Q&A: Probability and the Vilna Gaon’s Lottery
Probability and the Vilna Gaon’s Lottery
Question
There is a well-known story (it also appeared in the press at the time) about Rabbi Aryeh Levin, who used the Vilna Gaon’s lottery to identify the fallen members of the Convoy of the Thirty-Five when they were brought for burial at Mount Herzl.
There is a written protocol of the lottery in his own handwriting.
I recently heard a claim that in the modern period DNA tests were carried out and the identities of the fallen were confirmed. Does this (assuming it is true—I have not yet found clear confirmation) prove that there is something real to the Vilna Gaon’s lottery?
I calculated and found that the probability of correctly guessing 12 fallen soldiers is about 2*10^-9. That is not so far from the chance of getting 11 sixes in a row when rolling a die—not very likely, but not insane.
Is it correct to make such a comparison? Or here, since the guesses were made to order, does that change something?
(I would add that from the protocol and from the description of the case, it appears there was some prior knowledge about some of the fallen, which perhaps turns the guesses into informed ones and therefore makes them more plausible.)
Answer
I do not know the details of exactly how this was done, how they defined arriving at the correct name (after all, there are lots of degrees of freedom), and how they used the prior knowledge. So I also do not know how you did the calculation.
But assuming all the information is before you and you calculated correctly and the probability is very low, then perhaps there is indeed something to it.
Discussion on Answer
That is already a different question. In my opinion, no. “You shall not practice divination.”
As for halakhic rulings, certainly not.
With God’s help, 25 Shevat 5782
To Tirgitz—many greetings,
The matter of clarification by casting lots is mentioned already in Scripture as one of the ways of divine intervention, as it is written: “The lot is cast into the lap, but its every judgment is from the Lord.” Casting lots by opening a sacred book is mentioned in the Talmud: “Shmuel would check by a book.” A collection of sources on the subject can be found in Rabbi Aviner’s responsum about “opening the Rebbe of Lubavitch’s Holy Letters,” where he cites several great rabbis who said that not just anyone can “take hold of the Name.” And all the more so in matters of Jewish law, about which it is said: “It is not in heaven,” and they are not decided on the basis of prophecy or holy spirit.
With blessings,
Elieam Fishel Workheimer
In the playful atmosphere of the “snow day,” following your question I took a Hebrew Bible (Tanakh), opened it at random, flipped seven pages, seven verses, and seven words, and arrived at the verse: “Those who know Your name trust in You, for You, O Lord, have not forsaken those who seek You” (Psalms 9:11). From here there is a hint that the lottery is one of the ways in which God “will judge the world with righteousness,” but only when the matter is one of “a stronghold for the oppressed, a stronghold in times of trouble,” and only when it is done by “those who know Your name” and “those who seek You.”
Why is it so obvious to both of you that one cannot rule in Jewish law on this basis (and Elieam explained it by saying “it is not in heaven”)? If the lottery works, then every such successful lottery is a revelatory event of the Holy One, blessed be He, in might and power, and He is taking the trouble to bring up by lot that such-and-such Jewish law should be followed—and you say to Him: no sir, we rely on the Pri Megadim’s table because he ruled otherwise? Has anything this great ever been seen or heard? Those aggadic passages of the Sages in which they heard the Holy One, blessed be He, say such-and-such and nevertheless ruled otherwise, I interpret as exaggeration—that one does not pay attention to unproven tools based on fantasies. But if the tool is proven and the Holy One, blessed be He, is speaking with us mouth to mouth, then it is impossible in any way that there is anything more certain than that, and on what basis could we ignore the current and certain directive?
I calculated stringently (as I understand it):
Assuming that in each guess it could be any one of them, and that each guess is completely random (because from the Hebrew Bible you can derive whatever you want, especially since I saw somewhere that you can keep flipping pages in the lottery), then the chance of hitting the first is 1 in 12, the second 1 in 11, etc.
As stated, the product comes out a very small number (2 times 10 to the minus 9).
This is a very small probability, but it is not essentially different from a sequence of 11 die rolls that came up 6, which is not really impressive when it happens once.
The question is whether that comparison is correct.
With God’s help, Thursday of the portion “which you shall set before them,” 5782
To Tirgitz—many greetings,
If regarding Moses it was said, “And you, stand here with Me,” and the giving of the Torah to him continued throughout all the days of his life, then after him the Torah was sealed, and it was said: “These are the commandments”—meaning that a prophet is not permitted from now on to introduce anything new. Even Moses’ great disciple, Joshua son of Nun, was instructed by his God to resolve his questions in understanding the Torah through meditation and study of the Torah, as it is written: “This book of the Torah shall not depart from your mouth, and you shall meditate on it day and night, so that you may prosper in your way and then you will have understanding.”
And God did a kindness to His people by not “making life easy” and giving them understanding of the Torah through revelations from above, but rather through “hard work, with questions and answers, with lenient and strict arguments, and through clarifying the Jewish law” (as the Zohar says somewhere). And reason supports this, because what comes from outside remains external to the soul. But what is acquired through immense toil—”yes, at night my conscience instructs me”—is absorbed and internalized in a person’s soul, and wisdom in which one has labored becomes in his heart “his own Torah.”
For that reason, in matters such as identifying Achan and dividing the land, God spared Joshua and his people the need to strain their intellect to attain them, and revealed them to him by lot. But understanding the wisdom of Torah, God commanded him to achieve דווקא through “you shall meditate on it day and night,” through analysis and endless toil.
And likewise after the revelation at Mount Sinai, where God showed His people His great fire and made them hear His words from the midst of the fire, God commands Moses to place the laws “before them”—not only before exalted prophets, but before each and every person, who is tasked with toiling to understand with his own mind the words of the Torah and their reasons, so that God’s wisdom and will will become his personal possession.
With blessings,
Elieam Fishel Workheimer [free translation by the typist: the man in the study]
On the one hand we have a wondrous miracle before our eyes, in which the Holy One, blessed be He, reveals His דעתו by determining the outcome of the lottery, and on the other hand there is some idea learned at most from the words of the Sages saying not to relate to the words of the Holy One, blessed be He. This is a bit like: when you have the words of the master and the words of the disciple, whose words do you obey?
In short, the rule that Jewish law is not in heaven is weaker than an explicit directive from heaven. So either that rule is void, or it must be interpreted to mean that it cannot really be that heaven said it.
And how do you interpret that a prophet is not permitted to introduce anything new from now on, and that “it is not in heaven”? See my article about dreams (Midah Tovah, Miketz 5767), that even if there is a reliable dream it has no halakhic status.
And indeed, the medieval authorities (Rishonim) on Eruvin asked how they followed a heavenly voice to decide like Beit Hillel against Beit Shammai. According to your view, of course, there is no difficulty at all.
I do not interpret it. If one believes in the reliability of the message, then these rules make no sense, and I do not believe anyone would give them a glance. If one does not believe in the reliability of the message, then there is no need for these rules. And rules cannot tell us about the reliability of the message (because that is a factual judgment). And what is your own view?
And to Tirgitz—many greetings,
The “words of the master” stated it plainly: “You shall meditate on it day and night, so that you may prosper in your way and then you will have understanding.” There are no shortcuts; rather, you should labor and toil until you understand with your own intellect. Thus the Torah will be internalized for you and not remain external.
And as the Torah brings: “If a matter of judgment is too difficult for you… then you shall arise and go up to the priest who shall be in those days or to the judge… and they shall tell you the word of judgment.” Prophecy has a role in making decisions that depend on questions of future reality—whether to go out to war or not, whether to appoint this person or that person as king. But the principles and laws of the Torah are given over to the interpretation of the Sages and decision according to the majority of opinions.
All the more so with a lottery, which is only a kind of “small prophecy” that gives an indication and not a decisive clarification, since even by the natural course of events it is possible that the rare scenario will in fact occur. In a case where a rare coincidence appears like a hint from above against the considered ruling of the Sages, one should assume that the Sages will reexamine their ruling again and again. But if they checked, and checked again, and found that their reasoning is correct, then it is their duty to honor the method of clarification that the Torah laid out for them.
With blessings,
E.P.W.
I do not interpret it. All these rules make no sense, and I do not believe anyone would do anything based on them if he really believed in the reliability of the message.
My last message was sent by mistake.
With God’s help, 25 Shevat 5782
The topic of “It is not in heaven—Jewish law and prophecy” has been discussed extensively in the words of the Sages and in the writings of medieval authorities (Rishonim), later authorities (Acharonim), and scholars. See the articles in this category in the Asif Library. For example: Rabbi Abraham Isaac HaCohen Kook, “A prophet is not permitted to introduce anything new from now on”; Rabbi Tzefania Drori, “Holy spirit and determining Jewish law”; Rabbi Professor Neriah Guttel, “Indeed it is in heaven, in the laws of the Temple and its holy things—the essential exceptionalism of ‘Temple laws’ in Rav Kook’s halakhic thought”; Yaakov Bernstein, “Prophecy and Jewish law—Jewish law according to prophecy”; Aviad Biller, “Truth shall spring from the earth” or “righteousness looks down from heaven”; Eran Nazri, “A sage is preferable to a prophet,” and more. And “give to the wise and he will become wiser still.”
With blessings,
Yaron Fishel Ordner
I do not understand why there is even room for discussion. Can a minister give an order to ignore the king’s order?
To the Rabbi,
I do not know whether you missed my comment or did not see a need to continue the discussion from it.
I am bringing it again, with greater detail about the question at the end:
“I calculated stringently (as I understand it):
Assuming that in each guess it could be any one of them, and that each guess is completely random (because from the Hebrew Bible you can derive whatever you want, especially since I saw somewhere that you can keep flipping pages in the lottery), then the chance of hitting the first is 1 in 12, the second 1 in 11, etc.
As stated, the product comes out a very small number (2 times 10 to the minus 9).
This is a very small probability, but it is not essentially different from a sequence of 11 die rolls that came up 6, which is not really impressive when it happens once.
The question is whether that comparison is correct. That is, is it correct to say that the chance that Rabbi Aryeh Levin would perform the Vilna Gaon’s lottery and correctly guess all those buried is the same as the chance that Rabbi Aryeh Levin would declare that he is going to roll a 6 in 11 throws and indeed do so?
Because intuitively, guessing the identities of those buried feels more impressive. The question is whether that is a mistaken impression because the content of the probability is meaningful, or whether there really is some probabilistic or plausibility-related aspect here that I am missing?”
I did not understand a word. I do not see here the criterion for what counts as hitting on the correct name. How exactly is the lottery done? How do we know which name the verse points to? What do you do when a verse comes up that does not yield the name?
I very much doubt the ability to calculate anything.
All in all, you have shown that it is very likely that the story as told is false.
In the book With Might and Power by Avi Rat about Rabbi Goren (highly recommended), it is told how he rescued the drivers and jumped over the mines, etc., and some of those killed he knew personally from the synagogue and so on.
Bottom line, some of them had to be identified, and the families wanted the Vilna Gaon’s lottery, and he saw it as a fiction…
But he agreed because of the families’ distress; Rabbi Aryeh Levin was forced to agree, signed, and the government approved it.
And if the Vilna Gaon’s lottery were proven statistically correct, even though of course there is no physical law behind it, would it be possible to rely on it in Jewish law? Both to clarify facts and also to decide halakhic rulings?