Amateur armchair complaints about professional physics are not really a good look for winning arguments.

Black hole cosmology is well a established subfield of cosmology. Everything you just said is refuted by it.

So, I recommend you listen to scientists instead of pretending to know better than them.

To get started, Google Scholar lists over 300,000 studies on “black hole cosmology.” 62,000 on “black holes and other universes.” And 10,000 on “black holes and multiverse.”

But the article you are commenting on also does not depend on black hole cosmology anyway. Multiverse theories without black hole nucleation are also abundantly documented in the field. And none of my six arguments for multiverse theory being more probable than God depend on black hole models. So your argument is also fallacious. If multiverse theory is baseless speculation, then God is even more baseless speculation. Because comparing the two speculations, we have six good arguments favoring ours over theirs. Which is actually the opposite of “baseless.” So, to quote Inigo Montoya, “I do not think that word means what you think it means.”

That’s just a mathematical problem though. In other words, we don’t have mathematical tools to do that kind of calculation. We use exhaustion to the limit instead: we can graph the ratio for every value on a continuity and see the projection toward infinity remains constant. Thus we can assume there isn’t anything about infinity that changes that. It’s not like we can keep increasing the number of cows until suddenly two-headed cows instantly become as common as regular cows. One thing we do know is that physics doesn’t work that way.

Another way to look at this is how we do actual statistics: we randomly sample a population and then can calculate the probability that the ratio in the sample holds for the whole population. It has been shown that the effect of sample size is a constant, and thus not at all dependent on the population size. For example, no matter how large a population is (one million, twelve trillion, three gazillion bazillion), a random sample of 1000 members of that population will give a highly accurate result of true ratios in the population, because the probability of “randomly” getting an anomalous ratio goes down with every person sampled, regardless. For instance, if there is a 50/50 chance of getting an anomalous result for each sampled member of the population, then the probability of them all being anomalous is 0.5^1000, which is a vanishingly small number. You can do the math for every possibility (all anomalous but one, all anomalous but two, etc.) and run a curve and show that the probability that the ratio in a sample of 1000 does not correspond to the actual ratio in the whole population is a certain fixed amount (and an amount that’s quite low). You can increase the sample size (e.g. to 100,000) and astronomically decrease that probability even further. But at no point does the population size have any effect on these probabilities.

Thus it can be shown that even in an infinite population this remains unchanged, because the anomalous-sampling probability derives from the sample size, which is always finite. Therefore, we will always observe a ratio in a random finite sample even taken from an infinite population. So we know ratios continue to exist within infinite sets. We just have no mathematical tools to suss them by, because transfinite numbers do not adhere to the axioms of finite arithmetic, so “arithmetic” doesn’t work on them. Arithmetic is just a human invented tool though; so that it doesn’t work here is a fault of the tool, not the transfinite sets we want to extract information from.

Thanks so much for writing this very interesting response.

I think what you said solves a problem Alan Guth discussed, “In a single universe, cows born with two heads are rarer than cows born with one head. [But in an infinitely branching multiverse] there are an infinite number of one-headed cows and an infinite number of two-headed cows. What happens to the ratio?”

This is known as the measure problem in cosmology as you probably know. Anyway, again, thanks for your time and great response! 🙂

I’m not sure I understand your question. “Why is it that we’re not in one in the infinite set of universes that give false positives?” is straightforwardly “Because that’s improbable.”

For instance, if the “false positive sequence” has a probability of 1 in 1000, that means of all the universes otherwise identical to ours (assuming that’s even a thing that happens; more on that in a moment, but it seems to be the assumption you are operating on), only 1 in 1000 of them will witness that “false positive sequence.” Thus, there is only a 1 in 1000 chance we are in that universe. Therefore we can assume we probably aren’t. And that is exactly what we do assume: when scientists say there is a 1 in 1000 chance their results are a random accident, they are literally saying there is a 1 in 1000 chance we are in a universe where that mistaken observation is made. Which does mean we could be in that universe. It’s just unlikely that we are. That’s the whole point of stating it as a probability.

-:-

The underlying assumption might also be incorrect. But that’s a different matter. That infinitely many universes exist does not entail every possible universe does or will exist, because one of the funny things about transfinite quantities is that they no longer obey the one-to-one correspondence rule. So you can reach infinity before having gone through every configuration. We actually don’t yet have the math to figure that out.

For example, you can have an infinite number of different numbers but still not have every number. This is true in two different ways: (1) there are infinities larger than the set of all finite numbers (see Cantor’s Diagonal Argument), so there are actually more numbers than ever exist on a number line (there are infinitely many finite numbers, but also infinitely many transfinite numbers, and infinitely many imaginary numbers): so we can have an infinite selection of numbers that still leaves unselected infinitely many numbers, e.g. we can have all the imaginaries but none of the naturals, or half the imaginaries and half the naturals, etc. The more so if we can have repetition, e.g. if we can pick any number twice, we could have all the numbers except the number three, and in its place have a second two, and still have infinitely many numbers. In fact, and this is the really weird thing, we could have all the numbers except three—and we would still have infinitely many numbers! (We don’t have to add one back in) Likewise, you can have an infinite number of some things (let’s say, different sized balls) but still not have all possible things (e.g. we then won’t have any cubes).

So it’s actually not clear whether given infinite selections we will actually have gone through every possible selection. Because we can go through, for example, an infinite number of universes with planets in them and somehow never have gotten to a universe without planets in it. We have no math to ascertain the probability of that. It’s indeterminate.

Even so, I think it’s probable there are at least all plausible universes, so for instance there must be infinitely many universes with some version of you and me in them (in some sense), that will each be slightly different from this universe; and still infinitely many more universes without either you or me in them. But this being the case doesn’t really change anything as to the significance of probability judgments. Saying something is improbable just is saying we are more likely to be in a universe where that isn’t the case. More on this concept and what weird things it does entail see my article The God Impossible.

If there is an infinite number of universes, then wouldn’t science be undermined because probability goes out the window? After all, no matter how improbable it is for an experiment to give a false positive 4 times, it will inevitably happen if there is an infinite amount of trials in the multiverse.

Imagine a parallel universe in which everything is equal to ours, except the result of one experiment of General Relativity gave a false positive. Now, in another parallel universe, everything is equal to that universe, except for a new false positive (following the last one). If there is an infinite number of parallel universes in which the values of the constants and initial conditions are the same then you’ll find universes in which all experiments give false positives. So, one might ask “Why is it that we’re not in one in the infinite set of universes that give false positives?”

How would you respond to this challenge?

Thanks for your time!

Those are misleading statements, I’m afraid. I agree string theory is the best explanation for a variance in constants (indeed, even for the constants themselves, full stop), but it is in no way the only one viable and proposed in the literature. So the second quote is simply false (and note, you are quoting a philosopher, not a scientist; I’m afraid you just have a non-expert screwing up the facts there). The first quote doesn’t say anything as to string theory being necessary. It just says string theory entails variance; not that only string theory entails variance. Which is exactly what I just said (and note, that’s your only quote from an actual expert). When you actually read Dawid’s cited source (Vilenkin 1983), it nowhere says what Dawid does. Dawid confused Vilenkin’s proposal that we can explain variance with string theory, as saying we can only explain variance with string theory. Vilenkin has never said this.

Dr. Carrier wrote: “But that’s not true. The underlying laws of string theory can be the product of prior selection; and multiverse theory does not even require string theory (Chaotic Inflation, for instance, makes no mention of it).”

Well, it is true that the inflationary multiverse doesn’t require string theory in some sense; other bubbles will continue popping in other parts of the spacetime manifold. However, to have many variations of the constants of nature, one needs speculative extra dimensions.

“The fundamental theory of nature may admit multiple vacua with different low-energy constants. If there were just a few vacua, as in standard GUT models, then a few observations would determine which one corresponds to the real world. Predictions would then follow for every other observable in the low energy theory. However, it has recently been realized that in the context of string theory there may be a vast landscape of possibilities, with googols of vacua to scan.”

Alexander Vilenkin, “Probabilities in the inflationary multiverse”(2005)

“While the multiverse is rooted in the cosmological concept of eternal inflation (Vilenkin 1983), the string landscape is necessary for providing a physical basis for allowing different values of the cosmological constant and other parameters in each universe of the multiverse.”

Richard Dawid, “Philosophy of String Theory” (p.9)

No. I was not aware of that paper. But it agrees with what I argue in Six Arguments That a Multiverse Is More Probable Than a God. Thanks for the link.

“A New Fine-Tuning Argument for the Multiverse

Abstract

This paper has two aims. First, it points out a crucial difference between the standard argument from fine-tuning for the multiverse and paradigmatic instances of anthropic reasoning. The former treats the life-friendliness of our universe as the evidence whose impact is assessed, whereas the latter treat the life-friendliness of our universe as background information. Second, the paper develops a new fine-tuning argument for the multiverse which, unlike the old one, parallels the structure of paradigmatic instances of anthropic reasoning. The main advantage of the new argument is that it is not susceptible to the inverse gambler’s fallacy charge.”

https://link.springer.com/article/10.1007/s10701-019-00246-2