The Physico-Theological Argument — A Probabilistic Elaboration (Column 144)

A few comments:
1. Regarding the claim that that creature is blind to specialness: it seems to me the claim is that by the same token it is possible that you are blind to specialness (in a previous discussion you were indeed “blind” when I asked you about the sequence 3141592654 and you didn’t identify it…), and then it is possible that every sequence is special, so in effect none of them is.
2. Regarding the equal likelihood of B1 and B2 with a die, I don’t think that is reasonable, and it indeed depends on our assessment, which to some extent begs the question. For example, suppose I roll three times and get 666. Should one conclude from this that there is probably a guiding hand here? On your assumption of equality, yes, but we would all agree not to, because we assume that a loaded die or a miraculous throw is something whose probability is low.

1. As I wrote, blindness is indeed possible, but from the blind person’s point of view his decision is reasonable and called for. But to say that every sequence is special is not correct. There are entropy measures that quantify specialness (and not probability).
2. We would certainly not all agree otherwise. Without prior assumptions, if I had to bet on one of the two possibilities when a sequence of three consecutive 6s came up, I would bet that there was a guiding hand. It is not a significantly greater probability, but it is still greater. Clearly the significance in this case is relatively low, but still that probability is greater than the other. Beyond that, there is another problem: we have an assumption that a person is honest unless proven otherwise (a presumption of probity). And another assumption, that it is hard for a person to throw a die unfairly (we have no control over the outcomes of throwing a fair die). These two presumptions stand against that difference in probabilities (which would lead to the conclusion that he did cheat), and therefore a long and very special and significant sequence is required to create a specialness that will overcome the presumptions. A sequence of three 6s is not significant enough.

First of all, thank you for responding to what I wrote. I certainly understand the asymmetry. Still, I would ask that you at least consider this response of mine carefully, and if not, perhaps I would be glad to arrange a meeting—of course only if the rabbi has the strength and time (which does not seem likely, since the two series will probably both go to a seventh game). I would not trek all the way from the north to Lod if I were not almost mathematically certain of what I’m saying.

1. I have no idea how you concluded that Aharoni is with you, since he explicitly writes that he agrees with the idea I presented to him (that such a conclusion is sensible only because the special sequences have high selection potential, and therefore the alternative hypothesis to randomness is more plausible than for the other sequences). When he writes: "Indeed, I think you are right. There is nothing special about a sequence of 6s, except that for human beings it is different," he agrees that the explanation is as I said: because for intelligent beings it is different, there is a greater chance they will choose it.

2. You inserted things I already said I do not agree with: "Y bases the conclusion on our knowledge of the motivation of the generator of the sequence (the person who rolled the die). Therefore, according to him, if we have no information about his way of thinking and motivations (for example, if the die-roller is a demon), we will not be able to infer from the results that they are based on the intention of an intelligent agent."
My response: not true. In my article I explained that the specialness of sequences like all 6s is probably shared by most intelligent beings (and there I even justified this "theologically," precisely through the SETI example you brought here. My claim is that scientists too understand this intuitively: that intelligent beings formed in another universe would see something special in complex signals, and that is intelligence itself. If the mad demon sent signals that we identify as special, that itself shows that he sees something special in them, and therefore he did not send a meaningless signal. Therefore, if we accept that some intelligent being produced the special signal, we have already said that he sees something special in it). I find it hard to believe that there could be an intelligent creature such that if we present it with ten ordinary sequences (341264 and the like) and one thousand 6s, it would not see something special in that sequence. If not, it probably does not understand what numbers are.
I assign some prior probability to the existence of an intelligent being. Once such a being exists, special sequences are by definition ones with high selection potential from its point of view.

3. You wrote: "The reason for this is my assumption that if the result were a million ordinary digits (without specialness), there is no reason to assume that P(A/B1)=1. In such a case, the chance that there would be someone who wanted precisely that sequence is tiny a priori, and then the conclusion B1 does not rise as it did here. Note: this is not because I assume something about the character of the die-roller."
That is outright self-contradictory. The prior probability P(A/B1) is unrelated to the die result. It is an assumption that stands before the dice are thrown: "What is the probability that there is a thrower who would want the sequence 5641237?" Therefore there can be no justification for your equation (c is an ordinary world): P(A/B1)>P(C/B1) except by means of an a priori assumption about the nature of intelligent beings and the like.
Suppose that for the first time in the universe someone throws a die, and you and I are whispering on the side and thinking: what is the probability that the thrower intentionally wants 66666, and what is the probability that he wants 32143? If those probabilities are not equal, then this certainly stems from an assumption about the die-roller. This is prior probability, not probability that follows from the throws. I do not understand how you do not see that again and again you are implicitly assuming that there is a greater chance of an intelligent agent who wants a special world (or: that if there is an intelligent being, it will want a special world) than the chance of an intelligent agent who wants an ordinary world. Without this there is no justification whatsoever for your statement: "the chance that there would be someone who wanted precisely that sequence is tiny a priori," since, as stated, the prior probability does not arise from the result; it is, as its name says, prior.

4. Suppose there is an objective measure of specialness. What does that have to do with these conclusions? How does it connect? (See section 6.) By the same token one could describe a universe in which the sequence "6532791624583" is "holy," because it is the number engraved on God’s Throne of Glory. Suppose that with absolute certainty, 100%, nobody besides me knows that this number is written on the Throne of Glory—not even God Himself. I rolled the die and this sequence came out. Do you think there is any sense in concluding that someone caused it? How did he cause it, if nobody knows that this sequence is written on the Throne of Glory? If the supposed agent does not see anything special in this sequence, then his choosing it is not planning at all, but in a certain sense randomness.
Here there is already no doubt that the existence of an intelligent being who wants the holy sequence is exactly equal to the existence of an intelligent being who wants any other sequence. (And therefore you must be consistent: either for no sequence infer that someone caused it, including the holy sequence, or for every sequence infer that someone caused it.)

5. A challenge question for your approach. You wrote: "If that creature knows that this result is special for me and that it appeared before me, it too will infer that it has an intelligent cause. But if it appears only before him, then at least from his point of view there really is no indication that it has an intelligent cause."
What happens if the security cameras in that creature’s house filmed the occurrence of the "ordinary" result (a thousand 6s), and now he sends me that video. Should I infer that someone caused it? After all, now there is no reason to marvel at the fit between my preferences and the die result; now this statement of yours is irrelevant: "its appearance before him requires no explanation. But its appearance before us is an event with objective significance, since we see specialness in this result and precisely it appeared before us. This calls for explanation." On your view, in such a case one should not infer that someone cheated in the throws.

6. What misleads you into thinking it makes a difference before whom the phenomenon appeared is that sometimes the conclusion is that someone coordinated the result with whoever would encounter it (the specialness lies in the coordination, not in the result itself). For example, if slips are distributed with a supposedly random numerical sequence, and I specifically receive a sequence equal to my car’s license number, then I will infer that someone probably planned it; but if that sequence came to someone in Mexico with a different car number, he has no reason to be surprised (there is no coordination here, so there is no specialness at all).
Only here are your words correct: someone else who encountered this would not need to infer the conclusion, but I myself would.
But note that we are dealing with a case where we are not inferring specifically that someone coordinated my preferences with the die throw. (Even in a case where we are certain that the supposed thrower does not know that my preference is 666666, we would still infer that he planned this sequence.)

There is no such thing as "a special sequence is measured relative to the other results." In every inference in the world, the only way is to compare hypotheses regarding the specific event that occurred. The probability of obtaining a sequence randomly is equal for every sequence, and if for a certain sequence we prefer to say that someone planned it (and for others not), then it follows logically that in our view the probability that someone would plan a special sequence is greater than the probability that he would plan a certain ordinary sequence.

2. It seems to me we agree. I only said that there are special assumptions here (as you wrote regarding the other cases). Not only that most people are honest, but also that the very ability to cheat at this is probably not something common.

Yishai, how is it that as a skilled analyst you agree with the rabbi? Do you have answers to my questions in another message?

Y
Are you ordaining me thereby as an analyst? Just let me know when and where the ceremony is 😉
I didn’t read everything you wrote because it’s terribly long (and of course in choosing what to read there is ad hominem).
If I understand correctly, in your view the specialness is something that should exist for every intelligent being, but I didn’t understand why (as stated, I didn’t read everything, so it’s no wonder I didn’t understand).
Likewise, you disagree with Rabbi Michael’s idea that the low probability arises from the meeting of a certain number with a person who thinks it is special, and here too I don’t see any reason for doubt, because that meeting really does require explanation. If I roll a die (a polyhedron, for the sticklers) with 10 faces on which digits are written, and I get my ID number (without the check digit because it is not independent), and then those of my parents, siblings, wife, and children, I will of course think this was done intentionally; but if you see it, you won’t think so. Admittedly, you could argue that you too would think it special if you knew, because the ID numbers of people with family ties were grouped together—but it could be something almost entirely accidental, like the ID numbers of the last 10 customers who called me at the service center of Masouda and Sons Ltd. So suppose you threw 80 times and have the potential for 10 ID numbers, and you go look for the people, and if you have lots of information you will likely find some accidental connection like that among them, but it won’t move you; I, by contrast, as the person who just spoke with all ten and then got the result, will think that this requires explanation.

Yishai,
I seem to recall that several times you commented here with very interesting things in analytical fields.

1. True, I claim that most intelligent beings would see something special in such sequences, but that is not my main claim.
My main claim is that one can justify a conclusion about intelligent intervention only by means of an a priori assumption that a special sequence has a higher probability of being made by someone than an ordinary sequence. And in my view that is embedded (logically-mathematically) within our conclusion:
Suppose there is a die that was found fair in a laboratory test. Yet it produces a sequence repeating a thousand times: 1,2,3,4,5,6. We would all infer that someone is responsible for that.
Since the probability of getting such a sequence randomly is P1 (which is of course equal to (1/[6^6000]), and we prefer to say that an intelligent being created it, we are giving the planning option, P2, a probability greater than P1.
By contrast, for an ordinary sequence we do not infer that someone planned it, even though the probability of getting it randomly is also P1. That is, in this situation the planning option, P3, in our estimation is smaller than P1.
That is: P2>P1>P3

A conclusion that follows mathematically from this inequality is that, in our view, the probability that an intelligent planner would create some special sequence is greater than the probability that he would create some ordinary sequence (P2>P3). The justification for this inequality is the claim that most intelligent beings would see something special in such sequences.

Do you agree that this inequality is correct? If so, what is the justification for it?

2. Not true. I agree that sometimes a match between parameters is also a kind of specialness. The claim is that here one need not get to that.
For if the argument stems from the fit between the parameters, note that the conclusion is about a coordinator, meaning someone who knows my preferences and programmed the die accordingly. But note that we are dealing with a case where we are not inferring specifically that someone coordinated my preferences with the die throw. (Even in a case where we are certain that the supposed thrower does not know that my preference is 666666, we would still infer that he planned this sequence.)
What misleads you into thinking it matters before whom the phenomenon appeared is that sometimes the conclusion is that someone coordinated the result with whoever would encounter it (the specialness lies in the coordination and not in the result itself). For example, if slips are distributed with a supposedly random numerical sequence, and I specifically received a sequence equal to my car number, then I would infer that someone probably planned it, but if that sequence came to someone in Mexico with a different car number, he has no reason to be surprised (there is no coordination here, so there is no specialness at all).
Only here are your words correct: someone else who encountered it would not need to infer the conclusion, but I myself would.

I sent the article to Aharoni, who replied:
"In the meantime I spoke with mathematician friends and they reminded me of the following:

The only known precise definition of what a ‘rare sequence’ is (for example a sequence of 100 digits 6) is Kolmogorov’s, a Russian mathematician. The definition is this: a sequence is rare (or ordered) if there is a short computer program that generates it. For example, a sequence of one hundred 6s is obtained by a one-line program, more or less. The sequence of the first 100 digits of pi probably cannot save on programming—it is not cheaper to compute the digits of pi than to list them one by one"

I now realized that even a conclusion built on a coordination between parameters (like your example) has no justification for inferring intelligent intervention except together with the assumption that such a coordination has higher selection potential than the intentional pairing of two other numbers with one another.
Why is it that someone whose ID number is 32146126712, when he receives in the library card no. 32146126712, immediately understands that someone specifically wanted these sequences and that this was not a random lottery done by the computer, but when he receives just some number he will not think that someone specifically wanted it, and will have no problem thinking the computer did it? Again, that is only because the probability that an intelligent being would make such a match is greater than the probability that it would want to give you some specific number (as opposed to a random choice with the finger in a children’s counting-out rhyme). There is no escaping this.

Y, in my opinion your argument is incorrect because you are falling into exactly the same fallacy you accuse the rabbi of. What I am saying is a bit strange, but try to understand my point.

In your view, the definition of special is only in the eye of the beholder, and therefore it is an irrelevant argument. My claim is that your statement that, for example, the life-producing sequence would be chosen by an intelligent person fails at exactly the same point. For now I will ask you why you think an intelligent person would choose that, and your answer will ultimately be based on the fact that life is something special and therefore someone would choose it. But the basis of "life is special" is exactly the same fallacy you accuse the rabbi of. How do you know that an intelligent person would choose life? Just because you would do that??? There—you are like him, relying on your intuition that life is something very special. Underneath, that is exactly the rabbi’s same intuition.

I’m not saying you state this explicitly, but in the end that is what you are saying, because it is your implicit foundational assumption—you are simply bringing it from another direction.

This intuition too is based not on mathematics but on people’s subjective feeling that they would choose it. And where does this intuition come from?? Because it is obvious to them that it is special, so they would want it. There is no logic here, only intuition. And if you say that there is logic in choosing it, then you are admitting that it is special and you do not know how to explain analytically why. In other words, at the base of everything sits the intuition that something is special, and not the logical and analytical reasoning you demand from the rabbi.

Therefore either the rabbi is right or both of you are wrong.

Kakhagach, did you read what I wrote?
I am not accusing the rabbi of following intuition. I am disputing the analytics of the conclusion (if intuition is, from his point of view, the justification—which he did not claim—then my claim would be that I have an explanation of what it is based on and there is no need for it. One does not need intuition for the claim that, for example, in a die roll it is more likely that one of the numbers 1,2,3,4,5 will come up than 6. That can be proven mathematically).
My intuition stands at the tip of the pyramid, in assessing the structure of intelligent beings, and not within the relations in the mathematical equations—in the "reasoning" and not in the "calculation." I have a clear diagram: only if special sequences have high selection potential does this justify our conclusion.

That is not precise. Tell Aharoni (how he doesn’t know this is beyond me) to go back to his mathematician friends. This is a definition of the information contained in a sequence of numbers called Kolmogorov complexity, but there are two more definitions (I don’t remember whether they are equivalent to this one and equivalent to each other) that are also built on the concept of algorithm.

The first—that of Kolmogorov—is built on the notion of information compressibility.

The second is built on the notion of the typicality of a number sequence (specialness) or the randomness of a sequence.

The third is built on a notion called martingale, and it is a kind of betting, and it is built on the concept of predictability, or the "expectability," of a number sequence.

And there is yet another definition, simpler than these three, but weaker than them (there are sequences that by this definition would be special and by the three above would not). Or stronger than them. I don’t remember.

That is exactly my point. Intelligent people would choose it only because in their view it is special, not because there is any logic in it. If the fact that someone thought something is special requires a planner, then what Rabbi Michi sees as special also requires a planner.

You really did not understand. The fact that something is special in people’s eyes does not directly imply that there is a planner.
It causes the selection potential of this situation/order to be high, to the point that the planning hypothesis is more plausible.
When I come to the desert and see stones arranged like this:
*
**
***
**** up to a thousand in a row,
I infer that someone arranged them not because the sequence is beautiful to me, but because I assume it would be beautiful to a potential person who passed by here, so there is a very high probability (relative to the randomness option) that he arranged them that way.

I am glad to see this response of Aharoni’s, because here he says (in my claim: says again) that he agrees with my words and not with Y. He explains here that the specialness of the sequence derives from its various properties (those Eilon presents, or Kolmogorov complexity. It really does not matter. See also my book The Science of Freedom, chapter six, where I deal with such sequences from a somewhat different angle—following the book of my friend the mathematician Prof. Moshe Koppel. And indeed you will see there that Eilon is right). It is a plainly non-probabilistic property. If one randomly draws a number sequence, the probability of getting any such sequence, regardless of its Kolmogorov complexity, is the same as for any other sequence. And yet the entropy, the specialness, the structure, the information in it, will differ from one sequence to another. These are the properties I called specialness, and I said they are in the eye of the beholder because they do not depend on the probability of getting that sequence as a result. Thus, for example, in a place where the computer language is different, it may be possible to compute the digits of pi as simply as a sequence of 6s. For us it is less simple. To be sure, here one feels that there is an objective dimension to the specialness, but in any case it is not connected to the probability of obtaining the sequence in a lottery.

I will respond briefly:
1. Again and again, in my view, you are mistaken at the same point. I completely agree with the sentence you quote from Aharoni: "Indeed, I think you are right. There is nothing special about a sequence of 6s, except that for human beings it is different." That is exactly what I am claiming: despite the fact that its probability is equal to others, its specialness in the eyes of human beings is enough to prove that there is an intelligent agent that produced it. In my view, the specialness in my eyes, without entering into estimates of the producer’s thinking, is enough to infer that there is an intelligent agent that produced it. And I think that is what our disagreement is about.
I refer you to my response to Aviad (further below), who brought a response from Aharoni in which he again explicitly agrees with me.

2. So if that is the case, then you are indeed making assumptions about the producer—and in fact a rather wild assumption—and Kakhagach is completely right in his criticism of you. That is why I wrote that regarding a demon (who, I assume, could be built completely differently from us), you would not say this, and that is precisely where we disagree. And if you do say this even about a demon, then you really are making (wild) assumptions about the producer without a shred of justification. So what have you gained? It seems to me that this is exactly what Kakhagach pointed out. How can you assume that every intelligent creature sees a sequence of 6s as special, as opposed to a sequence of digits of pi or any other sequence? If its mind/intellect is built differently from ours, and in its eyes precisely that specific sequence looks special (or that is exactly its home address and zip code), why assume that it too sees specialness exactly as I do? This is nonsense. Even regarding human beings there is a fairly far-reaching assumption here (and Wittgenstein already addressed it in his argument about rule-following). So if even with human beings we are uneasy, what shall we say about demons?! A conclusion (that there is an intelligent agent) based on such a baseless assumption (that every kind of intelligent creature sees the same sequences as special; that the ranking of specialness is universal) is itself baseless.

3. I do not agree, and I explained this in the post (in the very next sentence, immediately after the one you quoted). I am actually avoiding making assumptions about him, and my conclusion follows from that and not from an assumption about him.

4. But I do not know that nobody knows of the existence of that holy sequence. That is exactly what I am putting to the probabilistic test: is there someone like that who knows it and wants it, or not. My claim is that even without knowing anything about the producer (including his very existence), I can infer from the specialness of the result that there is a producer and that he knows of this sequence and wants it. By contrast, if the sequence is not special, or at least that is not known to me, then there is no reason at all to infer this about someone else. That is what I explained in the sentence I mentioned in section 3. We are repeating ourselves.

5. I did not understand the challenge question. There is no challenge here. If I know that he is simply sending me a photograph, then this is not a random event, so what is the question. And if I do not know, then I will assume there was an intelligent factor (the photograph or another mechanism that generated the sequence sent to me).

6. I did not write that it matters before whom the results appeared. On the contrary, I wrote that it does not matter. Even if they appeared before someone else who knows that they are special in my eyes, then de facto they are special in his eyes too (their specialness is that they are special in my eyes). And if he does not know this, then indeed he is "blind" to that specialness, as I explained.

Your concluding paragraph of course only repeats the same mistakes again. So I too will summarize my position against your summary:
A. The probability is indeed equal for every sequence, and nevertheless there is specialness, as Aharoni explained (Kolmogorov or otherwise).
B. What determines the existence of an intelligent agent is the specialness (which is in the eye of the beholder) and not the probability (which is objective).
C. I further claim that there is no need to resort to any assumption about the producer in order to reach this conclusion. On the contrary, as I showed, it is important דווקא to avoid making assumptions about him.
D. And I further showed that you are making very wild assumptions about the producer, which cuts the ground from under your argument. As I wrote in section 2, according to your approach the conclusion that there is an intelligent agent is based on assumptions so wild that even if it follows from them, it has no force at all (because the assumptions themselves are not plausible).

In short, we really are repeating ourselves. Your comments here only strengthen my conclusion that I actually explained my position well in this post (since all your arguments here were already answered in the body of my remarks), and let the reader choose.

I didn’t understand the contradiction between the rabbi and y.
The rabbi presents the possibility that the intelligent creator will choose this world as 1, and the probability of his very existence as unclear.
Whereas you present the chance that the intelligent creator would choose the world as preferable to something else, and the probability of his existence as preferable to the rabbi’s probability.

The rabbi explains that according to his view it is not far-fetched that a situation would arise in which the creator created the world. And therefore he presents his very existence as unclear.
And you claim that the probability of this is lower than 1 but significantly higher than something else.

So it is not clear where the contradiction is here? It looks really identical. Your reasons are quite similar, despite the difference in how the data are calculated.

Rabbi, I’m sorry, but what you wrote reflects a misunderstanding, and some of it completely ignores my arguments.
1. If I sent Aharoni an explanation, and he writes, "You are right," it is utterly unreasonable to interpret the next sentence as one that does not agree with what I said. Principle of charity.
2. Indeed, it is a wild assumption, but I argued that we all assume this, and I proved it (according to my argument). If it does not seem plausible to you, then there simply is no proof of God—so what? I explained where Kakhagach is mistaken.
4. I asked if!
5. I wrote about a situation in which he rolled and got a thousand 6s, and just sent me the video. Would you infer from the video that some demon cheated in the throw? You answered no (as I understood it). There is no doubt that a demon cheated in the throws, even though they were not before me.

Hello Y.
I do not agree at all, certainly not with the strange inference regarding Aharoni (the question is in what exactly you are right). But forgive me if I stop here. Let the reader choose.

I don’t understand what inference is being referred to. I presented him with idea x (that special sequences have a higher chance of being chosen), and he says he agrees with me without any reservation.

To the rabbi

The key word, by the way, with respect to specialness is homogeneity. One can formulate specialness as rarity by claiming that the probability of a homogeneous sequence is negligible as the number of digits in the sequence grows, and as the number of possible digits to be inserted also grows. Here of course the question will be asked why homogeneity is specialness, and of course that is a basic intuition, but it seems to me that it is connected to the ergodic assumption (the one in physics): if we have a measurement of some variable of a thermodynamic system (a gas in a closed box with fixed energy), say volume or temperature, then the measurement takes a macroscopically negligible amount of time, but on microscopic scales the measurement time is long and the particles change their configurations (positions and velocities) thousands of times during a second. The assumption says that over the course of the measurement time, all configurations with the same energy will be occupied by the particles equally over time (in phase space, the point representing the value will dwell for equal lengths of time in every configuration having the same fixed energy of the gas).

This is a state of heterogeneity, corresponding to the fact that in a very large random sequence of digits we assume every digit will appear with equal frequency. If it turns out that for some reason the system occupied only a certain configuration or a certain group during the measurement time and not all of them—and that is the state of homogeneity of a sequence—then we would say that there is an influence from outside the system (as in the case of gas in a closed system, where only those configurations with the same energy appear. That happens because of the external constraint on the system. If, for example, there is no such limitation, then all configurations will appear with no restriction on their energy).

The ergodic assumption is somewhat like a law of nature, because it has proved itself in the successes of statistical mechanics. The only way this law would not be violated in the case of the appearance of homogeneity is, as I said, an influence from outside, which is a kind of creator (intelligence or something else).

1. In my opinion, calculations of conditional probability are not the right way to handle the problem. One can calculate probabilities when we have a known event space, that is, the possibilities are clear in advance and we can know the probability of each “atomic case.” That is how it is with a die throw: we know there are 6 possibilities, and by considerations of symmetry we assume that each of the possibilities has a probability of one sixth. In such a world I can ask questions like: if it is known that the sum of two throws is 8, what is the probability that the second throw was a six.
In our case, the space of possibilities is not known. We do not know whether there exists an intelligent factor that creates the world or not. We want to infer conclusions about the space of possibilities from the results obtained.
2. Regarding the problem Y raised—what is the difference between a sequence of 6s and any other sequence, since every specific sequence has the same probability of occurring.
First, with all due respect, it seems to me that the solution he proposes is plainly incorrect. According to what he says, after every lottery win we would need to set up a commission of inquiry, because there is someone who has a motivation to create the number sequence that came up, and therefore it is more reasonable to assume that he created the sequence than that the sequence was created randomly.
Moreover, according to what he says, every event—since its probability is very low—requires an explanation; it is just that we did not find an explanation because there is no factor that has a motivation to produce such a sequence. It seems to me that these things are far from common sense.
Now for the correct solution (of course in my opinion): it is worth noting that when throwing 1000 dice, the probability that we get a sequence whose probability is very low is 100%, since some sequence must come out whose probability of occurring is 1/6^1000. Therefore one should not infer anything from the fact that a low-probability sequence occurred. If there are 10 million lottery tickets and one of them wins, one should not infer anything from that, even though the holder of the ticket has an interest in producing it.
A sequence of sixes is different because even before the die is thrown, we divide the set of possible outcomes into two groups—the group of special results and the complementary group. When a result from the group of special results occurs, we are surprised, and rightly so, and therefore demand an explanation; then we begin to look for who had an interest in producing that result.
In our case regarding the world, the probability that it would arise by chance is very low; it is a very special result. Therefore we begin to look for explanations and introduce the intelligent factor into our space of possibilities. If the world looked random, there would be no need at all to begin looking for explanations; the space of possibilities as previously conceived, without the intelligent factor, fully explains the result.
In this context I wanted to coin the phrase: "Every event is exceptional, but there are events that are exceptionally exceptional."
3. According to the above, one must be careful in calculating the probabilities. Although the probability of three consecutive 6s is 1 in 216, it seems clear to me that a sequence of three consecutive 5s would surprise us to the same degree, so at most the probability here is 1 in 36 (the first throw does not matter; what matters is that all three are the same), and that is even before counting other special cases besides runs (such as 1,2,3). Therefore the significance here is very weak.
But when speaking of 1000 consecutive throws of 6, however we count the special cases, we have a very significant result of planning.

D, you are mistaken.
1. We do not investigate every lottery drawing because there are many organizers and many drawings. The planner option has to be examined relative to the randomness option, and therefore in a case where the randomness option is not negligible (because there are huge numbers of participants, etc.), then there is no need to prefer the planner option.
2. How do you respond to my logical-mathematical proof of what I say? So far everyone has ignored it:
Suppose there is a die that was found fair in a laboratory test. Yet it produces a sequence repeating a thousand times: 1,2,3,4,5,6. We would all infer that someone is responsible for that.
Since the probability of obtaining such a sequence randomly is P1 (which is of course equal to (1/[6^6000]), and we prefer to say that an intelligent being created it, then we assign the planning option, P2, a probability greater than P1.
By contrast, for an ordinary sequence we do not infer that someone planned it, even though the probability of obtaining it randomly is also P1. That is, in that situation the planning option, P3, in our assessment, is smaller than P1.
That is: P2>P1>P3

A conclusion that follows mathematically from this inequality is that in our view the probability that an intelligent planner will create some special sequence is greater than the probability that he will create some ordinary sequence (P2>P3). The justification for this inequality is the claim that most intelligent beings would see something special in such sequences.

1. The event space is either that there is an intelligent factor or there is not. Either the world was created intentionally by someone or randomly.
2-3. You are repeating what I wrote. See also the thread linked at the beginning of the post.

1. You are defining that event space in a completely arbitrary way; you have no knowledge of it. In exactly the same way I could define the event space so that only the possibility of a world like ours coming into being is possible, or that everything is only my dream, or any other option. It is simply the option you want to entertain.
2. To y—the fact that you keep saying your proof is logical does not make it so. I claimed that you have no knowledge at all about the probabilities. You derive P2 and P3 according to your needs. You raise the possibility of planning only when you encounter a problem. If I happened to think a moment before the throw about a certain sequence and it came up, you would begin thinking about all sorts of possibilities, such as that your thought controls the dice or that someone reads your thoughts and controls the dice. When nothing surprising happens, you have no need to raise those possibilities. When an ordinary sequence comes up, I have no need at all to raise the possibility that someone planned it. As I noted, there is a 100 percent probability that some unique sequence like that will come up. I could have predicted that before the throw. This certainly does not follow from my knowing that there is no someone who wants to plan this sequence.
Your answer regarding the lottery does not help, because the probability for the specific winner is very low.

D,
You are introducing here completely strange formal definitions: "you ask questions when something surprises you," and not addressing my equation. P1, P2, and P3 are not derived "according to my needs" but are prior givens.
If I rolled a die and got an ordinary sequence, I certainly can discuss the question whether it was by chance or not. True, usually we do not do this, but not because such a stage does not exist, but because its outcome is already clear to us in advance (that the randomness option is preferable).
Why is the proof not logical? When I receive an ordinary sequence I decide P1>P2—do you not agree with that?
When I receive a special sequence I decide P1>P3—do you not agree with that?
Why is no one here able to address the arguments properly? Don’t you see this is a logical domain in which there ought to be a logical explanation for our conclusion? There is no such thing as "encountering a problem" or "something surprises you"; these are just words that miss the simple logical analysis.

I did address it. I said that you do not know the probabilities P2 and P3, and you define them according to your needs in order to explain the result. When it is a surprising result, you define P2 as high, and when it is a low result, you define P3 as low because you have no need for it to be high. Even if I knew there were millions of creatures in the universe who could control the die, and each one liked a different sequence, I would still conclude that someone controlled the sequence of sixes and not the random sequence.

D, I already explained why what you are claiming is not reasonable. Please read what I wrote with openness.

The probabilities P2 and P3 cannot be related to the result. They are prior probabilities, exactly like P1.

"Even if I knew there were millions of creatures in the universe who could control the die, and each one liked a different sequence, I would still conclude that someone controlled the sequence of sixes and not the random sequence."
Well, that is completely absurd. For if all are equal in their probability of intervening in the sequence, then this is exactly a lottery in which each creature has an equal chance of taking over the throw and determining what special sequence will occur. They are essentially running a lottery among themselves over who gets to decide what number will come up in the throw.
The probability that the creature who likes the sequence 514134216 will win is exactly equal to the probability that the creature who likes 66666666 will win, and therefore your conclusion is absurd on its face.

Let us take a simple example:
Inside machine A there are 500 cards, marked with the numbers 1 through 500.
And there is also machine B.
By a random press on the machines, one of the cards contained in each machine is expelled.
I pressed both and entered the room, and I find a card marked with the number 239, and I am wondering from which machine it came.
The number 239 is a holy number, in the sense that it is inscribed on the Throne of Glory, but I have absolute certainty that no one besides me knows what the holy number is (including God Himself), so the only two possibilities for the source of the number are either machine A or machine B.
Now you claim: "Since the number is objectively holy, clearly one should assume it came from machine B."
That is of course a mistake, because deciding whether the number came from machine B or A depends on one and only one question: what is the probability that machine B would produce such a number, relative to the probability that machine A would produce such a number.
And that question is a prior question standing before us even before we activate the machines. It is an independent question.
If you decided that it is more likely that machine B produced this specific number, then by definition you have already decided that a priori it has a greater probability of producing such a number than machine A does (for example, because it has only 400 possible numbers in it, so the ratio between the machines is 4/5).
Now I ask you: why, when you get the number 453, will you no longer infer the same conclusion? How does the fact that a certain number is holy affect your decision?! In both cases the only question is what the machine’s prior (unconditional) probability is of producing such a number.
If you distinguish between the holy number 239 and the ordinary number 453, then it necessarily follows here (logically-mathematically) that machine B has a higher prior probability of producing a holy number than of producing an ordinary one.

The analogy to the die is simple. The planner is the substitute for machine B, and if only in special cases you claim he is responsible, then it already follows logically from this that the planner produces under his hand some special sequence with a higher probability than some ordinary sequence.

I ask you to read what I wrote carefully and with an open mind. The fact that I am anonymous and did not manage to convince Rabbi Michi does not mean one should dismiss what I say without examining it. (By the way, I asked Prof. Aharoni again in a clearer way, and he wrote that he does agree with what I say, that it is logically embedded here that there is a higher chance that a planner will create special sequences. I will publish his response later.)

P.S.: If every sequence had someone who saw something special in it, it might still be reasonable to infer a planner specifically for a sequence like 6666 and the like, because the intelligent beings common around us and close to us are such, and they have a greater chance of intervening.
That is why I gave an example in which all intelligent beings gather (fight it out, etc.) in a way such that each one really has the same chance to intervene (which of course leads to every sequence having the same chance of being chosen). Here it is already literally a lottery, and there is no logic in distinguishing between a special sequence and a non-special one. The two alternatives lead to the "special" result with equal probability (one divided by the number of possible sequences).

I moved D’s message here:

I think the one who is not addressing what I am saying is you. The example of machines A and B is a proof by contradiction. If I have no knowledge whatsoever about machine B and I know that A is random, and a sequence of sixes comes out, I will conclude that it probably produces sequences of sixes. If we receive a long random number repeatedly, I will again infer that this is probably the number machine B produces.
My basic claim is that all your probability calculations are made from the assumption that you know what the possible event space is. And that is not true. You adapt your worldview and your event space to fit the observation. You have no ability to make such a calculation a priori; the calculation is made after the fact and builds a world that will explain the results.

I do not agree. This question too has already come up. See the aforementioned thread.

You are not addressing my example. What does a sequence of 6666 have to do with it?
I am talking about a machine that randomly draws the cards inside it, and the holy number comes out (which nobody knows).

If I may intervene, we can take as an example Paley’s (self-replicating) watch argument. Upon seeing a watch, we know with certainty that it was designed, if only because the chance of a watch coming into being through a natural process is negligible. The same holds for a living creature, which is far more complex than a watch (whether self-replicating or not). That is the probabilistic argument in broad outline. Of course there are additional probabilistic arguments concerning the number of mutations over the time required for evolution, and one could expand on that as well.

To y, my conclusion would be that apparently someone does know the holy number after all…
I am not claiming that you are incapable of constructing an event space that gives you what you want. Certainly, if you assume that the creature capable of intervening draws a number and then intervenes on its behalf, there is no reason to assume anyone intervened, because every number has the same probability. And if you assume that the creature prefers a sequence of sixes, that justifies the conclusion that someone planned the sequence.
I am only claiming that you have no justification for these assumptions a priori; rather, you assume them in order to explain the results.

I already said that in order to make the case exactly parallel to the machine example, one must describe a situation in which you are certain that there is no one who knows the holy number.
This is exactly where my claim enters: if you infer a prior datum because of a psychological preference, then the conclusion is a mistake. A probabilistic finding in our case cannot teach you anything about a prior variable.

Suppose a person named Gad fills out a lottery ticket and wins.
Gad does not know the mechanism of the lottery. Suppose even that he lives in a kind of isolation from the world.
He only knows that he became a millionaire because a certain number he guessed was emitted by a mysterious mechanism, and that mechanism is capable of emitting one number out of a very large set of numbers.
Gad says to himself:
"Either an intelligent factor caused me specifically to win, or I won randomly. The probability of the second option is very low. Therefore there is almost certainly an intelligent factor that caused me to win!"
Clearly, Gad is mistaken.
What is the difference between the rabbi’s argument and Gad’s argument?

I explained exactly what the difference is. It is like inferring a conclusion from a random chain of die results, since the probability of getting it is very low (exactly like the probability of getting a bunch of 6s). Since in any case some rare result is supposed to come out, the fact that a rare result came out does not call for explanation, and there is no reason to infer that there is an intelligent factor behind it. But if a special result comes out (and not merely a rare one), that does call for explanation. All this is explained in the post and has been discussed ad nauseam.

The difference between the above example and evolution is that in evolution there are very few functional sequences relative to the possible space. Therefore, even given billions of years of evolution, the chance of finding a functional sequence remains very low. One can compare this to a person winning the lottery jackpot about 1000 times in a row. Be sure that already by the second time an investigation would be opened.

Rabbi, why? Winning the lottery is not only rare but also special. I think the difference is that there are many attempts and the probability is not so tiny. (About 1 in 20 million.)

Winning the lottery is not special. In every drawing someone is supposed to win. If the same person won a hundred times in a row, that would also be special.

In every drawing someone is supposed to win?!?!?!?!

In a lottery drawing, each participant chooses some combination of numbers. The machine draws numbers. If someone matched what came up, he wins (usually nobody wins).

Exactly. Some number always comes up in the drawing, doesn’t it?

What does that have to do with it? Someone also has to hit that number.

I do not know how a lottery drawing works, and I also do not understand where this strange discussion is going.
Someone winning the lottery is not something strange. Period. Even if it does not happen every time, it happens not infrequently. Therefore it is not essentially different from some result of die throws, for example, which is rare but not special. In both cases, when it happens there is no reason to look for a factor that tilted the result in the direction obtained.

Some number always comes up (theoretically—even if nobody participates), but not always has someone guessed the number. If I won, that is indeed special.

Well, I hope you will forgive me if I withdraw. It is hard for me to teach reading and writing here.

If the probability of hitting it is 1 in a million, then even if it happens once every five times and even if there are thousands of people, that means someone cheated.

gogo, far more than merely "thousands" of people participate. People do not win more than statistically expected, otherwise they would shut down Mifal HaPais.

I deliberately wrote that Gad does not know how the lottery mechanism works, and therefore from his point of view the mechanism produced a special number (it is special because it is the number he guessed and it is the number that changed his life). He does not know whether the mechanism sometimes produces other numbers, and he does not know whether there are others who guessed in addition to him.
How do you know you are not in Gad’s situation?

Sorry for the trouble. It is Torah, and I need to learn.

That is exactly the problem in evolution. According to evolution, the useful sequence developed again and again despite being rare in the space of possible sequences. Suppose hemoglobin developed. What is the chance now of also finding a functional cytochrome? And histone? And genes for wings? And genes for the mechanism of smell? And genes for the mechanism of vision? And genes for the mechanism of diving? And so on and on—thousands of times the winning sequence "came up in the drawing" along the evolutionary path. This definitely parallels a person winning the lottery jackpot again and again thousands of times. And I think there is a limit to every trick.

To Aryeh—

If Gad thinks he is the only person filling out the lottery and he won, he certainly ought to be surprised. Here his surprise would be a mistake, but that mistake is known to us and not to him. His surprise is justified according to the data available to him.
If he knows that millions of rows are being filled out, he should not be surprised.
Now to our world—if we see one universe in which life arose, and we think it is utterly improbable that this should happen by chance, the obvious conclusion is that it did not happen by chance. If there are other beings who know there are billions of universes, then they know our conclusion is mistaken. But from our point of view and given our knowledge, our conclusion is correct. A person has to reach conclusions on the basis of the best available reliable information possible. That is what there is.

What? Why does the fact that many people fill out the lottery change the probability that Gad will win?

See what D wrote below.

It doesn’t. It changes the probability that someone will win. Just as if I threw a die millions of times, I should not be surprised by a long run of sixes somewhere, even though in the specific die throws that produced a run of sixes the probability of that was the same as in the case where only those throws had been made.

In connection with this column, see Yishai’s message after the previous column and my response there:
https://mikyab.net/%d7%9e%d7%91%d7%98-%d7%a2%d7%9c-%d7%90%d7%99%d7%9b%d7%95%d7%aa-%d7%95%d7%9e%d7%95%d7%a9%d7%92%d7%99%d7%9d-%d7%9c%d7%90-%d7%9e%d7%95%d7%92%d7%93%d7%a8%d7%99%d7%9d-%d7%98%d7%95%d7%a8-143/#comment-14233

With all due respect, Eilon’s answer is better 🙂

But if someone had marked out in advance throws 458,334–458,345, and there there was a run of sixes, then that would indeed be special. And also in the lottery, if I win, that is special.

D’s claim is studied within a mathematical theory called Ramsey theory, by the way. It investigates how long (minimality) large sequences (and also the size of graphs, for example) must be in order for large ordered (non-random) combinations of any size we can imagine to appear in such a sequence. This is a subfield of combinatorics. One of the greatest researchers in this theory, by the way, is our acquaintance Paul Erdős. It is a theory with a markedly philosophical character.

Eilon, (I don’t know if you were referring to me; if not—ignore this) I know Ramsey theory very well. דווקא in this specific case it does not help. A sequence of sixes never has to appear.

To Wondering

Indeed I was not referring specifically to your remarks (nor specifically to anyone else), but I wanted to point the discussion to the fact that there is already a mathematical treatment of the issue he raised. True, the philosophy of the theory is that on large scales, order and organization will always appear at some point (like the monkey who, after a million years of typing, will produce a Shakespearean work), so it is the opposite of the philosophy the rabbi is dictating here. But indeed it is not relevant to our discussion, because of course that is the claim about an infinity of worlds without life. But I am fairly convinced that in the innards of the proofs of its famous theorems there are important insights for our matter.

By the way, here is an interesting argument regarding the existence of a designer for the world: suppose we find a robot with characteristics of a living creature—that is, it contains a replication mechanism and may even be made of organic material like DNA. Would such a robot constitute proof of design or of a natural process? According to evolution, we should assume it simply evolved, because it has characteristics of a living creature. But that is utterly absurd.

To Wondering, with all due respect, you are not special.

D
You say that the force of the argument is based on our (lack of) acquaintance with the way universes are formed. That greatly weakens the argument in my eyes.
If our knowledge about the formation of universes is next to nonexistent, then the correct answer to the question "What is the probability that the configuration of our universe was formed randomly" is "I have no idea."
Exactly as Gad should answer the question "What is the probability that I won randomly?"
You wrote that a person has to reach conclusions on the basis of the best available and reliable information possible. I do not accept that. In my opinion, a person should reach correct conclusions. And if he does not have available and reliable information, it is better not to infer any conclusion at all.

I do not agree on two counts:
1. It is not true that we have no information at all. We know that material objects do not come into being ex nihilo, and therefore it is very plausible that the same is true of universes. Beyond that, sometimes an a priori assumption (such as the principle of causality, which despite having no empirical source we all nevertheless assume in scientific contexts and generally) has force even without concrete information. That is how it is in science and in other contexts as well. For example, you know the law of gravity and the principle of causality here on earth. Would you not assume that both operate the same way on the moon or in space? Even if you have no specific information, that is a reasonable assumption until proven otherwise.
2. Even in the absence of information, one sometimes must make decisions. We do not always have the privilege of not deciding. Therefore, in the absence of information, the methodological assumption is that the probabilities of the various possibilities are equal. That is usually how decisions are made under conditions of uncertainty.

There is a difference between rarity, order, and specialness. Which of the following sequences is the most special? Why?

8, 5, 3, 2, 1, 1

7, 9, 2, 7, 5, 6

2, 1, 1, 2, 2, 1

8, 1, 5, 1, 3, 1

7. 0. 5. 1. 2. 4

And to that I commented that the monkey-at-the-typewriter theorem (/the die thrown infinitely many times) is not related to Ramsey at all.

I am copying from a new thread a message by Y:

Hello Rabbi.

After our discussion, I took holy advice and turned to the generation’s greatest authority on probability, namely the exalted sage, Rabbi Prof. Ely Merzbach, may he live long, founder of the journal Higayon (now included within Badad) and its editor, whom God has filled with wisdom to devise thoughts, reason in probabilities, and investigate statistics, and whose field of expertise and research is precisely the field relevant to the matter at hand. I laid out my arguments before him in full, and he agreed with me completely, without any reservation whatsoever.
And although I did not need the words of that sage, I was greatly rejoiced by this, for I had lodged in the depth of this halakhah, and through toil succeeded in understanding it thoroughly, contrary to my initial thought.
Rabbi Michi is beloved and his teaching beloved, but truth is most beloved of all. And since I came to the site of judgment and there was no man, I called and there was none to answer my arguments, and no one took it to heart to examine this issue properly and to read even one of my long messages carefully, much less to answer my arguments rather than disappear in the middle of the discussion as several here did, because I am anonymous (is it conceivable that I should be right against the minister of faith, may he live long), I saw fit to publish here the agreement of the above-mentioned great authority, and perhaps it will stir the holy community here to lodge in the depth of this halakhah, and not dismiss me with straw.
Here is the place to add my astonishment that your honor defined this issue as ‘uninteresting,’ for if I am right, then the proof for God (according to your current presentation) is null and void like the dust of the earth, unless one adds another assumption (which in my opinion is correct and not at all excessive, and is also ‘theologically’ embedded in everyone who accepts the physicotheological proof, though this is not the place).
And after the aforesaid gaon ruled so clearly in my favor, who am I, who counts, who is worth arguing with his holy words; and at the very least it is fitting for every Jewish person to reexamine the matter, and the halakhah follows Rabbi Ely in probability.
We are your students and we drink from your waters, and all this is only in a place my teachers left me room to distinguish myself.
I hope these words will stir the rabbi to examine this issue privately with complete openness and composure, and may it be that he discovers that the truth is as I say.
And to the various readers who commented on the rabbi’s post and did not pay attention to hear my arguments, I also ask them to reconsider the matter.
And thus was the correspondence between us (the emphases are not in the original, and their purpose is to show what is included in the gaon’s agreement):

Yair:

Hello Prof. Merzbach, my name is Yair.
I would be glad to consult with you on a philosophical-mathematical issue that troubles me.
It is a very substantial topic, and I have not seen anyone pay attention to understanding the logic of it until I thought about it myself.
I wanted to ask your opinion about the rationale behind inferring the intervention of some intelligent being from a rare and special event that occurred.
If someone rolls a die before us and gets a thousand 6s (and the die itself was found in the laboratory to be certainly fair, its mass uniformly distributed, etc.), of course we all draw conclusions, for example: the die-roller is cheating and throwing it in such a way that this special result comes out.
The question is: what is different about a sequence of 6s (and the like) as opposed to any ordinary sequence? After all, the chance of getting some ordinary sequence randomly is exactly equal to the chance of getting a ‘special’ sequence. So why would we not infer something similar from the sequence 21346213 (for example)? How does the fact that some sequence meets a criterion of ‘specialness’ change the conclusion that someone caused this result? And if a certain number were ‘holy,’ would that also work? Why should I care that an objective machine decided the number is ‘special’?
I thought about this a great deal and reached the unequivocal conclusion that the explanation is as follows:
Although every sequence (special and non-special alike) has an equal probability of occurring randomly, in the case of a special sequence the alternative hypothesis (that someone intervened) is more plausible than this hypothesis is in the case of an ordinary sequence.
And the explanation for this is: special sequences have a higher potential of being chosen by a person than a specific ordinary sequence, because of their beauty and specialness in human eyes.
A demonstration that special sequences have high selection potential:
If we present a classroom of students with one hundred sequences, only one of which is special (66666), and ask each one to choose a sequence, the choice will be distributed more or less equally among the sequences (1 choosing each sequence), except for the special sequence, which will be chosen by more than any other sequence (for example, 8 students will choose 666666).

My main claim is that one can justify a conclusion about intelligent intervention only by means of an a priori assumption that a special sequence has a higher probability of being made by someone than an ordinary sequence. And in my opinion this is embedded (logically-mathematically) in our conclusion:
Suppose there is a die that was found fair in a laboratory test. Yet it produces a sequence repeating a thousand times: 1,2,3,4,5,6. We would all infer that someone is responsible for that.
Since the probability of getting such a sequence randomly is P1 (which is of course equal to (1/[6^6000]), and we prefer to say that an intelligent being created it, then we assign the planning option, P2, a probability greater than P1.
By contrast, for an ordinary sequence we do not infer that someone planned it, even though the probability of getting it randomly is also P1. That is, in this situation the planning option, P3, in our estimation is smaller than P1.
That is: P2>P1>P3.
Some people claim that when it is something special, it is assessed together with all the other possibilities, and that this justifies the difference in conclusions, but that is of course not true. For every sequence that occurs, I am supposed to decide between the randomness hypothesis and the planning hypothesis, and the probability of obtaining it randomly is negligible.

Do you agree with this inequality and with my explanation?
Thank you, Yair.

Prof. Ely Merzbach:

Hello Yair (what is your last name?)
I agree with you completely. I would only add one small remark that complements your arguments:
There is a fundamental difference between prior probability and posterior probability (retroactively, in Hebrew).
Before the experiment, all the sequences have exactly the same probability (namely one divided by the number of possibilities), but after the die has been thrown many times, the probability is already different. It is equal to 1 for the sequence that occurred and 0 for all the sequences that did not occur.
Best regards,
Ely Merzbach

Prof. Ely Merzbach
Dept. of Mathematics
Bar-Ilan University
52900, Ramat-Gan, Israel

Yair:

Thank you very, very much for your response.
My name is Yair H., and the topic has troubled me greatly.
I asked several people, and some of them began to argue that the subject is connected to definitions of ‘regularity’ and the like, and I knew there is no connection whatsoever, and that everything depends on the fact that under the hypothesis the plausibility is higher.
It amazed me how people do not understand that this is simple logic.

Regarding your remark, I could not understand the depth of your intention.
Seemingly the matters are trivial, no? Did my words imply otherwise?

This issue also connects to the physicotheological proof of God’s existence, and I wrote two articles about it that clarify this principle and thereby answer quite a few of the objections raised against that proof.

The first article:
https://drive.google.com/file/d/0Bws0Lni1BgE-bWhxZm8zWURrZVE/view
The second article:
https://drive.google.com/file/d/1oGDe7oV2YfSMS6wGXzcCHncph9jgjz6O/view

Prof. Ely Merzbach:

Here is what I meant:

Many times people tell me that a ‘miracle’ happened to them, that on that very day something special happened to them, or they met someone they had not seen in a long time, and so on and so forth, and then they ask me what the probability of that event is. To their disappointment, I answer that the probability is 1 (that is, 100%), because it already happened!
This is yet another common mistake: failing to distinguish between the situation before and the situation after.
I explain this at length in my book The Logic of Fate (Reuven Mass Publishing Ltd.)

Best regards,
Ely

End quote.

As a side note, I saw fit to mention that the mathematician Prof. Yuval Roichman also agreed with me ("Hello Yair, your argument sounds plausible. Thank you for sharing, Yuval"), as did Prof. Maya Bar-Hillel, a researcher of probabilistic reasoning from the Center for the Study of Rationality ("Your solution is very nice. Thanks for sharing. Maya.").

And this is what I answered:

Exactly as in the case of Ron Aharoni, you are repeating your formulation of the question and their answer, and again simply not understanding what is being written to you. They all agree on the point that there is a difference between backward probability and forward probability. Which of course is trivial and obvious and does not require authorities of that caliber, but of course it also does not have even the slightest connection to the disagreement between us.

I think there is no disagreement between y and the rabbi (and y, pardon me, is insisting on not understanding this).
The letter y sent to Aharoni and now to various other great rabbis, containing his argument, is correct. I do not think the rabbi disagrees.
(The proof is built on the assumption that the probability that an intelligent factor would want to create life is much greater than the probability that randomness would create it.)
Y’s argument proves an intelligent factor.
The rabbi’s argument proves an intelligent factor that chooses to create the world.
The difference is in two points:
For y, the prior probability of the existence of an intelligent factor is greater than the prior probability of what the rabbi proves.
The advantage for the rabbi is that the conditional probability (if there exists an intelligent factor that wants to create the world, the probability that there will be a world) is 1.
For y, one has to take into account the probability that just some intelligent factor would simply happen to choose to create the world (which is of course greater than the probability that randomness would create the world).

In the end, y and the rabbi arrive at the same probability for the existence of God. (For the rabbi, it is the prior probability of the existence of an intelligent factor that wants to create a world, multiplied by something that comes out of Bayes’ theorem as explained in this post.)
For y, it is the probability of the existence of an intelligent factor multiplied by the probability that he would want to create a world. Exactly the same thing as for the rabbi!!!

Proposal,
Of course the conclusion is the same conclusion, because we both agree that a special result points to the involvement of an intelligent factor. That is not what the argument is about. The argument is about the reasoning for that conclusion. Therefore I completely agree with your calculation, but as I explained, if I understand his claim, there is nevertheless a disagreement between us in the reasoning: the question is whether in order to infer the conclusion that this is not a random result I am supposed to assume something about the intelligent factor that produces the phenomenon (6666). He says yes and I say no.

As I explained, if it is known to me that the fellow throwing the dice is a demon who may have a way of thinking completely different from mine, would I still assume that the result 6666 on the dice was not achieved by chance? It seems to me that again we both agree that I would. But he explains this by an a priori assumption that every intelligent being acts like me (an a priori assumption that even intelligent demons see something special in the series 6666), and only by virtue of this does he infer the conclusion that it is not mere chance. By contrast, I claim that one does not need that assumption. The very fact that the result is special for me means that the demon in this case (!) probably acted as I would (not that he is necessarily built like me and thinks like me in every other case). For me, the fact that he acts/thinks like me (in this specific case alone) is a conclusion from the specialness of the result, whereas for him it must be an a priori assumption about all intelligent beings. Thus, for example, from my point of view, if I know that this demon is throwing more dice, there is no reason for me to assume that again he will do something similar to what I would do. Y will assume so, because every intelligent being sees the same specialness in the same sequences.
There is no need to explain that his assumption is completely absurd (apparently there is a need, to my repeated surprise here). Why assume in advance that every intelligent being will see something special in the sequence 6666? What does that have to do with intelligence? This is a mental structure, not something objective. Could there not be an intelligent being built differently from me, no less intelligent, and yet seeing the sequence 6666 as something purely random? Of course there could be such an intelligent being. This is just stubborn insistence on nonsense, and it stems from a misunderstanding of the probabilistic argument (a failure to understand that subjective specialness is enough to infer the conclusion, and one need not make it objective by an arbitrary and absurd assumption).

???????????????????????????
"You simply do not understand what they are writing to you"??? "It does not have the slightest connection to our disagreement"???
Rabbi, there is no way to explain the bizarre response you wrote; apparently you did not read at all what I asked him.
I wrote to him explicitly:
"And the explanation for this is: special sequences have a higher potential of being chosen by a human being than a specific ordinary sequence, because of their beauty and specialness in human eyes."
"My main claim is that one can justify a conclusion about intelligent intervention only by means of an a priori assumption that a special sequence has a higher probability of being made by someone than an ordinary sequence," "A demonstration of this is…".

He answered me: "I agree with you completely"!!!!! c-o-m-p-l-e-t-e-l-y, including this point that the explanation is an assessment about the minds of human beings!!
He merely added another common mistake people make in probability (another one!), as he himself later clarified:
"This is yet another common mistake: failing to distinguish…"

It is legitimate that the rabbi does not have the strength to read what I write, but in that case it is better to refrain from responding and spare embarrassing responses like the one you wrote".

Rabbi, now I am terribly confused!
You told me that if a creature that does not see anything special in 6s gets such a sequence and sends me a video, I should still think someone caused it. And here you wrote that: "The very fact that the result is special for me means that the demon in this case (!) probably acted as I would," so if it came out before a demon and he only sent me a video, then we have no reason to marvel at the fit between me and the sequence.

If there is someone who is still reading what I write, I will explain where Rabbi Michi is mistaken, and once again puts words into my mouth that I did not say.
If this demon caused the sequence "6666666," and he did so not innocently, then that itself is because he sees something special in it and not in 3213426. And if he did it randomly, then again this mechanism is no better than ordinary randomness.
I am not necessarily saying that in the next case the demon will again choose such a sequence; not because he is a demon—this is also true of a human being. After all, there are far more ordinary sequences than special ones, but in a pairwise comparison between a special sequence and an ordinary one, the special one indeed has a higher probability.
A conclusion about an intervening demon does not necessarily claim that he was aware of my aesthetic tendencies to see something special in 6, and therefore created the sequence; therefore the claim that it is the fit between the sequence and a person who sees something special in it that requires explanation is completely absurd.

But truly, all these pixels I am wasting are in vain, for already from the first message the rabbi did not really read what I wrote (and the arguments put in my mouth testify to that a thousandfold).

And regarding a case where it is known that the demon does not see anything special in 6, I would still infer that someone caused it—but not the demon!! If from the demon’s point of view the sequence 666666 looks the way 2146233 looks to us, then the probability that he would create it is exactly like the probability of getting the number randomly! Unless one assumes that the demon knows what looks beautiful in my eyes, and therefore chose precisely this sequence (but that is not correct, since we do not necessarily assume/infer that he reads minds and the like).

What is the disagreement here? In this post (in the paragraph "Note: the point of disagreement"), the rabbi writes: because in my eyes this is a special result, the assumption that the demon also wanted this is not arbitrary. True, in this he contradicts what he said earlier ["I am not assuming anything about him"] and this requires investigation, but still this is exactly what y says.

I am done. I explained as much as I can.

Proposal,
Sorry for the delayed response.
Your comment that the rabbi contradicts his previous statements is correct; that is exactly my claim.
The datum, ‘the unconditional probability that an intelligent creature will create a certain world,’ is a prior datum unrelated to the result of the throw. It can be discussed even before the first throw in the world gets underway. Therefore it does not change even after the result 1,2,3,4,5,6 is obtained. The surprise is not at the fit between my preferences and the results of the throw, since I do not necessarily assume that that factor knew what my preferences were.

To the rabbi, hello,
With your Torah’s honor forgiven, but in my opinion the rabbi did not touch here on the stronger and more famous atheist question.
As is known, there are two possible ways for atheists to explain the world before us: 1. A world that was created and has a cause that is not God. 2. An eternal world.
The rabbi addressed only the first part of the atheists’ position.

The point is that according to the formula (as the rabbi used it), there are only two main parameters: a. the probability of the event itself. b. the conditional probability that given the event, the world would arise. And since we assume the probabilities of the events are equal (p), then where we have the option of assuming there is an intelligent entity, of course we will prefer to assume that… one need not be a great genius to understand that.

But!!! With respect to the atheist conception of an eternal world, here the rabbi’s answer is very problematic. Because in an eternal world the two parameters do not exist. There is only the first parameter. And because we do not know how to evaluate its probability, it equals p. Just as God equals p. (In addition, the religious conception also has to evaluate the conditional probability that God will create a world.)

Hence, the probability that the world is eternal without a planner is preferable! If only by virtue of Occam’s razor.

Again, I will begin by saying that my exalted Torah’s honor is waived for the gentleman. 🙂
But it seems you did not understand the focus of the discussion here. I am not dealing with convincing atheists that there was creation. I am explaining why, if one assumes there was creation, it is more plausible that there is a factor that created it and that it did not happen on its own. The dispute between me and Y was on this question: what is the role of the specialness, and is it the specialness or the probability that does the work. That, and only that, is what I dealt with here.
And by the way, the two options are not as you wrote: that there was a cause that is not God, or that the cause is God. The question is whether there was or was not a cause. If there was a cause, we call it God by definition.
The question of an eternal world is an entirely different question, and I dealt with it in the second and third booklets. Not here.

Okay, thank you very much.
In the second booklet you want to argue that if the world is eternal, it nevertheless requires an explanation, until you arrive at an explanation that breaks the regress and is its own cause.
And in the third booklet you say that it is preferable to argue that the explanation is volitional.

But assuming we give up the second booklet—for example, the idea that every entity that is not its own cause requires a cause—
then we are left only with the conclusion that it is preferable to argue that a complex thing requires a teleological and intelligent composer. (And not that every entity requires a cause.)
My question here attacks that idea.
Namely, if we enter only the realm of statistical calculation, then there is no advantage to God because He requires a calculation with two parameters, as opposed to the assumption that the world is without an additional cause (which requires only the calculation of one parameter).

Does the rabbi have a way to deal with this question? I would be glad if the rabbi could write even briefly, because I do not see a reasonable solution to it.

I did not understand why one should give that up. That is exactly the argument in favor of creation.
Beyond that there is also a problem with actual infinity (see the booklet there), at least regarding entities of the sort in our world. If it is one entity that exists for an infinite time, one can interpret the infinity as potential (there was no time at which it did not exist).
Beyond that, a complex thing requires an explanation regardless of whether it was created or not (this is the principle of sufficient reason, as opposed to the principle of causality, as I explained there).

As is known, there are difficult questions about the principle of causality in the cosmological proof, and also about the demand for sufficient reason for every entity, even one that is not complex (the rabbi wrote this there explicitly).

In any case, I understand that according to your view, in order to obtain a proof for God one must combine the two proofs together. They are not separate and standing on their own.
First, the cosmological proof causes us to accept that the world was created/caused by a first cause that is self-caused.
And the physicotheological proof causes us to understand that this entity is probably intelligent.

But without the cosmological proof in its various formulations (Kalam / Leibniz), it seems from your words that there is no reason to accept the physicotheological proof. I assume this is because of the reason I raised: that there is no advantage in positing an entity that causes the composition rather than assuming that the complex thing is self-caused. (Because that contains two parameters as opposed to one parameter p, as I said above.)
P.S. It now occurred to me that this is basically what Dawkins, may his name be erased, says in the great question, who created God, and if He is self-caused why not assume the universe is like that.
Indeed the only way to deal with it is not within the physicotheological framework but rather by going straight back to the cosmological proof.

Does the rabbi agree with this analysis?

First, I do not think Dawkins is wicked. He is mainly mistaken.
As to your point, even without the cosmological proof there is weight to the physicotheological one, since the complexity too came into being at some point in time, and beyond that it also needs a sufficient reason even if it was never created. The assumption, of course, is that the things in the world are not their own cause (perhaps that is what you call the cosmological proof).

I was talking about the assumption that the complexity is primordial and was never created.
I think this is the main issue I am raising here that the rabbi did not address in the calculation here in the post. If the whole universe has a cause, then I agree that it is preferable to argue that an intelligent entity would indeed create it.

I disagree with the principle of sufficient reason as an assumption that is always valid, i.e. that everything requires a reason (except for an entity that is its own reason). In the second booklet it seems explicit that the rabbi agrees with me and argues that this is a weak argument. Rather, only complex things require a reason, and there you mentioned that this belongs to the realms of the physicotheological proof.

If so, then my difficulty returns to its place: to claim that the universe has a cause requires two parameters, p + the probability that an intelligent entity will cause it. Whereas to claim that the universe will arise like this is only p.

Perhaps it would be easier to discuss this with an analogy similar to the one the rabbi brought in the second booklet.
When we encounter a very very special watch, and a heavenly voice informs us that it is eternal.
At this point we have two possible claims—either an intelligent creature (for example a human being) emanated it in a relation of emanation.
Or it has no cause and it simply exists.

According to the statistical calculation the rabbi raised here in the post, it would seem we should prefer the second option.
Because it has only one parameter to calculate: the probability of the world = p.
Whereas a human being would require two parameters: p + the probability that he will create a world.
In such a case Occam’s razor too would surely make it preferable to accept that a human being created the watch.

I do not agree. But I have already said what I had to say and I see no point in repeating it.

With respect to which part?
As for the issue of sufficient reason, in my humble opinion you wrote explicitly that it is not strong on its own.

The rest follows from the calculation in the post once one plugs in the data.

Perhaps the rabbi will explain why, if he sees an eternal watch, he would claim it is preferable to assume there is a planner behind it in a relation of emanation—without using causality, i.e. the cosmological proof?

By the rabbi’s instruction, transferred from the question:
Hello Rabbi,
I wanted to ask a question whose answer I did not really understand. I asked it elsewhere on the site, but it seemed to me that the responses there were not really related to the topic, and the answers also were not entirely related to the question. I would be glad if the rabbi could answer.
If there exists before us a complex and ordered thing (like a watch) but eternal [for the sake of the matter, a heavenly voice came out and revealed this to us], is it reasonable to claim that it requires a planner?
The advantage in the claim that yes, there is a planner, is that this claim has great explanatory power, so that it explains well why the unique phenomenon before us exists.
The disadvantage of this claim is that to some extent we are just pushing the claim of complexity one step backward. After all, the second complex thing (God, for example) also requires an explanation—for we are dealing with a unique entity for which we could imagine a different reality, and so on. Hence, in order to stop the chain, why should we not stop at the watch?
B. My assumption here is that even of an entity that is its own cause, one can imagine that it would theoretically exist in some other way. Can there be an entity that it would not be possible to think of as existing in another way? What would the status of such an entity be called? Only "a necessary existent"?! Or is there an intermediate reality such that, insofar as the entity exists, it could only be thus?
For such an entity, is it appropriate to ask regarding it the physicotheological proof? If not, then we have here an excellent regress-breaking entity. Is that not so?
I would be very glad if the rabbi could address the question. (And surely the dear readers here on the site as well ? )

You are bringing me back to the question why God Himself is not subject to the physicotheological or cosmological argument. I dealt with this in the booklets. Since I am looking for a regress-stopper, I have no choice but to assume that He is an entity of a different kind, self-caused. As for the universe itself, I wrote that it is not plausible to see it that way.
I did not understand the alternative you are proposing here. It seems to me that you are simply repeating the physicotheological argument.

The rabbi dealt with this in the booklets, but without addressing the claim of an eternal complex thing (an eternal watch).
In the cosmological proof, the rabbi wrote that an eternal entity still requires the principle of sufficient reason, but emphasized there that this is a weak principle for eternal things. It is strong only for complex things, and you wrote that this is the physicotheological proof.
And in the third booklet, the way of dealing with the fact that God does not require explanation was because the world was created…….

So first of all, there is no explicit treatment of this question in the booklets.
———-
The basis of my question here is perhaps about the definition of the plausibility of the hypothesis. The rabbi symbolized it in the article here as p.
If an eternal watch exists before us, then the claim says that we could have thought of an infinite number of other entities, most of which are not complex. If so, if there is a God for this watch, that explains well the existence of the watch.
But the question asks: regarding God too, we could have thought of an infinite number of other entities that might stand in His place (for example a broken watch). If so, why not stop at the watch?

So the possibility I proposed is that God is not self-caused but rather a necessary existent. And the practical difference between the two is whether we could have thought of another entity in His place.

The question is whether this criterion is at all part of p? For it will always equal 1/infinity.
Or if it is not part of p, then which term in the equation does an eternal watch contain? Such that we could think of another possible reality for it, namely a simple thing?

As for the booklets, I will check again. As for your point, I simply cannot understand it. What difference does it make for our purposes whether one speaks of self-causation or necessary existence? Choose whichever you want. The regress-stopper is God.

That one can think of something that is self-caused and yet could have been otherwise. Hence it can be a unique thing.

But a thing that is a necessary existent cannot be thought of as some other reality.

The rabbi writes that we have two possibilities to explain the world:
B1: There is an intelligent factor that created it.
B2: It happened randomly (there is a random universe-generator that draws universes, and this is what came out).
But that is simply not correct.
There is a possibility B3: that there exists a factor X which is not a being with will, whose property is to cause the creation of this world.
Hence the calculation collapses.

No. Because then the question is who created it. For if it is not intelligent, then the structure that emerged from it is a product of its own structure. That is, it itself is part of the universe we are discussing. This only pushes the question one step back.

Your Honor the rabbi,
The question you are now asking does not appear in any proof that you write.
For insofar as it belongs to the cosmological argument, then the conclusion of that proof is that there exists an entity unlike the entities in our experience, and it caused the world. But possibility B3—that there exists a factor X which is not a being with will, whose property is to cause the creation of this world—can also come out of the conclusion of the cosmological argument.
Now if we go to derive your claim from the physicotheological proof, it does not emerge from there either. For its power is only to characterize the cause found by the cosmological proof. But it has no power to create a proof of its own. After all, the rabbi agrees that if there exists a place with order (low entropy) that is eternal, then the physicotheological proof does not necessarily attack it. For it is not clear that it needs to be explained. And if we explain it, we can ask of the explanation (God) why He is this way and not another. So either we arrive at an infinite regress or we claim that God is self-caused. But then we could stop at B3, for it is not within our experience.
And therefore it sounds as though you are assuming a new proof, that every complex creation requires an intelligence that caused it. But the source of this understanding is not a statistical conclusion as you present it in this post, but an axiom of pure reason. But if so, the entire argument appearing in the PDF can be shredded.

Do not shred it so quickly. The claim is that if there is someone who created the world, he must be an intelligent entity (for if not, then he himself is part of the world and in need of explanation). Up to here I have defined the world under discussion. The probabilistic discussion starts from here and asks who created it. Now one must examine the option of random emergence versus an intelligent entity.
By the way, in the booklets I explained that there is a connection between the cosmological and the physicotheological proofs. They complement one another, and to some extent the distinction between them is only didactic.

You write that when there exists a deterministic process from entity B3 toward the world, then you assign B3 as part of the world.
But that is not correct. And there is nothing for that claim to rely on. For the assumption that the world requires a cause stems from the expanded principle of causality: it claims that the objects around us are not their own cause, and so they have an additional cause not in our experience, regarding which there is no point in asking about its cause because it is self-caused.
There is no doubt whatsoever that possibility B3 could exist, such that although it leads deterministically to the creation of the world, the expanded principle of causality (the basis of the cosmological proof) does not attack it at all.
The fact that the proofs complement one another is exactly the focus of my attack.

Hello,
You wrote regarding the argument here that—
The probability of hypothesis B1, that there is a planner, is P, just like the probability of the world.
And the probability that the planner will create a world is P(A|B1) = 1, because the intelligent factor is defined as one who wants and can create this
special world. Therefore his action is deterministic.
But perhaps you did not notice how with one stroke of the pen you skipped over the core of the argument. You must know the prior probability that God will create a world in order to calculate the likelihood ratio between B2 and B1. And moreover, otherwise how is this different from the claim that God would create just some random world?
You can see that here too (Stanford Encyclopedia of Philosophy) they treat this as highly important:
"which expresses that life-friendly conditions confirm the designer hypothesis and which likelihoodists such as Sober (2003) regard as at the core of the argument from fine-tuning for design."
And on this point there are many attacks: is it indeed reasonable to assume that the creator would create such a world, or not? If not, then of course the entire argument collapses.
https://plato.stanford.edu/entries/fine-tuning/#WeExpeDesiDesi

K, maybe related?
https://mikyab.net/%D7%A9%D7%95%D7%AA/%d7%91%d7%99%d7%a7%d7%95%d7%a8%d7%AA-%d7%A2%D7%9C-%d7%94%D7%98%D7%99%D7%A2%D7%95%D7%9F-%D7%9E%D7%9F-%D7%94%D7%AA%D7%9B%D7%A0%D7%95%D7%9F/

To Moavit.
You are indeed right that answer 1 there is almost exactly my question and request here.
But it did not advance me in understanding at all, because he repeats there exactly the same words he wrote in this post. I will quote selected parts below.

"Note that at no stage did I assume anything here about the nature of the generating factor (the die-roller) and his mode of thinking, and I did not need that in order to reach the result."
But if so, how is that different from just an ordinary random combination, where he would also say that the probability of creating an ordinary creation is 1?
"In such a case the chance that there would be someone who wanted precisely that sequence is tiny a priori." So it seems he is making an a priori assumption about the designer!!! But let us continue and discover that no???
"Note: this is not because I assume something about the character of the die-roller, but on the contrary because I do not assume anything special about him."
And regarding this G. E. Moore said, in the naturalistic fallacy, that if uniqueness is a characteristic (entropy), one cannot derive a norm from it! (motivation for creation)

Am I the only one to whom it seems that the rabbi in this argument is an implicit heretic; one only needs to expose to him the mistake he is making.