But you want to argue that even if we knew of a mechanism for producing universes, there is still almost certainly a God, 100% minus the chance of random formation, because there’s almost no chance of getting life, and they refuted that argument because everything has a low probability. Even the random result 3,3,5,2,1,5,6,4,2,3 has an almost zero chance, so why doesn’t that prove that aliens from Betelgez are responsible for it with probability 0.999999984?

Because I was brief, I didn’t show that they didn’t even refute that. Think of a case where you rolled a die and got 6 a hundred times in a row. Now you consider one of two possibilities: this is a random result, or an intentional one (there is a directing hand of God, or gods, or a loaded die). Would you also say of someone who concludes that the die is loaded that this is “statistics in reverse”? After all, the probability of such a sequence is the same as any other sequence. Real “statistics in reverse.”
What I’m claiming is that in his example he brought a rare result (low probability) but not a special one (because any result of the dice would have been equally rare), and from that indeed nothing can be inferred. That is statistics in reverse. But if the dice produce a special result and not merely a rare one (like the sequence of 6s I gave), the conclusion is called for.

Beyond that, you keep bringing up the option of aliens from Betelgez, which is one out of many possible options, so concluding specifically that is nonsense, whereas here this option is not one among many but the only one (either there is a directing hand or there isn’t), as I already noted in my previous comment.
In short, it’s nonsense.

Nice, you got me; the die example really is like life. But what exactly counts as “special”? Why is 6 special? And most importantly: how does its being special change the situation from any other result? Does that make it less likely than any individual alternative? Even when it’s special it has the same probability!
At this point my conclusion is that really even in the die case it isn’t right to think that someone / something caused it. Probably that’s just an illusion of the mind that misleads us. It would be interesting to understand where that error comes from.

You’ve now come back to one of the central problems of statistics (or probability), but you’re mistaken. If a sequence of 6s comes up, it’s clear there’s a directing hand. Just like if someone wins the lottery a hundred times in a row, it’s clear there’s corruption here and this is not statistics in reverse.
Indeed, the specialness is in the eye of the beholder, and yet that doesn’t contradict the objective conclusion that follows from it. It’s very confusing and requires explanation (I wrestled with this question quite a bit in the past). Briefly, I’ll say that the fact that the thing special in my eyes happened before my eyes is an objective fact. This is not the place to go into it at length.

I didn’t understand what the central problem of statistics is.
I also didn’t understand the second paragraph. Could you explain? This is so essential, and I haven’t found an explanation anywhere for why specialness in our eyes changes the picture.

The problem I was talking about is that defining the specialness/uniqueness of an event is in the eye of the beholder, ostensibly subjective, but the occurrence of such an event says something about objective reality itself. Like in the example of the sequence of 6s versus any other sequence: the specialness is seemingly only in our eyes, but the appearance of that sequence says the die is not fair (= a claim about reality itself).
So for example, if there were a creature built differently from us, and for it the sequence 1,6,3,4,1,2,5,5,1 was special for some reason, then its appearance would, from its point of view, have objective significance.
I explained that in my opinion the reason is that after you define the uniqueness of a sequence, the fact that precisely the sequence that is special in your eyes appeared before you has objective significance (the specialness is only in your eyes, but the correlation has objective significance). Of course, if it appears before me it will have no significance, because in my eyes it is not special.

You still haven’t explained how the fact that the sequence seems special to me is supposed to make me think someone created it.
And when you say that if there is a creature built differently from me and it sees some other sequence as special, and only it should infer that someone created it, while I shouldn’t—who is right here? Am I or is it? How can it be that for one person it is more correct to think A and for another person B?

There is also an “objective” definition of specialness (I put it in quotation marks because even the definition requires judgment, but it does answer the intuition of many people pretty well with regard to “uniqueness”), and that is order—that is, little information. In a sequence with lots of 6s there is little information. Likewise, a sequence of alternating pairs of 1,2 and onward has less order than the previous one but still a lot of order, unlike a random sequence of numbers. There is a mathematical theory that deals with quantifying the “order” or “specialness” of a sequence of numbers: algorithmic information theory.

Ailon, let’s say there is an objective definition—how does that mean someone created it? The probability of every sequence is equal, so what if some sequence meets the definition of “special”? Why in that case did someone specifically make it?

The moment there is a special sequence, it isn’t measured against every other sequence individually, but against all the others (which are not special). Now it is clear that the chance of getting it is tiny.
As for the question what someone else will think for whom it is not special: he won’t be able to know that someone created this sequence (because from his point of view it is an ordinary result), but the truth is still that someone created it. It’s like a blind person who cannot see what I see. It is still clear to me that what I see is correct and he is blind.

1. But that is exactly the question—why measure it against all the rest? So what if it feels to us like it has some specialness? Why does that imply it was created by someone? Any result you measure against all the rest has a tiny probability.
If I manage to program my brother’s brain so that he sees something special in 1634521, should he now think that someone is responsible for that number? How does the programming make someone responsible for the number?
2. If there really is some creature that sees 1634521 as special (and we don’t, so we won’t think someone is responsible for such a number when it appears), then is that actually our mistake? How can you know there isn’t someone who sees something special in it and therefore we are actually mistaken?

Alexei, I’d also add a question 3: as is well known, we are born into a reality in which complex things are pleasing and special to our eyes. But there is no reason to assume that this is how things are in objective reality.
The reason is that because of the reality we have grown accustomed to “communicating with” around us—the reality we grow up with and sleep with—it is naturally beautiful and special in our eyes.
This is a famous atheist claim.

Rabbi Michi, I’ve only now decided to step into the discussion. There is no doubt that some of what you say here is simply a complete mistake.
Granted, the Free Thought site is a broken clock, but as is known, even it can be right twice a day. In our case they were wrong in the reasoning behind their words, but some of the things themselves are absolutely correct.
I would be very, very happy if the Rabbi would read my words carefully, because it’s a shame that you’re missing such a central point that comes up again and again in so many different questions on the site and in general. It’s also a shame that a mathematical mistake should enter your trilogy (in the only calculation that appears in the notebooks).
I have not the slightest doubt that if you read what I write here, you will change your mind (and no, then I won’t have to write an article in response against you 🙂).
(Alexei, there are also answers here to all your questions.)

1) Your claim that the probability that God is responsible for the complexity of the world is 1 minus the probability of random formation is completely wrong mathematically, and I’m very puzzled how you didn’t notice it.
You mixed up two probabilistic data points, or two probability questions: 1. What is the probability that mechanism A will yield result X? 2. Given result X, what is the probability that mechanism A is what produced it?
The probabilities add up to 1 only with respect to the second question. We have some fact before us, and of course it has a source; the only question is which mechanism is the source. So if we add all the possibilities, we get exactly 1.
But regarding the first question, we are talking about the mechanism and not the result, so there is no sum of 1 here.
Therefore, if you want to calculate the probability that mechanism B is responsible for result X (assuming only A and B could be responsible for it), you need to examine the ratio between the two probabilities, and according to that ratio divide up the whole “pie,” and that is the probability that each mechanism is responsible for the result.

I’ll give a simple example:
Suppose there is a room containing two machines such that when you press their activation button, there is some probability that a watch will come out of them.
Machine A produces a watch with probability 1/20 (on average one out of every 20 presses produces a watch).
Machine B produces a watch with probability 1/10.
I entered the room at time t=0 and there was no watch there. I left the room and activated both machines by remote control. I came back into the room, and behold, I see a watch on the floor, and I wonder what the probability is of each machine being responsible for the watch’s appearance.
The correct calculation checks the ratio between the probability of machine A producing a watch and that of machine B. In our case, B has twice the chance of producing a watch as A, and therefore when dividing up the whole, we give it a portion twice as large as A.
That is, the probability that machine B is responsible for the watch is 66.6%, and the probability of A is 33.3%.
If you take the probability of A producing a watch and subtract it from 1, of course you do not get the probability of B producing a watch: 19/20 = 1 – 1/20 (even though certainly one of them is responsible for the watch!).
All of this is exactly because of what I explained above: there is a difference between the question of what is the probability that B will produce the special result, and what is the probability that it is the one responsible for this result, given that the result has already been obtained.
The probabilities of B and A producing a watch do not add up to 1 (in our case they add up to 3/20), and therefore obviously subtracting one of these probabilities from 1 will not give the probability of the other.

And in the context of the world, the two options are intelligent design and random lottery. The probability of a random lottery producing a world like ours is P, but that absolutely does not mean that the probability that some intelligent being is responsible for it is the complement of p. Here we need to evaluate intuitively what the ratio is between the probability that some intelligent being would create such a world (taking into account the prior probability that it exists) and p, and according to that compute the probability that God is responsible for the complexity, just as we computed above.

And there is nothing like showing that the Rabbi himself wrote this way in the fifth notebook, and these are his holy words:
"An example of the importance of comparison: Munchausen syndrome by proxy

The controversial psychiatric syndrome known as Munchausen syndrome by proxy (= seeking attention by harming another) is another example of the results of ignoring an alternative. A woman whose two babies died of crib death was accused of killing them. The argument was presented by Prof. Roy Meadow of the University of Leeds, who discovered the syndrome and was regarded as an expert witness on it. Meadow argued in court that the probability of crib death is about 1/8,000, and therefore the probability of crib death of two babies is about 1/64,000,000. The obvious conclusion is that it is improbable that the deaths of both babies occurred naturally (crib death), and therefore the mother probably murdered both her children. The mother was sent to prison for double murder. The end of the story is that after a lengthy period of imprisonment, the mother was released following the testimony of a mathematician, who explained to the judge the problematic nature of this argument. Meadow, who gave expert testimony in this case and won fame and a knighthood for discovering the syndrome (Munchausen syndrome by proxy), nearly lost his medical license.

What was the problem? Seemingly, the probability that the deaths were natural really is very low. Such a level of likelihood (1/64,000,000) would suffice in any criminal trial. The problem is that the judge and that doctor forgot to compare the low probability that two children would die of crib death with the probability of the alternative: that a mother would murder her two children with her own hands. Is that probability higher than 1/64,000,000? I don’t know. I’m not even sure anyone in the world knows. But if it is not higher, then why prefer the first interpretation over the second? And even if the probability of a murderous mother really is higher than the probability of crib death, the question is how much higher. Is that difference enough to count as evidence at a high enough level of certainty to convict a person in a criminal trial, and one of murder at that? Again, an unlikely interpretive possibility was dismissed out of hand here, while no one even bothered to compare it to the alternative and examine whether the latter was more likely. By this logic, one could really send to prison any mother whose one child died of crib death. After all, even a probability of 1/8,000 is no trivial thing."

If we translate Meadow’s mistake into mathematical language, he made exactly your mistake here. He is aware that there are (in principle) two possibilities for the babies’ deaths: the mother murdered them, or crib death. The probability of crib death is p, and therefore the probability that the mother murdered them is the complement to 1—and in our case, almost absolute certainty.
That is of course a mistake, as you yourself write, since the plausibility that the second option (murder) is what caused the babies’ deaths is also tiny, perhaps even less than the probability of crib death.
The probability that the mother is a murderer is not the complement of P, but the ratio between P and the probability that a mother would murder her two children with her own hands.
If, for example, the probability that a mother would murder her two children is ten times greater than the probability 1/64,000,000, then there is about a 90% chance that the mother is a murderer.

So too in our universe. The probability that some intelligent being is responsible for the complexity is not 1 minus the probability of obtaining it under randomness, but rather the ratio between the probability of obtaining it under randomness and the probability that God is responsible for the complexity (which is estimated intuitively).

That is the first point.

2) Alexei is completely right. One link is missing from your whole explanation. Even if a certain sequence is special in my eyes, that in no way explains why when we get such a sequence we assume someone created it. What is the connection at all between these two things? Maybe the fact that it is special in my eyes also means that whoever created it is called Moshiko?
Don’t you see that there is no connection between how something appears in my eyes and whether it is likely that someone created it? And even if there were an objective measure of specialness, that still would not explain why it is likely to assume someone created the special sequence! So what if the objective specialness-machine answers my question “Is sequence x special?” with “yes”?

Here too I have no doubt that if the Rabbi reads my words he will agree with them (the article I wrote in response to Ethologica deals with exactly this problem):

Suppose there is a die found to be fair in a laboratory test. And nevertheless it gives the repeating sequence 1,2,3,4,5,6 a thousand times. We would all conclude that someone is responsible for that.
Since the probability of getting such a sequence randomly is P1 (which of course equals 1/[6^6000]), and we prefer to say that some intelligent being created it, we are assigning the design option, P2, a probability greater than P1.
By contrast, for a meaningless sequence we do not infer that someone planned it, even though the probability of getting it randomly is also P1. That is, in this case the design option, P3, according to our estimate, is smaller than P1.
That is: P2>P1>P3

A conclusion that follows mathematically from this inequality is that in our opinion the probability that an intelligent designer would create some special sequence is greater than the probability that he would create some meaningless sequence (P2>p3). If we can justify this inequality, we have justified the conclusion—and that is Alexei’s question.

My explanation is that there is a higher probability that someone will choose a special sequence precisely because he sees something special in that sequence, and that causes him to want it more than a meaningless sequence.
That explains all the conclusions of this type about an intelligent designer (there is no need at all for entropy measures, or even objective specialness): an inscription of stones found in the desert, a die that gives 1,2,3,4,5,6, ten consecutive lottery wins, and so on.
The demonstration of this is simple:
Let us take 100 sequences of a thousand digits, all of them meaningless sequences, with no visible uniqueness.
We present the list of sequences to a class of 100 students, and ask each of them to choose one sequence.
We may assume that the choice will be distributed more or less evenly among the various sequences; that is, each sequence will be chosen about once. Why? There is no visible reason that would cause the students to prefer one sequence over another, and therefore their choice is random, a kind of lottery, and in such a lottery all the sequences have equal chance.
Let us repeat the same experiment with one change. We take 100 sequences of a thousand digits, 99 of which are meaningless sequences, and 1 of which is the sequence 666666…
Again we present the list of sequences to a class of 100 students, and ask each of them to choose one sequence.
Now it is reasonable that the distribution of results will be different. For example, there is a fair chance that we will find that out of 100 students, 8 chose the special sequence, and the remaining sequences were each chosen about once.
The explanation is that every number has the same basic potential to be chosen by the students (it is just one more possibility), but the special sequence has added value over all the sequences; it has an “additional property” that will cause the students to choose it, beyond merely being one of the options.
What we have really seen here is a demonstration that a special and aesthetic sequence has a higher chance of being chosen by a human being, and that of course explains what underlies our intuition from earlier, that P2 increases when it is a special sequence.

I’d be glad if you’d rethink these points.

Alexei,

Because of your question no. 1 (why measure it relative to the rest), I referred you to the mathematical field. This is not probability theory, and it is not connected to the probability of drawing a specific sequence, which indeed is equal to all the other specific sequences. It is a different mathematical field that studies something different from probability. If you study it, that question will disappear for you. You have a fundamental misunderstanding here, and this is not a question that should be directed specifically to the Rabbi, but to mathematicians too. It is a basic human intuition about the word “uniqueness”: something that stands out above all the rest. There have to be “all the rest,” gray background, and the something is “in color.” If there were only 2 possible sequences in the world, indeed the level of uniqueness of each sequence would be equal to the other.

Now there is another human intuition: if we see order or uniqueness, we assume there is an intelligence behind it that created it. This is exactly the claim that if you encounter an airplane on the planet Mars, you will assume it was made by aliens and not by the sandstorms that exist there. The parallel here to a special sequence is the three-dimensional configuration of the particles from which the airplane is made. This is a special configuration. Usually particles on Mars would be in the configuration of a flat pile of sand.

This intuition still requires study (not proof, but deepening), because there is indeed something a bit wondrous about it, since the concept of intelligence is something extra-physical.

Regarding your question 2, this is what the Rabbi would call a skeptical doubt. You can’t know who is right (if there even is a right here), but in the meantime no such someone has arrived, and when he does we’ll talk. But he won’t arrive. Or else we are crazy, because our perception is that existence in the world is objective, and therefore claims about order in it should be objective too. It’s like an alien coming and claiming that in the physics he experiences there is no force of gravity and in fact objects move upward and not downward. How would you know who is right? You could simply throw him onto the ground on planet Earth and then all the questions would be solved.

And that is also the answer to Feisterba. And about the wording of his remarks one may say: this is what we’ve got, and with this we’ll win.

Ailon, it doesn’t seem to me that Alexei disagrees that this sequence is special; he’s only asking what difference it makes that it is special. How does that cause someone to have created it?
And really you’re right, the same question exists regarding an airplane and the like.
There is no need for any study—I already explained the logic of conclusions of this type.

Alexei, I’m repeating myself. I’ll explain once more, for the last time, and that’s it.
1. When there is something special, it is measured against all the rest. When there is something rare but not special, it is measured against each individual alternative.
2. If you program your brain to see something special in a certain sequence, that won’t say anything—unless after the programming that very sequence appears. Programming after the sequence appears has no significance at all. If the specialness exists before the appearance, then the appearance has objective significance. My claim is that life is special (low entropy) independently of us, and was so even before us.
3. There is no connection whatsoever to the question whether we are mistaken or correct. As long as it is special in our eyes and exactly that appeared, that calls for explanation.
Therefore the atheists’ claim added here too (Feisterba’s) falls.

Y, I know Bayes’ formula very well (the formula of total probability). There is no need to write textbooks here.
My claim is that the sum of the conditional probabilities is 1. The probability (conditional) that if there is life (we got something special) it was created by random lottery is very small. Therefore the probability that if there is life, then there is something intelligent that created it, is large. Exactly as everyone would say about a long series of 6s from a die or winning the lottery. And that is exactly what you wrote and also what I wrote. And the explanation for that is indeed that if there is specialness, apparently the intelligent factor wanted it and therefore chose it (rather than it being chosen randomly).
Note that if regarding winning the lottery you can plausibly assume there is some corrupt person who did it intentionally because it is obvious to you that he has an interest in winning (he created the special result out of an obvious interest), then in die throws you do not see any such interest, and nevertheless when you get a special result you will certainly assume there is someone here who did it intentionally (and who apparently had some desire for this result). You do not need to know in advance that there is a desire for this specialness; it is enough that it is special in order to reach the conclusion.

By the way, your answer to Alexei regarding if someone arrives with different criteria of specialness is incorrect. Even if such a person arrives, it will change nothing. See the explanation I wrote him above about this.

??
Rabbi, you really didn’t address my arguments. I’ll try to do so briefly.
1. We did not write the same thing at all. You claim that these probabilities complement each other to one, and I claim they do not—and I proved it mathematically. If, say, the chance of getting a world like ours randomly is 1/100, you claim that with probability 99/100 the world is designed, and I showed that that is not so. Did you change your mind? How do you respond to the calculations I showed?
2. Not true. Even in a die result there is an interest. The interest is in getting a special and beautiful sequence. There is no need for the sequence to lead to victory or any monetary prize; it is enough that it has a high selection potential because of its beauty.
Obviously one need not know in advance the entity that wants to obtain the result; the special result itself is that desire.

Alexei is asking you what the legitimacy is of setting the special result against all the other results, and you did not answer him at all. So what if the truth-machine says it is special? By contrast, according to my explanation, there is no need to set it against all the rest. All sequences have equal probability of being obtained randomly, but only with the special ones is the design alternative more plausible than the random one, because special sequences are more likely to be chosen by an intelligent being, because they are aesthetically attractive and beautiful in its eyes. Just like winning the lottery attracts the cheater to cheat.

(As for the “by the way,” I didn’t answer anything like that to Alexei; I don’t know what you’re talking about.)

3) Do you agree with my inequality above (p2>p1>p3)?

Of course, my last remarks in section 1 are based on this sentence of yours: “The probability that God exists is exactly 1 minus the probability of spontaneous formation.” “The probability of spontaneous formation” is the probability that a universe like ours will arise spontaneously, not the conditional probability that given a world like ours, what is the chance that randomness is responsible for it.
If you meant a conditional probability, that sentence is simply not formulated correctly.

P.S. Not only is that sentence badly formulated if you meant a conditional probability, there is no way at all to arrive at a complementary calculation without introducing the probability that an intelligent being would create a universe like ours. Because, as I said, the probability that it is responsible for the complexity is the proportional part of the chance that it would create a universe like ours relative to the chance that a random lottery would lead to our universe. So that sentence has no meaning whatsoever.

Y, I answered everything and I’ll repeat briefly.
I explained that the probability of spontaneous formation means a conditional probability: assuming there was a formation, what is the probability that it was spontaneous.
The conditional probability—that is, the probability that given a world, it was created by chance—and the conditional probability that given a world, it was created by someone or something, add up to 1. That is my formulation, and that is also the formulation on the Free Thought site, and both of us mean the same thing.
I did not present here the calculation of the complementary probability that includes probabilities for the existence of such a factor. Precisely because in my opinion there is no way to estimate that, and there is no need to.
With the die, you guess (and do not know) that there is an interest, and you do this only because you got a special result. You have no information that there is a factor with such interests. Therefore, to infer the conclusion it is enough for us that a special result was obtained, and we need not know anything about the interests beyond that. And that is exactly what I wrote. The existence of interests is a conclusion, not an assumption of the argument.

The final reference was to Ailon’s words and not yours. I was mistaken.

1. Where do you see that this is the formulation of the Free Thought site? It absolutely is not! They explicitly write like me: “Now, scientists have calculated that the probability of life forming by chance is such-and-such, a very small number (say, for the sake of argument, 0.0001; in fact it is much smaller). Now, if this is the probability of life forming by chance, then the probability of its forming intentionally, the complementary event, is 1 minus 0.0001, namely 0.9999.”
2. If you yourself meant a conditional probability, then this “calculation” is pretty useless, because in order to get the conditional probability that the world was created randomly, we must know the probability that some intelligent being would create such a universe (to know the ratio between the unconditional probabilities), so in order to get the desired datum we are supposed to put into the equation a datum that is unknown to exactly the same degree. One cannot determine that the chance of an intelligent creator is high solely on the basis of the chance of random formation; part of the formula is to factor in the probability that an intelligent creator would create a world like ours, and in the end that datum is just as vague as the conditional probability that the world was created by intelligent design. But let’s leave that aside.
3. You didn’t understand me. I do know that special results (a tenth lottery win, a pretty sequence of 666666, an inscription of stones in the desert, and the like) have a high chance of being selected by some intelligent being (whose existence has some prior probability), and therefore if that result was obtained, I assume someone caused it (cheated in the lottery, in the throws, or arranged the stones), because the design possibility is more plausible than randomness.
I do know there is an interest in every special result. Maybe a weaker one, but there definitely is.
Here “interest” means: what is the probability that some intelligent being would choose this result. In the lottery it is high because you make money. In an inscription of stones it is high because it has meaning (“to be or not to be”). And in the die it is high because a thousand 6s is a beautiful sequence. I demonstrated the high probability of choosing such a sequence in my first post.
The assumption is that there is a high probability of choosing specifically this sequence, and the conclusion is that indeed someone chose it and it was not obtained randomly.

Alexei, did I answer your question?

Okay, we’re repeating ourselves. I’ll try one more time (even though everything has already been explained), and I suggest we end with this.

1. By the principle of charity, I assume he is talking about a conditional probability, because otherwise it simply makes no sense. According to the literal interpretation it is just nonsense (because the probabilities do not add up to 1). His term can be interpreted this way, and therefore I assumed this in order to show that even if he was talking about the right thing, he is mistaken. If he is just saying nonsense, there is no point in discussing it.
2. As I wrote to you, I did not calculate any probabilities. In my remarks I only used the sum of the conditional probabilities, and from that wrote that if the probability (conditional) that the world was created by chance is P (which is very small, not because of a calculation but because of considerations of plausibility), then the probability (conditional) that something created it is one minus P. That’s all. I wrote to you that I did not calculate these probabilities because I have no data about the unconditional probabilities and the ratio between them, and therefore there is no point in using the total probability formula. Still, this consideration is entirely logical and plausible, even if not quantitative. You keep repeating the claim, but this is a misunderstanding: what I did was an illustration, not a calculation.

Put differently: there is no a priori reason to think that the ratio between the unconditional probabilities—the probability of God’s existence and the probability of the existence of a random world-generator—is so small that it is on the order of magnitude of the probability that a random generator would produce such a complex world. If we assume that these probabilities are equal (in the absence of other information), or at least not different from one another by hundreds or thousands of decimal places, then the consideration remains intact with no need for any calculation. Whoever claims that they are so different bears the burden of proof. He is basically assuming what has to be proved (that God is totally improbable).
3. That is simply not true. You have no knowledge whatsoever of the interest or of the chance that such a sequence will be chosen. You only guess it because of the uniqueness of the results. Even if you had no familiarity at all with whoever rolled the dice and with his aesthetic preferences, you would still attribute the result to his intentional direction.

1. Not even the principle of charity will help here; he makes an explicit mathematical calculation.
2. I understood that, and I said that there is no plausibility consideration here and no illustration of anything, because the conditional probability of randomness itself requires the probability that a creator would create a special universe.

(Regarding “put differently”): This is simply wrong! One does not check whether the ratio between the unconditional probabilities of the existence of these objects equals the chance of the random mechanism creating a special world. The ratio I’m talking about is between the probability that God would create such a world and the probability that such a world would arise randomly. If, for example, that ratio is 1/10, that means that for every special universe I find that God created, the universe-generator created 10 such universes, and therefore if I encounter one such universe, it was most likely created by the random mechanism.

3. I most certainly do have such knowledge. I know with enormous plausibility that human beings see something special in the sequence 6,6,6,6 and there is a higher probability that someone would intentionally bring about such a sequence than some particular meaningless sequence. You don’t need to know the person in order to know that he has a preference for a sequence of 6666; it is built into every person, even if in practice he won’t choose it. Just as cheating in the lottery is a relatively high potential for every person, even if he won’t actualize it.
Even if the lottery had no monetary prize at all, you would still infer that someone cheated if he won 10 times. Exactly because there is a high potential to want to win 10 times.
Everything runs on the same axis of recognizing a result that has a higher chance of being chosen relative to another meaningless sequence; the difference is only quantitative, not essential. The conclusion is not that the sequence has the potential to be chosen—that I know beforehand. The conclusion is that indeed it happened.

y, I just finished reading your articles and also this whole discussion here—very nice, this is exactly what was bothering me, thanks.
In the article you explained the reasoning very well, but here you were brief; maybe that’s why Rabbi Michi doesn’t agree.
I’ll try to explain it to the Rabbi in my own very brief way, and I see no reason he shouldn’t agree.
Let’s take a similar example of two machines:
Inside machine A there are 50 cards, bearing the numbers 1 to 50.
Inside machine B there are 100 cards, 10 of them with the number 1 and 90 of them with the numbers 2 to 91.
With a random press on the machines, one of the cards inside each machine is ejected.
I pressed both and entered the room, and I find a card marked with the number 1, and I wonder from which machine it came. And of course I conclude that it came from machine B, since the chance of getting the card from machine A is 1/50.
Here they ask me:
Why wouldn’t you draw the same conclusion if you got the card 5? after all the chance of getting it from machine A is also 1/50, so what’s the difference?
The answer is that the question is always what the alternative is.
In the case where 1 came out, the alternative (machine B) is more plausible (probability 1/10), and therefore I choose it.
In the case where 5 came out, the alternative is less plausible (probability 1/100).

What y is arguing (as I understand him) is that although all die sequences are equiprobable, the probability that some intelligent being would intervene and produce the sequence 6,6,6,6,6,6,6 is greater than the probability that he would intervene and produce one particular meaningless sequence. We need to see the design option as a machine in which there is a greater probability that it emits special sequences than meaningless ones, just like machine B has a higher probability of emitting 1.
And here he showed with the classroom example, where each student chooses a sequence, that indeed there is a higher probability that some intelligent being would choose a special sequence than one particular meaningless sequence.
That is, it starts from the fact that the sequence is beautiful in someone’s eyes, and here one simply has to look at intelligent choice as a selection mechanism, with a higher probability of choosing the beautiful and special sequence than any one meaningless sequence by itself, and therefore when it is obtained we infer that indeed someone planned it. This is his equation (which surely cannot be disputed): p2>p1>p3. That’s all, really simple.

y, did I understand you correctly?

Alexei, you understood and explained it excellently.
I’m amazed every time anew how many mistakes and mistaken people there are in this field, and how much they turn it into mysticism or formalism (“the sequence is special and therefore it needs a creator”) without any ability to sketch a “tracking table” that would explain how the conclusion (there is a creator) follows from the premise (the thing is aesthetically beautiful in my eyes). The points are really simple. At least Rabbi Moshe Rat agreed with my articles.

Y, if you don’t have a motivation for the creator to do so, then you have a problem attributing it to him.
Remember that here you start from the fact that for the creator all the options are open to him, and then the question is only what he will choose.
In such a case you argue that it is more likely he will choose something desirable in his eyes.
But desire itself in the creative process requires motivation.
What desire is there in creation ex nihilo…?
It’s like you can’t say that Reuven was murdered by Moshe just because Moshe has a gun. You need a connecting reason, like Moshe hates Reuven….

Rabbi Michi completely ignored this point too. At least you are more in the direction of this point.

Second, if the probability of the sequence 35859566 is, say, 0.01, then given that it came out, Rabbi Michi claims there are two possibilities only: either it is random or it is designed.
On the side that it is random, that’s 0.01, and therefore he assumes that on the side that it is designed, that’s 0.99. Clearly this is not correct, and that is not how Bayes’ formula works (because it is relative to the rest of the overall set of probabilities), and therefore he needs to calculate separately the chance that a directing hand would create it.
And that, as stated, he did not calculate.

I just want to stress that it’s hard for us to find a reason for creation ex nihilo—certainly a world like this.
It’s like a sequence such as 36685986, for example.

Second, the Rabbi does not address that there is a very good reason to create God, and therefore the probability that g2 created g1,
(apart from the fact that it is preferable to the probability that g1 created the world) is much higher than the probability that g1 is his own cause (were it not for the claim that he is the necessary existent, which of course has other objections to it) …
and then we arrived at an infinite regress, or it is preferable to stop at the world instead.

Feisterba,
The example with choosing only demonstrates the fact that special sequences have higher selection potential than the others.
Even in a case where we didn’t tell a person to choose a particular sequence, we would still infer that he is responsible for it. The special stone inscription in the desert might not have been selected at all by the intelligent being, and yet he exists.
The motivation to create the special world is precisely because it is special.
As Alexei said, one has to look at the intelligent-creator thesis as a machine that performs actions with certain probabilities, and a special universe has a higher probability than a simple world.

As for the Rabbi’s calculation, I looked again in the notebook, and the wording definitely points to an unconditional probability. Two lines earlier it says: “We have already seen that the probability of spontaneous formation is negligible…” and afterward the probability of spontaneous formation goes into the formula. The big problem is that the Rabbi doesn’t understand that this is like the Munchausen syndrome case. Even if the chance of randomness is negligible, it is measured relative to the design hypothesis. If one does not agree to the inequality I presented, it is blatantly irrational to think there is evidence here.

Glad that at least you understand :).

Y, you keep ignoring the main point I raised: there is a difference between creating an inscription of stones and creating stones.
One who is capable of creating has no need of creatures; hence if he has no need of creatures, he has no reason to create them. A person cannot act by free choice without deliberation or intention; that is a basic condition of the concept of choice. Therefore, where no deliberation exists for him, your claim is irrelevant. Because God’s action would then be identical to a random action.

You also didn’t address that there is a very good reason to create God, even more than the creation of the world, and therefore the probability that g2 created g1,
(apart from the fact that it is preferable to the probability that g1 created the world) is much higher than the probability that g1 is his own cause (were it not for the claim that he is the necessary existent, which of course has other objections) …
and then we arrived at an infinite regress, or it is preferable to stop at the world instead.
Remember, it is also much more interesting to create g1 than the world.

Rabbi Michi, can I ask a small question here?
You wrote above that “there is no a priori reason to think that the ratio between the unconditional probabilities—the probability of God’s existence and the probability of the existence of a random world-generator—is so small that it is on the order of magnitude of the probability that a random generator would produce such a complex world. If we assume that these probabilities are equal (in the absence of other information), or at least not different from one another by hundreds or thousands of decimal places, the consideration remains intact without any need for calculation. Whoever claims they are so different bears the burden of proof.”
Which ratios exactly did you mean? I’m not sure I understood.
If we assume the prior probability of the existence of a universe-generator is 50% and the probability of God is 10%, and the chance that a world-generator would make a special world like ours is 0.001%, then here you claim the consideration remains intact because the ratio between the chance of God’s existence and the existence of a generator is 1/5, and this does not come close to the order of magnitude of 0.001%? Right?

Indeed.

So at the bottom line of the calculation, even after the conditional probability, the probability that God is the creator really is 1 minus the probability that a random universe-generator will create a special universe, right?

Yes. The conditional probabilities add up to 1.

Wait, but we forgot to enter one more datum: given that God exists, what is the probability that He would create a complex world? After all, it does not automatically follow from His existence that He would create a complex world (just as the generator does not necessarily bring about a complex world).
It’s like the example brought up here from Munchausen syndrome—that there is a small chance that the mother would murder children.

First, you are getting into the details of the calculation, and as I explained, I am making a schematic claim (plausibility, not probability).
As for your claim itself, the actions of the Holy One, blessed be He, are not examined through probability. A universe-generator creates universes randomly, and then one asks what is the chance that precisely such a universe will come out. But God does what He decides, and His actions are deterministic and not random. Therefore, given that there is a God who wants such a world, the probability that He will make such a world is 1.
Given a world as we know it, there are two possibilities: 1. There is a universe-generator and the world was produced by it randomly. 2. There is an agent who wanted it, and the world was produced by him deterministically. The sum of the conditional probabilities of these two possibilities is 1.

Obviously, I’m also talking about plausibility.
So why in the case of a mother who murders her children doesn’t it complement to 1?

I didn’t follow that discussion and I don’t know what is being referred to there (although the example there is from an article of mine). But it really doesn’t matter. In our case these two probabilities add up to 1.

Two babies died in one night. An expert claimed the probability of double crib death is 1/64,000,000, and therefore apparently the mother murdered them (there is no suspicion that anyone else did it).
And then you wrote there: “The problem is that the judge and that doctor forgot to compare the low probability that two children would die of crib death with the probability of the alternative: that a mother would murder her two children with her own hands. Is that probability higher than 1/64,000,000? I don’t know.”
According to what you’re saying here, they were not mistaken in their first decision, because the probabilities do complement to 1.

Incorrect. Those are not the conditional probabilities. What adds up to 1 is the probability that given that two children died, the mother murdered them, and that given that two children died, they died naturally. (For the sake of simplicity I’m assuming it is clear that no one else murdered them.)

I’m not getting it. So why in the case of God can you calculate the conditional plausibility that He is the creator as 1 minus the probability that a random generator would create life, whereas in the case of a murderous mother this is an error?
The two cases are completely similar as I understand them, and you say different things in them:

Event 1: death of two babies. The probability that random conduct would lead to this: 1/64,000,000. The probability that the mother is a murderer (given such a double death) is not equal to 63,999,999.

Event 2: formation of a complex universe. The probability that random conduct would lead to this: 1/64,000,000. The probability that God is responsible for the world (given that there is such a world) is equal to 63,999,999.

Don’t you see the contradiction?

There is no contradiction at all, so there is nothing to notice.
The probability 1/64,000,000 is not a conditional probability but an ordinary probability. You have before you 2 children; this is the chance that both die of crib death. We are talking about a conditional probability, which one must look at in reverse: given that two children died, what is the chance that this happened because of crib death versus what is the chance that this happened because of murder.

That much I understand!
So also when science finds that the probability of life-supporting constants is 1/64,000,000, that is not the conditional probability. Rather one has to set it against the probability that this is “murder” (the deliberate act of planning).
Why regarding murder do you write that “that a mother would murder her two children with her own hands—Is that probability higher than 1/64,000,000? I don’t know,” but regarding God it is clear to you that the probability that He would create a complex world is 1?

In short: the probability of randomness (unconditional) in both cases is x. Regarding God you infer that the conditional probability of His existence is one minus x, and regarding a murderer you suddenly agree that it is not?

Eli, that is exactly what I told the Rabbi earlier—that he ignores the fact that the formation of a complex universe does not automatically follow from God’s existence. True, this is not a random lottery because it is an intelligent decision, but the probability that this decision itself will be made is 1 in… (a thousand, two thousand, a million, I don’t know how many).
He treats it as though we are dealing with a probability of 100%, and that is how he reaches this error.
You are of course correct that this is exactly like the Munchausen case, where the Rabbi actually understands that even though the act of murder follows from a free choice, that doesn’t count as 100%, but as a lottery.

Feisterba, I don’t understand what is different about creating ex nihilo and creating from existing stuff. It’s not hard to raise speculations about why to create a world. In my opinion, creating (in whatever way) a special world has a higher probability than the random formation of such a world.

The alternative to the world having been created by chance is that there was someone who wanted it and created it intentionally. So if there was such a someone, the probability that he would create a world is 1. What is the probability that there is such a someone? I don’t know, but there is no a priori reason to assume it is small (certainly if the alternative is accidental formation).
But in crib death the options are that the mother murdered them or that they died naturally. If there is a mother who wants to murder, she will murder with probability 1. But the probability that there is a mother who would want to murder her two children is very small, or at least of the same order of magnitude as crib death of two children. Why? Because I know the nature of mothers in the world and the probability that such mothers exist (which is not true regarding the probability that a God of that sort exists, about which I have no information).

Rabbi Michi, sorry to wear you out; it’s important to me to understand.
The probability that there is a God who wants our world equals the probability that God exists times the probability that if He exists, He wants a complex world. Above you claimed that the calculation still stands, so you are basically claiming that the probability of the existence of a God who wants complexity equals the probability that there exists a natural universe-generator, and that seems completely implausible, for two reasons:
A. Why talk about a universe-generator at all and not just a random process that creates a universe, in which case the probability of its existence is 1? The probability that the airplane was randomly assembled from its parts does not need to take into account the probability that there exists a random airplane-generator.
B. Following the breakdown I suggested earlier, one could estimate that if God exists, the probability that He wants our world is small—almost 1 divided by the number of possible universes. No?
C. Suppose there had been an ordinary world before us, with no complex creatures. Why wouldn’t your argument apply there just the same? After all, here too the probability of random formation is negligible, and on the other hand regarding a God who wants this ordinary world too one could say your words: “there is no a priori reason to assume it is small (certainly if the alternative is accidental formation).”

You’re confusing motivation to do x within a decision that already exists for some action—where, as stated, you are right—
with motivation to act in the first place, x.
In the act of creation, that does not exist.

So add one more link to that chain of links: the probability that the intelligent factor will approach and make a decision to create something.
I really do not see that link as implausible to the point of matching the randomness option.

I’m about to post a column in which I’ll explain my position in detail and answer everything as best I can. See at the beginning of my remarks there my apology, which is also relevant to my disengaging from the discussion here.