## Devlin's Angle |

Both author and publisher made a considerable amount of money -- despite the fact that, as was immediately clear to both mathematicians and serious Bible scholars, the book's main thesis was complete nonsense.

Indeed, before the year was out, Maya Bar-Hillel, Dror
Bar-Natan, and Brendan McKay had shown that the
same kind of "amazing revelations" Dronin claimed
were hidden in The Bible could be found in the
Hebrew translation of *War and Peace* (and almost
certainly in any other work of comparable length).
Bar-Hillel and Bar-Natan are mathematicians at the
Hebrew University in Jerusalem, McKay is a
mathematician and computer scientist at the
Australian National University. In the latest issue
(Spring 1998) of *Chance*, the magazine of the
American Statistical Association, the three provide an
in-depth report of the result they first announced in
1997.

In a nutshell, the "secret code" by which Dronin claimed the Bible revealed hidden messages was that of the "Equal Letter Skip," or ELS for short. The idea is to start with some letter in the text and then skip ahead by some fixed number of letters to spell out . . . well, whatever you get. For example, if you start with the first (Hebrew equivalent of the letter) T in Genesis and skip 49 letters, the 50th letter is an O, the 50th after that is an R, and the 50th after that is an H. Wonder of wonders, you have just spelled out the word TORH, the Hebrew word for Bible (pronounced Torah). To the naive or numerically challenged, this might seem miraculous. But it's exactly the kind of thing you would expect to happen. The person searching for the "hidden messages" gets to choose which letter to start with and how big a letter skip to use, and only the successful choice is reported. With a text as long as Genesis -- 78,064 Hebrew letters long -- then you will almost certainly be able to find any moderately short word (say up to six letters long) by an ELS for some skip-number or other. Using a computer to search through all the possibilities, it's child's play to find them. For instance, the word TORH itself appears 56,769 times as an ELS for some skip number or another.

The utter triviality of the thesis that had turned Dronin
into an instant media star was illustrated when, in an
interview with the magazine *Newsweek*, Dronin stated
that "When my critics find a message about the
assassination of a prime minister encrypted in *Moby
Dick*, I'll believe them." Dronin was referring to the
claim made in his book that, using the secret Bible
Code, he had been able to predict the assassination
of Israeli Prime Minister Yitzak Rabin. Discounting
the rather obvious fact that many Middle East leaders
were always prime candidates for assassination,
McKay took up Dronin's challenge, and in no time at
all found that, when applied to *Moby Dick*, Dronin's
secret code revealed not only the assassination of
Rabin, but also those of Kennedy, Martin Luther King,
and Trotsky.

In fact, the "amazing" Bible secrets that made the headlines were not amazing at all. They are exactly what the mathematics will predict you will find, provided you search long enough -- perhaps a day or so if you have a fast computer. What posed more of a challenge to the mathematicians was a little known piece of research that had been carried out ten years earlier by another two Israeli mathematicians, Doron Witztum and Ilya Rips. They had discovered that when an ELS search was run on Genesis to look for pairings of names of prominent rabbis along with their birth or death dates (which are given as sequences of letters in Hebrew, with the first ten letters of the alphabet representing the numerals), the result was a success rate that seemed much higher than the mathematics predicted.

Subsequent examination of the Witztum and Rips
work by others seemed (I stress that word seemed) to
confirm their findings, and as a result, despite
continued skepticism by the statistical community at
large, their work was published in the respectable
academic journal *Statistical Science* in 1994. It was
this earlier publication that enabled Simon & Schuster
to proclaim, on the dustcover of Dronin's book, that
"The code was broken by an Israeli mathematician,
who presented the proof in a major science journal,
and it has been confirmed by famous mathematicians
around the world."

In fact, I am not aware that any famous
mathematicians confirmed the Witztum and Rips
finding. Rather, the ever-cautious statistical
community was not prepared to declare the result
bogus -- which is what they suspected -- until they had
concrete proof thereof. Now, thanks to some statistical
detective work by Bar-Natan and McKay, they have
that proof, and the *Chance* article presents it.

The problem was that, for the coding system Witztum and Rips used, Genesis did perform much better (in terms of pairing the rabbis with their dates) than any other text of comparable length. It was not the size of the ELS skip that was at issue, rather how do you select the rabbis whose names are to be looked for, which of the many ways of "naming" them do you choose (how many different ways do people refer to you, for instance?), and how do you represent their dates? When you are doing ELS letter searches, each of these makes a difference. The more freedom there is to make choices, the greater the likelihood of finding "something of interest" by an ELS search.

What made Witztum and Rips' Genesis result
tantalizing was that they provided a defensible
rationale for the choices they had made. To show that
Genesis was not special after all (in terms of providing
an ELS coding of rabbi and date pairings), Bar-Natan
and McKay had to find a coding system that
conformed to the Witztum and Rips rationale but for
which Genesis did not turn out to be special. In other
words, even though they suspected Witztum and Rips
had "cooked" their chosen rules to get the result they
wanted, Bar-Natan and McKay had to play by those
rules. It was like agreeing to fight an opponent using
the opponent's preferred choice of weapons. Despite
this difficulty, they were successful. They found a
coding system for rabbis and dates that conformed
with the Witztum and Rips rationale for which the
Hebrew translation of *War and Peace* fared just as
well as the Bible.

In their article in *Statistical Science*, Witztum and Rips
had concluded that "the proximity of ELS's with
related meanings in the Book of Genesis is not due to
chance." Bar-Hillel, Bar-Natan and McKay end their
recent *Chance* article by quoting that passage, and
adding their own conclusion: "It must therefore be due
to design. The design, however, may well be human,
not devine."

A final thought: The world we live in is indeed full of wonders -- many
of them genuinely "amazing" -- and mathematics and statistics
can help reveal those wonders to us. Moreover, whatever your
religious belief (or absence thereof), there is little doubt that the
Bible contains a great many "messages" that require effort to
"uncover". It is therefore a great pity that so much attention is
paid to the kind of nonsense peddled in *The Bible Code*.

For further details, see McKay's web site at: http://cs.anu.edu.au/~bdm/dilugim/torah.html.

** - Keith Devlin **

Devlin's Angle is updated at the beginning of each month.