I'm a rationalist and a skeptic, someone who safely separates faith from reason. But when I read a scientific paper titled "Equidistant Letter Sequences in the Book of Genesis," I confess I felt a strong urge to grow side-locks and a long beard and start atoning for my years of doubt. The article, published in 1994 in a prestigious, peer-reviewed journal called Statistical Science, argued with unnerving force that the first book of the Bible contains embedded codes that predict events that long postdate its writing and that these codes are, statistically speaking, "not due to chance." As I wrote in Slate two years ago (see "Cracking God's Code"), the paper's hypothesis, if correct, would all but prove both the existence of God and the divinity of the Torah (the first five books of the Hebrew Bible).
The paper startled me and many others. People became Orthodox Jews because of the codes. I know of one man who held off circumcising his son until the paper was published. It spawned a runaway best seller, Michael Drosnin's The Bible Code. It became a recruiting tool for ultra-orthodox Jewish yeshivas. And it amused, then frustrated, mathematicians worldwide. What made the codes especially eerie was that, while scientists were almost universally skeptical of them, nobody could figure out what was wrong with them. No one had published a rebuttal in a peer-reviewed journal. As long as that remained the case, even rationalists like me had to consider the possibility that science could support the most radical religious conclusions.
But the Torah codes' time is finally up. In the current issue of Statistical Science, Australian mathematician Brendan McKay and three Israeli colleagues have convincingly debunked them, and the former editor of Statistical Science who published the original paper has endorsed their rebuttal. For those of us who were freaked out by the codes, the new paper comes as a relief.
The codes' rebuttal has taken so long because the science behind the original paper is very sophisticated. (One of the authors, Hebrew University professor Eliyahu Rips, is a well-respected mathematician.) The original paper sought to test the anecdotal observation that pairs of conceptually related words tend to appear in close proximity to one another in the Torah, coded in what are called equidistant letter sequences. An ELS is a string of letters compiled by pulling letters out of a text at regular intervals. For example, if you start with the first letter of this paragraph and read only every fourth letter, you will find the word "TORT." Every text contains many such "codes," so the question was whether the observation of codes with apparent meaning in Genesis was a deliberate message from the almighty or mere coincidence.
To test whether the Genesis ELS were intentional, Doron Witztum and co-authors Yoav Rosenberg and Rips used a computer to search Genesis for ELS containing the names of famous rabbis and their dates of birth or death. These rabbis were all born long after Genesis was written, so their names could not have been encoded on purpose by any human author. Yet in the Genesis text--unlike in control texts such as a Hebrew translation of War and Peace--the rabbis appeared on average closer to their own dates than to the others'. This seemed to show that someone had actively encoded the text--someone who knew beforehand when rabbis would be born or die.
After years of onerous testing and retesting, McKay and his colleagues--Dror Bar-Natan, Maya Bar-Hillel, and Gil Kalai--have found the serious methodological flaws the peer reviewers missed. First, McKay et al. note, the codes are hypersensitive to small changes in the data. Excluding only four of the 32 rabbis essentially eliminates the effect, for example.
The core of their critique focuses on the manner in which the rabbis were named in the Witztum-Rips-Rosenberg paper. The names of medieval rabbis are not fixed in the way that modern names are; the great rabbi Moses Ben Maimon, for example, is often called Maimonides or the Rambam. Searching for the rabbis' ELS, therefore, required choices about what names to use for each particular rabbi. Witztum and Rips asked a consultant to compile appropriate appellations for each rabbi, but the rebuttal paper argues that the process used by this consultant was sufficiently subjective as to bias the results. (There is something indisputably bizarre in the spectacle of distinguished mathematicians squabbling about the correct names of 14th-century rabbis.)
In order to demonstrate that "data tuning" alone could account for the effect, McKay and his co-authors made their own alternative list of appellations for the rabbis, a list they describe as "of quality commensurate" with Witztum and Rips'. This alternative list produced no effect in Genesis but a huge effect in War and Peace. Then, McKay and co. sought to produce the most accurate list they could, using their own consultant. With this list, they found no statistical evidence of codes in any text.
Further evidence of tuning was found in other decisions Witztum and Rips made about their data. The authors of the first paper erred, McKay and his colleagues claim, in how they chose which rabbis to include. The rabbis were supposed to be chosen by an objective criterion--the length of their entries in a particular encyclopedia--but because of the "careless manner" in which this was carried out, rabbis were included who should not have been, while others were wrongly excluded. Birth and death dates were also flawed. The authors collected dates from a wide variety of sources, but apparently did not establish firm rules to decide among disputed dates. McKay and his co-authors also claim that aspects of the experimental design (such as the way distances were measured between rabbis and dates) were tuned. When McKay and his colleagues varied the experimental method, the choices of dates, and the way dates were expressed, the results almost invariably deteriorated.
T he rebuttal authors note still other problems in the original paper. The Torah's text has varied over the centuries, and when dealing with ELS, tiny variations can be ruinous. Yet when McKay et al. compared the text Witztum and Rips used to other Torah texts--some of which are probably more historically reliable--the Witztum and Rips text produced the strongest results. The authors also note that even using the flawed Witztum-Rips methodology, no book of the Torah besides Genesis shows any effect at all.
McKay and his colleagues do not accuse the original authors of fraud, speculate on how their data-tuning took place, or ask whether the tuning was consciously done. But they conclude that all the choices available to Witztum and Rips created "wiggle room," thus permitting the authors' biases to corrupt the results. "All of our many earnest experiments produced results in line with random chance," they conclude. "In light of these findings, we believe that [the] 'challenging puzzle' has been solved." For all but the true believers, the publication of the rebuttal paper seems likely to end the Torah codes debate.
But for the true believers, of course, the phenomenon was always more than a mere "puzzle," and they are not about to roll over. Rips was sufficiently enraged by Statistical Science's acceptance of the rebuttal paper that he retained a lawyer, who advised the journal that "the accusations in the article about to be published ... are untrue and libelous of Dr. Rips." Rips sought a delay in publication and the chance to respond to the critique in the same issue. (Statistical Science rejected his request but will consider publishing his formal comments in a later issue.) Rips contends that the rebuttal paper misrepresents the original experiment's methods and that it ignores subsequent tests that he regards as immune from data-tuning charges. He wrote me in an e-mail, "I believe that the evidence for the Torah Codes is now stronger than ever. I find the paper by the critics more than extremely unfair."
Those who want to believe in the Torah codes will always be able to find ELS that impress them. But there's a difference now. To believe today that the almighty wrote the Torah is once again, as it should be, a matter of faith. It's not a conclusion that can be forced on me--or anyone else--by statistical science.