Interesting.
1) And what about string theory? There, as I understand it, they really do talk about multiple universes with different laws. Is that too just speculation like inflation theory? And in general, is inflation not accepted by most scientists?
2) Sorry to correct you, but I assume you accidentally switched between the cosmological argument and the argument from complexity in this sentence: “even if they had different laws of nature from one another, that does not affect the physico-theological argument.” For the cosmological argument it certainly makes no difference, but it does refute the argument from complexity. There is no longer any wonder at the complexity.

1) The moment you have a theory, there is a structure behind it. There is no point getting into all these things here. Only a theory of pure chance could serve as a refutation (that is the theory that sees chance as an explanation for everything).
2) Correct. The moment you adopt the bizarre thesis that complexity doesn’t bother you, then it doesn’t bother you.
After all, regarding anything complex you can raise speculations that many different things were created and this is just one of them, so there is nothing surprising about its being complex. And then no conclusion at all can be inferred from complexity. For example, if you see before your eyes a die that falls a thousand times in a row on 6, you would not conclude that it is loaded, because maybe there were billions of throws and you just happen to be watching this one.

Sorry for continuing to bother the Rabbi, and on a fast day no less, but this is a fundamental issue and there’s no one else to ask (at least in our universe 🙂 ).
1) I didn’t understand what you meant by “the moment you have a theory, there is a structure behind it.” Who says it’s a complex structure (argument from complexity), and not just some plain structure (cosmological argument)? In the next section you say that indeed you meant the cosmological one and not complexity.
2) Obviously just making things up isn’t logical, but that is exactly science’s claim here: it isn’t just to evade God, rather it explains a great many scientific things in different and separate fields, so it’s the most reasonable thing to accept!
3) I just now saw on Wikipedia, in the entry “Many-worlds interpretation,” that in the list of advantages of the theory they write as follows: “The many-worlds interpretation also solves the problem of the anthropic principle and the problem of the fine-tuning of the universe: the universe was not specially tuned so that humans could exist in it; rather, it is one of countless possibilities, one of which is suitable for the existence of human life.” That implies they are indeed talking about universes with different laws.

Also, you have to remember that the logical conclusion is that there is an intelligent creator,
but then the atheists come and change the premise into a new premise unfamiliar to us: infinitely many universes exist, all just to evade the conclusion.

The point is that when there is no real basis or substance for changing the premise, we are left with no choice but to accept the conclusion. And we can’t just throw out basic assumptions without any basis unless we are simply not rational.

[Unless apparently they are authentic skeptics who see everything as 50/50. Maybe they’re inside a dream at all, even (and I’m not sure that’s less logical than adding infinitely many universes to the premise)….]

Yosef,
1) If that structure produces life and complexity, then by definition it is special.
2) Not at all. See the next section.
3) You are repeating what I said. That is exactly what I said: that multiple universes are intended to solve the problem of the anthropic principle, that is, to answer the physico-theological argument. In that way you could solve the problem of the die I described in the previous comment.
By the way, don’t draw any conclusion from their words (which imply that each universe has different laws. That isn’t true). These are not especially intelligent excuse-makers whose concern is to shore up their absurd worldview and avoid the obvious conclusion (belief in God). Of course, if you produce multiple universes ad hoc in order to reject the physico-theological argument, then you will produce universes with different laws.

Kobi,
Indeed. That’s what I wrote to Yosef.

Wait, Rabbi, I’ve already managed to lose track of you.
1) So are you claiming that even about a mechanism that produces laws in such a way that it produces everything (and in the process, inevitably, also a special and rare universe like ours), one can still ask a physico-theological question? Or only a cosmological one? What exactly is complex about something that tries everything and among all that gets a special result? I think I missed something, because that is exactly the anthropic principle, and in your booklet you wrote that the argument from complexity holds water only if two conditions are met: 1. the object is statistically rare. 2. not enough attempts were made to produce it. A mechanism that produces lots and lots of universes with different laws cancels condition 2.

2) When I said that the multiverse solves problems, I didn’t mean the fine-tuning issue, but other problems: in quantum theory, in strings, and in inflation. One explanation that solves three things is preferable to one explanation for each thing separately (as Rabbi Chaim said about that fool).

P.S. Thanks for the whole site.

I think there is a difference between adding more dimensions and laws of nature, all of which together are very well defined,
and then the question is still the same.

And adding universes that are not governed by the same laws of nature but by other laws of nature instead (and therefore by definition one cannot at all see or hear about them, which is the problematic and smelly part of the story).

Yosef,
1) I am claiming that if there are enough universes with different laws of nature to explain the specialness of the laws of nature (which means an imaginary number, in fact an infinite number, of universes with different laws of nature), even then the mechanism for creating universes still requires explanation. Assuming there is such a mechanism, then indeed the multiplicity of universes (the infinite multiplicity) can explain the anthropic phenomenon. I have already written more than once that the two arguments are connected to one another, and separating them is only for didactic purposes.
2) And that also solves fine-tuning, if such a thing exists.

Beyond that, the theory that will explain the totality of universes is itself some particular theory, and I am sure it too will be special (when it exists, and if it exists). So the question will arise about it as well.

I understand, you mean that the cosmological argument will still remain, and even a bit of the argument from complexity, because the mechanism will itself be complex.
On what basis is your assumption that the mechanism for creating universes will be special? Because in the end it arrived at a special result (our laws of nature)?
Maybe your intention can be explained more deeply this way: one can still say the following about the mechanism: “Out of all the systems of laws that could have been in the mechanism, only a tiny number lead to life” (or a mechanism that leads directly to life, or a mechanism that produces infinitely many universes and in that way reaches life).
What does the Rabbi say?

How large does the infinity have to be?
The set of all functions from R to R is aleph-2, isn’t it?
Assigning values to the constants is aleph-1, so that makes no difference here.
But the question is which functions exist. Is there a finite set of physical quantities between which one can define functions, in which case it really is aleph-2, or can one think of totally different things that would give a greater cardinality?

Yosef, it doesn’t actually have to be infinite, because the values of the constants do not have to be absolutely precise (there is a range within which similar properties will still exist for a sufficiently long time). But there still need to be masses of universes with masses of systems of laws. I don’t know what the issue of functions between constants has to do with this.

The issue of functions is that if there are universes with different laws, then what one needs to check is how many functions there can be between constants, for example between mass and force. It seems to me that it’s aleph-2.

Mass and force are not constants. Mass is a constant and it connects force to acceleration.
Maybe you mean how many functions there can be between physical variables, like acceleration and force. To that I say you need to remember that random laws of nature can be of completely different types from ours, with different variables (maybe a nature in which there is no motion at all, and then there is no velocity or acceleration), with a different number of constants and of course different constant values. By the way, they also might not be functions at all, and also laws with non-constant functions, and so on as far as your imagination takes you. Beyond that, the relation between the variables is differential and not a simple function, and that increases the number to completely different levels.

Thanks!!
But “powerful” does not necessarily mean special. A hurricane is also powerful. Maybe you meant “powerful” in the programming sense? And is the explanation I gave above correct?

Indeed, you understood what I meant. Even when there is no motion, there is a function connecting force to acceleration.
A differential equation that describes something physical is supposed in the end to yield a function, even if one cannot find it or write it in analytic form—it gives every X one unique result in R.
As for quantum theory, every X gets not a single result but a distribution, that is, a function, and then in fact one has a function from R to the space of functions from R to R, which would give aleph-3. Apparently one can complicate this as much as one wants and get as high a cardinality as one wants.

Yosef, no. It is indeed powerful in terms of properties, but not specifically because of our universe. Creating universes at all is a non-trivial capacity (to put it mildly).

Yishai, the function that one gets at the end does not connect force and acceleration, but gives a trajectory in space-time. That is not a law of nature. The equation is the law of nature. And in quantum theory one does not get a function but a distribution of possible results. But these hairsplittings are not really important for our purposes.

Of course it isn’t important for our purposes. It’s just for fun.
I still didn’t understand the point about differential equations. In the end, if every force has an acceleration, then there is a function here, and likewise between any two variables.
Why is a distribution not a function? A distribution gives every state a probability.

Take a spring, for example. Its equation of motion is that the force equals minus the distance from the equilibrium point times the spring constant: F=-kx. The force is the mass times the second derivative of that distance, and so here we have a differential equation whose solution is the position as a function of time. Something like: ( x=Bsin(at
The solution is a function, but it does not connect force to acceleration; the relation between those two is always linear (Newton’s second law) with the mass as the constant of proportionality. That does not vary between cases.
A distribution is a function of a random variable, or a function describing probability as a function of position. But it is not something that connects physical variables to one another.

Why should I care about the spring’s position? I care about the function connecting force to acceleration. There could be a universe where that relation cannot be expressed by an analytic function or even by a differential equation, but it is still a function.
Of course a distribution is not a function connecting physical variables to one another, but it does connect a physical variable in R (that is, cardinality aleph-1) to the function space of random variables (that is, cardinality aleph-2), and therefore if I’m not mistaken the set of functions that do such a thing would be of cardinality aleph-3.

We are apparently speaking two different languages. The function connecting force to acceleration is very simple:
F=ma. That’s all. It is true in all cases and under all circumstances, and there is no multiplicity here and nothing differential about it. It has nothing to do with differential equations or their solutions.
And indeed, this is a function that in another universe could be very different, which is exactly what I wrote.
As for distributions, our languages are apparently totally different. Even the cardinality of the continuum (C) is not necessarily aleph-1 (that is only the continuum hypothesis). A distribution also does not connect a continuous variable to a function space, but rather a random variable to a probability.
But I think this is not the place to continue this.

Hello Rabbi. I’m currently busy plowing through the responsa on your site, and I’m amazed by what’s going on here.
I came across one responsum that discussed the anthropic principle, and there the questioner asked you this: “Does the anthropic challenge exist only insofar as there is randomness in the universe?” (He meant real randomness, like in quantum theory.) And you answered him: yes.
So I understand that here too you meant that only if the mechanism for creating the laws of universes is random in a quantum sense—then the multiplicity of universes undermines the argument from design, and if there is no quantum randomness there—then the argument from complexity remains with the same force despite the infinite universes the mechanism produces.
So is that what you meant here as well? Were you speaking only about a completely random mechanism?
And in addition, I’d be glad for an explanation of why, if it is deterministic, then the multiplicity of universes explains nothing. That sounds very strange to me.
Thanks.

Hello.
The principle is this: if there is a die that falls randomly and after many throws you get a sequence of one hundred 6s, there is no probabilistic problem with that. Therefore if there is a random mechanism that creates masses of universes and one special universe comes out among them, there is no probabilistic problem with that.
There is still a problem in the formation of universes, because the mechanism for creating universes is itself a mechanism that requires explanation and requires an operator, and besides we have never seen such a mechanism, so this is baseless speculation.
When you have a die that is thrown deterministically, then no distribution is special. Whether you get a chain of one hundred different throws or one hundred identical throws, neither is more surprising than the other, because it is the structure of the deterministic mechanism that dictates the results. Of course, if that structure itself was created randomly, then the wonder arises as to how a structure that produces one hundred identical throws was formed randomly, and we are back to the random case.

Quantum randomness is not a solution to anything at all, because quantum theory itself is a special theory that requires explanation. The randomness occurs within it.

I understand that with a deterministic die there is nothing to “marvel at,” because everything was predictable. But the issue here is drawing conclusions by the argument from complexity, and if there is a mechanism that “tries everything” and in the process also arrives (inevitably) at our special universe, then our special universe is completely explained, and then it is proven that this mechanism is not special from the standpoint of creating our universe (perhaps it is special only from the standpoint of being a mechanism that creates universes), because it is not “targeted” at creating special laws. Then the anthropic challenge applies also to a deterministic mechanism for creating universes, because one already sees that the mechanism is not really special from the standpoint of our universe.
Like, for example, a deterministic machine that shoots a billion arrows in all directions, deterministically—true, in the end it will also hit the exact center of the target, but seemingly one should not infer from that that it is special (on account of the special hit; perhaps only on account of the mechanism itself), even though it is deterministic.
All this, of course, without even getting into the fact that this is all speculation to begin with.
[It now occurs to me that perhaps the Rabbi means that after we know there is a God from the cosmological proof, then we can more easily attribute to Him also the special result of the mechanism, since the mechanism is deterministic and its programmer is responsible for everything. That sounds right; but if we are talking about the argument from complexity itself, then the complexity disappears.]
Sorry for the length.

No mechanism can try everything. There are infinitely many “everythings.” Therefore this mechanism has a structure that selects what to create, and that is its specialness.