Reprinted with permission from: Bible Review, Vol. IX, Number 5, October 1995
Among the oft-derided Christian literalists, it is said that the Bible
is the wholly inerrant Word of God, and that Holy Spirit guided the mind
and hand of its human authors. Orthodox Jews are even more extreme in their
literalism: Among them, tradition holds not merely that every word of the
Bible is inspired, but that every letter of the Torah (the Pentateuch,
the first five books of the Hebrew Bible) was dictated directly by God
to Moses in a precise and unerring sequence. So-called "higher criticism"
and modern linguistic analyses have tended to undercut these claims, critiquing
them with what is generally regarded as superior scientific method.
Few of the methods used, however, meet the rigorous criteria of hard science
and mathematical statistics.
In 1988 an obscure paper was published-in a prominent, rigorous, indeed
premier, scientific journal-with results that may demolish the claims of
the "higher" critics, and support, rather, the Orthodox Jewish
contention as to the nature of the Torah. The paper, by Doron Witztum,
Eiyahu Rips and Yoav Rosenberg of the Jerusalem College of Technology and
the Hebrew University, is innocuously entitled "Equidistant Letter
Sequences of the Book of Genesis" and was published in the eminent Journal of the Royal StatisticalSociety.1 It generated a brief flurry of public attention (and a wave of activity
within Orthodox Jewish circles) but was ultimately lost from general view
both because of its rather technical nature and because of the sheer outrageousness
of its findings, which remain, however, unrefuted as far as I know.
The authors, mathematical statisticians, discovered words encoded into
the Hebrew text that could not have been accidental-nor placed there by
After publication, the authors continued their work and found that some
pairs of words were predictive-that is, they could not have been known
to the supposedly human authors of the Hebrew text because they occurred
long after the Bible was composed.
The authors submitted a subsequent paper to the referreed journal Statistical
Science (such review journals generally represent the pinnacle of scientific
publishing), where, not surprisingly, it met with considerable skepticism-but
also with admirable scientific objectivity. The reviewers insisted on a
somewhat larger-than-usual number of challenges and revisions, but in the
end, they published it. In the words of Robert Kass, the journal editor:
Our referees were baffled: their prior beliefs made them think the Book
of Genesis could not possibly contain meaningful references to modern day
individuals, yet when the authors carried out additional analyses and checks
the effect persisted. The paper is thus offered to Statistical Science readers as a challenging puzzle.
In August 1994, the paper was published in Statistical Science under the title "Equidistant Letter Sequences in the Book of Genesis."
I hasten to ward the reader that the results do not reveal any secret
messages encoded in the Bible, but they do demonstrate certain sequences
of letters forming words that cannot be the result of chance. The implications
are for the reader to decide.
The authors of course worked from the Hebrew text, not a translation.
They focused on the book of Genesis as transmitted in the Orthodox tradition
(the textus receptus or Masoretic text, usually abbreviated MT).
They regarded the text as simply a string of letters (without spaces),
as the tradition claims-in site of the many sophisticated, modern, apparently
scientific arguments to the contrary. The tradition treats the letter-by-letter
sequence as no less sacrosanct than the prima facie meaning and
intent of the words suggested by the word sequences. Was there meaning
cryptographically embedded in the text that went beyond the meaning of
the words as written? they asked.
To explain what they were about, the researchers used this illustration:
Consider a text that may either have meaning in a foreign language or be
a meaningless sequence of letters. Not knowing the language, if it is one,
makes it very difficult to decide between these two possibilities. The
researches go on to explain:
Suppose now that we are equipped with a very partial dictionary, which
enables us to recognize a small portion of the words in the text: "hammer"
here and "chair" there, and maybe even "umbrella" elsewhere.
Can we now decide between the two possibilities?
Not yet. But suppose now that, aided with the partial dictionary, we
can recognize in the text a pair of conceptually related words, like "hammer"
and "anvil." We check to see if there is a tendency of their
appearances in the text to be in "close proximity." If the text
is meaningless, we do not expect to see such a tendency, since there is
no reason for it to occur. Next, we widen our check; we may identify some
other pairs of conceptually related words: like "chair and "table,"
or "rain" and "umbrella." Thus we have a sample of
such pairs, and we check the tendency of each pair to appear in close proximity
in the text. If the text is meaningless, there is no reason to expect such
a tendency. However, a strong tendency of such pairs to appear in close
proximity indicates that the text might be meaningful.
This in effect is what the researchers have found embedded in the Hebrew
test of the Torah-a whole series of meaningful word-pairs in close proximity,
something that they demonstrate cannot have happened by chance. These words
they found in close proximity are not simply the words of the text (as
would be the case in the analogy above of an unknown potential language).
They were rather words composed of letters selected at various equal skip
distances, for example, every second or third or fourth letter. It was
as though "behind" the surface meaning of the Hebrew there was
a second, hidden level of embedded meaning.
The researchers were led to this phenomenon by an observation of a certain
Rabbi Weissmandel in 1958. The rabbi noticed that selecting sequences of
equally spaced letters in the text, he could find certain words or phrases,
such as, say, "hammer" and "anvil." He called these
"equidistant letter sequences" or ELS for short. However, he
had no way of determining if these occurrences were due merely to the enormous
quality of combinations of words and expressions that can be constructed
by searching out such "arithmetic progressions" in the text.
The mathematicians and statisticians who formed the research team decided
to study systematically the phenomenon that Rabbi Weissmandel had observed
to see whether it should be explained purely on the basis of fortuitous
The researchers in effect set out the text of the Torah in what mathematicians
call a two-dimensional array, which is simply all the letters in sequence
(without spaces) with so many letters in each row, row after row. The letters
of the word HAMMER might appear as:
and might run vertically, horizontally or diagonally, as in the examples
DECODING GENESIS. Searching for pairs of related words
embedded in the text of the Five Books of Moses, mathematical statisticians
treated the traditional Hebrew text as a string of letters, reading from
right to left with no spaces between words. They then divided the text
into rows of equal length and looked for associated words, running vertically,
horizontally or diagonally, with what they called equidistant letter sequences-that
is, with the same number of letters between each of the letters of the
desired word. As shown at right, they discovered "Zedekiah" (, red arrow), the name of Judah's last king,
reading from top to bottom beside "Matanya" (, blue arrow), Zedekiah's name before he ascended
the throhe, running backwards from left to right. In the lower sample,
the word "Hasmonean" (, purple arrow), the name of the family that
led the Jewish forces that recaptured the Temple from the Assyrians in
164 B.C.E., runs diagonally from lower left to upper right; next to it
appears "Hanukkah" (, green arrow), the Jewish festival that celebrates
this victory, which runs vertically from bottom to top. The scholars discovered
hundreds of similar word pairs naming people and events that post-date
the composition of the Pentateuch. Rigorous statistical analysis reveals
that the odds of such pairings having occurred by chance are extraordinarily
Color in these graphics is enhanced for clarity
The researchers in fact tested the Hebrew words for "hammer"
(patishe, PTYS) and "anvil" (sadan, SDN) in equidistant
letter sequences. These are short words and on general probability grounds
they may be expected to appear close to each other quite often in any text,
as in fact they do in Genesis. But they also found that even if they restricted
the search for such for such appearances to only the minimum equal
length skip distance, such word-pairs still occurred much too frequently
to be accounted for by chance. And other combinations also appear so often
that it begins to look not so much like a random happening, but like something
carefully embedded in the text. For example, the researchers also found
the pair Zedekiah ( a sixth century B.C.E. king of Judah), and Matanya,
Zedekiah's original name (see 2 Kings 24:17); and the pair Hanukkah (the
Jewish festival that commemorates the re-dedication of the Temple after
it was recaptured from the Assyrians in the second century B.C.E.) and
Hasmoneans (the family name of the leaders of the Jewish forces that managed
to wrest the Temple from the Assyrian monarch Antiochus IV Epiphanes).
Note that these names and events found encoded in the text of the Torah
involved people who lived, and events that occurred, long after the Torah
was composed, whether by a divine or human hand.
In their 1988 paper, the researchers selected, at random, 300 such Hebrew
word-pairs with obviously related meanings, and looked for the words embedded
in the text by treating the entire book of Genesis as a long cryptographic
string. They would start at the beginning until they came to the first
letter, then look to see if a second letter could be found two letters
away. If so, they then looked for the third letter two letters away; if
not, they stopped and searched for the next appearance of the first letter
and repeated the process. They continued until they found an occurrence
of the entire word spelled out at every second letter. If not, they performed
the same procedure looking at every third letter instead.
In this fashion they searched first every other letter, then every third,
and so on (including reverse order). When they found the first instance
(that is, at the minimum skip distance) of the first word of the
pair, they then searched until they found the first instance of the second
word of the pair, also at minimum skip distance, and measured its proximity
within the text-string to the first. They did this for all 300 word-pairs.
As a control, they performed the same search for the same pairs on numerous
random scramblings of the Genesis text. The authors found that each of
the 300 word-pairs were found in close proximity in the actual Genesis
text, but not in randomized control texts.
The published results show that this finding was significant at a level
of 1.8 x 10-17, that is, the odds of its occurring merely by
chance are less than 1 in 50 quadrillion. (A quadrillion is one with 15
zeros after it.) A finding in most scientific journals is considered significant
at chance levels of anything less than 1 in 20.
The capacity to embed so many, meaningfully related, randomly selected
word-pairs in a body of text with a coherent surface meaning is stupendously
beyond the intellectual capacity of any human being or group of people,
however brilliant, and equally beyond the capacity of any conceivable computing
device. Furthermore, that the word-pairs were randomly selected strongly
suggests that all possible word-pairs are so embedded.
Following publication of this paper, a public statement was issued,
signed by five mathematical scholars-two from Harvard, two from Hebrew
University and one from Yale.2 "The present work," they said, "represents serious research
carried out by serious investigators. Since the interpretation of the phenomenon
in question is enigmatic and controversial, one may want to demand a level
of statistical significance beyond what would he demanded for more routine
conclusions... [T]he results obtained are sufficiently striking to deserve
a wider audience and to encourage further study." The work was also
critiqued and endorsed by Dr. Andrew Goldfinger, a senior research physicist
at Johns Hopkins University in Baltimore, and by Harold Gans, an analyst
with the U.S. Department of Defense.
According to Jewish tradition, the Torah contains all knowledge; therefore
the codes embedded in the Torah also encompass information that transcends
the limitation of time. The Vilna Gaon, the great l8th century Rabbi of
Vilna, Lithuania, a child prodigy and one of the most brilliant men in
Jewish history, wrote that "all that was, is, and will be unto the
end of time is included in the Torah...and not merely in a general sense,
but including the details of every species and of each person individually,
and the most minute details of everything that happened to him from the
day of his birth until his death."3
Some may be reminded of the words of the Rabbi from Nazareth, seen in
a different light: "I tell you the truth, until heaven and earth disappear,
not the smallest letter,* not the least stroke of a pen,** will by any means disappear from the Torah [Law] until everything is accomplished"
(Matthew 5:18 ).
For their second paper, published in 1994, the researchers went one
step further, as if guided by the Vilna Gaon. Instead of looking for pairs
of related words, they looked for pairs of words that were time-related
from a period long after the Torah had been composed. They took the names
of the 34 most prominent men (measured by the length of their biographies
in a standard Hebrew reference book, the Encyclopedia of Great Men in Israel)
from the ninth to the nineteenth centuries, and (using the standard Jewish
way of abbreviating names***) they
paired the name with the date of the man's birth or death (Hebrew month
and day).**** There was no way
the author of the Torah could have known, at the time the Torah was composed,
of the existence of these men, and certainly not the dates of their births
or deaths-unless of course He was divine. Nevertheless, the researchers
were able to demonstrate that the names and the dates of their birth or
death were encoded into the text in close proximity; that is, using the
minimum skip distance the names and the dates of birth or death were found
embedded in the text of Genesis in significantly close proximity.
Understandably, skeptical scholars at the Statistical Science journal
then asked the authors to repeat the test on another sample of the next
34 most prominent men. In this group, the dates of death for two of the
men were not known, so the second test included only 32 men. The results
were the same, however. In short, for all 66 men, their names and birth
or death dates were found in close proximity.
The likelihood that this occurred by chance on the set of 32 names is
less than 1 in 50,000; on both sets, less
than 1 in 2,500,000,000. The first figure
is reported in the article in Statistical Science. The second number
is not included; as yet another measure of conservatism, the editors insisted
that after having found a successful result on the first set, the authors
repeat it on the second and report the results of the second set alone.
It is also significant the researchers tried to find the same phenomenon
by using the Samaritan Pentateuch, which varies slightly from the traditional
Jewish textus receptus. But the phenomenon was utterly lacking in
letter-level variants of the Pentateuch, such as the Samaritan Pentateuch.
Nor could it be found in other texts, sacred or otherwise. One of the reviews
had them try the same test on Tolstoy's War and Peace; so the researches
chose a section of the Hebrew translation that was the same length as Genesis,
but the phenomenon did not appear in War and Peace. With respect
to the other sacred texts, the phenomenon would not be expected because
even the best manuscripts of the text vary; there is no letter-for-letter
sacred text as there is for the Torah. Even the rest of the Hebrew Bible
outside of the Torah lacks such a tradition; hence there are innumerable
What are the implications of these findings ?
The phenomenon cannot be attributed to anything within the known physical
universe, human beings included. Moreover, the rigorous proof of the existence
and validity of the phenomenon requires both high speed computation and
only recently developed techniques of statistical analysis.
On the other hand, though statistically powerful, the phenomenon is
a relatively weak one. "Proximity" is defined only statistically,
and the phenomenon only makes itself apparent in the aggregation of many
examples that on average show much greater proximity than would
It should also be noted that there is no way of extracting the encoded
information without knowing it already. Because the information cannot
be extracted in advance, the method cannot be used to foretell the future.
(And of course the Torah itself forbids such practices.) The future long
ago embedded in the Torah must become our past before it can be retrieved.
How has the paper been received? The authors note with disappointment,
but not surprise, that responses so far have mostly fallen into two categories:
a priori acceptance or a priori rejection. The former, by believers and
enthusiasts (especially those without mathematical training), is indeed
not surprising. But the latter is-or should be. Since to date no one has
discovered a flaw in the authors' work, it is reasonable to ask of scientifically
trained, a priori skeptics (who are certain these results must be a fluke),
"What standard of proof would you accept as an indication that the
phenomenon might be genuine?" The most frequent answer by far is "There
is no standard. I will not believe it regardless."
One is reminded of the persistent (but after 80 years at last weakening)
skepticism that greeted certain results in quantum mechanics research:
for example, that what happens in every part of the universe instantaneously-or
even backwards in time-influences, in measurable degree, what happens everywhere
else. Should the "codes in the Torah" phenomenon remain undefeated,
perhaps in the light of such astonishing findings in modern science it,
too, will one day seem not so preposterous.
What then was the purpose of encoding this information into the text?
Some would say it is the Author's signature. Is it His way of assuring
us that at this particular, late moment-when our scientific, materialistic
doubt has reached its apotheosis, when we have been driven to the brink
of radical skepticism-that He is precisely who He said He is in
that astonishing, radical core document of the Judeo-Christian tradition?
*Literally iota, equivalent to the Hebrew yod, the smallest letter in the Hebrew
alphabet. **Literally tittle, a reference to the small decoration or "crown"
on some Hebrew letters in handwritten scrolls of the Torah. ***For
example, Rabbi Solomon [Shlomo] ben Isaac [Yitzchak] is regularly referred
to as Rashi. ****Numbers
are represented by letters in Hebrew.
Witztum, Eliyahu Rips and Yoav Rosenberg, "Equidistant Letter Sequences
in the Book of Genesis," Journal of the Royal Statistical Society 151:1 (1988), pp. 177-178.
H. Furstenberg (Hebrw University)00; I. Piateski-Shapiro (Yale University),
the renowned mathematician; D. Kazhdan (Harvard University); and J. Bernstein