Thanks. Survival bias is a bias that happens in data studies.
A famous example is a study from the 1970s, I think, that showed mutual funds beat the market. Later they showed that the study suffered from this bias because it checked the performance of funds over the last 5 years, but it didn’t take into account the funds that had already ceased to exist (presumably because of poor performance), and therefore didn’t complete 5 years.

As for our issue, I’ll phrase the question differently. Suppose the probability of intelligent life arising (or of a Boeing airplane arising from a junkyard — the example doesn’t really matter right now) completely randomly is epsilon.

Let’s imagine that the starting point of the Big Bang was duplicated one-over-epsilon times, each time in another universe.
It is very likely (without calculating the probability exactly right now) that there would be at least one universe in which the epsilon event happened.

The people there would sit and say: the probability that we arose randomly is epsilon, and that’s a negligible probability, so surely it wasn’t random. Of course they would be mistaken.

I didn’t find in the link to the excellent article you wrote any reference to this point.

A phenomenon like this is described in post 38 about the law of small numbers. In the context of evolution this is the anthropic argument. As far as I remember, it is also dealt with in the book and in the article.
What you’re saying is not entirely clear. Do you mean the probability of life arising within our system of laws, or within a random system of laws? But both claims are addressed there.
If what you mean is the probability of life arising within the framework of our laws, that is what I called there the formulation “within the laws.” That is easy to answer even with a calculation that presents bounds on the number of attempts to create life in our universe, which is not of a sufficiently large order of magnitude (de Duve’s calculation). Beyond that, you assume that in our universe there are laws that allow life, and within them the probability is epsilon. But now I will ask: why are the laws here exactly such as to allow life? This is a very, very special system.
They also tried to answer that by means of the thesis of the random formation of universes with different systems of laws.
Briefly I will say that we have no indication whatsoever of the formation of universes and their spontaneous destruction (each time with different laws of nature, since not every system of natural laws even allows the formation of life). And even if there is such a thing — who is responsible for the fact that such universes with different laws are constantly being created? That too is not supposed to happen on its own.

What I mean is within the framework of our laws. I don’t understand biology or chemistry. But I understood that there is some chance of life arising randomly.
If the counterclaim is that there is no chance of life arising randomly, that is a sufficient answer.

But the claim that the probabilities are so low that there must be an intelligent designer is not sufficient.

I already explained all this, and I’ll repeat it again.
As I wrote, there is a small chance of life arising within the laws (that is, given the laws of our universe), but as I wrote, the number of attempts (according to de Duve’s calculation) is not enough for that probability to be realized. Therefore it is indeed a good argument.
Moreover, I wrote that outside the laws there is no mechanism at all for random formation, and therefore there a small probability rules out that possibility.
So in my opinion the argument in favor of an intelligent designer is excellent.

My point is only about “within the laws.” If there is a small probability, epsilon, for life to arise, then the statement “the number of attempts is not enough for this probability to be realized” has no meaning. Because if life really did arise randomly, then we would today be in exactly this situation.
Another way to explain this: I’m a bridge player. The probability of a specific card distribution in a four-player game is one in billions, I think. To date I’ve played tens of thousands of random bridge deals. The probability that exactly those deals would happen to me a priori is so low that even if all the Chinese had existed since the beginning of the universe and had done nothing but deal cards nonstop until today, the chance of getting those specific deals would have been very close to 0.
According to your method, those deals therefore were not random.
Am I missing something?

If I understand correctly, Aran basically means something like Douglas Adams’s puddle: “Imagine a puddle waking up one morning and thinking, ‘This is an interesting world I find myself in — an interesting hole I find myself in — fits me rather neatly, doesn’t it? In fact it fits me staggeringly well, may have been made to have me in it!’”

Roughly, yes. It’s more like saying that one could argue from the bridge example I gave earlier that because the probability was so small and it still happened, that is proof of intelligent rather than random design of the card deals in bridge games — which is obviously nonsense.
And therefore it doesn’t matter how small the probability is; as long as it exists, you can’t argue that because it is small it is impossible.
Because then we’d say that every time something happens with very small probabilities. But such things happen all the time.
Every day (or cumulatively over a few days), random things happen with unimaginably small probabilities. But they are still random.

Just another example: if we take all the lottery draws over the last 30 years, the probability of getting exactly the draw results that actually came out is probably even smaller than the random probability of life arising. So is that proof that the lottery draws are not random? (That’s a probability of one in a number with several hundred digits; I don’t know if that’s enough.)

You are indeed missing something very fundamental.
There is no connection at all to the lottery example. If in rolling a die you got 6 a hundred times in a row, wouldn’t you wonder what the reason was? Would you continue to think it was fair? Here too your argument applies: after all, the probability of that is exactly like the probability of any other string of a hundred outcomes. But this is a special outcome. Life too is a “special outcome” (low entropy).

Now you are getting to the matter of plausibility. That is, one can say one of two things: either the formation really was random (which is possible), or there was intelligent design. You argue that because our event, as human beings, has a “special” interpretation (100 times a 6 on a die, or the formation of life), we should greatly increase the probability that the event was not random.
But I argue that we really have no ability to quantify those probabilities. For example, suppose I claim one of two things: either reality as we know it is entirely real, or the world was created yesterday and all of us had memories of reality implanted from that point in time.
Which is more plausible? After all, both are possible and explain everything that happens. How can one assign a probability to something about which we have no prior experience? (We exist only once.)
Most people will argue that actual reality is more plausible, but on what basis? I am not claiming that one is more plausible than the other, but rather that it is impossible to assign probabilities here at all.
Therefore I would say that the matter of plausibility is a possible argument, but not a decisive one, and certainly not a “proof.”

There are quite a few mistakes here (and I addressed them in my book). But instead of getting into them, I’ll say that you didn’t answer me, so I’ll repeat my question: if you get a 6 a hundred times in a row, would you infer something from that? I’d be happy with a yes-or-no answer.

It depends. If you now say, let’s throw the next 10 throws, then yes.
But if you show that at some point this happened, then not really, because with enough throws (and thank God, a lot of dice are rolled in the world) there is a reasonable chance that this will happen at least once (the birthday problem).
And more to the point, there are 2 issues here regarding the question and why it is not valid. The first is that if I see, say, that now you throw 100 times and get 6, I would estimate that you brought a fake die that would do that. Why would I estimate that? Because I know such dice exist, or can be produced. In other words, in the analogy, I know how an intelligent designer would cause life to be created. And we don’t really know that, because he didn’t explain it to us and we haven’t seen such cases.
The second point is that asking what the probability is that life would arise is not the right question. Rather, one should ask what the probability is that some “special” thing would happen. Because even if life had been different, or we saw other phenomena not related to the formation of life but still special, we would always say this. Therefore one should ask what the probability is that one of the special cases would happen. After all, the question of the formation of life is asked only because life formed; we wouldn’t ask it if we hadn’t come into being (survivor bias).

Another way to challenge it is with the following thought experiment. Let’s imagine that we built a machine that randomly produces some kind of intelligent creatures. Let us assume that the probability of producing a human being like us from all possible intelligent creatures is, for the sake of discussion, the same as the probability of life arising.
The human being who is produced does not know that other intelligent creatures were produced; he knows only himself. That person will calculate the probability of his own formation and say: the probability is so low, and after all I am intelligent and special, so there must be intelligent design…
In other words, who says that we are “special”? There may have been countless other special possibilities that we are not counting.

Hello.
I asked a simple question: if you see before your eyes a die that is rolled and gives 6 a hundred times, would you say that this is chance? You answered no. Why? Because you know about the possibility of making a fake die. But even if you do know that — you still decided that because the possibility that the die is fake is more plausible than the alternative.

Now I will ask: and if you know nothing at all about fake dice, but also have no information ruling out their existence? Would you then say this is chance? Please, only yes or no. No additions.

It is very plausible that it is not chance.

Now someone comes and tells you: perhaps this die was rolled countless times in the past (and will be rolled in the future), and you just happened to encounter only the “successful” case. What would you say to him? Would you change your position? Again, please just yes or no.

I would not change my position.

Why wouldn’t you change your position? After all, it is possible that there were many rolls that you didn’t see and didn’t know existed.

What he told me added no information. The fact that the die may or may not have been rolled is exactly the same as the situation I was in before he said anything. Or in other words, what he said was already known before he said it.

Of course. I was only asking for the reasoning behind your previous answer. I’m going step by step.

That was the reasoning: the possibility that something may have happened changes nothing.

B. That is not a reason. I asked why it changes nothing. After all, there is another possibility — how do you rule it out?

A. And while we’re at it, one more short question that I forgot earlier: why do you think a sequence of a hundred 6s is “special” (and therefore you inferred it wasn’t chance)? After all, its probability is the same as any other sequence of a hundred outcomes.

(The numbering is reversed because that was supposed to be the order of the questions.)

1. You asked why it changes nothing, and the answer is that it doesn’t, because it was already known in the previous question. And I did not rule out the other possibility; I only argued that it is less plausible.
2. As for the short question: the sequence you described has the same probability as any other sequence, true. But what is special about it is that this combination can be explained in other ways with higher plausibility (like: the die always gives 6 because it is built to always give 6).

By the way, I understand that you are going step by step (it’s hard in writing instead of a conversation :)), but I’ll just note that the die question is not similar to the question of the formation of life.

A. Sorry that I’m not replying continuously; I add an answer each time I get to a computer.
B. It is indeed hard to proceed step by step, but in my experience a discussion that isn’t conducted that way is even harder.

1. You still haven’t answered me. I asked why you ignore the possibility that there were additional rolls and that this is just a random sequence. [In parentheses I’ll only remark that “to rule out” does not mean to reject categorically. There is certainty about nothing. To think it is less plausible is what I call ruling it out, that is, reaching a different conclusion. I’m asking why you think it is less plausible.]
2. In my opinion that is not correct. Suppose for the sake of discussion that you are unfamiliar with the possibility of making an unfair die. Or alternatively, suppose for the sake of discussion that after the rolls you checked the die (you weighed it from all sides and felt it) and discovered that this die is in fact fair. Would you now assume that the sequence of a hundred 6s is random? Your answer here implies yes (since now there is no possibility that explains it). In my opinion you would assume that the thrower of this fair die simply knows how to direct the result somehow. From this it follows that the conclusion that this sequence is special is not connected to the possibility of creating an unfair die. You decided that this sequence is special from merely looking at it.

First of all, thanks for the patience in all the answers. I didn’t introduce myself: I work in probability and statistics for forecasting in finance.
1. I’m not ignoring the possibility that there were additional rolls; I just pointed out that there always could have been more rolls, and someone telling me that didn’t change anything. As for why the possibility of that doesn’t matter: because you are describing a case where you now came and showed me 100 throws all coming up 6. You didn’t say beforehand that this was what would happen; you didn’t know to say in advance that something special would happen here. So the fact that the results could have been different does not change the fact that I still saw something predefined as rare and it happened. That is similar to your telling me in advance exactly what the 100 throws would be and being right.
By contrast, if you were showing me a historical case in which that outcome came up, and you saw it after it happened and that’s how you heard about it, that is completely different. Then it would be more plausible that it was random.
2. I didn’t understand why you disagreed with me, because I said the same thing, and you gave a possible explanation (that the thrower knows how to direct the die).

Pleasure to meet you. 🙂

Sorry that I’m being insistent, but that is my purpose in breaking the discussion into stages. So I’ll try to be more precise before moving on.
1. Indeed, the definition of the situation was that I did not say in advance that this would happen. It simply happened. Contrary to what you say, there is no difference whatsoever between your seeing it happen in front of you and your seeing or hearing that it happened in the past, so long as you don’t know of additional throws. Therefore it is not at all similar to a successful prediction of a hundred throws (where I would not ask why you think this is surprising or special).
In our case there is nothing that marks the sequence you saw as “special,” and its probability is identical to any other sequence of the same length, and therefore I ask again: why do you assume there is a mechanism that produced it, rather than it being pure chance?

2. The difference is crucial for our purposes. You based the specialness of the sequence of results on prior information you have — namely that you already know it is possible to create an unfair die. To show you that your treatment of such a sequence as special does not depend on prior information you have, I asked what you would say in a situation where you have no such information.
Note that you have no knowledge that anyone has the ability to obtain a desired result in die throws, and nevertheless, when you see such a sequence, you said (in your last message) that you would infer that the thrower probably has such an ability (or alternatively that there is some other mechanism that produced it).
But if we agree on 2, then as far as I’m concerned that’s perfectly fine. The question of relevance will become clear later, if necessary. For now I’m only waiting for agreement/reaction to item 1 here.

1. In my opinion there is a difference between my seeing it happen before me and hearing about it from the past. Because in life there are more cases than dice rolls. I won’t hear about rare events that happen all the time if they have no meaning in human eyes. But I will hear about ones that do.
For example: a person dreams at night about a plane from a certain airline crashing, and it turns out that it happened (this occurs every few years).
Or a lottery draw that repeated itself a few weeks later (a real case that happened in Israel in 2010).
In other words, the reason I heard about the event in the past is because it happened and was unusual. Therefore the odds of hearing about some “special” event are much higher than they seem (the birthday problem).
By contrast, if you tell me tonight I will dream that a plane crashes and you are right, or in the next lottery draw the previous numbers will repeat and you are right, that is different. Because then the truth of the prediction is tested on that specific case, not on a general cluster of countless cases from which I happen to hear of one.
As for 2, for now we agree.

Here is a link to the article that appeared at the time about the lottery draw that repeated itself. Several respectable people made mistakes, at least according to what the article says. Following that, a few years later I gave a lecture at the Weizmann Institute at a conference on games of thought, in which I showed that not only is what happened not rare, it is even plausible. Of course, if one asks the right question.
http://www.ynet.co.il/articles/0,7340,L-3970398,00.html

Let me say in advance that the examples of the plane in the dream and the lottery draw are poor. After all, I know there are many dreamers and many planes that don’t crash, and there is nothing astonishing in this happening once. I also know there were many drawings in which it didn’t happen, and therefore there is nothing astonishing in its happening once. The question is what you would say if there were one such case and it succeeded. It really doesn’t seem to me that the Weizmann Institute needs a lecture to understand this (as a graduate of the institute, I am offended on their behalf 🙂 ). After all, we are not asking after how long it will appear, but once in how many drawings there will be a sequence of two such events a month apart. That is a completely different question. I vaguely remember seeing that article once and finding it very amusing.

As for your remarks, I do not see a difference between a situation where someone tells me and one where I see it. According to your approach, the person who experienced it himself should draw a different conclusion from you, who heard it from him? Not plausible. I am speaking of a case where you have no information about additional events, and therefore there is no difference at all between you and him. But it doesn’t matter for our discussion, because before us there is a world with laws and a very special mode of operation, and this is not a rumor we heard about one world among many. So for purposes of our discussion here, that is enough for me.

To be continued.

As for the lecture at the Institute, it was for a broad audience that included students and others. And you may be surprised, but when it comes to probability I am always surprised anew by the confusion there is even among educated people in the sciences.
As for the drawing itself, the probability of a drawing repeating itself exactly after a month is about 1 in 2.3 million.
But that is of course not really the question. When I broadened the question to what is the probability that in a year there will be 2 drawings that repeat themselves, we got down to about 1 in 3300. And when I finally checked whether in the last 20 years, in some year, in some country out of 20 countries, this would happen, I got to a probability around 50%.

I think I understand the root of the disagreement here. You claim that the lottery draw is a bad example because there are many of them, and I claim it is a good example.
You are basically saying that the formation of life happened once, and therefore the lottery example is not similar, because the draw repeats itself.
I look at the formation of life not as one case, but as one among many “specials.”
The collection I am looking at does not need to be of the same type (lottery drawings, plane crashes), but rather “specials.”
In fact, even for the lottery drawing, the real question is not what is the probability that at some point the drawing repeats itself (which is your argument), but what is the probability that at some point we will hear about something “special,” whether in the lottery, a plane, or the formation of life. (Let’s leave the precise numbers aside for now; obviously the lottery case is not in the range of “special” in terms of probabilities.)

You are not phrasing correctly the question I asked. What I wrote was: what is the probability that there will be a drawing with two identical results a month apart. That is not identical to the wording “what is the probability that a drawing repeats itself.” That is actually a version of the question you asked.
By the way, even a probability of one in several million is not implausible if you think about all the drawings in the world in all countries over the years. But as I said, that is not what I was talking about.

As for our matter, when I have time I will address it in more detail and get to the main point.

Yes, but what you wrote is the question is not the real question. Take the lottery example. In the article there is someone who calculated the probability that a drawing would repeat itself exactly after a month, which by the way is the same probability as that any six numbers come up.
But he is calculating something uninteresting, because what the readers of the article are really asking themselves is: what is the probability that an event would happen that would generate an article in the world of lottery drawings? After all, if the drawing had repeated itself after one or two drawings, or 17, they would also have written an article — and that is the point.

Fine, I completely disagree, but there is no point getting into that discussion here.

I will summarize what we have brought up so far:

1. The situation: I throw a die and a sequence of a hundred consecutive 6s comes up, and that’s all, and I don’t know that there were any more throws.

2. Regarding such a situation, we accept the following three claims:
A. Such a sequence is special. [Even though every sequence of a hundred outcomes has the same probability.]
B. I do not take into account that maybe there were more throws before or after or elsewhere, and that I am observing one random sequence. Although this is possible, if I have no information about additional throws, it should not be taken into account.
C. Under these circumstances, the conclusion is that this sequence was not formed randomly. Of course this conclusion is not certain, but it is the plausible conclusion. [This is what I defined as rejecting the assumption of randomness.]

3. We distinguish between two situations:
A. If I have information that an unfair die is possible, I will prefer that interpretation.
B. But even in the absence of such information (or if I checked and it turned out that this die is fair), I would still assume this is a special sequence and look for another explanation (that is, reject the assumption of randomness). For example, I would assume that the person throwing the fair die probably knows how to control the outcomes somehow, and he is the one who produced them.

Agreed?

Yes.

Hello.

Now I move to the requested analogy (in my opinion). Note that I’m formulating straightaway the argument outside the laws (that is, I am not entering into the question of conditional probability — given our laws of nature, what is the probability that life would arise — but rather discussing the implications of the specialness of the system of laws itself).
The formulation, of course, follows exactly the summary in my previous comment regarding the die.

1. The situation: I see before me a world in which there is a very special system of laws. It allows the formation of life and contains biological laws that allow its continued existence. I do not know of other worlds with different systems of laws.

2. Regarding such a situation, we accept the following three claims:
A. Such a world and such laws are special. [Even though, for the sake of the discussion, it is plausible to assume that every system of laws has the same probability.] Note: this is the fine-tuning argument (that every small deviation in the values of the constants in our world’s laws of nature would prevent the formation and existence of life). The specialness of life (and therefore of the laws that allow it) is essential and objective (in scientific terms: life has low entropy, just like a sequence of a hundred 6s in die throws).
B. I do not take into account that perhaps there were other universes/systems of laws before or after or elsewhere, and that I am observing random specialness. Although this is possible, if I have no information about additional universes, it should not be taken into account. This is the rejection of the anthropic principle.
C. Under these circumstances, the conclusion is that this world and these laws were not formed randomly. Of course this conclusion is not certain, but it is the plausible conclusion. [This is what I defined as rejecting the assumption of randomness.]

3. We distinguish between two situations:
A. If I have information that there is a mechanism for the formation of worlds with special laws (= an unfair die), I will prefer that interpretation. But then I will ask about that mechanism itself: who is responsible for its existence? And I will go through the whole argument again (goto 1).
B. But even in the absence of information (or if I checked and it turned out that there is no such mechanism), I would still assume that this is a special world and look for another explanation (that is, reject the assumption of randomness). For example, I would assume that its creator probably knows how to control the laws he creates (this is not a random formation of the system of laws), and that he is the one who created them.

Before we move on to discussion and to raising new objections, I suggest that you go over your remarks throughout the thread and tell me which of the claims you already raised still remain valid against my formulation here. I don’t find any such claim.
This suggestion is meant to make sure the discussion remains orderly — that is, to prevent raising new claims before we have exhausted the previous ones (because my move until now was meant to answer the claims you already raised. New ones, if there are any, we will discuss afterward).

The disagreement is about item 1. The analogy between throwing the die and “I see before me a world with a very special system of laws” is not valid.
Because I saw the die throw forward, so to speak. That is, we discussed a case where you call me over and show me, from now on, the throwing of 100 dice. The world I see backward. That is, I am already aware of its existence.
In research, the parallel is seeing a phenomenon in data, and then no matter how rare it may seem, the odds of its being random are much greater than they appear (simply because we discovered the phenomenon by looking at the data and did not think of it in advance), as opposed to making a forward claim (“100 dice throws yielding 6 are not plausible as random”) and then throwing the dice.
In other words, if we had not come into being, we would not be talking about the formation of life. We are talking about it only because we “discovered” it.
For the analogy to be valid, we would have had to come into existence not as we did but in some extra-universal way, look at the universe (or the cosmic potential) from the outside, and claim that the formation of life is very rare. Then we would “run” the universe and see what happens. And if we then saw that life did in fact form, we would be in the die argument.

Look again at the summary I proposed. That’s what I made it for.
We spoke about die throws without predicting in advance that this is what would come out. We already agreed that when one sees such a sequence of outcomes, it is special (if we do not know of additional throws). Are you now retracting that agreement?
If not, then I now see before me a special world, and that is exactly like seeing before me a hundred throws of 6. There is no difference between the cases (assuming I know nothing at all about the existence of more throws or more universes).

Your comparison to a situation in which I see a special phenomenon within a given data set is not relevant. There you are looking at part of the data and you know there is more data you did not look at. But here I made sure to include in my summary that the existence of more data is not known (more throws in the case of the die, or more universes and systems of laws in our case).

Your claim that if we had not come into being, we would not be discussing it — that is the anthropic claim, and it is a completely different claim, and of course it too is mistaken. It reminds me of Hawking’s example of the condemned man standing in front of a skilled firing squad at a distance of 10 meters, and a hundred shooters all miss him. Hawking argues that the condemned man has no reason to marvel at the “miracle,” since if he had not survived he would not have been able to marvel at the phenomenon. That is total nonsense, of course. Only if there had been many shootings by that same firing squad, and one time someone (= me) survived, would there perhaps be room to attribute it to chance (assuming there really were many shootings).

Let me try to sharpen the point.
You wrote, “We talked about throwing dice without predicting in advance that this is what would come out,” and I agree. You wrote, “So I now see before me a special world, and that is exactly like seeing before me a hundred throws of 6. There is no difference between the cases.”
Here I disagree. Because I knew the world already before you talked with me about it. The case of the world is similar to the case where, after (emphasis on after) someone threw dice, you show me the result.
And not where someone will throw and we cannot predict in advance what will come out.

I don’t understand.
If you see a movie that describes how a year ago a die was thrown a hundred times and every time it came out 6, is that special or not? What is the difference between that and seeing such throws with your own eyes (assuming there is no information about additional throws)? Do you think the cameraman who filmed it is supposed to marvel at the result, whereas you, who watch it, are not? There is no difference at all.
I am sure that if you hear of such a drawing that was done once (to the best of your knowledge), and such an outcome came out, you would send the police to investigate what happened there. Exactly as if you saw it with your own eyes (so long as the source saying it happened is reliable).

And how did the cameraman hear about that die throw? He heard about it because it came out the way it did.
That is, the filmmaker was looking for something strange and interesting to make a film about, and came across the die story. He looked for many events in our world, from planes to lottery drawings and more. And in the end he found the very strange case of rolling a die 100 times and getting 6.
If he had found a person who dreamed 20 times about a plane crash of some airline at a certain hour, wrote it on his website, and the date he predicted really came true — or if he had found some other unique thing — that’s what he would have published.
And therefore the case becomes not “what is the chance of a 100-time die throw having some significance to human beings” (the same number or a pattern like 123456 that repeats itself, etc.), but “what is the probability that at some point some event happened that looks like crazy, rare luck?”
By contrast, if now someone says to me, let’s throw a die 100 times, I know I am checking this case and only this case, and not a collection of all the random (or not) things that were ever possible.

I’ll try again, although this is already beginning to look hopeless (maybe I should have written all this out in advance and shown it to you, instead of writing it before your eyes 🙂 ).
I came to Reuven and said, let’s throw a die a hundred times. We threw it, and to our astonishment it came out 6. There was a camera on the wall that filmed it. Reuven took the film from the camera and showed it to you. Neither of you knows of any additional throws.
Please answer the following two questions:
A. Is Reuven supposed to be astonished (that is, is this a special result from his perspective)?
B. Are you supposed to be astonished (that is, is this a special result from your perspective)?

Reuven yes, and I no (or more accurately, less. I’m speaking at the principled level and not calculating anything exactly right now).
What you describe has happened to me many times. So I’m not talking only about something theoretical, but about something empirical.
And I’ll ask you: would Reuven show me the recording if a result that wasn’t “special” had come out? I assume you would say no. That is, I see the recording only in special cases (survivorship bias).
Reuven, by contrast, would in any case have watched the dice, whether something special came out or not. And I remind you that a priori, before the die was thrown, Reuven could not know that a special result would occur.

Don’t tell me that seeing an event like a hundred 6s when you don’t know of additional throws does not arouse wonder in you. At most you would assume there were additional throws and that they showed you only the special result. That is exactly why I asked about a case where there were no additional throws, or you do not know of additional throws.
You keep returning again and again to bias (survivorship bias), and I keep asking again and again what would happen without bias (which is the situation in our world). I asked about a case where they show you the film and you know of no additional throws and, as far as you know, there were none. In such a case there are no biases.
All right, I see no point in continuing.
All the best.

I think there is a bias in the example you gave, but apparently I’m not managing to explain well enough what that bias is.
I thank you very much for your time.

Perhaps. With pleasure.
All the best.

For the benefit of whoever reads this responsum:

Aran failed by making a mistake that somewhat resembles that of Ido Hadi, against whom I wrote a critique here: https://mikyab.net/%D7%A9%D7%95%D7%AA/%D7%9E%D7%90%D7%9E%D7%A8-%D7%AA%D7%92%D7%95%D7%91%D7%94-%D7%9C%D7%90%D7%AA%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%A7%D7%94/

Ido argued that one can infer that the die is unfair only if I raised that hypothesis early enough.
Aran, somewhat similarly, argues that one can draw a conclusion only if I saw the rare event with my own eyes, and not if someone told me about it after the fact.

I keep being amazed by how much confusion there is in this area (Aran wrote that he works in statistics and probability(!)), even though the matter is completely simple.
And here is what I mean: as common sense says, there is absolutely no difference between a situation in which I see with my own eyes a die that gives 6 a hundred times, and a situation in which I later watch a video documenting such an occurrence.
Either one should conclude that the die is unfair or one should not. How can a fact relating to the person affect his right to draw conclusions? This of course creates a bizarre paradox in which the thrower himself can infer a conclusion from the throws, while the viewer of the video after the fact cannot draw similar conclusions, even though it is the same die, and there is no information in the thrower’s hands that is not known to the viewer of the video that could explain this difference. And since that is so, if the viewer has no right to draw conclusions, then we are telling him: “Indeed, the die is unfair, but you are forbidden to believe that, because you didn’t see it with your own eyes.” Another possibility, no less ridiculous, is to say that the die can be fair and unfair simultaneously, depending on who wants to draw the conclusions (a quantum die?).
It cannot be that the thrower can draw a conclusion that the viewer of the video cannot draw.
Of course, this is in a case where one does not have relevant information that is unknown to the other (for example, that there were many attempts with this die); rather, it is a case in which both have exactly identical knowledge.

By the way, Aran’s challenge is not so absurd. One could call it a “horizontal anthropic challenge,” in which we are not claiming that there were very many throws and therefore one should not marvel at the special sequence of throws (as in the original anthropic challenge), but rather that there were very many domains in which lotteries were conducted, and therefore it is plausible that in one of the domains a rare and special outcome would be obtained, even though in that domain there were not many attempts.
An example: an Olympics in which a million competitions are held in completely different sports, and in each competition there is a special result whose probability is one in a million. If in one of the competitions we got precisely the special and rare result, there is not necessarily reason to suspect anyone, because a million competitions took place in parallel, and it is plausible that in one of them there would be a special result (whose probability is one in a million).
In any case, it does not matter how I came to the information about the special event, whether by direct observation of the die, or from a story told me by a friend, or a video I watch — the conclusion must be identical in all the cases.
Aran wrote: “That is, the filmmaker searched for something strange and interesting to make a film about and came across the die story. He searched for many events in our world, from planes, lottery drawings, and so on. And in the end he found the very strange case of throwing a die 100 times and getting 6.” This is not an absurd argument, but it is equally relevant to the die thrower himself, and it undermines his ability to draw conclusions from the throws, because the world is like the Olympics above, and therefore no die throw is surprising even if these were the only throws ever made with a die, because when there are infinitely many occurrences of all kinds, it is plausible that in one of them something special will occur.
Something special and rare had to happen: either there would be a special result in a lottery drawing, or in dreams about plane crashes, or in die throws. Therefore one should not marvel that something special came out in the die throws, even though no additional throws were made with this die, or with dice in general.
That is what I called a “horizontal anthropic challenge.”

Happy holiday. First of all, the name is Aran, not Eran.
You wrote: “And here is what I mean: as common sense says, there is absolutely no difference between a situation in which I see with my own eyes a die that gives 6 a hundred times, and a situation in which I later watch a video documenting such an occurrence.”

I claim there is a difference. Because what you see with your own eyes has exactly the probability that 6 will come up 100 times.
Whereas the video after the fact you will see with higher probability, because you will only see videos with events you perceive as “special.”
In other words, you are seeing this video because it came out 100 times 6.
And therefore the question is no longer what the probability is that 100 times 6 will come out, but what the probability is that at some point something special happened that was filmed and will interest you.

I suggest leaving it to the readers to judge.

Hello Aran (sorry about the spelling mistake), and happy holiday.
I think you are making a very serious mistake, from which your error follows.
If the viewer of the video were drawing the conclusion that the die is unfair from the “surprising” fact that the special video reached him, and that he in particular is watching it, then indeed you would be right that he cannot draw any conclusion. With very high probability, a video documenting a die falling a hundred times on the number 6 would reach all corners of the globe.
A person cannot say “how fortunate I am” that such a special video came to his attention, because there is a high probability that such a special video would reach the general public.
Moreover, even if we assume that the probability that such a video would reach even any one person in the world is one in infinity (and there are not infinitely many people in the universe), the conclusion would at most be that I am lucky, and that someone who really loves me caused me to become aware of this video. The conclusion in any case would not be connected to the die, or to the throws. The throws only make the video special, and so I would be wondering what I did to deserve that the video reached me, despite there being almost no chance that it would reach anyone at all. The probability that the video reaches me could be negligible even if it were some other interesting video and not necessarily one documenting a rare and special event — for example, a video in which the local bank manager gives a 10-digit number and says that whoever comes to the bank with this number will receive a million dollars.
You are conflating the probability that the video will reach me with the probability that the event it documents occurred randomly.
The negligible probability of its reaching me is, of course, different from the probability that the die would fall a hundred times on 6.

The point is that the viewer of the video does not draw the conclusion about the die from the fact that he watched the video, but from the *content* of the video, which only became known to him through watching it.
The die thrower himself as well (and you admit that he can draw conclusions from the throws) does not draw the conclusion from the fact that he “won” to see such special throws, but only from the simple fact that his eyes convey to him: “the die fell a hundred times on 6.”
There is no difference whether that information came to him by his eyes, or by artificial eyes (a video, in the vernacular).

When I now throw a die 100 times, the probability under the assumption of a balanced die is one-sixth to the 100th power.
The probability that I will see a video in which that same die is thrown is the probability that I will receive and watch such a video.

In the first case, before I throw the die, I know exactly what I want to do and what its probability is.

In the second case, I receive and watch videos only for some reason. There is a reason the video reached me and a reason I am watching it.
If there were a video of 100 die throws with a distribution roughly similar across all the numbers from 1 to 6, there is a very low probability such a video would be distributed, and even if it reached me, I would not watch it.

You wrote: “The point is that the viewer of the video does not draw the conclusion about the die from the fact that he watched the video, but from the *content* of the video, which only became known to him through watching it.”
If the viewer does that, he is mistaken.
I’ll give you an example that happens a lot in financial forecasting.
A person comes claiming he has a winning method. He shows you that he tested it in the past, and the probability that its success is random is very low — say one in 10,000.
You check and see that indeed everything is true.
Is the probability that the method is not random really one in 10,000?
No.

Why not?
Not only because you see many such cases, and not only because 10,000 people making random systems produce such systems and the one random success reached you.

The reason is that he came to me only because he got a good method. If he had gotten a bad method, he would not have come to me, and I would not have heard of him.
Even if he is the only person in the world who tried to develop a method, that is still true.

The same goes for the video. I see it because it came out 100 times 6.
I see it because it was interesting and special. I would not see it if it had distributed randomly.
And it is not that I saw it because I am looking to watch videos in which 100 times 6 came out, or 100 times 1, or 50 times 1 and then 50 times 6, or all the numbers in order from 1 to 6 again and again, etc.
I am looking to watch videos with interesting things of some kind.

And therefore the probability of seeing the video is the probability that some weird thing happened at some point, out of the whole world of possible weird things.

And therefore the probability of seeing it is lower than the probability in the first case.

Aran, you are falling into exactly the same errors I pointed out above.
1) You wrote: “In the second case, I receive and watch videos only for some reason. There is a reason the video reached me and a reason I am watching it.” The heavy burden of proof is on you to explain why the fact that certain data reached me for certain reasons makes the data irrelevant. If we agree that a thousand die throws that yield 6 indicate that this is not a random die, you need to explain why the fact that the probability that this story would reach me is high means I cannot relate to the data once it has reached me.
2) You wrote that if the viewer of the video infers that the die is unfair from watching the video, “he is mistaken.” Well then, if he is mistaken, so is the original viewer.
Regarding the example of the financial method, you explained why you cannot infer a conclusion from the data the developer brings you: “The reason is that he came to me only because he got a good method. If he had gotten a bad method, he would not have come to me, and I would not have heard of him.” And I ask: ???? And if it were your father telling you every day what happens at his job, then as his child you can believe that the method is successful? After all, now the story did not reach you because of its rarity and specialness. But now when you tell it to your friend, suddenly there is no evidence in these data. Truly bizarre.
How can the fact that the information reached you for a certain reason affect your ability to accept what the person says? It makes no sense at all.
If you add the fact that there were many more attempts, and therefore it could still be random, then of course the developer of the financial method also cannot infer the conclusion from the method’s success.
As I explained in the previous comment, this rule could be relevant only if my conclusion came from the fact that I *encountered* the video, in which case there would be no reason to marvel at that, because the probability of that is high. But since drawing the conclusion is not connected to the *arrival* of the data to me, but to the data itself, the question how and why it came to me, and how probable it was that it would come to me, is irrelevant.
There are data from which a certain conclusion arises, and you come along and add a strange rule according to which: “If those data reached you for a certain reason, and not in a natural way (like a rumor about an ordinary event), you may not infer the conclusion called for by them.”

The matter is sharp and clear on the logical level.
Your claim is this: Reuven, who watched the die with his own eyes, should conclude that the die is unfair.
Shimon, who watched only the video, cannot conclude this.
This is the same die, so there are only two interpretations that can explain your claim:
1) The die splits quantumly into two dice, and therefore at the same time two opposite values are possible for the question whether the die is fair or not.
One die is indeed unfair (the thousand throws proved it), and the second die is fair (that is, we have no evidence that it is unfair). The question is who is holding which die, and who will use it in the next throw (Reuven or Shimon).
2) The die has only one value under the property “fairness.” It is indeed unfair, as the throws showed. But there is a prohibition on the viewer of the video from believing the conclusion called for in light of the throws, for reasons unrelated to the objective reality of the die itself.

Please explain which possibility you mean, or present another possibility, and then we can continue the discussion.

In closing, if you are allowed to invent a rule that makes no sense at all, then I’ll invent one too:
My rule: if certain data (including data that came to me directly through my own eyes), such as a thousand throws yielding 6 (from which it clearly follows that the die is unfair), are remembered by me only because of their specialness (= the probability that I remember them is very high), then one may not infer any conclusion from them, even one that clearly follows from them, because the probability that I would remember them is very high.
After all, all the ordinary die throws you made in your life, you certainly don’t remember. By contrast, the thousand throws that yielded 6 you certainly would remember, and therefore you cannot infer any conclusion from that.

Now here is your rule: if certain data, such as a thousand throws yielding 6 (from which it clearly follows that the die is unfair), came to me only because of their specialness (= the probability they would come to me is very high), then one may not infer any conclusion from them, even one that clearly follows from them, because the probability that they would come to me is very high.

I find no difference whatsoever between the two. And what you are saying is really a logical contradiction.

You wrote: “How can the fact that the information reached you for a certain reason affect your ability to accept what the person says? It makes no sense at all.”
The issue is not whether to accept what the person says or not. It is a question of probability, and the probability that the event really was random is greater than if I now perform the die throws.

If I now receive a video from a friend with the title “You have to see this, unbelievable,” and I see 100 times that 6 comes up,
the probability that the event was random is greater.
Why?
Let’s go back to the first case.
If before the die throws it is established that 100 times coming up 6 is the implausible event that would rule out randomness, and then we throw the dice — then yes, I agree.
But if nothing was said, then the situation is different, because even if 100 times 1 or 2 had come up, or 50 times in a row 2 and then 50 times 3, or a repeating sequence of 123456, or many more examples I could give here, we would say, unbelievable, that’s special.
Therefore the probability of the special event is not one-sixth to the 100th power, but the probability of some special event occurring — which is smaller.

Now when the video is received, the probability is smaller still, because I would receive any video with some special event in the world.
It could be a die, cards, an event in nature, and many other things. Therefore the probability of randomness is much smaller.
Because the a priori question is not what is the probability that 100 times 6 will come up, but that something special will happen. And the probability of that is much higher.

And regarding the financial event, since I will receive methods only when they succeeded, and since there may be many such methods, the probability of randomness is much greater. Therefore both theoretically and empirically, from extensive experience, I can say that the probability of a worse outcome for the method in future reality is very high. Or in other words, the probability of randomness is higher than the probability of randomness when looking at the method on its own.

And therefore in practice, both regarding the financial method and the die throws, what one does in research, after one discovers a finding “by chance” or if someone told me about it without a prior hypothesis, is simply to test it again prospectively or on another “clean” data set.
Then if in the next 100 throws 6 again comes up, or the financial method replicates what I saw before me, the probability of randomness is lower.

First of all, let us set aside additional testing of the hypothesis raised. We are speaking only about drawing conclusions from an event that already occurred (1000 throws yielding 6), and not discussing what is the best way to arrive at the most correct conclusion regarding the die. I too would test the die more times, and even in different ways.

Now you have changed your claim, and so I would ask for clarification from you. You wrote: “But if nothing was said, then the situation is different, because even if 100 times 1 or 2 had come up, or 50 times in a row 2 and then 50 times 3, or a repeating sequence of 123456, or many more examples I could give here, we would say, unbelievable, that’s special. Therefore the probability of the special event is not one-sixth to the 100th power, but the probability of some special event, which is smaller.” The explanation you gave here is equally relevant to the die thrower and to the viewer of the video.
Please explain exactly what case you are talking about, in which the direct viewer is supposed to infer that the die is unfair, while the video viewer is not supposed to infer that.
I want us first to talk about a case in which I am playing with a die at home for fun, and I get a thousand throws of 6. Before they came up I did not think at all about the possibility that special throws would come up.

After you clarify exactly which case you are talking about, I will again ask for an explanation of your claim about the die.
This is one die and two people who know exactly the same thing, except that one of them learned of the event by watching it (that is, he would have learned of it anyway, regardless of the outcome), and the second learned of it only because the event is special.

Now I come to these two people and demand that they decide whether the die is fair or not.
You argue that the direct viewer should answer me that it is not fair, and the viewer of the video should say that it is fair.
What is the meaning of your claim? Are both answers correct? Does the die contain two values under the category “fairness”?

See quantum mechanics.

Dudi, if that were what Aran meant, indeed everything would fall nicely into place. I would only ask to see the evidence that the die obeys the principles of quantum mechanics (and would happily inform the physicists that Schrödinger’s cat has been found). But I assume that is not what he means, and in this way I am showing him that he cannot give a logically coherent description of his thesis. Simple logic says that given two people with exactly the same information about a certain event, it cannot be that one of them can infer a conclusion that the other cannot.

You’re right, I raised 2 claims.
The first claim is that even in the first case, the probability is lower than one-sixth to the 100th power for the reasons I mentioned above.
And the second claim is that in the second case the probability is even lower for the reason I wrote in the post above:
“Now when the video is received, the probability is smaller still, because I will receive any video with some special event in the world.
It could be a die, cards, an event in nature, and many other things. Therefore the probability of randomness is much smaller.
Because the a priori question is not what is the probability that 100 times 6 will come up, but that something special will happen. And the probability of that is much higher.”

Note: you keep relating to my claim as a logical problem. But that is not so — the issue is purely probabilistic. And I showed that the probability in the two cases is different, because the probabilistic question is different.
In the first case: what is the probability that something special will happen in 100 die throws.
And in the second: what is the probability that something will happen that will lead to a video being sent to me.

Aran, did you read my whole comment? Did you notice that you ignored most of it?
1) I ask you again for an explanation, on the logical level: what is the real status of the die (that is, what is more plausible to bet — that it is fair or that it is not)? Does it receive two values under the category “fairness,” or not? Who is closer to the truth, the one who watched the die itself (and will bet that it is unfair), or the one who received the video by email (and will bet that it is unfair)? Are there two truths?
In another case, where Reuven knows that there were billions of throws with that die (and therefore there is no reason to marvel that it yielded a thousand 6s), and Shimon is unaware of that datum, Reuven’s conclusion is the correct one, and Shimon is the one who is mistaken, because he does not have all the data in hand. The die is fair (probably), it has a single answer under the question “is the die fair?”, and also under the question “in light of the data known to us, is the die fair?”, and Shimon misses the correct answer because of lack of information. I am still waiting for a parallel explanation in our case.
2) I again ask for clarification as to what case you are talking about. I want first to discuss a case in which the thousand throws that yielded 6 came about without any prior statement such as: “If a thousand 6s come up now, that will rule out randomness.” I was just playing with a die for fun, and a thousand throws came out. At the end of the throws I said to myself: “What an idiot I am, apparently the die is unfair.” At that point I sent you this information about the die (of course I wouldn’t have sent it if an ordinary sequence had come out), and according to you, you cannot infer that the die is unfair. Do you agree that this is the case we are discussing?

I also ask for a response to this new point:
3) Suppose that every day I film all the actions I do, and in the evening I send you, my good friend, the video of the day that passed. And today I threw a die a thousand times and got only 6s. Within the full video I sent you, documenting my whole day (the shopping I did, taking the kids from preschool, etc.), there is also the filming of the die throws. In this case, can you infer that the die is unfair? After all, now the video reaches you regardless of the content inside it, and not because it is special and rare, since even if the die had yielded an ordinary result you would receive documentation of those throws, because as part of my quirk I always send you a record of my whole day.

I’ll try to answer in order.
1) You ask for an answer on the logical level. But there is no logic here, only probability.
Let me try to explain more fully.
First of all, let us begin with the first case. I’ll simplify it so that for the die thrower there are only 2 possibilities: the die is random, or it is not random.
How do we determine after the 100 throws what the probability is that it is random?
The thrower must assume before throwing the die what the probability is that the die is not random. Let’s call that probability Y.
Let us assume for the sake of simplicity that the only event that would change Y for me is only and precisely that it always comes out 6.
(That is, if it always came out 3 etc., that is not interesting — again, for simplicity’s sake.)
Let us call the a priori probability that it always comes out 6, X.
After 100 throws, what is the probability that the die is random?
For that we calculate a conditional probability.
Well then, if Y and X are equal, the probability is about 50%.
If Y is much smaller than X, then the probability that the die is random is still very high.
If X is much smaller than Y, then the probability that the die is random is very low.

And if you say that the person did not estimate Y but just threw the die for fun,
the answer would be that one cannot determine the probability of randomness.

You can say that I’m just talking nonsense here, and that any sensible person who throws and gets 100 times 6 will understand that the die is not random.
But what you are really saying there is that clearly Y is much smaller than X.
Even if Y was not fixed a priori.

After that introduction to your question: the probability of randomness in the first case, assuming Y is much greater than X, is very low.

In the second case the person’s information is different, and therefore the probabilities change. This does not require Schrödinger’s cat; rather, the probability of the event depends on the information available. And the 2 people have different information.

You ask whether there are 2 truths. As far as I’m concerned, I stick with the answer in terms of probability. So yes, there are 2 different probabilities for 2 different people who hold different information.

2) The answer is yes.
3) The probabilities are not identical. Let us assume of course that I watch your daily videos for some reason consistently.
Still, in daily life other things also happen to you in which there was potential for “strange” things, like lightning striking a tree and causing branches to fall in a way that spells “not random,” for example. Therefore the probabilities of randomness are lower.

Try to respond to what I am claiming in probabilistic terms. This is a probability question.

Aran/Eran,
how does one measure Y — “the probability that the die is not random” — assuming we do not actually have real knowledge about the world?
Or in our analogy,
how does one measure the probability of God?

P.S. Regarding the world, unlike the die we also do not have an understanding that it is random; rather, we just don’t multiply entities and therefore think that the world has no explanation and is therefore random.

By contrast, with the die the basic presumption is that it is random. So regarding the world, who says that even a little bit of uniqueness requires a designer? Unlike the die, where one has to exceed probability X by a lot.

And besides, in the world it may be that every law of nature requires an organizer in any case. (And therefore in that measure Y immediately jumps as a logical continuation of describing God, as opposed to X, which is completely nullified.)

Aran is the name 🙂
In our analogy, of course it is impossible to measure Y. And worse than that: the question was not asked a priori, and therefore we are biased in calculating Y.
But suppose we were looking at the universe from the outside — then we would have to come with some estimate of Y. Or be in a situation where we would not know the probability of randomness.

For example, suppose I give you 2 possible explanations of existence. One possibility: everything you know in reality is true.
The second possibility: the world was created yesterday, with all the existing information — that is, all your memories from before yesterday are inventions, etc.

Which is more likely?
In order to answer that one needs data. But there isn’t any. You live only once.
One can say that there are not really only 2 possibilities, because there is also the possibility that the world was created two days ago, three days ago, etc.
That is true, but the multiplicity of cases does not change anything probabilistically.

My answer to that question? In my opinion one cannot say what is more plausible. That does not mean the probability of the two things is 50%, but simply that there is no answer.

As for what you wrote in the P.S., that is true, but it still does not change anything probabilistically. It just means Y is different.

Aran,
I see that the conclusion is pessimistic 🙁 🙁 … regarding such a basic and meaningful question. May God have mercy on us. Maybe that is why revelation is needed if God wants to claim that He exists?

In any case, are you familiar with this (I’m not very knowledgeable in the matter, I only once heard a short lesson about it), that in philosophy of science they tend to claim that the prior probability of hypothesis Y,
A. is derived from how well Y fits our general knowledge.
B. and most importantly, how simple the hypothesis is.
And since the hypothesis that there is a God is such a simple hypothesis (it has no boundaries at all and stands by one entity alone), it is far preferable to the hypothesis that the world is random (which hangs on very many complex entities).
And also it fits our general knowledge (“go and see” that there is almost no culture without some supernatural factor behind it, even on the dollar of secular America: in God we trust).

The fact that this is about probability does not change the fact that every claim has to be examined logically and has to be completely clear. We need to understand which person is closer to the correct understanding of the die’s reality. In a case where one has information that the other lacks, clearly he is closer to the truth. In your case there is no addition in information (see below), and yet there are differences in the conclusions of the two people, and it has to be clarified which conclusion is more correct.

1) There is no difference whatsoever whether I fixed the prior probability that the die is unfair before the throws or after them. To claim there is a difference means saying that my thought affected the fairness of the die. And the test for that is this: if I present you with two dice, both of which gave a thousand throws (their only throws) of the number 6, except that with die A the thrower thought after 10 throws about the possibility that it is unfair (so that 990 throws remained that “confirmed” this possibility), while die B was thrown in a room empty of people, so that no one raised the possibility that it was unfair until the end of the throws — now I tell you: choose a die and we’ll take it to a laboratory. If it is found to be unfair, you will receive a billion shekels. Every rational person will say there is no advantage to the die near which someone happened to raise the possibility during the throws that it is unfair. According to your method, it is clearly preferable to choose the die near which stood a person who could raise the possibility that it is unfair. I do not accept this mysticism.

I again find a contradiction in your words, because in item 2 you claimed that you accept the case I described (where we did not say before the throws that a thousand throws yielding 6 would decide that we are dealing with an unfair die), while on the other hand you wrote that one must assume before the throws what would prove that the die is unfair. I will continue relating from now on as though you agreed that there is no need to determine a priori the probability that the die is unfair (Y in your notation).

You wrote: “In the second case the person’s information is different, and therefore the probabilities change.” In my understanding, “information” means “certain data,” so knowledge can be shared fully with another person, and we can arrive at a state in which both people under discussion hold equal knowledge. The die thrower can transfer all the information in his possession into the hands of the viewer of the video, and indeed that is exactly our case — there is no information that one has and the other does not. Exactly the same information!
And nevertheless you argue that each of them should have a different conclusion from the die throws. Since the information is the same, it is clear that you are confusing *information* with *the way in which the information came to my attention*. And as I explained at length, a difference in the way the throw data came to me cannot change my conclusions.

3) I did not understand why in the case I described here the viewer of the video cannot infer the conclusions of the thrower. After all, he is like an extension of the thrower’s eyes.
As stated, here too there is no difference in the knowledge of the two people, no difference at all. And if there is, let them sit over coffee and close the gaps, because that is exactly the point at issue.

1) You wrote: “There is no difference whatsoever whether I fixed the prior probability that the die is unfair before the throws or after them.”
I didn’t claim otherwise, except that as a human being you will be biased, but if we put that aside, there really is no difference.
I didn’t understand where you inferred that from what I wrote.

But without an a priori determination of the probability of randomness one way or the other, we won’t be able to say anything.
Suppose we did not make any a priori estimate or calculation of randomness. And we threw the die 100 times and got 6.
Why should we think the die is not random? After all, the event is possible and it happened, so what is the problem with randomness?
In order to claim that this event causes us to believe the die is not random, one must determine that before throwing the die, the probability that the die is not random (Y) is much greater than the probability of the special event (as we defined special events — but for simplicity let us assume only a sequence of sixes is special).
After all, you would agree with me that if a higher power had “revealed” to us that the die is not random with probability one-sixth to the millionth power, then after throwing the die 100 times we would determine that the die is random.

What you are really arguing (in “probabilistic” language) is that it is obvious to the thrower that the probability of non-randomness is much greater than the tiny number one-sixth to the 100th power. And therefore it is “reasonable” that the die is not random. The “reasonableness” comes from a different assumption of Y; the “logic” itself is not logical at all.
Y can be fixed whenever we want, provided we do not take the results of the throws into account when fixing it.

Regarding the issue of “information,” the information in our case is the number of possible events that would determine uniqueness out of the total set of possible events.
In the first case that number is different from the second case. Therefore their “information” is different.

3) The probabilities are not identical, in the sense that the probability of a special case right now is higher, because I am looking at more things that have potential for weirdness.
What I mean is the probability of the special case of 100 times 6 as against all the special cases that could happen to a person during the day.
But as between the viewer and the original person, if I am watching everything that happens to him then there is no difference. It is just that both of them differ from the case of a special video that reached me because it is special.

To Ido: why a pessimistic conclusion? I personally am a believer, and I think the conclusion is actually very optimistic. If it were so easy to prove God’s existence, then what need would there be for faith / belief?
Besides, I believe that the Holy One, blessed be He, already revealed Himself to our people at Mount Sinai. You can’t keep pestering Him every few thousand years. There’s a limit 🙂
As for what you wrote, I’m not a philosopher. I’m only into probability and statistics. So from my point of view, if Y cannot be determined, then it cannot be determined. Not everything is possible.

1) I did not dispute the fact that someone who claims that 100 throws yielding 6 prove the die is unfair has assumed some prior probability for the possibility that the die is unfair (Y). I simply think there is no need to give exact numbers and values, and one can certainly leave this in the realm of plausibility rather than probability. Even if I find a book in another galaxy, I will assume that some intelligent being composed it, because there is some prior plausibility that there is an intelligent creature that could have created the book. Even though I cannot assign numbers to that plausibility, the conclusion is still quite strong.

I thought you were demanding prior conditioning because of this sentence (and what followed it): “If before the die throws it is established that 100 times coming up 6 is the implausible event that would rule out randomness, and then we throw the dice — then yes, I agree.”

2) As I said, the meaning of the word “information” is certain data. Data, by definition, can be transferred from one person to another. If what you call “information” cannot be transferred by the viewer of the die to the viewer of the video even if they sit for hours over coffee and close the gaps, then by definition this is not “information” but a “position” — that is, why and how a certain datum came to my attention. A gap in information can be closed; you are not talking about information, and therefore that cannot be closed.
My logic says that no matter on which side of the river you stand (= whether you watched the die yourself or only received a video), the probability that the die is unfair is equal.
It cannot be that when I am the observer of the die, it is more reasonable for me to bet that it is unfair than it is for my friend who only received a video.

Dudi means David,
The conclusion is pessimistic because if regarding such a fundamental fact we cannot know, how will we know how to aim the cannon of life?

In any case, I think it is quite clear that one can evaluate Y based on the simplicity of the explanation and prior knowledge. Think of a murder case where we suspect A, Y, and D.
We know that Y’s fingerprint was at the scene, and Y was in that area at the time of the murder. Those are the pieces of evidence in the case against Y.
But Y claims that D hates him and wants to put him in jail because Y once sent him to jail. Therefore D placed Y’s fingerprint at the scene. And the reason Y was in the area that night is that he was helping watch over his grandmother and went out to smoke a cigarette, etc. etc.
Would we believe Y? Probably not. Why? Because it is a complicated explanation! The simple explanation is that Y murdered him.

Likewise regarding the laws of nature: for any given set of findings, one can draw infinitely many “lines” —
functions that describe the findings as a general law of nature… etc. etc.
But we will always prefer a law of nature based on addition laws (provided, of course, that it fits the findings), rather than multiplication. And multiplication rather than exponents, and exponents rather than roots, etc. etc. The simpler the mathematics of the laws of nature, the more likely they are to be correct.

And because God is such an incredibly, incredibly simple hypothesis, He takes the whole pot on this question.

In any case, the biggest big question, in my opinion, is what is the probability that that God would create such a world. Does such a simple and perfect entity [God] have a reason to create such a world — human beings with limited freedom and evil all around in the world?
If the probability of that is high, then clearly there is a God. And if not, then it is not clear at all.

——
1) Regarding the revelation at Mount Sinai that you mentioned — do you believe in it without additional support from the side, such as the reality of God? And from what argument? I’d be happy to hear.
2) P.S. It sounds from your words that you believe much more than you *know*. Am I right?

To y,
You wrote that if you saw a book in another galaxy you would assume there was an alien behind it.
Indeed, I agree with you, and what’s more, I think people greatly exaggerate with Occam’s razor in this matter, and one’s hand should be much quicker on the trigger when it comes to adding an entity to the explanation.

But what happens in a place where you find no reason at all that someone would create this book? There simply is none, none exists, **no** reason at all. Would you assume someone created it? Presumably you would prefer to assume it happened by itself. How, you don’t know. But that is much preferable.
For example, if you find even a little reason for it, of course you would assume someone created it. For example, if you see a Coca-Cola bottle (far, far less special than a book!), you would assume the aliens made it (assuming no human beings arrived there).
And even if you knew they have no ability to drink, you would probably still assume they tried to imitate human civilization. The main thing is to find some conceivable reason for it.
But if you examine it and find *no* reason, then you would certainly assume that no one created it.

And the question is whether regarding God it isn’t like that. Does such a simple and perfect entity [God] have a reason to create such a world — human beings with limited freedom and evil all around in the world?
If the probability of that is indeed high, then clearly there is a God. Even if it is close to negligible, it still stands to reason that there is one (like the alien trying to imitate human civilization).
But if not, then it is not clear at all that there is a God.

What do you think about that, Mr. y?

Rabbi Abraham, I feel we’re going in circles because of some communication short-circuit. Instead of answering the questions, I’ll try to restate my claim.
In the first case, the probabilistic question is: what is the probability that in a hundred die throws a “special” sequence will be obtained (the same number, alternating, etc.). Let’s call that probability A.

In the case where I saw a video, the probabilistic question is different: what is the probability that A or some other “special” event happened? (a random output of ordered numbers, shuffling cards and then drawing them in exactly their order, lightning striking a tree and knocking down branches that spell out “I am God,” etc.)

The probability in the second case is higher.

And in another matter, there is another way to attack the argument that low probability therefore means intelligent design.
Suppose there are 2 possibilities for the state we are in today.
One — intelligent design, in which case we would always arrive at our current existence (let us assume).
The second — randomness, in which case everything is random and with some probability X we arrive at our current existence.
Which is more likely?
Since one cannot know the prior probability of the 2 cases, one cannot know which is more likely.
What you are really arguing is that the prior probability of intelligent design is much greater than X.
On what basis?

And I will formulate my answer to this new wording, and the matter will become sharper.
As I said above, you are raising a challenge I called a “horizontal anthropic challenge,” where the claim is that one should not marvel at a special result (whose probability is, for example, 1 in 1000) that occurred in domain a, because there are many additional domains (b, c, d, e — and for simplicity, 1000 more domains) in which no special result occurred (again, for simplicity). Therefore it is plausible that when there are 1000 domains, in one of them a special result will occur whose probability is one divided by the number of domains (and in each domain the possible special result has probability 1 in 1000).
That challenge is certainly possible — see the Olympics analogy from the previous comments — but that is not what I want to discuss, because the sting of your claim is different.
You claim that when I watch the die itself, then I do not need to take other domains into account (planes crashing or “lightning striking a tree and knocking down branches that spell ‘I am God’”). You formulated this claim as follows: “the probabilistic question is what is the probability that in a hundred die throws a ‘special’ sequence will be obtained.”
Whereas when I watch a video documenting the special die throws, I need to take additional domains into account. You formulated this claim as follows: “the probabilistic question is different: what is the probability that A or some other ‘special’ event happened?”
That is exactly what I do not accept. There is no basis whatsoever for taking other domains into account when I watch a video of the die any more than in the case where I watch the die directly. It makes no difference at all that I am watching the video only because it is special, and that but for its specialness I would not have become aware of it. The information is the same information, and it does not matter what the reasons were that brought me to be exposed to it.
When I come to draw a conclusion about the die, the question by definition is: “what is the probability that such a special sequence would occur?” And there are two possibilities that must be decided between: (1) the probability is 1 in 1000, and therefore the die is probably unfair (in this possibility we do not take other domains into account). (2) the probability is quite plausible, because there are 1000 additional domains in which there is a special result whose probability is 1 in 1000, and therefore in one of the domains something special “had to” come out. I cannot marvel that it happened specifically in the die rather than in another domain (a plane crashing, or the tree falling as above), since there is nothing special about the fact that the special result occurred specifically in the domain called “throwing a die.” In whatever domain that result had occurred, I would have “marveled” and asked the same question, and therefore the question and the marveling are mistaken. This is similar to a person marveling that the following perfectly ordinary lottery result came out: 6127361573. That same person would have marveled at some other ordinary result too, and therefore it is clear that his marveling is mistaken.
I am not trying to decide between those two possibilities; I am only saying that this is a question that stands on its own, and has no connection whatsoever to the question of how the information about the die reached me.
In your formulation, there is no reason to replace one probabilistic question with another just because certain data reached me for a certain reason. It is not logical that what determines whether we adopt possibility 1 or 2 above is the position in which I am situated (watching the die, or the video).

And regarding the argument against the proof of God (that we do not know the prior probability of His existence), I already said that I am not trying to give a precise formulation with equations, but only to explain the simple intuition.
Your question attacks in exactly the same way the inference to an “intelligent author” when on another planet stones are found scattered in a pattern forming a quotation of a million English words from a famous book. After all, the probability that such writing would come out is equal to that of any scattering of stones. How do you know the prior probability of the existence of a creature capable of writing such an inscription? If in such a case you do not infer the existence of an intelligent author, then at least you are consistent. I suspect that is not the case.