Several years ago, astonishing statistical evidence was published regarding the existence of a hidden code in the Book of Genesis, relating to future events. New research deprives this evidence of its import by proving that the same code can be found in the Hebrew translation of War and Peace.
Maya Bar-Hillel Dror Bar-Natan Brendan McKay
A previous issue of Galileo contained an article by Zvi Atzmon titled: The Torah codes -- The unbearable lightness of the computer. Here we wish to describe the research of Witztum, Rips and Rosenberg1, which Atzmon only touched upon at the end of his article, and to present new research which casts serious doubt on their findings.
If you start from the first T in the Book of Genesis, and skip 49
letters, the 50th letter is an O. Skipping over another 49 letters
brings you to an R, and a final 49 letter skip brings you to A, thus
spelling the word TORA (which in Hebrew has just four letters) in
equal-letter-skips (ELSs). This amusing fact was discovered several
decades ago by Rabbi Weissmandel. What Weissmandel saw with the unaided
eye can nowadays be sought with the aid of computers, spanning much
longer text segments, and much larger letter skips. Such a search shows
that the word TORA can also be found as an ELS in War and Peace (the
Hebrew translation), for example, in the translation of the following
text from chapter one: ' "... said Anna Pavlovna. "You'll spend the
whole evening with me, I hope?" "And the fete at the English
ambassador's? ...", said the prince. '
A computer search for the names of two of the present authors,
Maya and Dror, finds them, too, in Genesis (chapter 40, verse 1) as
ELSs. Indeed, if a word is not too long (say, up to 6 letters), or its
letters not too rare (e.g., in Genesis, the tenth letter yod is thirty
times more common than the ninth letter tet), then there is an excellent
chance of finding it as an ELS in any sufficiently long text (Genesis,
for example, is 78,064 Hebrew letters long). The computer allows an easy
search not only for single words, but for pairs of words as well. It can
happen that thematically related words (such as the names of the authors)
would appear close to each other, as in the phrase just cited.
In the mid '80s, Doron Witztum, a Jerusalemite born-again Jew,
started looking for all kinds of words and word combinations in Genesis.
His findings are described in his book: The Added Dimension2 (in
Hebrew), which was also mentioned in Atzmon's article. The fact that
"in any text of sufficient length ... it is possible to find various
words as ELSs" (Atzmon, p. 34) did not escape the notice of Witztum and
his collaborator in letter skipping, Professor of Mathematics Ilya Rips,
another born-again Jew. They decided to run a kind of statistical test,
and check whether the letter skips they were finding in the Torah were
exceptional, or were merely an artifact of the multitude of letters and
possibilities which the letter skipping method allowed. In his article,
Atzmon called the results of this test "a line of statistical findings
that could really trouble skeptics" (p. 32), and said that it "cannot be
ignored, and is certainly disturbing" (p. 38). Atzmon was unaware that
meanwhile research had been done which undermines the results that
bothered him, and strips them of their significance. But before we
describe that research, we should get a grasp of the nature of those
statistical findings, which were even published in a scientific journal.
The Encyclopedia of Great Men of Israel, edited by Margaliot,
contains short biographies of Jewish Rabbis who lived between the 8th and
the 19th centuries. Sometimes the biography contains a death date or a
birth date. Witztum and Rips (many regard Rips as the central figure in
ELS research, but we shall talk of Witztum and Rips, in the order in
which they chose to author their joint paper. Rosenberg only did the
programming for them, and will not be mentioned further) listed those
rabbis to which the Encyclopedia devotes three columns and upwards of
text, and mentions a date of death or birth. They found 34 such rabbis
(actually, they erred slightly in composing the list, both in column
counting and in missing one rabbi), searched for their names and dates of
death or birth as ELSs in Genesis, and computed a kind of distance
function between the name of a rabbi and his date (for brevity's sake, we
shall talk only of dates of death. There were very few birth dates
anyway). Their assumption was that if there is, indeed, a hidden text in
the Torah, then thematically related words will appear in proximity, as
they do in any meaningful text.
The exact manner in which they computed the distance is
technically complicated, and of no importance to the present story.
Interested readers can find the details in the original article. Anyway,
a list of numbers was obtained, which describes the "distance" between
the name of each rabbi and his date of death (in some cases, no ELS was
found for a rabbi's name or date, and then, of course, no distance was
computed). Here and there some rabbi was particularly close to his date
of death. At the same time, many rabbis were actually closer to some
other man's date. So to test if there was an extraordinary closeness
between the rabbis' names and dates, a statistical significance test was
required. "Statistical significance" is the probability of obtaining a
certain result by chance. The smaller the significance, the less the
probability of getting that result by chance. The question was whether
the distribution of distances that was found in the rabbis' list in
Genesis was statistically significant.
The original method whereby Witztum and Rips computed the
statistical significance of their results was erroneous. Prof. Persi
Diaconis, a world reknowned mathematician and statistician who
specializes in uses and abuses of statistics to support fantastic claims,
was one of the experts consulted by the scientific journals in which
Witztum and Rips hoped to publish their results. He suggested a
different method, which they used in the Statistical Science article.
For the present story, we will assume that Diaconis' method was used all
along, and describe no other.
Imagine that each rabbi is paired not with his own date of death,
but rather with some other date, sampled at random from the list of
dates. It is possible, of course, to compute the distance between the
rabbis' names and such random dates. If there is anything special in the
Book of Genesis, and the rabbis' names really appear exceptionally close
to their dates of death, then the distances between correct name-date
pairs should be, on average, closer than between random name-date pairs.
Diaconis suggested running a kind of "race". 999,999 permutations of the
34 rabbis were chosen at random. In every permutation, each rabbi was
paired with the date against which the permutation pitted him. For each
of the 999,999 permutations, the distances between the rabbis' names and
the date they happened to be paired with in that permutation were
computed. The original, correct, list of distances was compared to
999,999 lists of distances in which each rabbi was paired with a random
date. Lo!, the correct pairing achieved one of the first places in this
"race"! If there were nothing special in this list or in the Book of
Genesis, there would be no reason for it to excel like that. The
probability that of all lists, the correct one would excel thus by pure
chance is minute. In other words, a latent code was discovered in
Genesis, with a very small statistical significance (as said above, the
smaller the statistical significance of a result, the greater its
actual significance). It is almost impossible that what was found, was
found by sheer coincidence.
This and more: Witztum and Rips took various other Hebrew texts,
and ran their test on them, too. For example, they took the first 78,064
letters of War and Peace. There, too, the computer searched for the
names of the rabbis in ELSs, their dates of death or birth in ELSs, and
the distances between names of rabbis and their respective dates. There,
too, the list of distances obtained was compared to 999,999 other lists,
which were obtained by permuting the names of the 34 rabbis. In War and
Peace, the correct list did not at all excel in the race. Its
performance was kind of middling. These, then, are the results which
Atzmon, and the editor of Statistical Science, found so astonishing.
It is noteworthy that the only thing that Witztum and Rips
claimed in their article is that they found in Genesis a phenomenon of
extraordinary statistical significance, namely, one whose probability of
being sheer coincidence is vanishingly small. They did not offer a
possible alternative to chance. But there was no need to say explicitly
that which everyone understands: since the rabbis were born and died
decades after the Torah was written, only a clairvoyant could have
introduced the secret code into it. If you will, Witztum and Rips had
discovered a statistical proof of the divine origin of the Book of
Genesis.
Now that we have presented - albeit without the technical details
- the main essentials of the statistical method whereby Witztum and Rips
proved the existence of a secret code in the Torah, it is time to look in
detail at the lists they worked with. If hitherto an impression might
have been formed that each rabbi was represented by a single name and a
single date (or two, if the encyclopedia mentioned his birth date as
well), this turns out not to be so. The rabbis were known by many names
and appellations, and they entered the list with many names and
appellations. For example, Rabbi Yosef Terani appears in the list with
9 names [approximating the Hebrew for the benefit of non-Hebrew
speakers: Rabbi Yosef, M'Terani, Yosef Terani, Teraani (another
spelling for Terani), M' Teraani, MHRIM"T (an acronym), HMHRIM"T,
MHRI"T, HMHRI"T]. Dates also appear in more than one form. For example,
The Gaon of Vilna had a birth date and a death date, which are listed
under a total of 9 forms. [For the benefit of readers not familiar with
Hebrew, we note that Hebrew dates are written using letters rather than
numerals, with letters having numerical value, in a manner resembling the
use of digits to write numbers. 13 would be written as JC -- J=10, C=3,
JC=13. We will not list the 9 date forms here, but we note the
following: First, each date was written in three forms, roughly
analogous to: June first, on June first, first of June. Second, the 15
and 16 of the month are typically written as 9+6 and 9+7, respectively,
rather than 10+5 and 10+6, because of a kind of religious taboo on the
letter combinations corresponding to the latter form. Witztum and Rips
listed both forms. The Vilna Gaon's 9 forms included a 15th of Nissan
date, hence the multiplicity of forms]. What is going on here? Are
these, perhaps, ALL the possible names and appellations of the rabbis, or
ALL the different ways in which their dates could have been written, and
so we simply see a comprehensive list? The answer is: not at all.
Indeed, it is in the multitude of possibilities for writing names and
dates, and the even greater multitude of possibilities for choosing among
them, that the key to the Torah codes puzzle lies.
To demonstrate what is meant by multitude of possibilities,
consider January 1. In addition to January first, the frst of January,
and on January first, we also have on the first of January, January
one, on January one, New Year's day, on New Year's day, etc. If a date
has 12 forms (as, for example, 1 of Tishrey does), and one can choose
among them, there are almost 4 million ways in which a subset of these 12
forms can be chosen. The 16th of the month of Nissan can be written in
as many as 20 forms. How were the particular names and date forms in
Witztum and Rips' lists chosen?
Witztum and Rips' article gives a partial answer to this
question. Written and oral exchanges with them give a more comprehensive
answer: The names and appellations were supplied by Prof. S.Z. Havlin, a
bibliographer from Bar-Ilan University, and the date forms were supplied
by the late Dr. Yaakov Orbach. It is not quite clear who is responsible
for the fact that many of the dates mentioned in Margaliot's Encyclopedia
were altered, corrected, discarded, or exchanged, so that the dates in
Witztum and Rips' list are not identical to those in the Encyclopedia.
Be that as it may, whomever was responsible for the choices made, the end
result is that in spite of Witztum and Rips' declared intention of
running their statistical test on a "uniform, objective" list, the list
they actually ran was neither uniform nor objective: it necessitated the
discretionary judgment of experts; judgment which, as we shall presently
see, is open to question.
It is worth noting that the objectivity of the list is redundant
if the list is a-priori. For present purposes, a list is "objective" if
anyone who would try to reconstruct it would get the same list
(incidentally, Havlin has admitted in writing that if he were to draw the
list of rabbis again, it might look different). On the other hand, a
list is "a-priori" if it had been set in advance of any knowledge of how
the words in it "perform" as ELSs. For statistical purposes, the
importance of being a-priori far outstrips that of being objective,
because the significance test described above assumes a-prioricity, but
it does not assume objectivity. This can be clarified by the following
example: Suppose someone claims to have telepathic powers, which enable
him, say, to "read" numbers without seeing them. Suppose he is subjected
to a statistical test: he is asked to guess the serial number on a 100NS
bill -- and he succeeds. Since there are ten digits in the serial number
on such a bill, the probability that the success is mere coincidence is
tiny (about 1 in 1010). But suppose that the testee produced the bill
out of his own pocket. In this case, one might suspect that the bill was
not chosen a-priori; namely, that the chosen bill had been peeked at
earlier. In this case, of course, it is impossible to compute the
probability of a successful guess from purely combinatorial arguments, as
just done. The fact that the bill was not chosen in an "objective"
manner is important only insofar as it raises a suspicion that neither
was it chosen in a "a-priori" manner; and a-priori choice is important
because the computation of the statistical significance assumes it. The
probability of successfully guessing the serial number on a bill is not
the same whether or not it had been peeked at in advance. Likewise, the
probability that a particular list will excel in a race against other
lists is not the same whether or not one knows in advance that it
contains some "stars" (i.e., rabbis whose name is very close to their
date of death).
Was Witztum and Rips' list a-priori? Since it fails the
criterion of objectivity, they must be asked. They claim that it was.
In particular, they claim that the list of names, and perhaps also of
dates, was supplied to them as is by Havlin, with neither them nor him
knowing what would happen when they would be subjected to the
computerized search described above. It follows, for example, that the
eyebrow raising decision to look for the 15th of a month using the
unconventional form, was based on a-priori considerations, without
knowing that this is a fortunate choice. Should we base our attitude to
the Torah codes on Witztum and Rips' claim that their list is a-priori?
Here's the irony: if one is willing to take their word for it, one can
give up on objectivity all along. Any list at all, constructed any way
at all, is acceptable if it is a-priori. Objectivity is meant to remove
the need for an act of faith. Lack of objectivity in the list raises
suspicion that it is not a-priori, either. Later on, we shall present
strong statistical evidence that the list indeed was not a-priori, but
first we need to complete another stage in the story.
Out of concern, or out of suspicion, that the statistical
significance testing was not carried out in a clean and a-priori manner
as required, Diaconis (the same Diaconis mentioned above in connection
with the permutation race) recommended a repeat test on a fresh sample.
A new list of rabbis was extracted from the Encyclopedia, this time those
to whom between 1.5 and 3 columns of text were devoted. 32 rabbis were
found this time (there were some errors again). The second list was
constructed and tested exactly according to the same rules which governed
the first list, and it, too, came almost first in a field of one million
contestants.
On the face of it, the second list answered the concerns raised
by both the lack of objectivity and lack of a-prioricity of the first
list. In other words, all the "degrees of freedom" (a technical term
which roughly means "choice possibilities") appear to have been already
exploited by the first list, and the second list was bound to the choices
made in the first list. Diaconis hoped that the constraints set by the
first list would guarantee the objectivity of the second list, and this
objectivity was supposed to make it more credible that it was also
a-priori. But in fact, we shall presently see that the rules and
constraints laid down by the first list left sufficient room for
maneuvering in the second list, allowing for the "cooking" of a second
list which would be no less successful than the first list. By "cooking"
a list we mean playing around with the options it affords until it looks
good enough.
Where did any degrees of freedom remain in the transition between
the first list and the second? In regard to the date forms, the second
list did indeed follow the first list accurately. The same three forms
of date writing (e.g., July 4th, on July 4th, 4th of July), and the same
two ways of writing the 15th or 16th of a month. But in writing names
and appellations, there aren't rules as strict and binding as there are
for date writing. For example, Rabbi Yehosef Ha'Nagid was called
Yehosef, while Rabbi Yosef Terani was called Yosef. This is not
inconsistency in spelling the names -- rather, this is how these names
were actually spelled (or so the experts tell us). Rabbi Abraham Saba
was also named after one of his books, while Rabbi Abraham the Angel was
not. This is not an inconsistency in choosing appellations -- rather, it
reflects reality.
Since different people, even if given the same name at birth, may
come to be called differently in the course of their life time (a Robert
can be Bob, Bobby, Rob, Robby, Bert, Bertie, etc.), allowing nicknames
and appellations makes it difficult to specify an "objective" list of
names governed by strict rules. The appellations are included because
the person who draws the list thinks they should be included. It is a
matter of discretionary judgment. Indeed, Havlin, in a written
description of his considerations when constructing the list of names and
appellations, admitted explicitly that he used a great deal of judgment
when constructing the list. It follows, therefore, that the second list
did not solve the problem it was intended to solve, namely, gauranteeing
that the second list could not be fiddled with and "cooked" to success.
The reader might wonder at this point: Is it really possible to
"cook" a second list, following exactly the rules set by the first list,
so that it would be as successful as Witztum and Rips' second list
actually is? Many of those who readily see that the appearance of words
and of word combinations as ELSs, even in proximity, is possible in any
text, find it hard to believe that even under the heavy constraints set
by the first list of rabbis, Witztum and Rips' results (namely,
outstanding performance in a permutation race) can also be replicated in
any text. But very recently, this too has been unambiguously
demonstrated.
Dror Bar-Natan and Brendan McKay, assisted by Prof. Menahem Cohen
of the Faculty of Jewish Studies at Bar-Ilan University, undertook the
following challenge: to take some text of the length of Genesis, and
cook a list that would excel in a list race run on this text, yet such a
list as would follow the guidelines governing Witztum and Rips' first
list just as closely as their own second list did. The text chosen for
this purpose was War and Peace (the first 78,064 letters), for the simple
reason that it played the role of "any old text" in Witztum and Rips'
original article, when they tested their second list on it, and it
failed. Bar-Natan and McKay's list was constructed as follows:
1. The list of rabbis was chosen by Witztum and Rips' criterion, namely,
rabbis to whom the Encyclopedia allotted between 1.5 and 3 columns of
text, and whose entry included a date of death or birth.
2. The dates, including their form, were identical to those used by
Witztum and Rips.
3. The computational details were the same as those used by Witztum and
Rips, with the following exception: Witztum and Rips included two rabbis
even though they had discarded the dates given them by the encyclopedia,
thus leaving them unpaired in the correct list. Bar-Natan and McKay's
list discarded these rabbis, as well as one other who didn't belong in
the list in the first place.
4. Only in the list of names and appellations were significant changes
made. Out of close to 90 names and appellations in Witztum and Rips'
list, twenty were dropped, and 30 were added. For example, the name
"Oppenheim" spelled with a single Hebrew letter yod was exchanged for
that name with a double yod spelling. The deletions and additions were
all based on research, and were governed by principles and consistency
considerations to the same extent as Witztum and Rips' list was.
Additional detail can be found in Bar-Natan's and McKay's Internet
sites.
In a race of ten million permutations, the modified up list came
in 12th place! It is possible to summarize matters thus: Except for the
"small print", i.e., within the boundaries of trivial changes, all of
which are justifiable, consistent and legitimate no less than Witztum and
Rips', the astonishing result from Genesis can be replicated in War and
Peace.
Of course, from the fact that a list could and was cooked for War
and Peace, it does not follow that Witztum and Rips cooked their list for
Genesis. They persist in claiming that their list, unlike Bar-Natan and
McKay's, was a-priori; that it was chosen in good faith, and the choices
were blind with respect to its success probability. Since none of the
critics and skeptics were around when the list was drawn up, the decision
whether or not to believe the a-priori claim regarding the second list,
just like regarding the first one, remains an act of faith. Nonetheless,
there are other findings, also statistical in nature, which indicate that
if Witztum and Rips' list was not cooked, then its creators enjoyed a
fantastic stroke of luck, to say the least. These findings, to be
described below, raise serious questions, but we shall leave the readers
to draw their own conclusions.
Every researcher in every research must make many methodological
choices. So too, Witztum and Rips, or their consultants, faced many
choices and decisions. It is convenient to demonstrate this with respect
to dates.
1. Witztum and Rips could have settled for dates of death only (they
would have lost but one rabbi out of 66), or they could have taken dates
of birth as well as dates of death (it would not have been practical to
take just birth dates, because only 7 rabbis had them). The choice was
between one date, or two (where possible).
2. Witztum and Rips could have written the 15th or 16th of a month by
the conventional form only, by both forms, or even just by the
unconventional form.
3. There were many degrees of freedom regarding the form of writing
dates. Recall, Witztum and Rips chose three particular forms, but they
could have added a fourth form; they could have settled on a single
form; they could have stuck to the form used by Margaliot; etc.
These are just a sample of the choices presented by the dates.
They faced choices in other areas as well, primarily in the form of ELS
searching and the distance computation. We cannot go into further
detail, due to technical complexity and space limitations, but it is
important to note that there were a great many choices.
Suppose, now, that all these choices were made, as claimed, in an
a-priori fashion, namely, without knowing how the choice would affect the
outcome. It stands to reason that where a choice could have been
resolved in one way or another, it would turn out aposteriori that the
blind choice was fortunate (i.e., improved the ranking in the race) about
as often as it was unfortunate (i.e., hurt the ranking). However, wonder
of wonders, it turns out that almost always, if not always, the allegedly
blind choices paid off: just about anything that could have been done
differently than it was actually done would have been detrimental to the
list's ranking in the race. That is the case, for example, with regard
to all the date choices listed above. Even the decision on which of the
five books of the Pentateuch to carry out the test was fortuitous: in
each of the other four books of the Torah, the list does not perform any
better than chance. Of course, the probability of blindly choosing so
felicitously again and again and again diminishes rapidly with the number
of such choices. By the same statistical logic which gave power to
Witztum and Rips' results, the results of the present analysis suggest
that the chance of drawing up such a successful list blindly is very
remote.
This analysis completes the critique of the seemingly astounding
statistical results which were published in Statistical Science. A list
was presented there which performed most surprisingly and impressively in
Genesis. That list perfomed quite poorly in War and Peace, and in
several other control texts (though it also performed poorly on Exodus,
Numbers, Leviticus, and Deuteronomy). However, another list, as accurate
and correct as the original list, did achieve on War and Peace a measure
of success as impressive as that of Witztum and Rips' list. So what
remains of the "scientific" experiment and the statistical significance
testing? We are back to square one. We started by showing that words in
ELS form can be found in Genesis -- as well as in any other sufficiently
long text. Now we see that even a list of rabbis, whose ELS names were
remarkably close to their ELS dates in Genesis -- can be found as well as
in any other sufficiently long text. To be sure, the probability that
Witztum and Rips' results are due to mere chance is very small. But the
alternative to "mere chance" turns out to be not that whomever wrote the
Torah inserted the codes into it, but rather that whomever found the
codes in the Torah did not find them by mere chance, but rather by
diligent tinkering.
Several months ago, Maya Bar-Hillel lectured about this work in
the Statistics Department of Tel Aviv University. Doron Witztum was
present. At the time, the "cooking" of the War and Peace had not yet
been completed, and Bar-Hillel reported that the cooked list was ranked
at about 60 in a field of one million. "Only 60?", interjected Witztum
mockingly from the audience. "If I were to cook a list for War and
Peace, I could get it to perform much better than that". "Indeed you
could", replied Bar-Hillel. "I believe him. I suggest you all do,
too".
Table of Alterations in Second List
This table lists only the differences between Bar-Natan and McKay's list
and Witztum and Rips' list, in a manner accessible to an English language
reader. The original list appears, in Hebrew, in Witztum, Rips and
Rosenberg's article, and in the Galileo article. + Denotes added
appellations, - denotes deleted appellations.
1. + RAB"D sheni (second Raabad)
3. - H'Malakh (The Angel)
4. Removed, for lack of any date.
6. - Maasey YHVH (the Hebrew spelling for Yahweh); + Maasey H'; Baal
Maasey H'
7. - Oppenheim (single yod); + Oppenheim (double yod)
8. Removed, for lack of any date.
10. + MHRX"A, + H'MHRX"A (acronyms)
11. - Benvenesht, + Benveneshty, + H'Rav HBI'B, + H'Rav H'HBI'B (acronyms)
12. - Kafusi, + Kaafusi, - Baal ness, - Baal H'ness
15. + Yehuda Segal
19. + R"Y Terany, + R"Y Teraany, + H'R"Y Terany, + H'R"Y Teraany
20. Removed, doesn't meet inclusion criterion.
21. + Mimongil (family name)
22. - Khaagiz, + R"I Khagiz, + MHR"I Khagiz
23. + Yakov Levi, + MHR"I Levi
24. - HR"I Emden, + R"I Emden, - H"RIEB"C
25. - Horowitz, + Horovitz, + Ytzhak Levi
26. - Krochmal, + Krochmaal
27. - Zacuto, - Zacuta, - Moshe Zacuto, - Moshe Zacuta
30. - AX HE"R, + AHE"XR, + Hon Ashir (book)
31. - Sar Shalom, - Mizrahi, - H'MHR$"$
32. - Xeelma, + Shlomo Xelma
33. Rabbi Meir Eisenstaadt, erroneously omitted from the original
second list.
Notes
Readers interested in further detail are invited to read Witztum, Rips &
Rosenberg's original article; Atzmon's article; and the following
Internet sites, where some of these res ults appear:
1.http://cs.anu.edu.au/~bdm/dilugim
2.http://www.ma.huji.ac.il/~drorbn/Codes
Prof. Maya Bar-Hillel of the Center for the Study of Rationality at The Hebrew University studies biases of judgment and decision making. Dr. Dror Bar-Natan of the Department of Mathematics at The Hebrew University studies quantum algebra and low dimension topology. Dr. Brendan McKay of the Department of Computer Science at the Australian National University studies combinatorics and computational proof.
1. Witztum, D., Rips, I. & Rosenberg, Y. (1994) Equidistant letter
sequences in the Book of Genesis. Statistical Science, vol. 9(3),
p. 429-438.
2. Witztum, D. (1989) The Added Dimension: On Two-Dimensional Writing
in the Torah. Self-published in Israel in the Hebrew language.