The Issue of Letter Skips and Codes in the Bible (Column 640)

With God’s help

Disclaimer: This post was translated from Hebrew using AI (ChatGPT 5 Thinking), so there may be inaccuracies or nuances lost. If something seems unclear, please refer to the Hebrew original or contact us for clarification.

A few days before Passover, an old friend sent me a video about encoding information in the Torah. The topic is hackneyed and not new—and perhaps also boring—but for me it’s always accompanied by a sense of intellectual dishonesty (on both sides of the divide). I thought this was an opportunity to touch a bit on the question of honesty in such debates. I will deal with the question of encryption, but only as a vehicle through which I wish to make claims about how the discussion should be conducted and the honesty it demands.

What are we talking about?

There are persistent claims about factual information from different historical periods (up to our own day) being encoded in the Torah in various ways. Needless to say, there are many charlatans involved in this field (some even published books about it), and their “findings” are meaningless. But that in itself doesn’t prove that there’s nothing to the phenomenon. It should be examined on its own terms, and it seems most people don’t bother to do so. The starting positions you bring to the discussion dictate your attitude and the entire debate. Needless to say, this is true of both sides: both those convinced that there are clear findings there and those who deny it. This is an example of the lack of intellectual honesty that is very common in such debates. In this column I wish to address this fraught topic a bit, and point out issues that require clarification when formulating a position regarding it. For me, the main takeaway is the need to insist on intellectual honesty even when we have an a priori stance.

One root of the issue can be seen in the age-old interest in gematria. Gematriot tie together concepts and try to prove and learn various things from the numerical value of letters and words. It’s clear to everyone that gematria is a highly dubious tool, and it’s not reasonable to build a serious argument upon it. Similarity in the numerical values of two words or verses can be purely coincidental. It’s a single finding and therefore, almost by definition, lacks statistical significance. But in recent generations we’re offered a more “scientific” and systematic use of similar techniques of encoding in the Torah, such as equidistant letter sequences (ELS). In these contexts, claims are raised that the findings are serious and based on statistical significance—unlike gematria—and therefore can be relied upon. I will therefore begin with the topic of gematria, and only afterward move on to the modern codes and encryptions.

Introduction: A look at gematria

There’s the well-known early homily on “im Lavan garti” (“I sojourned with Laban”)—“and I kept 613 commandments”—which plays on the gematria of the word “garti.” (Here it may be mere letter rearrangement rather than even gematria.) Does anyone seriously think the Torah actually intended to say that? Very likely not. It looks more like a homiletical game (from the root “derosh,” as opposed to “midrash”). The Sages themselves tell us that gematriot are “desserts for wisdom” (see Avot 3:18). I surmise (or at least hope) that they mean nothing substantive should be built upon them. It’s a homily that hangs a principle that may be true in its own right (or at least we’d like it to be true) on a gematrial play—no more. I already wrote in the past (see, for example, in Column 52 on the difference between derush and pilpul) that the common rule “no refutation to homily” is based on the fact that the conclusion of the homily is correct, and therefore there’s no need to be punctilious about whether the argument leading to it holds water (usually it doesn’t).

We also find skepticism regarding this esoteric tool among the early commentators. Thus, for example, on the verse, “And when Abram heard that his brother was taken captive, he armed his trained servants, born in his house, three hundred and eighteen, and pursued as far as Dan” (Gen. 14:14), the Talmud (Nedarim 32a) says that Abram’s 318 trained men are merely a code for Eliezer, Abraham’s servant, since “Eliezer” equals 318 in gematria. Yet Ibn Ezra, in his commentary to this verse, writes:

“Counting the letters of ‘Eliezer’ is homiletical, for Scripture does not speak in gematria; for one can derive whatever one wants, for better or for worse, but the word is to be understood literally.”

For him it’s clear that nothing can be learned from gematria, since you can do with it whatever you wish. These words are worthy of Ibn Ezra, one of the greatest homilists and word-play masters. He certainly knows what he’s talking about.

Already here we should note that the numerical identity between the number of Abram’s trainees and the gematria of Eliezer is indeed a rare phenomenon, and seemingly one might see in it an indication of a substantive connection. Such a connection rests on the claim that it’s unlikely for such an identity to be coincidental, and if it exists then it likely comes to teach us something. But of course, upon further consideration there’s no real impediment to such an identity occurring by chance. Comparisons based on numerical value can lead us to utterly bizarre places. The word “בראשית” (Bereishit) has a gematria of 913, which is exactly the number of commandments plus three hundred, or: “only 613” (rak taryag)—a “clear” hint to the prohibition of “bal tosif” (not adding commandments), and to R. Moshe HaDarshan’s derashah cited by Rashi there.

Indeed, we also find in rabbinic literature some halakhic gematriot. For example, from the verse “until the days are fulfilled, which he consecrates to the Lord; he shall be holy” (Num. 6:5), the Mishnah (Nazir 5a) learns:

“An unspecified term of naziriteship is thirty days.”

The Gemara there brings a source from the verse cited:

“From where are these things [derived]? R. Matna said: Scripture states ‘kadosh yihyeh—he shall be holy.’ ‘yihyeh’ in gematria equals thirty. Bar Pada said: corresponding to the [appearances of] ‘nazir/nazro’ in the Torah—thirty minus one.”

So, unspecified naziriteship is thirty days because the gematria of “יהיה” (yihyeh) is 30, or because of the number of times the root נזר appears in the Torah (and here they add the “kolel,” as always when the gematria doesn’t quite fit).

It’s no wonder that the Rosh writes there in his commentary:

“‘yihyeh’ in gematria equals thirty. It seems that it is a received tradition, and they merely supported it by this gematria, for [gematria] is not among the Thirteen Principles by which the Torah is expounded.”

According to him, it’s only an asmachta, while the law itself was transmitted by tradition. I’ll just note that the expression “gemara gamiri lah” isn’t necessarily “a law from Sinai,” as Rashi explains in several places. In the Netziv’s introduction to the She’iltot, known as “Kedmat Ha’Emek,” he records a dispute between Rashi and Rambam about this: according to Rambam, it’s a derashah that the Sages expounded in the past; the resulting law reached us, but the source was lost.

In any case, the Rosh’s reasoning here is that gematria isn’t among the Thirteen Principles of Derash, and therefore there must have been a tradition. On the face of it, this is a rather weak argument. First, gematria appears among the thirty-two principles of R. Eliezer b. R. Yose HaGelili. Moreover, there are countless derashot in rabbinic literature carried out with techniques other than the Thirteen (or the parallels of the school of R. Akiva). It seems more likely he means that gematria cannot be a valid principle of derivation because of its reliability—just as we saw above in Ibn Ezra.

No wonder Ramban writes at the beginning of his Sefer HaGe’ulah:

“A person is not permitted to judge by gematriot and to derive from them any matter that occurs to him.”

I wonder what would constitute a proper engagement with gematria for someone who doesn’t “derive from them any matter that occurs to him.” What’s the criterion? I don’t see any criterion other than knowing from another source that the gematrial conclusion is true; then there’s no objection to using it, and “one does not refute a homily.” But certainly not to build a new halakhic ruling on gematria. It cannot be a creative homily. The implication is that, unlike midrash, by definition derush is supportive (confirmatory), not generative.

Describing the problem: From gematria to ciphers

Similar games can be found in tools that differ slightly from gematria—though they’re no more reliable. Thus, for example, the game in the Passover Haggadah about the number of plagues at the Sea—fifty according to R. Eliezer and two hundred and fifty according to R. Akiva. It’s hard for me to believe anyone takes those numbers seriously (their meaning is also unclear: what exactly does it mean that they were struck by 50 or 250 plagues at the Sea?). This is a bizarre, quirky homily, certainly not something on which to build any precise claim. Gematria and such midrashim look, on their face, like kinds of ciphers by which one can extract this or that information from the Torah—but these ciphers are quite dubious, and it’s very likely they aren’t ciphers at all. They’re mere amusements.

The reason for the dismissive attitude toward such arguments is that the textual phenomena on which they are built could be coincidental. To claim something on the basis of some cipher, at least one of two conditions must be met: 1) We were explicitly told that information is indeed encoded in the text, and usually, in parallel, we were given the key by which to extract it. 2) If we weren’t given such information/key, we can still claim that if the textual phenomenon is very rare and puzzling and cannot be accidental, then clearly it was written deliberately to teach us something. Returning briefly to gematria: even if I assumed that the tool of gematria was given at Sinai, it’s clear we don’t use it every time we find a connection between the gematrias of two expressions. The use of this tool is very rare, and not for nothing. Unrestrained use of gematria can “prove” anything you want. Therefore, even in cases in which the tool and key of encryption were handed over, there must still be significant statistical significance before we can learn anything from such a gematrial comparison.

In other words, to infer anything from a given cipher you must show that the encoding is substantive and not accidental. That is, you must present a comparison between the chance it’s coincidental and the chance that information or an idea is indeed being encoded there; and if the claim of coincidence is far-fetched (highly improbable), then one can claim that information is encoded there—and that’s an argument in favor of the extracted content.

As noted, in recent generations claims have begun to surface about a more systematic and well-founded use of encryption techniques in the Bible, mainly in the form of letter-skips. Notably, in those contexts no one claims that the tool or key (ELS) was transmitted by tradition. There, clearly, we’re dealing with the second mechanism: the claim is that the statistical significance of the phenomenon proves there is encryption here. To that end, some have used modern statistical tools to analyze these mechanisms and findings, and their claim is that statistically significant results have been discovered—results that cannot be ignored. This, they say, isn’t gematria but something scientific.

A look at intellectual honesty in this debate

These claims sparked a fierce debate even among experts. It’s hard to ignore that differing views on the codes correlate with one’s a priori stance on the Torah and its divine origin. Those who believe in these codes are usually people who believe in the sanctity and divinity of the Torah, and they use codes to prove it. Their opponents are usually (though not always) people who don’t accept the Torah’s divine origin, and therefore, for them, it’s a priori impossible for future information to be encoded in it. From their perspective, it’s clearly impossible, and so all that remains is to refute the arguments raised by supporters. But there is, of course, another possibility they ignore: acknowledging that there is indeed clear statistical significance and drawing the appropriate conclusions. If information about the future is encoded there, then the author likely knew that information—hence one must abandon the view that the biblical text is purely human. I assume I won’t surprise you by saying this doesn’t really happen. There are also religious people who don’t accept the claims about Torah codes. A prominent one is Prof. Barry Simon, a very well-known emeritus professor of mathematics at the University of Chicago and Caltech, and there are many others (I, in my small way, tend in that direction too). Conversely, there are almost no secular people who do accept them. It’s worth noting that there are a handful of exceptions in that direction too, such as Prof. Haim Shore of Ben-Gurion University, who has written and lectured quite a bit on Torah codes, and videos on these topics have been published.

I’m reminded of an amusing anecdote (to me, at least). While serving grandly as Purim Rabbi at the “Netivot Olam” yeshiva in Bnei Brak and environs (a yeshiva for ba’alei teshuvah), I went up on stage with a goblet of wine and, after the kiddush, expounded with a mighty hand and outstretched arm on matters of Purim. Among other things, I said that I had just discovered an astonishing finding of letter-skips in Tanakh: the place where the word “Esther” appears with the minimal skip in the entire Tanakh is in… the Book of Esther. A skip of 1, of course. If that doesn’t bring us all to repentance, I don’t know what else to do with such stiff-necked folk. There were quite a few people there (including some of the ramim) who were shocked that I mocked the fundamentals of the Torah like this. Letter skips in the Torah were considered by them part of the Thirteen Principles of Faith. Some even told me that my words could cause people to abandon their religious commitment. I answered that in my opinion it’s better that they abandon it. If their commitment is based on such nonsense, then it’s already a mistaken commitment and is null and void. The seeds of my heresy (heaven forfend) were already sprouting there.

But back to our topic. Since there are prominent professionals among both the proponents and the opponents, we can assume that, at least when we’re dealing with their arguments (as opposed to the aforementioned charlatans), it’s not utter nonsense on either side. Precisely because of that, the question arises: why is there such a marked correlation between people’s worldviews and their attitudes toward encryption? If there are very strong arguments on both sides, how is it that specifically religious people adopt the arguments for, and specifically secular people adopt those against? One could, of course, try to reverse the order of causality. But I presume no one will seriously claim that these people’s religious or secular stance is the result of studying the question of codes. For the vast majority, it preceded it. If so, this seems to be an indication of intellectual dishonesty among the participants in the debate. It seems people are subordinating professional and scientific positions to theological worldviews.

On the face of it, this is true on both sides of the divide, but interestingly, among religious people you will find many who do not accept the code thesis, whereas among secular people you’ll hardly find any who accept it (barring rare exceptions). There can be several explanations for this difference: 1) Secular people are less intellectually honest. From my impression that seems less plausible. 2) The presence of codes flatly contradicts secularism; but unlike those fools from my Purim homily, a religious outlook doesn’t require such codes. But this explanation merely says that secular people have a stronger incentive to be dishonest, and yet the conclusion remains that they are less intellectually honest (albeit now with a psychological explanation). That’s certainly possible. 3) The codes are not true, and therefore, if there’s bias, it’s only toward accepting them (i.e., some religious people will accept them despite the lack of basis because of their belief). There’s no logic that would produce a bias toward an incorrect position (i.e., a secular person accepting codes despite being secular).

I must say explanation 3 is implausible to me. If serious experts present arguments (incorrect, by my current assumption) in favor of codes, that means they’re not obviously foolish arguments. If so, it’s hard to accept that not a single secular person—certainly an amateur in math and statistics—fell into those same mistakes. It therefore seems we should conclude one of the first two explanations (with the second being more plausible), namely that there is likely bias here, more pronounced on the secular side.

And yet—intellectual honesty

To complete this a priori view, I should present another possibility that explains the distribution of opinions in a somewhat more charitable manner. The claim is that if there are decent arguments either way, it’s reasonable that a person will remain with the position he or she held before the discussion. That is, the secular person doesn’t specifically adopt the arguments against codes and reject those in favor, but rather says that since there’s no decisive verdict either way, there’s no reason to abandon secularism. And likewise for the religious person who accepts the codes. This may be true mainly for those who haven’t examined the arguments on their merits (either because they aren’t experts or because they haven’t engaged with the topic). But for the experts who have examined the arguments and expressed unequivocal positions for or against, there it’s more reasonable to adopt one of the three explanations above (with the second, as noted, being the most reasonable).

I’ll bring a parable I have used before in discussions of spurious correlations (see, for example, Columns 30, 571, and others). When Reuven becomes religious, many of his secular friends explain this step by a psychological crisis he underwent (a loved one died, he broke up with his girlfriend, etc.). His new religious friends say he finally became courageous and wise and discovered the truth. In other words, the secular are psychologists and the religious are philosophers. What happens with Shimon, who leaves religion? There the roles are reversed: his religious friends explain that he wanted to permit sexual licentiousness—i.e., they are psychologists—while his secular friends say that finally he understood his mistakes—i.e., they are philosophers. So who’s right? On the face of it, both sides are right. Anyone who makes a change in life—certainly such a radical one—is driven by psychological motives and also finds philosophical justifications. Therefore one can explain such a step in both the psychological and philosophical planes. So why does each side choose to address such a step specifically in one of the planes, and why specifically the one they chose?

In truth, it would be appropriate to address only the philosophical plane, since a psychological discussion about someone’s step is none of my business and irrelevant to our discourse on the merits. If someone becomes religious, I should examine his arguments and not hit him below the belt; and likewise for one who leaves religion. But each of us tendentiously chooses one plane: the one for whom the step is congenial (a secular person regarding leaving religion, and a religious person regarding becoming religious) explains it philosophically; the one for whom it’s uncongenial explains it psychologically. Apparently we’re all being dishonest.

But note that this conclusion isn’t necessary. Think from the perspective of a religious person. He believes religious faith is true and secularism is mistaken. Therefore when he sees someone becoming religious, he explains it philosophically—because in his view that person truly discovered the truth. But when he sees someone leaving religion, he believes there’s no philosophical justification for it and therefore attributes it to psychological motives or influences. And conversely for a secular person, of course. This explanation parallels my final proposal above for the codes controversy. There too there may be an explanation that leaves the sides more honest, at least partially. Of course, if a person is unwilling to reconsider and insists on assuming his stance and deriving from it all conclusions—that’s biased thinking with no justification. The justification I offered here can apply only where the arguments themselves really aren’t unequivocal.

Conclusions

In any case, it’s clear that when we look at any controversy, we must examine both sides’ arguments as objectively as we can. Biases lead us to dishonest conclusions. A secular person should take into account that perhaps the ba’al teshuvah’s arguments are strong, and he should consider them and adopt his path. He needn’t stubbornly cling to his secular stance, dismiss the teshuvah-seeker’s arguments, and attribute them to psychology. He must be open to the possibility that he is wrong. The same goes, of course, for the religious person regarding someone leaving religion.

In conferences of religious educators, it’s very common to treat students’ questions and departures from religion dismissively. In many cases we’re told that so-and-so’s questions are “answers,” not questions—that is, he raises them only to justify a step he had already decided upon. This approach is problematic for several reasons. First, even if the student is driven by an agenda, if he’s raising questions, he apparently needs that justification and mere psychological motives don’t suffice for him. Therefore it is appropriate to address his questions and answer them substantively—and perhaps that will influence him despite his a priori motives. Beyond that, in many cases the reason for the educator’s attitude is that he himself doesn’t really know how to answer those difficulties, and so it’s easier to dismiss them and attribute them to psychological influences and biases. An honest educator should answer the questions even if he’s right that they’re really “answers.” Moreover, he should be willing to consider the possibility that they are very good questions and, if he has no answers, perhaps he too should draw conclusions (leave religion, or adopt a thinner theology). Of course, the same applies to secular educators.

Entrenchment in an a priori position may be a psychological explanation for stubbornness in theological debates or in the debate over Torah codes, but it’s no justification for that stubbornness. Accusing someone of psychological bias isn’t a substantive argument within the debate itself. After you’ve answered the questions on the substantive plane, you may conclude that if someone still insists, he’s likely psychologically biased. But you must first examine the arguments substantively, and only afterward draw such conclusions. Psychological claims can be conclusions of the discussion, but not arguments within it. The debate itself must be conducted solely on the philosophical plane (see Columns 517 and 571 for more points on lack of honesty in such debates).

Intellectual honesty in fraught debates

The phenomenon of non-substantive debate characterizes discussions on fraught topics, such as arguments around religious faith or ideological positions. In Appendix B of my book God Plays Dice I dealt with several such examples. The subject of codes was one of them, and it’s worth seeing there how the scientific community discussed them. It’s a paradigm of intellectual dishonesty. Each side entrenches itself, and the arguments appear mainly to justify a priori stances.

The subject of that book was evolution. In that same appendix I also described the debates around evolution, which are usually conducted very dishonestly. Neo-Darwinists sometimes conceal information that might play into the hands of creationists; and the creationists, of course, pounce on every problem a researcher presents, without context and without mentioning the arguments and findings supporting evolution. Both sides behave like a fanatical religious sect with articles of faith that cannot be denied. The priests of the atheist church would not shame, in their zeal and fervor, Amnon Yitzhak or Amram Blau; and of course their devotees resemble those devotees as well.

Another case I discussed there was an article by several physicians on the effect of prayer on healing patients. It was an outstanding example of dishonesty. A scientific article surveying a set of experiments that examined the effect of prayers on healing. Of the experiments reported there, all those conducted with full and careful scientific methodology showed a significant effect. There were experiments that showed no effect, but all of them suffered methodological flaws. To my astonishment, the authors’ conclusion was that in light of their review there is no clear evidence for the effect of prayer, and each person may hold his own view. They chose cautious wording—namely, not that there is no effect, but that the question remains open and believers and skeptics may remain in their stances. But they were so biased they didn’t even sense the problem in their article. After all, their own review says exactly the opposite, and in fact there is a clear scientific conclusion. Their biases overpowered them, and it was very important for them to leave us all with the possibility of being biased and not letting the facts influence us.

To complete the picture, I’ll add that in an appendix note there I brought harsh critiques of the methodology of the successful experiments as well, and therefore I’m far from certain that this is indeed the scientific conclusion. But as far as the content of their article goes, that should have been the conclusion had they maintained real intellectual honesty. Needless to say, the experiments were conducted only on Christians who prayed and not on Jews, of course. Once again we see that Christians truly believe in their dogmas—not like us. Among us, no one really believes that prayer has an effect. Many declare it passionately, but let’s see one of them willing to put it to an empirical test. For that you have to be a real religious zealot, and among us there are none. Oh, I forgot: the Sages already saved us from this trouble. It’s forbidden to test God except regarding tithes. Thus we remain covered and forever right—not like the simple-minded Christians who put it to empirical test and risk failure.

By the way, even regarding tithes—where testing God is permitted—I know of no scientific experiment that examined this. There are only old wives’ tales about miracles that happened to so-and-so who tithed his money or produce. Let someone do serious scientific work here, with a sample group and a control group, with success metrics determined in advance, and examine the statistical significance of the results. When that happens—even if the experiment fails (as I expect)—then you can tell me that someone truly believes in it and not just declares sticky, pious slogans.

Another introduction: Between rare and exceptional

More than once I’ve highlighted the distinction between rare and exceptional. If we roll a die a hundred times and it comes up 5 every time, we’ll find it very odd. It’s reasonable to infer the die isn’t fair or that the roller has some ability to influence the outcome. But for some ordinary sequence of outcomes we’ll perceive nothing special. Yet statistically there’s no difference in the probability of getting a hundred 5s or any other random sequence of a hundred outcomes. The chance for each such sequence is 6^-100 (tiny, of course). Why don’t we marvel at every result we get? After all, it’s extremely unlikely. Well, it’s indeed reasonable that such a result would occur. On the contrary, with a hundred rolls we can know in advance with certainty that we’ll get a highly unlikely result (every result is). So how does a hundred 5s differ from other sequences? In that it is exceptional. It has special order, and it’s unlikely to have happened by itself. Note: exceptionality is a different measure from rarity. We might say all outcomes are equally rare, but the exceptional ones are each exceptional in its own way (Anna Karenina; see Columns 17 and 286).

One mechanism that turns a rare result into an exceptional one is pre-specification. If someone predicted in advance the exact sequence of die rolls, then we’d be amazed if that very sequence occurred—even if it’s one of the ordinary (non-exceptional) sequences. Because the sequence was pre-specified, it becomes exceptional. If it’s exactly what we get, there’s something in need of explanation.

The flip side of the coin is the phenomenon called “cherry picking” (see, for example, in the Q&A here). People tend to collect selective evidence that supports their a priori position and see it as reinforcement. If we take the question of Torah letter-skips, I can find the name of Sadat’s assassin in a minimal skip near “Sadat,” and likewise “Brutus” near “Julius.” But I won’t find the other assassins near their victims. A charlatan will use those two results as proof that the text is divine since it encodes future information. But it could just be coincidence. To see that the text is indeed significant, we must test whether it predicts all assassins and victims—or at least a meaningful quantity—especially in comparisons with other books (there were comparisons to War and Peace, and debates raged about those too). In addition, it’s important to see how unambiguous and single-valued the method is. If the code is flexible enough, you can always tweak it to find “significant” results. This is indeed one of the accusations against Rips and Witztum: that they define the cipher too flexibly (percent closeness over percent of text, and there are different ways to arrange the biblical text—they play with the lengths and widths of the text). A code of sufficient flexibility will give me whatever result I want from any book I choose.

Choosing the examples that confirm my view while ignoring the others is the fallacy aptly called “cherry picking.” For example, people tell old wives’ tales about miraculous rescues from terror attacks and missiles (a Book of Psalms in a pocket that stopped a bullet), but no one did serious statistics comparing other cases and groups. Did anyone check how many soldiers had a Book of Psalms that didn’t save them? Or how many soldiers had a pornographic magazine that did save them? And how many soldiers were saved with no book at all? As long as that isn’t done, it’s a mere anecdote—cherry picking. Likewise, there’s no problem choosing a successful example in the Bible and building mounds of theological theses upon it. In any book one can find successful cases. The main debate surrounding letter-skips is precisely this: are the successful cases statistically significant, or are they just anecdotes—cherry picking?

Additional demands from a cipher

Similarly, there are debates about how flexible the cipher is and whether it’s defined a priori. Of course, I must first choose the cipher and only then test whether it works on the text. If I choose the cipher after trying and finding one that works, it’s meaningless. In any book I can define an ad hoc cipher after testing many possibilities and discovering which yields fruit. I must also define the cipher rigidly enough and not allow adjustments that enable me to reach results by tuning parameters. All these are claims raised regarding the ciphers proposed by Rips and Witztum.

These two were the first to propose professional scientific work that yielded significant findings. It’s hard to doubt their professional ability, and the debate around their paper spilled far beyond the bounds of the journal that delayed it for many years before publishing it with a caveat (see about this here). Committees of top-tier professionals were formed and they too struggled to reach decisive conclusions. The debate hasn’t ended to this day. One must understand these questions aren’t simple, and even for experts it’s very hard to define the proper method for testing such a thing; but among laypeople, everyone readily forms an opinion—one way or the other.

Another anecdote. Once I was sent by the “Netivot Olam” yeshiva to hear a lecture by Doron Witztum, delivered in a private home to a group of several dozen professional statisticians. It was quite amazing to see how at a loss they were, and how much they followed their a priori leanings. It was very hard for them to present systematic, professional critique of his claims. I don’t say this to disparage them—it’s truly hard. What’s needed is systematic professional work by experts who will sit with this subject and analyze it deeply. Most critics didn’t do that. Incidentally, for that reason I returned to my mentors at the yeshiva and told them I couldn’t give them a professional opinion on the matter. I felt that to examine it I’d need to sit seriously for a long time and analyze things. As long as I hadn’t done so, it would be irresponsible to give an opinion.

My stance is a priori skeptical. I didn’t examine things in depth—it would take a huge amount of work and requires non-trivial statistical tools. Therefore I remain with my a priori position; since it’s my a priori stance, I hold it and place the burden of proof on those who claim otherwise. But for the sake of intellectual honesty, I add—and I’ve said in the past as well—that this is an a priori stance and I am far from denying the possibility that there’s something to these codes (similarly I’ve written more than once regarding various mystical phenomena).

The video

As noted above, what prompted me to address the matter was an almost six-minute video from Oren Avron’s channel about encoding information in the Torah. You can see it here. There are of course many such videos, but I’ll use this one to illustrate the points raised above. I will describe his findings with critical notes according to the order of presentation.

The introduction

In general, the video deals with occurrences of the well-known irrational number π in various forms in the Book of Genesis. His claim is that the significance here clearly proves the text is heavenly—that is, it couldn’t have been written by a human being (not even by one who knew π?). He prefaces by saying that π is used in mathematics and science very intensively, and therefore it’s interesting to examine specifically it. This is already an important point. Note that I could have chosen any number; if you want special irrationals, we have π, e, the golden ratio, √2, and so on. There are countless such numbers, and therefore it’s clear one can always find some number that will show up in very impressive ways in any text you like. One need only test the findings again and again for many numbers and choose the one that works. Alternatively, one can collect the digits that appear in all the attempts and then build a number out of those digits. Then present that number to the viewers and show that it appears in a very pronounced and impressive way in the text. This reflects the importance of an a priori definition of the target, not an ad hoc one. π is special enough to be exceptional and not merely rare, even without pre-specifying it (recall the sequence of a hundred 5s in the example above). It is not like any other irrational number I might have chosen (just as any random sequence of rolls I might choose in the example above).

He prefaces by noting that information about π reached us long ago, but it was partial: about the first five digits were known some 2,000 years ago; about 1,000 years ago we already knew roughly ten digits. But the Torah predates those dates, and therefore the presence of such information in the Torah shows its source is heavenly. Someone who knew all this wrote the Torah and also knew how to encode this information in it.

He continues and explains that biblical Hebrew doesn’t have digits, and therefore one must use gematria. This is the natural way to translate letters into numbers. Again, note that we could have chosen a different mapping, and then again could have produced ad hoc whatever finding we wanted. We could translate alef as 512, bet as 138, gimel as 1941, and so on. One can always find a mapping that will look amazing for any text. Gematria has an advantage here because it isn’t arbitrary: it wasn’t invented ad hoc to prove these findings, but is known for millennia, long before we had tools to test its significance for Torah encodings.

One more remark before I begin: I don’t intend to verify his findings, and for the sake of discussion I’ll assume he’s accurate. I’ll only try to see whether they’re significant enough to conclude anything about the Bible’s divinity.

The first five findings

He opens by noting that the word “Torah” has a gematria of 611. The first verse of Genesis has a total gematria of 2701. If you take the first 611 digits of π (you can find them here), then summing them yields exactly 2701. This seems quite an amazing coincidence. But note that it could also be pure chance. I could take the value of the phrase “Tablets of the Covenant,” “Ark of the Covenant,” one of the Divine Names, “Bereishit,” and so on, and look for their gematria in any verse or biblical phrase I choose. Ad hoc matching will bring me as wondrous results as you like. I can try across any book, test thousands of words and thousands of sentences, and find a pair that satisfies such a relation—and then present it as a marvelous, significant finding. It may be rare, but not exceptional. As I explained above, the choice must be a priori, not a posteriori.

Beyond the choice of word and verse, I could also count digits after the decimal point of π or include the leading 3. I could sum every second digit, or digits at Fibonacci positions, the sum of squares of the digits, etc. Note the flexibility here, which raises question marks about the finding’s significance. When there are many degrees of freedom and ad hoc matching of a target, there’s always a chance the relation we found is just an ad hoc choice and therefore not very meaningful. Note that in the traditional system, final letters have different gematria values, and he chose to ignore that. Again, there’s problematic flexibility that casts doubt on the significance. One could also choose alternative numeric values for letters and tune the matter to produce a “surprising” result. All these are ways to do it ad hoc, and the great flexibility increases the chance of finding such results ad hoc.

But one should be fair. The word “Torah” is indeed a natural choice here, and the first verse of the Torah doesn’t look like an ad hoc choice. Gematria is the common numeric value of Hebrew letters and wasn’t invented for this test. It’s an ancient and natural mapping to use. All these relations look fairly natural and not artificial choices made merely to fit. In short, it’s hard to categorically state this isn’t significant at all. One way to check would be to perform similar experiments in other books to see if one can ad hoc find relationships like this between a thematically important word in the book and its first (or last) sentence—with a relation that is natural and not chosen ad hoc. If you take War and Peace and search for a similar relation between the value of the word “war” or “peace” and the value of a key sentence (first or last), in a way where the numerical relation is natural and not tuned to fit, I doubt you’ll succeed. That’s the first finding.

But it doesn’t end there. Now he defines the “small” gematria of letters and words—that is, gematria without zeros: tav is 4, lamed is 3, and so on. The word “Torah” has a small gematria of 17. The first verse has a small gematria of 82 (I checked; that’s true). Astonishingly, the sum of the first 17 digits of π is 82. Here too we have all the flexibilities described above and more—but note this is a repeating pattern obtained in exactly the same manner (in both cases we sum the first digits of π according to the gematria of “Torah,” and it yields the gematria of the first verse). That’s the second finding—and you must admit it now looks more significant.

He then shows that the sum of the 17 digits immediately following the first 611 digits again yields exactly 82 (!!!). That’s a third finding pointing in the same direction. I’m already starting to itch. Granted, there’s great flexibility here. Had it come out 83, or 82 squared, or 164 (twice 82), etc., we could also have flagged that as a surprising (exceptional) finding. In addition, it’s interesting what happens with the next 17, or with the 17 following twice 611, and so on. This shows how problematic the finding is and how much flexibility lurks behind it. And yet, I doubt a test in a comparable book would produce similar results. It’s also important to see whether he’ll manage to show consistency—that is, that by the very same method he continues to find the same results in the Torah. That would greatly strengthen the significance, of course. This is the third finding.

Next: we now take the first 82 digits of π after the decimal point. The sum of their squares again yields exactly 2701 (!!!). This is the fourth finding along the same path. Here too note that we could have used cubes, square roots, doubling, and so on—countless possibilities. And yet, to be fair, this choice is fairly natural and simple, even if not unique. Hence there’s also a significance here that’s hard to ignore. This is the fourth finding.

At this point I would expect him to continue and test the sum of squares of the first 17 digits and obtain exactly 82, paralleling what he did above. But for some reason that doesn’t happen. I assume he didn’t get a suitable result there. That already raises questions. Even if the finding is surprising, if God indeed encoded this information unambiguously, I’d expect Him to do so consistently and perfectly. Remember, there’s no impediment to doing so if you plan the text in advance. Even humans with good software could do something like this today. This is another indication of problematic significance in these results.

On the other hand, even though I have a difficulty, if the results are significant and unlikely to be coincidental, it still tells us something. At most I’ll infer that the author is divine—and I’ll have a question about why He didn’t carry it through consistently. An analogy is Paley’s watchmaker argument for the creation of the world. Paley argued that if we found a watch lying on the ground, we’d assume it didn’t come about by itself; its complexity indicates a maker. So the world—which is much more complex—was certainly created by a maker. Many object that if the world has an omnipotent maker, we would expect the process of life’s emergence not to be evolutionary. Evolution produces much waste: many creatures die and go extinct along the way, some in great suffering. Why not create directly the world you want? But this objection has limited force. Assuming the world’s complexity is highly significant and unlikely to have arisen unguided, that implies a maker. If you don’t understand why He acts as He does, you have a question—but that doesn’t topple the argument for His existence. Likewise, if I found a watch that runs on a 23-hour day, lagging behind the true hour, that wouldn’t refute the claim it’s a very complex object unlikely to have arisen by itself. It would still be appropriate to infer there’s a watchmaker—only that I don’t understand his thinking and action.

The next two findings

The first verse has 7 words and 28 letters. The sum of the first seven digits of π yields exactly 28! In addition, the arithmetic mean of the gematria values of the first letters of those seven words yields exactly π (22/7, to two digits after the decimal). Needless to say, there’s substantial flexibility here too. Why take the arithmetic mean and not the geometric mean? Why take the first letters and not the second or last? To what precision does the finding cease to be implausible? Remember, 22/7 is a very common approximation of π. So if there are seven words, it’s tempting to sum some set of letters to get 22 and then divide by the number of letters. Here the smell of ad hoc choice is already strong.

He adds that the chance of getting such a result in a random book is absolutely nil. Of roughly two hundred million books in the world, there’s no chance of getting such a finding in any of them by accident. But of course this claim is problematic, since that calculation is far from unambiguous given all the flexibilities described thus far. I could do a similar exercise in any book, find the gematria of its first sentence, say it comes out 20,496. What’s the chance of that? Quite small—but that would be equally “true” for any number I get. I remind you again of the difference I showed above between rarity and exceptionality. The chance of getting a random sequence of a hundred die rolls is tiny—and yet we will always get such a sequence. As I explained, that’s a rare but not exceptional finding. A probability calculation reflects rarity, but not necessarily exceptionality. The number he presents is one quadrillion (10^-15). If you calculate a hundred die rolls, you’ll find a number much smaller than that. The event of a hundred rolls has a probability much smaller than the one he’s talking about, and yet I can tell you with certainty that if you roll the die a hundred times, you’ll get such a sequence. I’m sure you won’t be astonished by that result (unless it’s a hundred 5s or something comparable—exceptional, not just rare). In short, the big question isn’t the degree of rarity (which probability represents) but the degree of exceptionality, and that depends heavily on the search method’s flexibility.

Exceptionality depends, of course, on the finding having emerged unexpectedly and not chosen ad hoc. For example, take the second verse of Numbers and look for links to e. You can always do that. Now if you do a probability calculation, of course it will look miraculous. If I pre-specify that I want a verse where the sum of the first 82 digits of e equals its large gematria, and the sum of the sixth roots equals the verse’s small gematria—then go over War and Peace to see if any sentence satisfies this; or go over all the books in the world and look for one where the first sentence does. You can always find such a finding.

Intellectual honesty

So what’s the conclusion from all this? I don’t have one. My a priori inclination is to reject these findings. I don’t trust them. But there are indeed rather impressive findings on their face. The flexibilities that determine the degree of exceptionality show that presenting a probability calculation for the finding’s significance is almost impossible—certainly not for laypeople in statistics, who can be easily impressed by such displays (see examples in Columns 38, 88, 210, and others). As I explained above, since I don’t see a clear decision either way, I see no reason to abandon my a priori stance. In that sense I indeed remain with my position despite the findings—and to me that is an honest posture.

Nevertheless, everyone else has a very emphatic stance on the matter—both those who support the findings and their significance and those who oppose them. I don’t. The task of checking this seriously is extremely difficult—nearly impossible for me—due to its complexity and dependence on various assumptions. Therefore, the honest path for me is to say that there are, on the face of it, impressive findings, though their meaning and significance are not decisive. For some reason, balanced statements like this are almost never heard amid the emphatic stances in this controversy. I’ve already presented my critique of that emphatic posture and the proper way to approach it in the first part of the column.