Feb 26 2021

Multiverse Again

I interviewed philosopher Philip Goff for the SGU (the show will air tomorrow with an edited version, and the full 1 hour discussion will be available for SGU members) about the multiverse and the fine-tuning problem. I was hoping by the end of the discussion one of us would have been convinced the other was correct (and I don’t care which, I just want to be confident that I understand this problem). In the end, we did not resolve our difference, but we did really clarify the issues well. This is a good exercise in logic, and also demonstrates how difficult it can be to deal with some statistical issues. I still admit I could be wrong here, I just don’t understand why. But here is the follow up.

First – here is Philip writing about our conversation and why he thinks he is still correct. In this post I will summarize where I think the discussion is and why I am still not convinced.

Here are the points of common ground (approved by Philip):

1 – The probability of our universe existing is unaffected by the presence or absence of other universes. To think otherwise is the inverse gambler’s fallacy.

2 – The probability that some universe capable of evolving complex life exists (assuming the premises of the fine-tuning problem) is higher if there are multiple universes than if there is only one universe.

3 – The key to the question of inferring a multiverse from the observation of our universe (again, assuming the fine-tuning problem and that there is no other solution) is therefore asking the right question – do we consider the probability of our universe existing or of some universe existing?

4 – There is a selection effect in that only a universe capable of evolving sentience would be observed (assuming no external observer).

Philip adds another concept for consideration – that of improbable improbability. Essentially, in a random distribution all outcomes are equally unlikely, but some may have a-priori meaning. For example, that someone wins the lottery is not unlikely, so if John Smith wins the lottery he is specifically unlikely, but not special and no less likely than anyone else. However, if the wife of the person drawing the numbers wins the lottery, sure she is just as unlikely as John Smith, but she is not the same. We don’t need a special explanation for why John Smith won, but we certainly would want one if the wife of the lottery number picker won.

Similarly, any configuration of natural laws (let’s stick with the – 10^229 possibilities) is just as unlikely as any other configuration, but the tiny minority of outcomes that allow for life are special. Philip explains it this way:

What’s the difference between the two cases? The fact that Steve Novella won the lottery is improbable, but it’s not improbable that it happened by chance. Why is that? Because there’s no (non-ad hoc) non-chance hypothesis that would render it much more probable.

Philip also hangs his hat on another analogy involving IVF, again attempting to account for the selection filter. Let’s say you are the product of IVF and you learn that the doctor was only going to implant your egg into your mother’s womb if he rolled 6 on 100 dice on his first attempt (chance is 1 in 6.5 x10^77). You were born, so obviously he successfully made this roll. Can you infer from this that the doctor did the same thing with other implantations? Philip thinks that intuition strongly favors no, but I think you still can infer this. The example is just rigged to give a false intuition. The chance of someone being implanted is greater with multiple attempts, and only on a successful roll would someone be around to contemplate their own improbability.

But I prefer another example, playing off his Joker-Monkey-Typewriter analogy. Let’s say you pop into existence, never having existed before. You are sitting in a room. In front of you is the god Loki and next to him is a monkey and a typewriter. Loki tells you that you can ask him anything about what is happening in this closed room, but nothing about what is happening outside the room. Through many questions you find out what a monkey is, that he essentially bangs randomly on the typewriter. Further, Loki was only going to magic some being into existence if, in a 10 minute period, the monkey typed out a sentence in English. That sentient being could have been anything, Loki is mercurial, but based on the sentence (I like that bananas are yellow) he made you.

So, it is clear that your existence is very improbable. Can you infer that your existence is more likely if Loki did this experiment in gagillions of rooms? I think yes – especially if you realize there is nothing special about you, that any creature created would be in the same position, and there would be no one to observe their own non-existence in rooms that failed.

Philip and I agree that what this all comes down to is whether or not we should be considering the probability of our universe existing or of some universe existing. He thinks we should consider the latter, on the principle of improbable by chance, but also because we should be considering all the information we have available to us. We don’t just know that some universe exists, we know that our universe exists, so that is the information that we should be using as our starting point.

My counter was – yes, but we also know that there is a selection filter. If we include that information, then the probability of our universe existing is transformed into the probability that some universe exists. Therefore, if we know that a filter is in place, we can infer a multiverse because that would render a highly improbable event (like, extremely close to zero probability) into a highly probable event. That is the key – would the multiverse render our universe more likely. I maintain it does because of the selection filter, which means “our” universe is effectively “some” universe capable of supporting life.

If your brain is now broken – that is part of the point of all this. Human brains have terrible intuition for statistics. Even far simpler problems, like the Monty Hall problem, are challenging. There are statistical illusions that fool even professionals. I am also very aware that, apparently, statisticians agree with Philip and not me (although it seems this is still a debated issue). But I have searched (I still have a lot of searing to do, but so far) and I find their arguments equally unsatisfying. For example:

“Proponents of a Multiverse correctly state that its existence would increase the probability of life existing in some Universe, but this is only relevant to the probability of life in this Universe if one identifies any Universe with the same properties as ours with our Universe. Such an identification may be suggested by the (weak) Anthropic Principle, but its is by no means implied by it, and one should realize that the inference of a Multiverse from the FTA implicitly hinges on this additional assumption.”

But does it? Isn’t the selection filter enough to equate any universe with this universe? This universe is only special because it is the one that happens to exist, like the winner of a lottery. But that is post-priori special, not a-priori special. Any universe capable of evolving life would observe itself to be highly unlikely, and therefore because any universe with such properties would observe itself, any such universe is probabilistically equivalent to some universe. In any case – if I am wrong about this I am still searching for an argument that I can understand to explain why.

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