There’s nothing like a good ad hominem, from Prof. Ron Aharoni, in response to my presenting the idea to him (quoting my message below):

“Hello Yair,

Indeed, I think you are right. There is nothing special about a sequence of 6s, except that for human beings it is different.

The relevant concept is entropy, a measure of order. Entropy expresses degree of rarity—the rarer an event is, the lower its entropy.

But what is ‘rare’? According to the measure of the human being. Think about the effort invested in arranging a dictionary in alphabetical order. You invest a lot of energy, and get something that externally resembles a jumble of unordered letters. Where did the invested energy go? Seemingly the entropy did not decrease. But in fact it did decrease, if you look at the right system: not the dictionary alone, but the dictionary together with the human mind. An ordered dictionary + a brain is more ordered than a jumble of letters + a brain.”

My message:

This is a very essential issue, and I haven’t seen anyone pay attention to understanding the logic behind it until I thought of it myself.
I wanted to ask your opinion about the rationale behind drawing conclusions about the intervention of some intelligent agent following a rare and special event that occurred.
If someone throws a die in front of us and gets 6 a thousand times (and the die itself was found in a lab to be unquestionably fair, the mass is uniformly distributed in it, etc.), of course we would all draw conclusions, for example: the person throwing the die is cheating and throwing it in such a way that this special result comes out.
The question is: what is different about a sequence of 6s (and the like) as opposed to any random sequence? After all, the probability of getting any particular random sequence by chance is exactly equal to the probability of getting a ‘special’ sequence. So why wouldn’t we conclude something similar from the sequence 21346213 (for example)? How does the fact that some sequence meets a criterion of ‘specialness’ (what does that even mean?) change the conclusion that someone caused this result?
I thought about this a lot, and came to the unequivocal conclusion that the explanation is as follows:
Although every sequence (special and non-special) has an equal probability of occurring randomly, in the case of a special sequence, the alternative hypothesis (that someone intervened) is more plausible than that same hypothesis in the case of a random sequence.
And the explanation is this: special sequences have higher selection potential by a person than a specific random sequence, because of their beauty and specialness in human eyes.
A demonstration that special sequences have high selection potential:
If we present a class of students with one hundred sequences, only one of which is special (66666), and ask each of them to choose a sequence, the choices will be distributed more or less evenly among the sequences (1 will choose each sequence), except for the special sequence, which will be chosen more than any other sequence (for example, 8 students will choose 666666).

Oz, if it interests you, we’re discussing the topics in the article here:
https://mikyab.net/dwqa-answer/%d7%aa%d7%a9%d7%95%d7%91%d7%94-%d7%9c%d7%aa%d7%99%d7%a7%d7%95%d7%9f-%d7%a9%d7%92%d7%99%d7%90%d7%94-%d7%9e%d7%91%d7%99%d7%9b%d7%94-%d7%91%d7%9e%d7%97%d7%91%d7%a8%d7%aa-%d7%94%d7%a9%d7%9c%d7%99%d7%a9/#comment-14068

If the Rabbi has already ruled that this does not count as ad hominem, I’ll add the second part of our correspondence:

y:
At the next stage I thought about a case where we come upon a computer program that randomly rolls a die based on swiping a finger on a touch screen, and the result 6 is obtained a thousand times. Let’s assume we are certain that no person intended to sabotage the program so that it would specifically produce 6; still, we would all conclude that this is probably a bug. Now again the question arises: why wouldn’t we also conclude the same in the case of some random sequence, one that was determined without any connection to the finger swipe—that is, that there is a bug in the program? After all, the probability of all sequences is equal.
And here one has to say that if we trust our intuition, the only reason to justify such a conclusion is that there is a higher probability of a bug that causes the program to produce 6 a thousand times than of a bug that brings about some random sequence that was determined without any connection to the finger swipe on the screen. Gadi Alexandrovich also told me that such malfunctions are more likely.
What do you think of that?

Ron Aharoni:
Nice idea, agreed.