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I think this episode came off as “weird and testy,” as I described it to one friend, but I like weird and testy!  Here is the audio, video, and transcript.  Here is one excerpt:

COWEN: How do you think the many-worlds interpretation of quantum mechanics relates to the view that, just in terms of space, the size of our current universe is infinite, and therefore everything possible is happening in it?

DEUTSCH: It complicates the discussion of probability, but there’s no overlap between that notion of infinity and the Everettian notion of infinity, if we are infinite there, because the differentiation (as I prefer to call what used to be called splitting) — when I perform an experiment which can go one of two ways, the influence of that spreads out. First, I see it. I may write it down; I may write a scientific paper. When I write a paper about it and report the results, that will cause the journal to split or to differentiate into two journals, and so on. This influence cannot spread out faster than the speed of light.

So an Everett universe is really a misnomer because what we see in real life is an Everett bubble within the universe. Everything outside the bubble is as it was; it’s undifferentiated, or, to be exact, it’s exactly as differentiated as it was before. Then, as the bubble spreads out, the universe becomes or the multiverse becomes more differentiated, but the bubble is always finite.

COWEN: How do your views relate to the philosophical modal realism of David Lewis?

DEUTSCH: There are interesting parallels. As a physicist, I’m interested in what the laws of physics tell us is so, rather than in philosophical reasoning about things, unless they impinge on a problem that I have. So yes, I’m interested in, for example, the continuity of the self — whether, if there’s another version of me a very large number of light-years away in an infinite universe, and it’s identical, is that really me? Are there two of me, one of me? I don’t entirely know the answer to that. It’s why I don’t entirely know the answer to whether I would go in a Star Trek transporter.

The modal realism certainly involves a lot of things that I don’t think exist — at least, not physically. I’m open to the idea that nonphysical things do exist: like the natural numbers, I think, exist. There’s a difference between the second even prime, which doesn’t exist, and the infinite number of prime numbers, which I think do exist. I think that there is more than one mode of existence, but the theory that all modes of existence are equally real — I see no point in that. The overlap between Everett and David Lewis is, I think, more coincidental than illuminating.

COWEN: If the universe is infinite and if David Lewis is correct, should I feel closer to the David Lewis copies of me? The copies or near copies of me in this universe? Or the near copies of me in the multiverse? It seems very crowded all of a sudden. Something whose purpose was to be economical doesn’t feel that way to me by the end of the metaphysics.

DEUTSCH: It doesn’t feel like that to you. . . . Well, as Wittgenstein is supposed to have said (I don’t know whether he really did), if it were true, what would it feel like? It would feel just like this.

Much more at the link.  And:

COWEN: Are we living in a simulation?

DEUTSCH: No, because living in a simulation is precisely a case of there being a barrier beyond which we cannot understand. If we’re living in a simulation that’s running on some computer, we can’t tell whether that computer is made of silicon or iron, or whether it obeys the same laws of computation, like Turing computability and quantum computability and so on, as ours. We can’t know anything about the physics there.

Well, we can know that it is at least a superset of our physics, but that’s not saying very much; it’s not telling us very much. It’s a typical example of a theory that can be rejected out of hand for the same reason that the supernatural ones — if somebody says, “Zeus did it,” then I’m going to say, “How should I respond? If I take that on board, how should I respond to the next person that comes along and tells me that Odin did it?”

COWEN: But it seems you’re rejecting an empirical claim on methodological grounds, and I get very suspicious. Philosophers typically reject transcendental arguments like, “Oh, we must be able to perceive reality, because if we couldn’t, how could we know that we couldn’t perceive reality?” It doesn’t prove you can perceive reality, right?

And this:

COWEN: A few very practical questions to close. Given the way British elections seem to have been running, that the Tories win every time, does that mean the error-correction mechanism of the British system of government now is weaker?

DEUTSCH: No. Unfortunately, the — so, as you probably know, I favor the first-past-the-post system in the purest possible form, as it is implemented in Britain. I think that is the most error-correcting possible electoral system, although I must add that the electoral system is only a tiny facet of the institutions of criticism and consent. In general, it’s just a tiny thing, but it is the best one.

It’s not perfect. It has some of the defects of, for example, proportional representation. Proportional representation has the defect that it causes coalitions all the time. Coalitions are bad.

COWEN: You have a delegated monitor with the coalition, right? With a coalition, say in the Netherlands (which is richer than the United Kingdom), you typically have coalition governments. Some parties in the coalition are delegated monitors of the other parties. Parties are better informed than voters. Isn’t that a better Popperian mechanism for error correction?

I also tried to sum up what I think he is all about, and he reacted with scorn.  That was an excellent part of the conversation.  And here is a good Twitter thread from Michael Nielsen about the Conversation.