing if they win, long enough to lose again in some cases, but have to stop if they lose too much. While this seems to make sense, it is wrong. The house wins entirely because the odds are in their favor, and the loser absorption wall has no effect on this outcome. This is because players are just as likely to win or lose after they go bust, so going bust does not prevent them from winning more than it prevents them from losing even more.

I do think I have identified where the inverse gambler’s fallacy goes wrong in arguing about the multiverse. I am going to copy the entire argument that Goff is making to be clear I am fairly representing it:

You wake up to find yourself in a room sat opposite the Joker (from Batman) and a monkey called Joey on a typewriter. The Joker tells you that while you were unconscious, he decided to play a little game. He gave Joey one hour to bash on the typewriter, committing to release you if Joey wrote some English or to kill you before you regained consciousness if he didn’t. Fortunately, Joey has typed “I love how yellow bananas are,” and hence you are to be released.

In the above story, you could not possibly have observed Joey typing anything other than English—the Joker would have killed you before you had a chance—just as we could never have observed a non-fine-tuned universe. And yet the inference to many monkeys is still unwarranted. Given how unlikely it is that an ordinary monkey would come up with “I love how yellow bananas are” just by randomly bashing away, you might suspect some kind of trick. What you would not conclude, however, is that there must be many other monkeys typing rubbish. Again, what you need explaining is why Joey is typing English, and the postulation of other monkeys doesn’t explain this. By analogy, what we need explaining is why the only universe we’ve ever observed is fine-tuned, and the postulation of other universes doesn’t account for this.

The problem in this analogy is you. You wake up in front of the Joker and a monkey. This makes the analogy simply confusing, and is just distracting from the more straightforward logic of this situation. This is, as I said before, the lottery fallacy. It is very unlikely that you will win the lottery, but it is very likely that someone will win the lottery. By using you in his analogy, Goff is pre-selecting the winner. Yes – it is very unlikely that you will be alive in the Joker scenario, regardless of whether or not there are other monkeys on other typewriters. But that is not the fine-tuning problem. We don’t need to explain why our universe is compatible with life, just that there can be any universe compatible with life.

There is no perfect analogy for this, and all the analogies put forward to explain the application of the inverse gambler’s fallacy fail on this account. But let me try to give at least better analogies that are cleaner. Let’s say that you are a reporter investigating the lottery – a single lottery with a 1 in 1 billion chance of winning. Those running the lottery announce that John Smith has won. Is it more likely that John Smith is the only person that played the lottery and bought a single ticket, or that millions of people played? The latter, of course. And we don’t need to explain why John Smith won. In fact, if John Smith bought the only ticket, you would want to investigate further for fraud. You would not accept that it’s just a massive coincidence that the one ticket purchased was a winner.

Remember, in the fine-tuning argument the claimed chance of our universe winning the cosmic lottery is 1 in 10^226. We cannot wrap our heads around how unlikely that is. To say that this happened entirely by chance is absurd. If there are as many universes, then that is a possible explanation. Again – we don’t have to explain why our universe exists, only that there can be a universe compatible with life.

Here is another, hopefully helpful, analogy. Let’s say that we encounter a super-advanced alien race. They claim they created the Earth (and for the sake of argument, let’s say their claim scientifically checks out). The features they decided to give the Earth were determined at random. They reveal the process they used to determine these factors, and by their own calculation there was only a one in 1 quadrillion chance that the Earth would be compatible with life. Now – is it more likely that Earth is the one and only planet they created, or that they go around the universe creating lots of planets? Do we need to explain why Earth specifically is compatible with life?

The bottom line is that, given these premises, we can infer that it is more likely (not a certainty) that the aliens have been creating lots of planets, so that there is a good chance that at least one is compatible with life.

A lot of the discussion in the previous thread was about the fine-tuning argument itself. This is not relevant to the logic here, however. In this case we are assuming as premises that – the constants of the universe are determined at random and only a tiny proportion of possible universes are compatible with life. These premises are assumptions, we do not know that they are true. We don’t know how the physical constants are determined, if they can vary, with what probability distribution, and exactly what possibility space of outcomes allows for life. We also don’t have independent evidence for a multiverse, or what other universes are like. Personally I remain agnostic toward all of these possibilities.

The only cosmology I rule out on probability alone is that there is only one universe, and the probability of that universe allowing for life is something like 1 in 10^226 and that we simply bought a single cosmic lottery ticket and got fantastically lucky.