Faith – Lesson 19

Last time we finished the cosmological argument, which is an argument based on the existence of things in general, without assuming anything specific about the nature of the things that exist. The claim was that every thing, at least of the kind we encounter in our experience, must have a cause, and therefore if things exist, then there is a cause that created them, and that is God. And I said that for the purpose of the cosmological argument, the definition of God is: the one who created reality, the cause of reality, or the creator of reality, the Creator, let’s call it that.

The next argument I want to begin today is the physico-theological argument; the terminology is Kant’s. The physico-theological argument is not an argument from the mere fact that something exists, but an argument from the special character of what exists. What is that special character? There are a few versions here: there is an argument from complexity, there is an argument from design, from fit, from adaptation—these are all different shades of the same kind of argument. And what it basically says is that if something complex, designed, coordinated exists—something like that—then it did not create itself; something must have produced it.

It’s very similar to the cosmological argument, but as we’ll see there are differences between them that raise many other discussions. The cosmological argument is important also because it complements this argument, since the basic logic could really have been built on it. The cosmological argument is simpler, and the basic logic there—the understanding of why an infinite regress is a failure, why “so then what is the cause of God,” and all the refutations and objections we encountered in the previous argument—those also come up in this argument. What I already answered in the previous argument, I won’t repeat here. What I do want to discuss in this context are the things unique to this argument; there are additional aspects that come up specifically in relation to this argument, and those are what I want to focus on.

So maybe it’s nice to begin with a midrash from Otzar HaMidrashim by Eisenstein, from Midrash Temurah. “It once happened that a heretic came and said to Rabbi Akiva: ‘Who created this world?’ He said to him: ‘The Holy One, blessed be He.’ He said to him: ‘Show me clear proof.’ He said to him: ‘Come to me tomorrow.’ The next day he came to him. Rabbi Akiva said to him: ‘What are you wearing?’ He said to him: ‘A garment.’ He said to him: ‘Who made it?’ He said to him: ‘The weaver.’ He said to him: ‘I do not believe you; show me clear proof.’ He said to him: ‘What can I do? Don’t you know that the weaver made it?’” That is how that heretic answers him. Then Rabbi Akiva says to him: “And you—don’t you know that the Holy One, blessed be He, created His world?”

The heretic left, and his students said to him: “What was the clear proof?” Meaning: what, you didn’t explain it. What do you mean “the world testifies to the one who created it”? Why? Why does it testify? In what sense? He said to them: “My sons, just as a house testifies to the builder, and a garment makes known the weaver, and a door the carpenter, so the world makes known the Holy One, blessed be He, that He created it.”

There’s a structure here that also reminds me of “you brushed him off with a reed and to us what do you say,” as Rabbi Yohanan’s students say to him. All kinds of arguments with heretics where somehow the arguments are a bit of a shutdown, and then the students come and say, wait, open it up for us more. What exactly was wrong with his claim, and what did you answer him? You brushed him off with a reed—what did you answer him?

I think what they really want to say to him—and this really reminds me of modern dialogues about God—they want to say to him, I think I’ve mentioned more than once already my favorite distinction between an English-English dictionary and an English-Hebrew dictionary. In an English-Hebrew dictionary, you take an unclear word and explain it with ten other words that we know. In an English-English dictionary, you take an unclear word and explain it with ten words that we know even less. So many times someone asks you a question, and you explain it by means of another principle—but that other principle is no clearer than the question they asked you.

After all, they asked you: how do you know someone created the world? So Rabbi Akiva turns around and asks him: tell me, and how do you know that someone wove the garment you’re wearing? And at that point the heretic’s claims were silenced. He said to him: like the garment, so the world. The students ask: wait, wait—you asked a great question. Really, regarding the garment too, who says so? That’s not an answer. That’s an English-English dictionary. You explain one question that we don’t know—the question of how the world testifies to its Creator—with another question that gives us the illusion that we know it, but actually we can ask that one too. Who said the garment testifies to the weaver? There too I can ask: maybe it created itself?

Okay, indeed Rabbi Akiva’s students are basically asking him—so it seems to me—if all due respect, you brushed him off with a reed, but really there is a good question here, and the question applies both to the garment and to the world. What do you answer to that?

Except that if that really were the line of the discussion, then Rabbi Akiva’s answer is not so clear. He said to them: “My sons, just as the house testifies to the builder, and the garment makes known the weaver, and the door the carpenter, so the world makes known the Holy One, blessed be He, that He created it.” What has been added here beyond what came before? It just repeats itself; he doesn’t really explain. He says: the world testifies to the Creator. And they asked him: why does it testify? Who says it testifies? Like the garment—who says it testifies to the weaver? So Rabbi Akiva is simply repeating once again what he had said to that heretic. So what did we gain from this whole exchange?

We were supposed to understand that there’s a good question from the students here, but if so, it isn’t clear what the not-so-good answer is that Rabbi Akiva gives them.

So notice: there is a certain difference in wording between what Rabbi Akiva said to the heretic and what Rabbi Akiva says to the students. When Rabbi Akiva spoke with the heretic, he didn’t explain to him at all that the world testifies to its Creator and that a garment testifies to its weaver. He only said to him: look, by your own method you too accept things without explanation, because the fact is that regarding the garment you’re wearing, you don’t ask who wove it; it’s obvious to you that the weaver wove it, without getting into the question of why at the moment. So what do you want from the world? By your own method you cannot ask that question. He didn’t even say to him that the garment testifies to the weaver and the world testifies to the Creator. That does not appear in the dialogue between Rabbi Akiva and that heretic. All that appears there is that the heretic himself does not ask these questions regarding the garment, so why are you asking these questions regarding the world? But it is not written there that the garment testifies to the weaver and that the world testifies to the Creator. No, that’s not in their dialogue. He only says to him: don’t you know that the Holy One, blessed be He, created His world? You do know that. What does that mean—how does he know that? That the world testifies that someone created it? That’s not written in the dialogue between Rabbi Akiva and the heretic. It appears in Rabbi Akiva’s answer to his students.

There he says: the world testifies to its Creator just as the garment testifies to the weaver and the door to the carpenter. There is something in the world itself that testifies to the fact that someone created it. That really is a point that did not appear in the dialogue between Rabbi Akiva and the heretic. What is that thing? What is it in the world that really testifies that someone created it? Or in the garment, that someone wove it?

So apparently it is their complex structure. Or in other words, this is exactly the physico-theological claim, which says that something complex was probably made by someone. A complex thing does not create itself. It requires some directing hand to create the complex thing. That is basically what Rabbi Akiva answers his students. That is the answer that lay behind the answer he gave that heretic. In other words, there is a logical argument here. He is not just saying: by your own method you don’t ask these questions regarding the garment, so don’t ask them regarding the world either. Fine, then that heretic should have answered Rabbi Akiva: you’re right, now I’m asking the same question about the garment too. That is basically what Rabbi Akiva’s students answered in place of that heretic. So now what do you answer me?

Now we’ve moved on to an English-Hebrew dictionary; we’re done with the English-English dictionary. Now explain both phenomena to me—the explained word and the explaining words—now explain everything. And to that Rabbi Akiva says: what do you mean? Look at the world. It’s complex. Just as the garment is complex—except the world is much more complex. Now a complex thing obviously doesn’t create itself just like that. Therefore it is clear that the world testifies to its Creator just as the garment testifies to the weaver. It’s even an a fortiori argument, because the complexity of the garment is much less than the complexity of the world, so clearly the world testifies to its Creator even more.

In the picture there are additional examples that appear, say, in Maimonides in the Laws of Idolatry, at the beginning of those laws. He brings the rabbinic midrash about our father Abraham: that Abraham lifted his eyes heavenward and said, “Lift up your eyes on high and see: who created these?” There is an entire functioning, coordinated world here; the stars move in their courses, and so on. What is this, just there for no reason? It just happened to exist? It just happened to come into being? Someone created it. But there it is not focused on complexity, although one could interpret it against the background of complexity. Here, in this midrash, I think it is really, really the physico-theological argument, in a completely explicit sense. It’s not some interpretation or another; it is exactly what Rabbi Akiva is answering.

In more modern formulations of this argument, yes, the atheists always cite it in the name of Reverend Paley. This is a Christian minister from the end of the nineteenth century, and he basically brings a version of this argument. He says: suppose you’re out, I don’t know, walking on the seashore. You see a watch lying there on the ground. You pick up the watch and ask yourself: how did it get here? How was it made? Who is responsible for this watch? Did it create itself—what’s the problem? Was it assembled by some accidental mechanism? That’s not an answer you would accept. Why not? Because a watch is a complex, coordinated thing, and it has parts; the design is evident in it, because someone made it so that it would function and show the time. Therefore it is clear that there was some watchmaker who built it.

So Paley says: if regarding the watch you say this—and its complexity is far less than the complexity of our whole world, our whole universe—then clearly with regard to the universe, it’s no worse than a watch. If it exists here, then someone created it. Okay?

The atheists love to mock Paley’s watch argument, and this usually works like this: when you have answers, you mock. But this argument is a very good argument in my view. We’ll still have to go some distance to see that; there are objections and refutations and answers. But right now I’m just laying out the argument itself.

And I’ll finish with yet another formulation, and this one really drives the atheists crazy. Sorry that I’m always speaking in the name of these anonymous atheists; I’ve just run into so many websites and people repeating these claims that I don’t even have names for them anymore. It’s the same thing everywhere.

The third formulation—why does it drive everyone crazy? Because it was formulated by a very, very well-known physicist named Fred Hoyle, an astrophysicist. And when it comes from our own backyard, that really makes people angry. The atheist backyard, yes? Science is perceived by them as the private property of atheists. You’re not allowed to bring matters of faith in there; science belongs to atheists. By the way, strangely enough, believers also cooperate with this idea—fundamentalist believers—who also say yes, science is the property of atheists.

In any case, Fred Hoyle—yes, the famous airplane example of Fred Hoyle. Fred Hoyle says that the probability that life arose by chance is far less than the probability that a tornado passing over a junkyard would cause the scrap there to arrange itself into a functioning airplane. In other words, the wind would throw all the parts around and they would somehow connect to one another and a functioning airplane would emerge. So he says: if someone told you such a thing, you’d have him hospitalized. Now when you say that the world was created by chance, or that life was created by chance, the probability is even lower than that. And somehow that is perceived as a rational position. That’s what Fred Hoyle says.

And on atheist websites, in many places, this is called “Hoyle’s fallacy.” They don’t even bother arguing with him, as though it is already known and obvious that this is a mistake. Fred Hoyle got confused here; it’s an error. Fine. So I’m going to try to argue that it is very much not an error. Fred Hoyle is right, and the ones confused are his critics. But we’ll get to that later.

In any case, if I summarize for a moment all these arguments, which basically share a common structure, the point is this: there is a universe with a certain special structure—complex, designed, coordinated, whatever; there are different formulations. That is premise A: first of all, it exists. An empirical premise. There is a universe and it is complex. Premise B: a thing with a complex structure does not arise spontaneously; it does not arise for no reason, arbitrarily, on its own. Conclusion: apparently something created it. If it is not spontaneous, then there is something that created this complex thing. We call that something God. Okay?

You can see the structure—it is very similar to the cosmological proof, except that here we are not merely assuming that something exists and therefore something is needed to build it, to create it. Rather, we assume that something complex exists. We need the character of the thing that exists, not just the fact that it exists. The mere fact that it exists—that’s the cosmological argument. Here I assume special properties or characteristics, special characteristics of the thing that exists, and on that basis I build the argument.

If it turns out that what we call the anthropic principle—that there are several constants that… we’ll get there. We’ll get there, get there. Fine-tuning, yes. We’ll get to those things. “Anthropic principle” depends who you ask. The anthropic principle of the religious people is what I just said. And the anthropic principle of the atheists is what I’ll talk about later. They also call their objection the anthropic principle.

Anyway, the claim basically, in the end it seems to me—or before the claim—here the same objection arises that we saw in the cosmological argument. It arises here too. Therefore I won’t go back over everything we said there, only what is new. For example: people immediately ask, yes, so who created God? If God created the world and He is so sophisticated and complex and can produce such a world, then He too is something complex. And if He too is something complex, then who created Him? Basically they tell you that you are entering a chain, an infinite regress.

I spoke about that at length in the previous argument. The claim is that—okay, the one who created Him is God prime. And the one who created Him is God double-prime. And so on. In the end, in the end, we remain with an infinite regress. And then what does that mean? If we remain with an infinite regress, then that essentially means that an infinite regress is a failure, as we saw there. Therefore we have to assume that somewhere in this chain there exists something that was not created by something else, because otherwise it is an infinite regress. But every complex thing, according to our assumption, needs something to create it. So this is exactly the same move I made there, so here I’m doing it briefly.

What I want to argue is that certain things have to be excluded from this principle. Complex things of the type we know probably have something that created them. But if there is a thing that was never created, or that is not of the kind we know, then with regard to it maybe one need not assume that something created it. And I’m saying not just maybe as a mere possibility—it must be so. Because otherwise the alternative is an infinite regress. Okay? Therefore I’m claiming that I prove the existence of such a thing, one for which there is nothing that created it. Not that I’m saying, no, there’s some possibility that such a thing exists. No no—it must exist, because otherwise we are in an infinite regress.

So why not say that the world itself is such a thing? The world itself exists without—yes, it is complex but no one created it. Because the world is of the type of things we have experience of. And we’ll see the matter in more detail later. And regarding those things, we know that they do not arise spontaneously. More than that: we also know that the world was created. It did not always exist. Fourteen billion years or something like that is what they estimate today. So if that’s the case, then the question arises: who created it? Regarding God, we do not know, we are not familiar, so it may be—and what I showed earlier is, there must be something that begins this chain, something that itself was not created, there is nothing that created it. And that thing is basically called God.

Now this point is different from the cosmological argument—I’ll sharpen it a bit. It’s different from the cosmological argument in that in the cosmological argument we assume that everything must have a cause. The existence of every thing, regardless of its character, must have a cause. Then I qualified that and said that this is only for things in our experience, of the type of things familiar to us, okay? Because otherwise it is an infinite regress.

Here the move is similar, but the second premise in the argument is different. There, the first premise is: a world exists; everything that exists must have a cause; conclusion: there is God. Here the structure is: a complex world exists—an empirical premise that is a bit different. And the non-empirical premise, the meta-empirical one, let’s call it philosophical, is also different. There the premise is the principle of causality in the sense that everything that exists must have a cause. Here the premise is that a complex thing must have a composer, an arranger, something that puts it together. Okay? It is parallel, but not the same. Conclusion: there is God.

And notice that the God being discussed here is the God who is supposed to be sophisticated enough—the engineer sophisticated enough—to engineer the world, to create its complexity. As distinct from the God in the cosmological proof, where maybe He is omnipotent, or at least has very great powers—He created the world ex nihilo, regardless of complexities. There He is not an engineer; there He is a Creator. Here He is the engineer. Okay? So, as we already said, every argument assumes some definition of the concept of God, and that definition is expressed in the premise.

Okay, now, why indeed do I exclude the Holy One, blessed be He Himself, from this premise that a complex thing does not come into being or does not exist just like that without having some arranger or composer? Here we have to enter into something that I really could also have entered into in the cosmological argument, but it was more convenient for me to illustrate it here.

We basically have two principles. One principle says that a complex thing does not arise spontaneously; something created it. The second principle says that if you adopt this straightforwardly, then you reach an infinite regress, and that cannot be right. So basically this contradiction requires some kind of solution. We have two conflicting considerations. On the one hand, every complex thing must have a composer—we’ll see later that this is even a statistical principle. On the other hand, we arrive at a philosophical failure. Meaning, if we assume it, then we arrive at an infinite regress. Or in the context of the cosmological proof: everything must have a cause, but if we assume that, then we arrive at an infinite regress; therefore it cannot be that everything has a cause. A contradiction, one thing and its opposite.

I’ll perhaps bring a legal example. Among jurists there is a principle called lex specialis, preference for the specific. What does that mean? If, say, the Torah forbids murder—“You shall not murder.” The prohibition of murder is a very severe prohibition. On the other hand, the Torah says, “Those who desecrate it shall surely be put to death”; someone who desecrates the Sabbath is liable to death. Seemingly these are two principles that contradict one another. It is forbidden to murder a person, so how can we sentence someone to death? What do we do? A Sabbath desecrator comes before us. On the one hand there is the prohibition “You shall not murder”—it is forbidden to kill him. On the other hand the Torah says you must kill Sabbath desecrators. We have two conflicting principles. What do we do?

Jurists call this preference for the specific, lex specialis. What does that mean? The specific principle always takes precedence over the general principle. In other words, this principle that one must kill Sabbath desecrators applies specifically to people who desecrated the Sabbath—with witnesses and prior warning. The principle “You shall not murder” applies to every person as such; it is a more general principle. The specific principle always prevails. Therefore one must kill him and thereby override “You shall not murder.”

Why is that so? Because if we prefer the general principle—that it is forbidden to kill—and apply it here too, then the instruction to kill Sabbath desecrators is emptied of content; it cannot be implemented in any case. Yet it is written in the Torah. So something here cannot be. Whereas if I prefer the specific instruction, the instruction “You shall not murder” is not emptied of content. In every other case it is forbidden to murder, except for Sabbath desecrators, whom I exclude; the general rule does not apply to them. You see the similarity to our case.

That means that if I have two principles that both seem correct, I cannot give up either one. I am not willing to give up that infinite regress is a failure, and I am not willing to give up that a complex thing does not create itself. But these two principles contradict one another. What do I do? I have to choose a way out that leaves the maximum of both alive, or valid. I exclude one of them in the most minimal way I can, so that both still remain valid.

And therefore what do I basically say? What do I have to remove from the principle that every complex thing must have a composer in order not to contradict the infinite regress problem? I could throw out altogether this premise that every complex thing must have a composer, but that is not reasonable. We accept this premise; it is a correct premise, a reasonable premise. Therefore reason says to exclude from it the minimum necessary in order to solve the contradiction. What is the minimum necessary? One entity. That is enough. It is enough that there be one entity that starts the causal chain, and regarding it I do not assume that it needs something else that created it, and that solves the whole problem. I can remain with the principle that every complex thing must have a composer except for that one entity, or except for a certain kind of entity, but generally speaking, aside from exceptions, it is true. And the infinite regress does not arise; I have solved it.

Therefore the accepted solution is basically to exclude the minimum possible from the one principle so that it will not contradict the other principle. And that is what I did here. So now instead of assuming that every complex thing must have a composer, I qualify it a little. I say: every complex thing—almost every complex thing—that came into being and is of the type of things we know from our experience, must have a composer. So I have excluded a certain kind of thing, apparently very small and rare, regarding which I do not assume this, because otherwise there is an infinite regress.

And now I return to my argument and say this: every complex thing in our experience, that came into being at some point, must have a composer. That is the philosophical premise. The empirical premise: a world exists, and it is complex. Conclusion: the world has a composer. Now you can ask: and what about that composer—does it belong to the class of things that need a composer? Maybe yes, maybe no. If yes, then it too has a composer—a prime composer. Okay? If not, then we’re done. If it has a prime composer, then what about the prime composer? Is it of the character of things that need a composer or not? In the end, in the end—because otherwise it’s an infinite regress—it’s clear that at some point I will say that in fact it does not need a composer. That entity is God. Okay? And this exists according to my premise. There are such entities, so this is not a contradiction. My premise does not say that every complex thing must have a composer, but rather every thing of the sort familiar to me or within my experience must have a composer. So now everything is fine, and this argument is basically the updated formulation of the physico-theological proof. And as I said, there are ancient formulations of it too, but in the end this seems to me to be the most sophisticated formulation.

Now I want to explain a little more what this business of “complex” means. What is “complex,” and why must every complex thing have a composer? And why do I—why does this require explanation? Seemingly it is intuitively obvious. But why does it require explanation? Because this point is often attacked in debates about this proof.

There are people who say: what do you mean by complexity? There are many kinds of complexities. The anthropic principle—but this time of the atheists—we’ll get there. But people often attack this point. There are many kinds of complexities, and fine, there can be situations in which all the complexity is in the eye of the beholder. To you something seems complex; to someone else it won’t seem complex, and something else will. It’s a matter of taste, like beauty, like I don’t know what. Complexity is not something objective; it’s something you choose to look at. So if you want to prove the existence of God, then you assume that the world is complex and such a thing cannot arise by itself. I don’t know, a table is also complex and a log is also complex. No, you say that it isn’t. Why not? Where does the threshold of complexity lie? What is complex at all? You can define lots of kinds of complex. You can use statistics or something.

Right, exactly—that’s what I intend to do. What I’m basically using is the concept called entropy. That’s statistics for physicists. In other words, entropy is basically the following concept. I want to claim that the concept of complexity—contrary to what you’ll find, once again, on very many websites and in many arguments—the concept of complexity is an objective concept. It is not in the eye of the beholder.

By the way, we never spoke here about Occam’s razor. One of the criticisms of Occam’s razor—Occam’s razor says I prefer a simple explanation over a complex explanation. One objection to the razor says: what is simple and what is complex? That’s in the eye of the beholder. Why is one thing simpler than another? Because you decided so, because it’s your taste, or because that’s how your mind is built. Just a completely arbitrary matter. How can you infer conclusions from that and choose a scientific theory about the world based on it? It’s just your own mental structure.

Yes, so in many places this claim comes up—that complexity is in the eye of the beholder; everyone with what he defines as complex. So I want to claim: not so. I want to claim that there is an objective definition of complexity. It is statistical. And the conventional name for this thing in the scientific world—in physics, in biology—is entropy.

And to explain this, let’s take an example. Yes, entropy is one of the fundamental concepts of what is called thermodynamics, or statistical mechanics, in physics. And one of the examples on which this whole business was, it seems to me, built—the whole picture of statistical mechanics—is what is called an ideal gas. Let’s take a gas that has a collection of free molecules, with no strong bond between them. It’s a gas; it’s in the gaseous state. Now I put this gas into a container, so the molecules roam freely through the container. Now suppose I somehow managed to gather all the molecules to one side of the container and closed them off with some sort of nylon sheet, okay? And now they’re in the upper-left corner of the container. Now I tear the nylon and release the molecules. What will happen? They will spread through the whole container. Right?

So molecules that are gathered in a certain corner of the container—if I leave them alone, if I release them—they will return to being dispersed throughout the whole volume of the container. Okay? But the reverse will not happen. Molecules that are dispersed throughout the volume of the container never gather themselves so that they are all in one corner. And the great puzzle of thermodynamics is why. Because on the face of it, this contradicts the basic principles of physics or mechanics, because all the basic laws of mechanics—today almost everyone says this—are reversible in time.

Suppose you show a film of a mechanical event that happened, and I project it for you backward. You have no way of knowing which projection is forward and which is backward. Both processes are legitimate processes from the standpoint of the laws of mechanics. Okay? Think of billiard balls on a table. Someone strikes one billiard ball, which strikes two other balls, which strike more balls, and so on. Now I show you the movie backward. When I show it backward, it is completely legitimate mechanically. If all the balls that flew off at the end had flown like that and struck those balls that continue flying like that and then went backward, they would have sent the original ball backward. The path is completely reversible.

So what does that actually mean? It means that in microscopic mechanics—here I’m ignoring friction and the like, of course—but if the laws of microscopic mechanics are symmetric, then why is macroscopic thermodynamics not reversible? It is not reversible in time, because the fact is that a collection of molecules at the edge of the container spreads through it all, but molecules spread throughout it all do not suddenly all gather together in one corner.

Or if you prefer: if a flowerpot falls from a rooftop, it falls down and shatters. But I’ve never seen a collection of shards fall from a rooftop and become a flowerpot down below. Become a built, intact flowerpot. Okay? The process is not reversible. There are one-way processes that are lawful in physics, but if you run the film backward—it is wildly improbable, it doesn’t happen. Okay?

Now how does that happen? How can it be that the motion of every particle is reversible in time, but when you talk about large systems, suddenly irreversibility emerges? This is the great puzzle of the irreversibility of time. By the way, this is usually believed to be what gives rise to the directionality through which we all experience the time axis. Time always flows forward, right? What gives “forward” priority over “backward”? Why don’t we start becoming younger? Where does the directionality of the time axis come from? In space, for example, there is no directionality, right? Just as I can go right, I can go left; up, down, forward, backward—it’s completely symmetric. Okay? In time I can’t go backward, only forward. So that means that time, somewhere, lost its symmetry; it always flows forward. The claim is that this is because of thermodynamics.

But as I said, that’s an English-English dictionary. What does “because of thermodynamics” mean? And in thermodynamics itself, where does that come from? How can that be? The explanation for this—the accepted explanation today, yes, the explanation of statistical mechanics for thermodynamics—the accepted explanation today is the following.

Let’s suppose—let’s see if I can show this. Do you see this chain? Think of it this way: I take some space, like the gas box in which the gas is enclosed. But like physicists, you know, we begin with something one-dimensional, and not points in space but little boxes in space, or little squares in space, okay? So here there are ten squares in a row in one dimension. We have a space with ten places, ten spots. Okay? Just to illustrate the point.

Now we have one particle, drawn here. You see this particle. Okay? That’s the particle. The particle can be in any one of ten places. Okay? Now suppose we have three particles, or two—let’s say two. Fine? So if I have one particle, how many states can there be? Ten, right? Either it’s here, or here, or here, here—ten possibilities. One particle in a chain with ten cells gives ten possibilities. What happens if there are two particles? Let’s say non-identical particles for the sake of discussion. Okay? If they’re non-identical, then for the first I can choose ten places to put it, and for the second one of the nine remaining, so that gives ninety possibilities. If they are identical, then it’s 45 because you divide by two. Okay? So then it’s 45 possibilities, if we’re talking about identical particles.

By the way, I think I once talked about this in relation to Amos Oz, who says that as Judaism progresses from Sinai to us, it’s like a room that fills up more and more with furniture until finally there’s no room to move. Creativity ends, it ossifies completely; you can’t interpret, you can’t move. And I once wrote to him, and also told him, that he has a mathematical error, because the more furniture there is in the room, the more possibilities there are for creativity and interpretation, not less. Think of a room shaped like a chessboard, eight by eight squares, okay? And you have one chair that occupies one square. Exactly like the problem I just described—you have one chair occupying one square. How many ways are there to arrange that chair in the room? Sixty-four, right? Eight by eight; you can put it in any square. If there are two identical chairs for now, how many possibilities are there? 64 times 63 divided by 2. That’s about 30 times more, right? If there are three chairs? 64 times 63 times 62 divided by 3 factorial, okay? Divided by 6. In short, much more. Once again, say another factor of 25, whatever.

So the more chairs you add into the room, into the given space—or area in this case—the number of possible arrangements grows. Or interpretive creativity is required more and grows more, or finds greater expression, the more principles there are to which I am committed. The more furniture there is in the room, the more creative possibilities there are for arranging it, not fewer. The space is smaller, but empty space allows no creativity at all. In empty space you can create nothing. Empty is empty. Creativity is what you do with things that are inside the space. That’s what creativity means.

So here too: the more particles there are, the more arrangements there are within the chain, not fewer. Okay, I return to our chain. So now, if there are two particles, say, then it’s 10 times 9 divided by 2—45 possibilities. If there are three particles, it’s 10 times 9 times 8 divided by 3 factorial possibilities. Okay? So it’s already much more. About a hundred and something—120 or something like that. So there is an increase in the number of possibilities as the number of particles grows. The more populated the room, the more possibilities there are.

Now let’s look at the following definition. Suppose I have three particles and I know—let’s go to the diagram. Look at the picture below. See it? I have three particles in this chain, and I placed them at positions 4, 7, and 10. Okay? For the sake of discussion. That’s the state. I have one particle at 4, one at 7, and one at 10. How many possibilities fit this situation? Of course here it could be particle number 1 or 2 or 3, and here too it could be particle 1, 2, or 3, and here too. Basically there are six possibilities here, right? Here one of the three particles, times here one of the two remaining, and the third here. There are six possibilities.

What happens if all three particles are on the right side? One, right? All the particles are on the right side. The distinction I made here is called the distinction between macroscopic and microscopic states. What does that mean? Macroscopically, I tell you: look, there is one particle at 4, one particle at 7, one particle at 10. That is the description of the state as a whole. If I want to know microscopically, then the macroscopic description actually hides beneath it several different states. For example, particle 1 here, particle 2 here, particle 3 here; or particle 2 here, particle 1 here, particle 3 here; and so on. There are several such states—six. There are six such states.

So that means that for one macroscopic state there are six microscopic states that fit it. Okay? What happens here? Here the macroscopic state is one. How many microscopic states fit it? One. No more. All the particles are at the far-right point, in cell number 10. Therefore, one state.

This means that in this state there is more information than in this state. In other words, if you give me the macroscopic state here, I can also tell you the microscopic state. I have complete information. If you give me the macroscopic state here, and I ask you, okay, but microscopically what’s happening—where is each particle?—it’s not clear. The information is incomplete; I have six possibilities. The information is not… I do have some information: I know the particles aren’t here, here, here, or here. Fine, I’ve ruled out many possibilities. But there is still freedom; the information is not complete information. Okay?

Now when I look—think back to our gas in the container, and suppose the particles are moving around freely throughout the whole space. Okay? The state in which all the particles are on the right side of the container is much less likely than the state in which they are spread across the entire container, right? Why? Because if I tell you they’re spread through the whole container, there is still very little information there. It may be that particle 1 is here, 2 here, 3 here, 4 here, 5 here. It could be that particle 5 is here, 4 here, 3 here, 2 here, and 1 here. There can be many, many possibilities. So if the particles move freely and each particle moves independently of all the others, then for the overwhelming majority of the time, when we look at the container, we will see that it is filled evenly throughout its volume. The times when all the particles are clustered on the right side of the container—this almost never happens; it’s such a rare state that it practically never happens.

Therefore, in physics we identify the amount of information with the likelihood of the state, the probability of the state—and that is what is called entropy. A low-entropy state is a state in which I have a lot of information. A rare state, an ordered state—I have a lot of information. All the particles are on the right side—that’s an improbable state. Okay? A state in which I have less information is a more probable state, and that is called a state with more entropy. Entropy is minus information—okay, it’s inversely proportional, actually minus the log of the information. But it goes with minus information: the more information there is, the less entropy there is. Okay? Or the log of one over the information.

The claim basically is that there is an objective definition here of what is called an ordered or complex state and what is called a simple or disordered state. And the claim that a shattered flowerpot is a disordered state, while a whole flowerpot is parallel to the situation in which all the particles in the container are in the same point or the same region—therefore it is a less probable state. And therefore, usually, if we drop very many flowerpots from the roof, they will almost always shatter. A very rare case would be one that doesn’t shatter, but usually it shatters. If we throw particles from the roof, there would be a very, very rare case in which all the particles fall and somehow land in the form of a whole flowerpot. But that probability is so tiny that it simply won’t happen; we won’t see it.

So physics is reversible; it is symmetric in both directions of these processes. But statistics does not allow us to see that. What creates the irreversibility is the statistics. Just to stress: it’s rare, but it’s possible. There is a theorem of Poincaré that says it will always happen. Maybe it will take trillions of years, but right. What does “always happen” mean? Assuming the process is ergodic on phase space—that is, if it goes through all the states—because if it doesn’t reach those states, then it won’t happen. But if the system can reach all states, then if you wait long enough, it will also reach them.

Anyway, all I’m doing in this really short lesson in elementary physics—or really mathematics—is just to show you what the meaning of the definition of complexity is. Complexity is not in the eye of the beholder. Complexity has an objective definition, and the definition is minus entropy. When entropy is small, that means the state is complex, coordinated, special. There is a lot of information in it; it is improbable. When entropy is high—well, when entropy is low that means the state is… sorry, when entropy is high it means the state is dispersed, the particles are throughout the whole container, and so on.

In this language, when you look at a living body, a living body is a body with very low entropy, because it is a coordinated, ordered, complex, very special body. If you took all the particles that make up a human being and randomly assigned them an arrangement, the number of times you would get a functioning body is negligible. You understand? You see the analogy? And therefore this means that a living body, or a biological system, is a system with low entropy. And the emergence of systems with low entropy from some initial state that is, say, unordered, random, accidental—that is a process that is statistically improbable. Okay? That is basically the complexity claim.

And now I move to the second law of thermodynamics. After we’ve understood what thermodynamics is, now the second law. The second law basically says this—and notice, this is a scientific law or a scientific statistical law. It has nothing to do with beliefs or philosophies. Okay? It has to do with statistical calculations. And what this law basically says is that a system does not move from high entropy to low entropy on its own. In other words, a system does not become more ordered by itself. A system—what’s called an isolated system—is a system with no outside involvement, but rather it moves by its own forces, and then the entropy will never decrease. It will either increase or stay the same, but it will never decrease. Order will not just emerge by itself. Go back to the flowerpot. Yes, when the flowerpot falls in the wind and there is no someone here who planned the fall of the flowerpot, directed it—there is no guiding hand—but rather it is a system operating autonomously, with nothing from outside interfering, then the level of order will only decrease, or the level of entropy will only increase. Because more order never emerges for no reason. Exactly like the gas in the container. When the gas is arranged on one side and we leave it alone, now there is no involved hand; it will spread throughout the container. If we want to return it to one side of the container, that will require someone’s intervention. The gas won’t do it on its own. When the system is isolated, closed, it will not happen by itself. It requires the intervention of someone from outside to do it, and only then can a process of order actually come about. Okay?

And that is basically the physical or statistical claim that underlies the premise of the physico-theological proof. The premise of the physico-theological proof basically says that a complex thing does not arise without a composer—which is nothing other than the second law of thermodynamics. The second law of thermodynamics basically says: there is a situation in which a system is isolated, nothing from outside is involved in it, it is in a state with a given degree of order, entropy is the measure of order, and the order will not increase—or the entropy will not decrease. That won’t happen if the system is isolated. If it is open to external influences, it can happen. Someone from outside can do it.

Yes, there are all kinds of puzzles—Maxwell’s demon, for example. I’ll elaborate on it because these really aren’t random examples; it clarifies the proof. Maxwell—I think it was he who proposed this paradox against the second law of thermodynamics. He says, let’s say there are little balls flying around in a container of ideal gas, and we’ll treat the particles as little balls moving at various speeds in different directions inside the container. Okay? You put a door inside that container, and next to that door you place a demon. And this demon opens the door every time a ball comes from the left side toward the right side. The door is in the middle of the container, dividing it in two. Every time a ball comes from the left and hits the door wanting to go right, he opens the door. Immediately after that he closes it. Slowly, slowly, you understand that all the little balls will move from left to right.

Now the system is closed: demon plus balls plus container. All of that is one closed system. You understand that after some time it will become more ordered. Why? Because the balls will cluster in the right half of the container. And we said that when they are clustered in one place, that is more ordered. How can that be? This is the paradox of Maxwell’s demon.

The accepted explanation of this problem—and this really is somewhat philosophical—the accepted explanation is that someone invested information here. Information. And incidentally, in information theory they actually measure information in terms of entropy, because information compensates for entropy. What does that mean? This demon has a policy: when to open the door and when to close it. Whoever programmed this demon—it could also be a computer, yes—whoever programmed the demon basically inserted into it a directed system and embedded information in it that determines how and when it should act. If you put information into the system, it can organize it. That is basically the claim.

By the way, that information becomes less and less usable as time passes, because once all the balls have moved to the right side, the demon becomes inactive, right? Because no ball comes from the left anymore. So you could say the information stopped functioning, the information went down, and order increased. Therefore the total entropy remains constant. The claim is that you also have to include the information—or the effective information—in the calculation, and then you will see that entropy still does not go down. And for it to go down, you need someone outside the container to intervene and create order there among the balls. Only then can a higher order suddenly emerge. Without the intervention of someone external, or information that he inserted into some system inside the container—but someone external did it, okay?—it cannot happen. And this is a theorem in physics. A physical law.

Now the claim is—again, there are objections to this and we’ll still discuss them; I just want to present the thesis—the claim is that this is basically the meaning of the second premise in the physico-theological argument. A complex thing—complex meaning ordered, with a lot of information, that is to say with lower probability, less likely to emerge—such a thing does not arise on its own. What does “on its own” mean? When the system is isolated, there is no involvement of an external factor, the system will not become more ordered. That simply won’t happen.

If you see a system becoming more ordered, with lower entropy, that means it is not isolated. It is not closed. There is something from outside involved in the system, causing the entropy to decrease. It doesn’t happen by itself. If you see shards of a flowerpot falling from a roof and when they reach the ground they arrange themselves into a whole flowerpot, you understand that someone planned that process; it is not something that happened by itself spontaneously. There is an external factor that was involved in the matter. That is basically the claim.

Now when we look at the world, there is complexity and structure in the world and so on. This means that if we started from the point of a Big Bang, something that has no very, very clear internal structure, and suddenly we see around us human beings and animals and plants and all kinds of things with very low entropy, or with enormous complexity, enormous information—all synonymous terms—then it means that this system is not isolated. Someone from outside the world caused this. The world is the container, yes? Someone outside the world caused some sort of order to arise within it. That cannot happen without the involvement of an external hand.

Now the involvement of that external hand can take place through the laws of nature. The laws of nature merely channeled the system so that it behaves from the point of the Big Bang to the safari we see around us today. So the laws of nature are responsible for this. But notice: the laws of nature are Maxwell’s demon. The laws of nature are a system with laws, with some policy, operating on reality in the world so that its entropy decreases. What does that mean? That someone built this demon and placed it by the door so that it would allow the balls to pass according to its policy. There must be someone who programmed the demon, who put into it the information that allows it to create order here. Or in our analogy: if the laws of nature create order here, that means someone programmed the laws of nature to do so. Because it doesn’t happen on its own. The laws of nature are Maxwell’s demon.

Therefore, even if you tell me that the laws of nature are doing all this, as people always claim in this context, that does not solve the problem. Just as Maxwell’s demon does not violate the second law of thermodynamics. So here, of course, I’ve gotten ahead of myself; we’ll still get there. I just want you first to see the picture. This is the picture. This is the physico-theological argument in a more modern formulation. And basically this is the argument that is in the midrash, and in Paley, and in Fred Hoyle, and so on.

Now we—not now, but next time—will begin to see various objections that arise in relation to this argument, and I’ll try to deal with them, each according to the honor it deserves. Okay. Does anyone want to comment or ask?

Seemingly an air conditioner cools the room, decreases the entropy in the room—but of course there is external intervention here; I’m increasing the entropy outside, and that decreases it inside the room. The outside and the inside—that’s another whole issue that I’ll still get to. But for now I’ll be satisfied with the fact that someone built that air conditioner; it didn’t create itself. The air conditioner is Maxwell’s demon. And someone built it in such a way that it would see to it that the entropy here decreases. Okay? So from my perspective, the air conditioner is the demon. True, it comes at the expense of entropy outside, and we’ll talk about that too. That’s part of the objections. But we’ll discuss that later.

Yes, Rabbi. Yes, yes. Low entropy, high entropy—all that—does it affect the probability, or does it also make the thing impossible? No, it’s not a matter of impossibility. It’s all a matter of probability. It doesn’t affect… what is probability? Entropy is the probability, or minus the probability. But we are not saying there is no possibility. It could be that… we’re not saying there is no possibility. The probability is small. No, there is a possibility. The probability is small. Okay. We’ll get there. That too gets addressed; objections are raised about that too.

Fine, so if you wait a very long time, it will happen even though the probability is small. We’ll deal with all these objections later. Okay? Okay, thank you. Anyone else? Have a peaceful Sabbath. Okay, have a peaceful Sabbath, goodbye.