[The February, 1996 issue of Bible Review contained
many letters commenting on Dr. Jeffrey Satinover's article on the "Codes
in Torah" (ELS patterns), "Divine Authorship?", which had
been published in the October 1995 issue. We reprint here Dr. Satinover's
response to these correspondents. Note that their actual letters are not
reprinted here, nor are correspondents' names. These are the only edits
made to Dr. Satinover's response as published in Bible Review.]
The robustness of the Torah codes findings derives from the rigor of
the research. To be published in a journal such as Statistical Science,
it had to run, without stumbling, an unusually long gauntlet manned by
some of the world's most eminent statisticians. The results were thus triply
unusual: in the extraordinariness of what was found; in the strict scrutiny
the findings had to hold up under; and in the unusually small odds (less
than 1 in 62,500) that they were due to chance. Other amazing claims about
the Bible, Shakespeare, etc., have never even remotely approached this
kind of rigor, and have therefore never come at all close to publication
in a peer-reviewed hard-science venue. The editor of Statistical Science,
himself a skeptic, has challenged readers to find a flaw; though many have
tried, none has succeeded. All the "first crack" questions asked
by BR readers – and many more sophisticated ones – have therefore
already been asked by professional critics and exhaustively answered by
the research. Complete and convincing responses to even these initial criticisms
can get fairly technical. I can here clarify only up to a point some of
the misunderstandings in the letters. But I will also send more complete
private responses to each writer whose comments are not fully answered
here.
A number of writers think it a weakness that an event must occur before
it can be found in the text. This seems to me like watching an elephant
fly backward through time only to complain, "But why isn't it traveling
into the future, too?" What the research doesn't do in no way detracts
from what it does. Nonetheless, there are ways to evade this constraint,
as [one letter-writer] suggests, though there are difficulties. Verifiable
results depend upon a sufficiently large and uniform data set, which is
not easy to assemble. Isolated examples can rarely generate statistically
valid results: Looking for one's own name, or for Jesus', is therefore
an uninterpretable enterprise, even if you find what you're looking for.
If the research is eventually disproved, no one serious will bother
using the text of Genesis as an oracle. But should the body of rigorous
findings expand, some will even so be inclined to ignore the primary meaning
of that same text – including its cautions. The Torah itself casts this
most typical of human inclinations at the center of its most distressing
dramas – e.g., the garden, the snake, "ye shall be as gods,"
etc. – and it suggests that what follows is more consequential than the
mere "demerits" of scouting, pace [another letter-writer].
[A third correspondent] quickly identifies a major conflict between the
higher-critical (more generally modernist) worldview and the implications
of the codes research. He reminds us that there is a huge mass of Bible-related
data that is convincingly synthesized in line with the conventionally anti-supernatural
assumptions of modern scholarship. [The third writer's] chief objection
– and one of [a fourth writer] – is to what the codes research appears
to imply concerning the integrity of the Masoretic Genesis, that is, that
what we have today is the 100-percent error-free replica of the original.
But, as will be explained below, he has not found the flaw in the research
he thinks he has (and that he seems to have felt he had better find quickly!).
Neither is the integrity of the text so evident.
In a similar vein, [the fourth letter-writer] recognizes that no text
can be both densely encoded and at the same time tell a previously established
story. Rather, no human being could. [This writer] also correctly notes
that researchers with a computer can just "keep trying until it does
get lucky" so as to "yield any damn-fool message." He thus
pointedly raises the important question of unreported "hidden failures,"
a well-known bugaboo in all scientific research. To exclude this possibility,
the referees insisted that the researchers repeat their positive findings
on a separate set of individuals selected according to the referees' own
criteria. The paper reports on the results for this second set alone.
Related to the question of unreported failures is the potential for
hoaxes. Given the many frauds science has unfortunately fallen prey to,
especially of late, I'd better play the straight man: I am not joking and
I have no reason to suspect anyone else is. To rule this out, the referees
were given the computer programs to do with as they pleased. Furthermore,
the data – the text of Genesis, the names and dates of the individuals
– have long been published in public-domain texts. They cannot be faked.
Anyone may start from scratch and arrive at the same results, as has been
done repeatedly. Nonetheless, perhaps one day I will be shown to have been
a fool in this matter and, along with others, a boyish one at that (my
translation of "puerile") – but neither a liar nor practical
joker. As for simple chance explaining it (in contrast to unrecognized
error), well, we know exactly what the odds are – 1 in 62,500; it's what
makes the case, not breaks it. And more is in the pipeline, with even more
daunting odds.
Now on to some details. Some writers ([the third correspondent]) conclude
that the shape of the snippet of text is subject to whim and determines
which word-pairs can be found. Others ([the fourth correspondent]) assume
the method is so generous that one can find anything at all. These would
be serious weaknesses indeed were they as described. However:
(1) The identical search and analysis procedure is followed for Genesis and for all controls. As there is nothing in either procedure that
favors any set of data, the results in Genesis should differ from the results
in the controls by no more than small, chance variations. But the results
in Genesis are dramatically different. The odds are vanishingly small that
this exceptional difference has occurred merely by chance.
(2) The search method is precise and highly constrained. It does not
depend upon a particular rectangle of text such as those in the illustrations.
(These are only used to calculate minimal proximities.) One may more easily
envision this by first considering a simple string of the entire text,
some 78,000 letters long. The search-and-find part of the procedure is
carried out on this entire text string, not on snippets of it. Roughly
described, both words of a pair are located by finding where each appears
at its own respective minimum equidistant letter sequence (ELS). In theory,
these minimum sequences may be any number of letters (though no longer
than c. 78,000 divided by one less than the number of letters in the word);
in practice, they tend to be quite short relative to the total length of
Genesis. But as we will see, the actual ELS does not bias the results.
In a string, the proximity of two terms in a pair may be defined in any
number of ways: For instance, from the beginning of the right-most word
(Hebrew reads right to left) to the end of the leftmost (this would give
the largest distance); from the beginning of the leftmost word to the end
of the rightmost (this would give the shortest distance); between the midpoints
of each, etc. Even for this simplification, defining proximity in a uniform,
meaningful way for many such pairs of words, mostly of different lengths
and letter spacing, requires care. It would be meaningless, for example,
to treat a four-letter word spread out over the entire text (ELS of about
26,000) as "close" to every other word.
(3) The specific method used in the research to calculate proximity
is more sophisticated than counting letters on a string and is designed
to avoid the problems inherent in linear measures. First, the portion of
Genesis that includes all of both words and everything in between is cut
out from the text after the words have been found. For words that are very
far apart, or have large ELS's, this is a huge piece of text. The resulting
string is then wrapped into a rectangle (more precisely, a helix, forming
a cylinder). The rectangle is reshaped until the two words are as close
together – "compact" – as possible. Despite this manipulation,
words that were far apart in the original string, or with widely spaced
ELS's, can never form as compact a configuration as words with short ELS's
that were close together. The most compact rectangle is used in every case.
Remember, this method is applied to Genesis and all controls. The procedure
therefore favors none.
(4) In addition to searching for pairs of historically connected names
and dates, the researchers performed identical searches and measurements
on sets of unrelated pairs, created by matching one person's name with
another's date. (This aspect of the research addresses questions 9-11 of
[the first letter-writer]. There are 32! (that is, 1 X 2 X 3 X ... 31 X
32 = c. 2.6 X 10 exponent 35) possible mismatched sets. From these, 999,999
were selected at random, which, along with the set of actual name-date
pairs, made a total of 1,000,000 sets of pairs. The researchers allowed
for variant spellings of names and alternative death dates, and also generated
four different proximity statistics for every one of these 1,000,000 sets,
both when running the test on Genesis and when running it on control texts.
They then ranked the 1,000,000 sets in ascending order of compactness (rank
1 = most compact). In all four measures, the rank of the actual historical
data, and only in the actual Genesis text, stands out starkly as many thousands
of times closer to 1 than the false sets of data either in Genesis or in
any control text. The proximities of the false pairings, however, fell
well within the range that would be expected by chance, whether located
in Genesis or in the controls.
(5) The examples shown in the article are good illustrations. But they
are also fairly typical. Indeed, they are of the most common class, showing
words fairly close together: More than 1/9 of the true name-date pairs
are in the top 1/25 of proximities. But not only is the average proximity
of names to matched dates in Genesis far smaller than expected (or than
is found in controls), the distribution of the different individual proximities
that make up the average is also remarkable. When charted, they do not
form a bell-shaped curve, for instance, with a peak that merely yields
a lower than expected mean. Nor is it a random-appearing distribution that
happens to have a low average. Rather, its highest point is at zero distance,
indicating that the largest number of paired words appear right beside
each other, and the distribution (the number of pairs at a given proximity)
drops off smoothly and rapidly as the proximity (the distance between the
words) increases to the maximum possible (about 78,000). By contrast, the
distribution for the controls is a flat line (a "uniform distribution")
– as expected. All possible proximities between pairs are equally represented,
and the average (composed of all these) is therefore about half the length
of the text. This reflects the fact that in the controls the location of
any word is independent of any other word – every such location being a
matter of pure happenstance, as most people would presume should be true
for Genesis as well, but isn't. What might the distinctive shape of the
distribution indicate? First, to return to one of [the third respondent]'s
and [the fourth respondent]'s concerns, one possibility is that perhaps
the text we have is in some small measure not precisely the original, though
it must be close to it. Because of the aggregate nature of the phenomenon,
introducing more and more small errors into the text will slowly degrade
the robustness of the findings, but won't entirely efface them – until
a certain critical degree of error is exceeded. (Studies by outside experts
have already begun to quantitate this.) Perhaps (some of ) the greater
than zero proximities are due to such errors having slowly crept into the
text. However this cannot account entirely for the peculiar spread of proximities,
since if there were no other additional cause(s), the distribution would
consist of one sharp spike at zero proximity, and a random, approximately
equal scattering of other proximities, small and large, caused by the errors.
Second, since more than one death date for the same person can't be correct,
we know that at least some of the spread must be due to inaccuracies in
the historical data. But here, too, such errors alone (or in combination
with textual errors) would leave a sharp spike at zero against a random
scattering of other proximities. So, there must be an additional reason
for the spread. (My own guess is that the phenomenon is intrinsically probabilistic
– as is the ultimate reality it points to. Though counter to our intuitive
understanding of, say, predestination, similarly strange ideas have unexpectedly
been found at the foundation of the physical world as well.) [The first
letter-writer] has well expressed the balance of both skepticism and seriousness
that the unusually high quality of this research demands. Rigorous investigations
of the present research are being published by independent outside experts;
one such piece (by Harold Gans, a senior mathematician with the U.S. Department
of Defense) not only confirms the original findings using different techniques,
it also shows that the cities of birth and death of the rabbis in the Witztum
et al. study are also encoded in Genesis. The odds that the results of
this new study occurred by chance are less than 1 in 200,000. Witztum et
al. have themselves submitted a new paper, on a completely unrelated data
set, also tested in Genesis, with odds of 1 in 250,000,000. There are many
(myself among them) who would like nothing more than for the results not
only to continue to hold up, but to be extended further. Nonetheless, if
the work is in error, it would be best for this to be demonstrated not
just quickly but well. Casual dismissal can no more accomplish the latter
than uncritical acceptance will accomplish the former. In a recent interview,
David Kazhdan, professor and chairman of mathematics at Harvard, cautioned
hasty skeptics of the Torah codes, "The phenomenon is real. What conclusion
you reach from this is up to the individual."
—Dr. Jeffrey B. Satinover, February 1996
—Reprinted with permission
