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Some Bible code related experiments and discussions
By Mark Perakh
First version - January 10, 1998
Last updated July 10, 1998
(Appendix 2 added on December
- How common
ELS regarding Jesus
a superhuman mind necessary to create code?
"simple" statistical proofs of "code" authenticity
About the meaning of ELS phrases in the Bible
the "amazing" discoveries by Drosnin, Satinover, etc.
the "scientific" proof of "code" by Witztum, Rips, and Rosenberg
- Appendix 1
(Discussion of "simple" calculations of probability)
- Appendix 2.
About WRR's formula for the calculation of the expected number of ELS
I would like to report on some simple experiments I conducted in
order to see for myself whose claims in the ongoing war between the proponents
and the adversaries of the authenticity of the Bible codes conform to facts.
Also, I would like to offer some conclusions I have formed in regard to the
question whether the Bible codes are real or imaginary.
I am a Professor of physics (Emeritus). I have taught physics and
related disciplines at several universities, first in the former USSR, then in
Israel and in England, and finally in the US, at University of California,
California State University, and University of San Diego. Among the courses I
have the privilege to teach is statistical physics, which I have taught for both
undergraduate (physics majors) and graduate students. I have published nearly
300 scientific articles, several books, and was granted a number of patents.
Although I never did any research per se in the field of
mathematical statistics, I used quite extensively statistical methods in my work
in the areas of magnetic Phenomena and of electrochemistry.
I have acquired the information about the Bible Code controversy from
the following sources:
- A book by Grant Jeffrey, titled The Signature of
- A book by Michael Drosnin titled The Bible
- A book by Jeffrey Satinover titled Cracking the Bible
- A number of letters posted on the Internet, including the exchange
of criticisms between Rabbi Daniel Mechanic, Guy Cramer and Lori Eldridge, and
some other people (see http://www.discoveryseminar.org/response.html; http://jewsforjudaism.org/codes/jesuslb.htm; http://www.yfiles.com/;
- Excerpts from the book by Pastor Y. Rambsel, titled Joshua, The
Hebrew Factor, as posted on Internet. (See http://home.cvnet.com/crm80/)
- An article by Doron Witztum, Eliahu Rip, and Yoav Rosenberg as
reprinted in the book by M. Drosnin.
- A set of articles by Dr. Brendan McKay of Australia as well as
papers by Dr. B. McKay with Dr. Dror Bar-Natan, Alec Gindis, and Aryeh Levitan.
- Articles by Dr. Barry Simon of Caltech, by Dr. Gil Kalai of the
Hebrew University of Jerusalem, and by Dr. James D. Price of Chattanooga (see,
for example http://www.math.gatech.edu/~jkatz/Religions/Numerics), an article by D.E. Thomas (see http://www.cscop.org/si/9711/bible-code.html); articles by Dr. R. Haralick (see, for example http://www.prophezine.com/tcode/Obj15.html) and some other publications on the Web.
Whatever views various participants of the dispute adhere to, the
focal point of discussions is the so called ELS, which stands for
Equidistant Letter Sequences. This term denotes any meaningful words that
are formed by characters, which happen to appear in the text at equal "skips."
For example, look at the word "denotes" in the previous sentence. Letters d, o,
and s in that word, which are separated from each other by the same skip of 2
characters (e and n between d and o, and t and e between o and s) form the word
DOS which is an acronym for Disk Operating System, and therefore
it constitutes an ELS.
The dispute between pro-codes and anti-codes camps is whether ELS
appear in the text of the Bible just by chance, or they constitute a
deliberately inserted code. While all pro-code people believe that the creator
of the code cannot be a human being, some of them (as, for example, Dr. J.
Satinover) attribute the authorship of the codes to God, while some others (for
example, M. Drosnin) attribute it to extra-terrestrial visitors to our planet.
Various participants of the dispute who do not believe that the
"codes" are deliberately inserted in the Bible, approach the problem from
different angles and use different sets of arguments. However, they usually
complement rather than contradict each other. They consider each otherís efforts
as contributing, from different viewpoints, to the same goal, namely to the
assertion that the "codes" are fictitious and do not testify to the authorship
by a non-human mind.
On the other hand, there is no unity whatsoever in the "pro-codes"
camp. Indeed, Dr. Satinover, who, like M. Drosnin, believes that "codes" are
real, expresses in his book the opinion that M. Drosninís book "presents the
Bible code in a most unfortunate light... It has the potential to discredit the
serious research..." (Page 261 in J. Satinoverís book). One of the most prolific
defenders of the codesí authenticity, L. Eldridge relates to M. Drosninís book
with the utmost contempt. Dr. Eliahu Rips, to whom M. Drosnin makes numerous
appreciative references in his book, had disavowed Drosninís book in quite
resolute terms. Rabbi D. Mechanic has a high praise for the work of Rips,
Witztum, and Rosenberg, but dismisses with disdain the books by Y. Rambsel, and
by G. Jeffrey. In their turn, G. Cramer and L. Eldridge value the books by Y.
Rambsel and G. Jeffrey, but vigorously repudiate Rabbi Mechanicís articles, and
Studying the publications of the "codes" proponents makes it rather
obvious that the disagreements between them are due mostly to different
agendas underlying their efforts.
In this paper I shall try to clarify the controversy, supporting my
conclusions by observations of facts rather than pursuing any
The dispute in regard to the authenticity of codes essentially
revolves around three topics, to wit:
1. What is the statistical probability that the ELS occur in the
Bible by chance?
2. Do similar ELS occur in texts other than the Bible?
3. Are human beings capable, with or without computers, of creating
complex arrays of ELS such as found in the Bible?
The people who are "pro-code" usually answer the first question with the
assertion that the probability in question is extremely small. To the second
question the "pro-code" people usually answer with "No." Likewise, the people who believe in
the Bible code usually also believe that the answer to the third question is
I will try to test all three answers in this article.
The numerous examples of the ELS found in the Bible and demonstrated
by Witztum, Rambsel, Drosnin, Satinover, and others, have made a strong
impression on many people. Indeed, it seems hard to imagine that so many
coincidences could've happened by chance. Therefore, after having read the books
by Jeffrey, Drosnin, and Satinover, I decided, as a beginning of my exploration
of the matter, to test how often various ELS appear in any randomly chosen
texts, in various languages.
For my first test I chose one page from a letter I wrote in Russian
to my friend in Moscow. That page contained the total of 2025 Cyrillic
characters. Using WordPerfect word processor, I removed from the text in
question all spaces between the words, as well as all commas, periods, etc. The
text thus converted into a continuous string of characters. That is how it has
been done in the Bible code studies. Then, without using any computer program, I
started looking for ELS that would simply pop up from the text. I discovered in
that sole page over 30 ELS, with skips ranging from 15 to 60 characters. At that
point I stopped looking for more ELS. Most of those ELS, as it could be
expected, turned out to be just three letter words, but a few four-letter words
jumped out of the text as well. Certainly, by using a computer and extending the
size of the skip to larger values, many more ELS could be found in that page of
my letter, and much more in a larger text.
Then I switched to English. I conducted tests with three texts. One
text (let us call it E1) was one page from a letter I wrote to the USA embassy
in Kazakhstan. The other (E2) was a part of the first page of a story I wrote
years ago in Russian. I translated it into English. The third (E3) was the first
page of another story of mine, also first written in Russian and then translated
into English. Again, I stripped the texts of commas, periods, spaces, etc.
Text E1 contained 2107 characters. I identified in that text over
forty ELS, and after that I stopped searching for them. While three-letter words
appeared most often, there were a number of 4-letter words ELS (for example
rest, male, root, the name of Vice-President Gore, and others.)
In most of the sources dealing with ELS in the Bible, a special
significance is attributed to the simultaneous appearance of several words
related by meaning, in a proximity to each other. I was curious to see, if such
occurrences can pop up in the tested page. At one location, the following four
words appeared, three of them having a common letter (T), while the fourth word
(ARE) was situated across the other three. Of the three words that had a common
letter T, two were oriented symmetrically along the sides of an isosceles
triangle. The third word (TEN) was aligned with the triangle's diagonal. This
"array" of ELS spelled BRIT TITS ARE TEN. The skips were 47 (for TITS), -43 (for
BRIT), and 45 (for TEN). Of course, one may either agree or disagree with the
quoted sentence, but its appearance hardly could be attributed to any non-human
entity. (A copy of the text in question can be viewed at brit.cfm).
Text E2 contained only 520 words. Even in that small sample 34 ELS
popped up at once, at first glance, after which I stopped looking for them.
Among those ELS three words happened to be 4-letter ones, the rest were
Text E3 contained slightly below 2000 characters. As in the previous
examples, ELS were abundant. There were some 5-letter words, a little more of
4-letter words, and a whole enchilada of three-letter words. Right in the middle
of the page, there was a 6-letter word TORVIL. Parallel to it, in the adjacent
vertical, there was word ICE with the same skip of 45. Across the page, there
was word DEAN, with the skip of 47. Close to both Torvil and Dean the word WIN
appeared twice. Of course, Torvil and Dean used to be famous champions in figure
ice-skating. Since the story in question was written years before TORVIL and
DEAN demonstrated their skills on ICE, having twice WON championships, one may
suggest that I predicted event which would occur later, and had encoded my
prediction in the form of a combination of several ELS placed close to each
other in the text of my story. Sorry, I did not possess such abilities. Among
the 4-letter words were LAND, (not far from a 3-letter word SEA), LULL, TILT,
ODOR, etc. (A copy of the text in question can be viewed at torvil.cfm).
Finally, I had written. especially for this Web page, a short poem
whose contents relate to the "code" dispute. The slightly shortened
version of that poem can be viewed at Poems.cfm. The full length of that poem is only 558 letters. Then I stripped
its text of spaces, punctuation marks, etc, converting it into a continuous
string of letters, in a conventional way used by all ELS researchers. It took
about 50 minutes to compose the poem. It took only about 15 minutes to
locate in it 37 ELS, after which I stopped searching for them. I found a
funny feature in that text, namely three symmetrically situated appearances of
the same two words, as it is shown and described at trihen.cfm.
These simple tests have shown that the phenomenon of ELS is very
common, and a very large numbers both of individual ELS and of ELS clusters
necessarily appear in any text. The reason for that is of course the fact that
any language consists of a vast number of words.
I performed the described non-computerized tests before I came across
the Web publications by Dr. B. McKay and D.Thomas. I was gratified to find that
my conclusion turned out to be well in agreement with the multiple examples of
ELS clusters found by Dr. McKay in a number of non-Biblical texts, most notably
in Moby Dick, as well as with many examples of similar clusters of ELS in
English texts demonstrated by D.E. Thomas (they both used a computer program to
locate the ELS).
Now let us take a look at the works by Grant Jeffrey and Pastor Y.
Rambsel and at their criticism by D. Mechanic. Grant Jeffrey first refers
favorably to the work done by Witztum, Rips, and Rosenberg. Then he switches to
the results reported by Pastor Rambsel. In Mr. Jeffrey's view, the article by
Witztum et al should be accepted as a proof that numerous occurrences of
the ELS in the Torah indicate a non-human authorship of the Bible. Mr. Jeffrey
believes that God had deliberately inserted into the text certain codes in the
form of those ELS. In this point, there seems to be an agreement between
G.Jeffrey and Y. Rambsel, on the one hand, and D.Mechanic, on the other.
However, soon they drastically part their ways.
Jeffrey, following Rambsel, insists, that the Torah contains numerous
references to Jesus in the form of ELS which prove that Jesus was the Messiah.
Rabbi D. Mechanic suggests, on the other hand, that there is a
significant difference between the works of Witztum et al, on the one
hand, and those of Rambsel and Jeffrey, on the other. According to D. Mechanic,
the work of Witztum et al represents what D. Mechanic refers to as a
legitimate Bible code research, based on scientific methods involving
mathematical statistics. On the other hand, says D.Mechanic, the works of
Rambsel and of Jeffrey represent an effort to use the legitimate results of
Witztum et al in order to validate Rambsel's unfounded, and sometimes
even fraudulent claims.
Guy Cramer and Lori Eldridge, in return, accused Rabbi D. Mechanic of
Let us look at the arguments by D. Mechanic and his opponents. Rabbi
D. Mechanic indicates in his article that the ELS that spells the four letter
Hebrew word Yeshua, which is considered to be the shortened version of Yehoshua,
the Hebrew name of Jesus, is mathematically expected to appear in the Torah
by chance, over 10,000 times. It is also expected to appear as many times
in any other Hebrew text of comparable size. Therefore locating this word as
ELS, as it was done by Rambsel, in the Torah, has no meaning.
Out of curiosity, and to see whether R. Mechanic's assertion can be
verified by some simple tests, I decided to try to locate word Yeshua in some
non-Biblical Hebrew texts. I randomly pulled from a shelf a few Hebrew books.
The first one happened to be a book by a contemporary Israeli writer Dahn
Ben-Amotz, published in Tel-Aviv in 1979 by Metziuth Publishers. The title of
the book is Ziunim Ze Lo Ha Kol, which translates as Screwing is Not
Everything. (The cover of that book is reproduced at amotzcovr.cfm
and its inside title page in English, at amotinsd.htm). I decided to look for occurrences of ELS that would
spell the 4-letter word Yeshua, as well as some combinations comprising both
Yeshua and some other words, such as Yeshua Shmi, Yeshua Moreh, Yeshua Khali,
Yeshua Iakhol, Dam Yeshua, etc. These phrases are examples of Pastor Rambsel's
findings in the Bible, which, in his opinion, constitute the "codes" proving
that Jesus was the Messiah. Sometimes Y.Rambsel uses instead of a four-letter
form of Yeshua (Yud-Shin-Vav-Ayin) a shorter, three-letter version
(Yud-Shin-Ayin). Likewise, I decided to look for such three-letter version
occurrences as well. Since I did not have the text of the book in question in my
computer, I could not remove from it the spaces between the words, the commas,
the periods, etc. Obviously, if the spaces, commas, etc, are preserved in the
text, and counted as meaningful characters, it makes locating ELS more
difficult. In such a case some of the sites in the characters strings are
occupied by meaningless spaces etc. So, if I could locate ELS, counting the
spaces etc as characters, then it would mean that indeed the ELS in question are
quite common. Then I would repeat the search for ELS spelling Yeshua, Yeshua
Shmi and the like, this time ignoring the spaces, commas, periods, etc.
Including the spaces, commas, etc, into the string, I
discovered, on the very first page of the Ben-Amotz's book, ELS spelling Yeshua
with a skip of -68, as well as Shmi (My name), right next to Yeshua, with a skip
of -60 (all these skips included the spaces between the words).
Then I switched to a search for Yeshua Shmi by counting
only letters, and ignoring the spaces between the words, the commas, hyphens,
etc. I leafed randomly through the book, and soon I located, on page 47, right
in its middle, ELS spelling the words Yeshua Shmi one right after the other,
both with a skip of only 2. Then I leafed more, randomly, through Ben Amotz's book and found the following clusters (or
arrays, if we use the term used by Satinover) of ELS.
On page 23, within only three lines of text, words Dam (Dalet-Mem)
and Yeshua (Yud-Shin-Ayin, which Rambsel and Jeffrey consider a legitimate
spelling for Yeshua) meaning Blood of Jesus, occurred one right after the other,
both with a skip of only 3.
On page 27, within only three lines of text, the same words Dam
Yeshua, appeared, both with the same skip of 4.
On page 63, within only 2 lines of text, word Yeshua appeared twice,
once as a three-letter version (Yud-Shin-Ayin) with a skip of 3, and once as a
four-letter version (Yud-Shin-Vav-Ayin) with a skip of -1. In the same two lines
of text word Moreh (Mem-Resh-Hey, meaning teacher) appeared 3 times with
skips of 3, 4, and -6. In the same lines word Mori (Mem-Resh-Yud) meaning My
teacher appeared with a skip of -5. The characters of words More and Mori
appeared interspersed with the characters forming ELS for Yeshua.
On page 164, within three paragraphs, ELS for Yeshua appeared 4
times, three times as a three-letter version (with skips of 2, 4 and -6) and
once as a four-letter version, with a skip of 7. On the same page, within the
same three paragraphs, the four-letter word Yakhol (Yud-Khaf-Vav-Lamed)
appeared with a skip of 51. The characters of the ELS for Yakhol were
interspersed with those for Yeshua. The phrase Yeshua Yakhol means Jesus
Can or Jesus is Able, and, when found by Y. Rambsel in the Bible, was
interpreted by that writer as one of the proofs of his claims.
A copy of the above paragraphs on page 164 of Ben Amotz's book,
provided here as an example, can be viewed at yeshyakh.cfm.
On page 315 an ELS for Yeshua (as a four-letter word) appeared with a
skip of -6. Overlapping that word, word Khali (Khet-Lamed-Yud) appeared
with a skip of -3, letter Yud being a part of both ELS for Yeshua and
Khali. Word Khali was translated by Rambsel as "Polished Jewel" and the phrase Yeshua Khali, when
found by Rambsel in the Bible, was interpreted by him as another proof of his
views on the codes and Jesus.
All the above ELS have been listed by Cramer and Eldridge as those
for which the "significance index" (see the explanation below) was found to
be extremely small and therefore the ELS in question, in
Cramer & Eldridge's opinion, must
have been deliberately inserted codes in the Bible.
At this point I decided to try some other Hebrew text. This time it
happened to be a book by an English-speaking writer Michael Moorcock, titled in
English The Stealer of Souls. It was translated into Hebrew and published
in Tel-Aviv in 1978 by Am Oved Publishers. On page 13 of that book, two clusters
of ELS appeared, both anchored around word Yeshua. One cluster, which all was
within only three lines of text, contained the four-letter version of Yeshua
(Yud-Shin-Vav-Ayin) with a skip of 5. Following it, ELS spelling Shmi (My
name) appeared with a skip of 7, and right after that word, another ELS appeared
spelling Khali with a skip of -18. (Khali was translated by
Rambsel as Polished Jewel). The other cluster on the same page contained the
three-letter version of Yeshua (with a skip of 5) followed by an adjacent
ELS for Shmi with a skip of 11.
At this point I pulled one more book from a shelf. This one happened
to be a translation into Hebrew of Ernest Hemingway's The Old Man and the Sea published
in 1977 in Tel-Aviv by Am Oved Publishers. On the second line of the first page
of that book, the three-letter word Yeshua with a skip of -4 popped out at once.
Having leafed randomly through the famous Hemingway's story, I saw, on page 17, the four-letter
version of Yeshua with a skip of -7. Of course, I looked around that word to see
if there are there any phrases like those touted by Rambsel. I don't know why,
but besides the two-letter word (Ayin-Zayin, skip of -11) meaning strong,
which probably would delight Rambsel, if located in the Bible next to Yeshua, I
found, next to the Yeshua sequence, an ELS which had a common letter (Ayin) with
Yeshua, and spelled (with a skip of -11) a Hebrew word (Ayin-Kaf-Bet) meaning
crook. I am sorry, I had no intention to find an ELS with a negative
connotation. My conclusion though had become unambiguous, namely that a
variety of ELS, including combinations of word Yeshua with various other words
occur quite commonly in any text, in non-biblical texts as well as in the Bible.
Therefore their appearance in the Bible does not constitute a proof of
anybody's views or beliefs.
To locate all the listed ELS and their phrasal combination, I did not
use any computer program and did not rearrange the text in the way it is
routinely done in the Bible codes studies. There is little doubt that by
applying a computer program and by spending more time on that effort, many more
examples of ELS would be located in the books I tried, those ELS seemingly
related to whatever topic one would choose.
There seem to be at least two possible interpretations of the facts
presented. One is that God (according to Rambsel, Jeffrey, Cramer-Eldridge,
Satinover, and others) or extraterrestrial visitors (according to Drosnin) not
only had dictated the text of the Bible to Moses but also continues to dictate,
character by character, every book, and even every piece of text anybody
endeavors to write. The other interpretation is that all those allegedly amazing
ELS in the Bible have not been deliberately inserted but rather occur there by
chance. Of course, the burden of proof is on the shoulders of the "pro-codes" people. Those who do not believe that
codes have been deliberately inserted in the Bible, do not need to prove
anything as they do not make any extraordinary claims. If the people choose to
believe in the authenticity of "codes" they are expected to present convincing
explanation as to what is the difference between the ELS found in the Bible and
the same ELS found in non-biblical texts. Given the extraordinary
character of the claims about the "codes," the explanation in question is expected to
be factual, unambiguous, and not based on vague concepts such as "relevance," "proximity," etc.
The proponents of the Bible "codes" claim that the
alleged creator of the "codes" must have possessed superhuman abilities, since
neither a human mind nor the best computers available to us are capable of
creating such a complex web of ELS.
This statement betrays a plain ignorance on the part of those who
offer it. I would like to refer here to a book titled "The Codebreakers" by
David Kahn (Weidenfeld and Nicolson Publishers, London, 1967). In that book one
can find a plethora of information about the ability of men and women to both
encode and decode information using methods whose complexity and sophistication
make the alleged Bible codes look as a children game. Even the crossword puzzles
that are being printed daily in local newspapers look as pinnacles of
sophistication as compared to the "codes" in the Bible reported by Rambsel,
Indeed, even in the book by J. Satinover, who believes that the
"codes" are real, there is an example of a method of encoding/decoding which is
one of the simplest tools that had been used for encoding secret
information. Nevertheless it can easily produce "arrays" of ELS quite similar to
those allegedly "encoded" in the Bible. The method in question was apparently
invented by the renown Italian mathematician and writer Girolamo Cardano in
16th century. It has since been used many times for encoding
moderately important secret messages. The method in question is as follows. A
grille, which is a sheet of a stiff paper, is used in which a set of
holes has been cut forming a template. Each hole has a size enabling one to
write one letter through it. The template is placed over a sheet of blank paper
and the message to be encoded is written through the holes, letter by letter.
Then the grille is removed, and the blank spaces between the letters of
the secret message are filled with a text that has some innocent contents. The
letters of the encoded message thus become parts of the overall text, but now
are separated by "skips." To decode the message, a grille identical to that used
for encoding is placed over the text, and the secret message is read through the
holes. When the holes are cut at equal distances, it constitutes the "simple"
Cardano grill. It, of course, produces ELS exactly like those discovered
in the text of the Bible. In those uncounted cases when this method was
successfully used, no superhuman mind was ever required.
When I was a kid of about 12, in the city of Odessa in Ukraine,
myself and a few of my friends had fun playing a game in which we sent to each
other secret messages in the classroom right under the nose of our teacher. To
encode a message, we used several techniques. One of them was the use of the
Cardano grille, even though we had no idea that it was invented in Italy in
16th century. I do not remember now, how we came across the idea of
the grille. Sometimes we used a grille with equidistant holes ("simple" Cardano
grille) thus creating sets of ELS not unlike those found in the Bible. On other
occasions we used a grille in which the distance between the holes would either
increase or decrease in a regular way from letter to letter. It thus produced
encoded messages where the "skip" changed uniformly from character to character.
As I will show later in this paper, similar "codes" with regularly increasing or
decreasing "skips" can be easily located in any text as well as the ELS. I don't
believe any of my 12-year-old friends possessed a superhuman mind.
Especially for this paper, I decided to try to encode again, like I
did it as a 12 year old, some simple phrase, being willing to spend on that task
not more than 10 to 15 minutes. I did not make any Cardano grille, but
simply counted the letters manually. First I wrote the following phrase:
Rabin Will Die which, in the parlance of cryptology, would be my
plaintext. The choice of this particular expression was due to
the widely publisized alleged prediction of Rabin's assassination given in the
book by M. Drosnin, which will be discussed later in this paper. I wrote
the letters of the above expression on a piece of paper, leaving spaces between
letters which would enable me to insert 10 other letters between any two
consecutive letters of the above expression. Then I wrote between
the letters of that expression a text which, even if it is not very
sophisticated, is nevertheless meaningful. The entire exercise took 9
minutes. Here is the result:
Rivers are dAmningly roBust in the
Indian coloN ies,
moving Water unerrIngly, thus aLleviating
Lust for the Drinks,
forcIng people rEcognize.....
This is how the ciphertext looks:
Rivers are damningly robust in the Indian colonies, moving water unerringly,
thus alleviating lust for the drinks, forcing people recognize....
The presence of a plaintext encoded in the above two lines as
an array of ELS is not evident to an uninitiated reader. However,
the intended recipient of that message, knowing the skip (10 in this case) would
have no problem in decoding the message.
Of course, if a serious need existed for me to prepare a secret
message using Cardano grille, doubtlessly I would be able, by spendng more time,
to write a much more sophisticated ciphertext. The conclusion is
inevitable, namely that a human mind is quite capable of creating arrays of ELS
not unlike those found in the Bible.
A quite impressive factual confirmation of the contention that ELS
clusters like those found in the Bible can quite easily be produced by regular
men and women, came from Mr. Gidon Cohen of York, Great Britain. The story is as
follows. Grant Jeffrey, who authored several books about the Bible code and who
maintains that the "codes" are real, has suggested that the sheer complexity of
the ELS in the Bible points to its creator being God. As one of examples of
supposedly amazing arrays of ELS in the Bible, Mr. Jeffrey pointed out
the array which contains, within a segment of the text of a relatively small
length, names of 25 trees "encoded" in the form of ELS. Mr. Jeffrey was amazed
by that array to such an extent that he issued, on radio, and in several
conferences, a challenge to anybody to compile a text, of about the same size,
in English, which would also contain ELS spelling the names of any 25 trees.
Being confident that simple men or women, and even Moses himself, were not
capable of performing such a task, which only could be done by God, Mr. Jeffrey
offered to pay $1000 to anybody who would successfully fulfill the above
It did not take long until Mr. Gidon Cohen presented a piece of a
meaningful text, in English, consisting of less than 300 words (the total of
1139 characters) in which the names of 29 trees had been encoded in the
form of ELS. Mr. Cohen performed the task without using a computer program, by
manually counting characters. When a computer program was used (by Dr. McKay and
Mr. D. Thomas) they discovered in Mr. Cohen's text additionally ELS spelling the
names of at least 5 more trees plus a number of ELS for various related words
such as forest, copse, bark etc, and plus a dozen ELS for plants other than
trees. (Any reader who wishes to see the text by G. Cohen, can request it
via e-mail: email@example.com).
To Mr. Jeffrey's credit, he admitted that his challenge was met and
paid the promised amount. However, it did not make Mr. Jeffrey retract his
statement about the alleged Bible codes.
Lest I will be misunderstood, I would like to point out that by
refuting the claims about the necessity of a superhuman mind for the creation of
the alleged codes in the Bible I was not at all suggesting that the ELS in the
Bible had been created by men or women. The explanation best compatible with the
factual evidence is that arrays of ELS appear in the Bible not by design but are
rather chance coincidences. One more argument in favor of the above explanation
is the fact that, after Mr. G. Cohen had compiled his short text, in which he
"encoded" deliberately the names of 29 trees, a computer analysis of his text
revealed there many more ELS spelling names of more trees, as well as of other
plants, and also 35 names of animals, as well as various names of people,
including that of Dr. Rips. Mr.Cohen did not place all these additional ELS in
the text deliberately. They appeared there by chance.
As I have mentioned earlier, many participants of the dispute about
the "codes" try to calculate the probabilities of the appearance, by chance, of
various ELS in the text of the Bible. Indeed, the most highly acclaimed
publication which has become the pivotal point of the recent Bible code
controversy, namely the paper by Witztum, Rips, and Rosenberg, was published in
1994 in Statistical Science magazine. This fact underscores the role
ascribed to statistics for the problem in question. There are several good
publications, mainly on the Internet, providing criticisms of the paper by
Witztum et al. I would like to indicate, in particular, articles posted
on the Web by Gil Kalai, Brendan McKay, and Barry Simon.
Unfortunately, many of the people who are interested in the Bible
code controversy, either could not or would not read either the paper by Witztum
at al or the criticisms of it by G. Kalai, B. McKay, and B. Simon, since
much in this material is not intended for laymen. On the other hand, more people
read and are influenced by some other publications, which pretend to treat the
problem from the scientific viewpoint. I believe that even if Witztum at
al announced that they were retracting their statements about the codes (I
don't expect this of course) many other proponents of the codes, such as Rambsel
and Jeffrey, would not abandon their efforts to prove the codes' reality.
(Recently, Guy Cramer and Lori Eldridge, who used to be among the most prolific
defenders of the "codes" have announced, commendedly,that, in view of the
evidence, they do not any more support the beliefs in the codes'
authenticity. Very courageous and honest of you, Guy, and Lori ).
Scientists such as G. Kalai, B. McKay, and B. Simon, while being
involved in a discussion with Witztum, Rips, and Rosenberg, evidently do not
consider it worth their time to argue with writers of allegedly statistical
treatises that are not on the same scientific level. Hence the claims of many
proponents of "codes" other than Witztum et al remain largely
Unfortunately, many of these claims are characterized by errors and
misconceptions and produce unreliable values of probabilities. I believe that,
for the sake of many unsuspecting readers, it is desirable to explain the errors
in those claims.
An example of such a faulty calculation is the one which was once
offered by two code proponents, whose names I would like to omit because, since
the publlication on the Web of their calculation, they both changed their views
and do not support the "codes" any longer. I will refer to them as
XY. It may be instructional to analyze in detail those old calculations of
XY as a warning example.
XY first agreed that some of the ELS found by Rambsel can indeed
happen in the Bible by chance, because the probability of their occurrence as
they have calculated it, turned out to be not very small. On the other hand, XY
had singled out eleven ELS found in the Bible by Rambsel, and insisted that the
appearance of those ELS by chance has such a small probability that these
11 ELS must be deliberately inserted codes. To demonstrate their point, XY
suggest a certain procedure (they call it formula) for the calculation of
the probability of an ELS appearing in the text by chance. For certain ELS found
by Rambsel, that alleged probability turns out to be very small (between 1/99
for some ELS, and down to about 1/58,507,687 for some other ELS).
XY calculated for each of the 11 ELS they believe to be a genuine
"code" a quantity they call "significance index", which is the same as the
probability of a sequence of characters to appear in a text by chance. A
detailed discussion of XY's caculation of probabilities is given in an Appendix to this
article. It is shown in the Appendix that the calculation of probabilities
was conducted by XY in a way contradicting some basic rules of the Probability
Theory and therefore the values of "significance index" calculated by those
writers are meaningless numbers.
Now, let us consider the question: what if, regardless of the values
calculated by XY, the actual values of probabilities in question are
indeed very small? Does it mean the occurrence of corresponding ELS must be
attributed to a conscious design? Not at all.
Again, as an example, let us turn to XY's treatment of the
probabilities in question. As we shall see, XY's interpretation of those
probabilities is based on a misconception. It invalidates their conclusions that
some ELS found by Rambsel must be deliberately inserted codes.
The error in question stems from XY'se misinterpretation first of the
meaning of probabilities in general, and second of the meaning of the quantities
they calculated, in particular.
Let us see how XY explain the meaning of probability. What they say
is as follows. If the calculated probability of a certain ELS in a given text
is, for example 0.001, then, according to XY, one has to look through 1000 texts
of that size to encounter an ELS in question. This explanation is wrong. The
actual meaning of probability is as follows. If it is 0.001, it means that if a
very large number of tests has been performed (that number being much
larger than 1000) then the ELS in question will appear, on the average,
approximately once per every thousand tests. In order for that to happen,
the number of tests must be very large indeed. The more tests are performed
under identical conditions, the closer will be the number of occurrences of ELS
in question to the calculated probability (in this example, one occurrence,
on the average, per one thousand tests). If the number of tests tends to
increase indefinitely, the number of occurrences of ELS in question will
approach the calculated value of the probability. However, nothing can be
asserted as to what would happen in any particular thousand of tests.
Theory of Probability can not and does not predict whether an event
will or will not occur. Even if the calculated probability of an event is very
small, it does not mean at all that that event will not happen. All what Theory
of Probability can assert is that in a very large number of tests the
average number of occurrences of a specific outcome will approach the calculated
value of probability for this outcome along with the increase in the number of
tests. Not more and not less than that.
Consider an example. Nearly 100 times a year, a lottery is played in
California. I, and you, and your cousin, and every John Doe who buys a ticket,
have been told more than once that his/her chance to win the big prize in the
California lottery is about 1 in eighteen million! (The precise number, as it
can be easily calculated, is actually 1/15,890,700). Nevertheless, millions of
tickets are sold every three or so days. Why? Do those results of the lottery
game contradict the theory of probability? Not at all, if one understands
properly the meaning of the quantity called probability.
The value of probability does not predict how many times one must
play to ensure winning. One may well win having bought just one ticket (as it
had happened a few times) and one as well may never win even buying tickets
millions times in a row.
Why some lucky guy wins almost every time the lottery is
played, despite his chance to win being that small? The explanation is quite
simple. The chance for a particular ticket to win is indeed 1 in about 16
million. However, the chance for some ticket out of all the tickets sold,
to win, is much larger. If several million tickets are sold, then the
probability of some ticket (and we never know in advance which one) to
win becomes so large, as to approach certainty. So, we witness about 100 times a
year how an event whose particular probability per se is only about
1/16,000,000, actually happens with the utmost regularity! This fact in no way
contradicts the laws of probabilities. It fully conforms to the mathematical
expectation for some ticket (but not known in advance which one) to win,
whereas the mathematical expectation for the particular ticket to win
still is very small.
How is all this applicable to the ELS found in the Torah and spelling
Yeshua and some combinations of Yeshua with other words, such as Shmi,
Yakhol, or Moreh? The chance to find in the Torah a particular ELS
may be small (but still much larger than calculated by Cramer & Eldridge)
but the chance to find some ELS, combining the word Yeshua with certain
other words is much larger. The reason for that is that the Hebrew language (and
any other language as well) contains so many different expressions and phrasal
constructions, that the chance to come across some meaningful combination
of Yeshua with some other words in the Torah is quite large. Indeed, when
Rambsel sets out to locate meaningful phrasal combination in the Torah, he is
not after any particular expression. Were it the case, the probability to
locate such an expression could be small indeed (which still does not mean at
all it would not be found by chance). But since he is looking for any
combination of words which seems to support his contention that the creator of
the Torah encoded in it a message about Jesus being Son of God and the Messiah,
then the probability of coming across many such suitable phrasal sets is not
small at all. Like in the California lottery, where an event whose individual
probability is only 1/16,00,000, happens, on the average, twice a week, so
Rambsel's quest for suitable ELS in the Torah is expected to reveal many such
combination of words almost on every page. Obviously, also many expressions,
which contradict Rambsel's beliefs, would necessarily be encountered. However,
either consciously, or subconsciously, such undesired phrases would be ignored,
most often before their full length has been revealed. This is a phenomenon that
happens in every research. Scientists know very well how difficult it is to
accept anything contradicting their expectations and how easy it is to see a
confirmation of a preconceived view where no such confirmation really exists.
The fact that many expressions found by Rambsel in the Bible, were
also located, and quite easily, in non-Biblical texts, may serve as a
confirmation that calculations of probabilities, like that offered by XY, are
meaningless and cannot be used to justify any conclusions as to the reality of
"codes" in the Bible.
In view of the above considerations, what is striking is how actually
poor Rambsel's catch has been. While, on the one hand, people like Drosnin,
Satinover, Witztum, etc, have found a big number of what they believe are
detailed predictions of many events, such as Rabin's and Sadat's assassinations,
AIDS epidemics, and the like (we will discuss those finding a little later), on
the other hand, for such pivotal event in the history as the emergence of
Christianity, all what Rambsel and his followers could discover in the Torah is
only a number of grammatically lame, ambiguous phrases.
Let us recall that the name of Jesus of Nazareth does not appear even
a single time in the open, not-coded text of the Hebrew Bible. If the creator of
the Bible wanted to send a message to us, humans, about Jesus Christ, why would
he resort to a code while avoiding any direct reference to Jesus?
Of course, the name of Jesus appears overwhelmingly in the text of
the New Testament, whose original, unlike the Old Testament, was written in
Greek rather than in Hebrew. When the New Testament was translated into Hebrew,
the name of Jesus was transliterated by the translators as a four-letter
Hebrew word Yeshua ( in Hebrew Yud-Shin-Vav-Ayin). Actually, though, Yeshua is a
shortened version of the five-letter Hebrew name Yehoshua
As the name of Jesus in the Hebrew translation of the New Testament
has been traditionally spelled as Yeshua, Rambsel was looking for and has found
in the Old Testament many occurrences of the four-letter version
(Yud-Shin-Vav-Ayin) and of the even shorter version, the three-letter word
(Yud-Shin-Ayin), but not the five-letter version spelling Yehoshua.
Of course, if one believes that the ELS in question occur in the
Bible just by sheer chance, then it is natural that a five-letter ELS would be
encountered about twenty times less often than a four-letter ELS. It would be
even more true for phrases containing, besides ELS for Yehoshua, also such
accompanying ELS as Shmi, Khali, Rimon, (see below the discussion of these ELS)
etc. On the other hand, if one believes that the ELS are deliberately inserted
codes, then unavoidable question is, why Yeshua rather than Yehoshua?
While in the Hebrew language Yeshua and Yehoshua are indeed two forms
of the same name, there is a semantic difference between the uses of the
five-letter and of the shortened four-letter form. Letter Hey which is present
in the five-letter version but is absent in the shortened one, is considered by
the Bible scholars to be a link to the name of God (which is in Hebrew
Yud-Hey-Vav-Hey). Indeed, that letter, according to the Bible, was added by God
to the name of Abram, converting it into Abraham, thus linking the name of the
patriarch to the name of God.
Let us imagine that in a historical book about Franklin Delano
Roosevelt he is consistently referred to as Frankie. Of course, Frankie is a
shortened form for Franklin, but obviously referring to the late President as
Frankie is not the same as referring to him as Franklin Delano Roosevelt. It is
even more true in the case of Yehoshua's name, given the special significance of
letter Hey which is omitted in the four-letter version, Yeshua. The four-letter
ELS for Yeshua, and even more so its three-letter version, are diminutive
forms. They have in Hebrew the connotation of either familiarity, or even of a
certain lack of respect for the person bearing that name. Does it not look
strange that the alleged creator of the "codes," if he wished to encode
references to Son of God and the Messiah, would use in those codes, so often, a
diminutive form of Messiah's name?
Obviously, the alleged creator of "codes" would have no difficulty to encode the
full five-letter version Yehoshua as many times, instead of, or at least along
with its diminutive form.
Now, if the author of the Torah wanted to encode in it a message
about Jesus, would it not be expected that Jesus would be at least somehow
identified in the "code"? For example, the encoded words could have spelled
something like Yeshua Ha-Notzri (Jesus of Nazareth), or, perhaps Yeshua ben
Yoseph (Jesus son of Joseph), or maybe Yeshua ben Miriam (Jesus son of Mary),
or, say, Yeshua Nolad beBetlechem (Jesus born in Bethlehem), or any other of
numerous possible identifications. Nothing of the sort has been discovered by
Rambsel. So, if any phrases found by Rambsel has indeed been deliberately
encoded (which, of course, is not proven at all), then who is Yeshua these
"codes" refer to? For example, it could very well be Yehoshua (equivalent of
Yeshua) Bin Nun (Joshua the son of Nun) who led the Israelis into the promised
land after the death of Moses. (While in English the name of Yehoshua Bin Nun is
transliterated as Joshua, and that of Yeshua of Nazareth as Jesus, in the
original Hebrew it is the same name Yehoshua or, in a diminutive form, Yeshua.
In some other languages both Joshua Bin-Nun and Jesus are referred to by the
same name, which, for example, in Russian is transliterated in both cases as
Yisus). At least the not coded, "surface" text of the Torah speaks a lot
about that Yehoshua. It could be any other Yeshua, as this was not an
uncommon name in Israel.
Now, what is the meaning of those expressions Rambsel and
Jeffrey attach so much significance to? For example, what is really the
meaning of words such as Yeshua Shmi (Jesus is my name)? What can this possibly
mean except of some Yeshua (and there is no indication as to which Yeshua is
meant) to announce that his parents named him Yeshua? What hidden meaning has
the expression Yeshua Rimon (Jesus pomegranate)? To mean "Jesus is a
pomegranate" that expression in Hebrew should've been Yeshua Harimon, or Yeshua
Hou Rimon. As it spells, it really has no meaning by itself. Maybe some Yeshua
likes pomegranates? Or grows pomegranates? Or has red cheeks and is nicknamed
pomegranate? Obviously, the expression is ambiguous.
One more expression touted by Rambsel is Yeshua Yakhol (Jesus can, or
Jesus is able; or Jesus is allowed. The word Yakhol means will
overcome only in conjunction with another word, a noun or a
pronoun, denoting somebody or something being taken over, and with prefix
l' before that other word. If the word following Yakhol is a verb
preceded by prefix l', it means can or is able or is
allowed. The meaning of Yakhol standing alone is ambiguous, and its exact
meaning becomes clear only in context). Moreover, again, which Yoshua
can, or will overcome, or is able, etc? And
can what? Yehoshua Bin Nun obviously was able to perform, and did
perform, according to the not-coded text of the Bible, many feats. To assert
that the phrase in question refers to Jesus of Nazareth is an example of an
arbitrary interpretation of the text, which by itself has no clue as to its
possible meaning. And, most telltale is the fact that practically all
expressions found as combinations of ELS in the Bible and discussed above, have
been found as well in texts other than the Bible.
As mentioned earlier, some of examples given by Rambsel employ
imprecise translation of Hebrew words, or choose out of several possible
meanings the one fitting their goal. For example, consider the expression
Yeshua Moreh. The word Moreh, which has several meanings in Hebrew, does
not mean at all "Teacher of Righteousness", as they claim. The most common
meaning of that word is simply teacher, and it can be a school teacher of any
subject, or even driving instructor, tourist guide, etc. but the word
Righteousness was added by out of thin air.
Another Rambsel's example is the occurrence of the combination
Yeshua Khali, which allegedely translates as Jesus polished jewel. First,
if the meaning were to be Jesus is a jewel, it must be Yeshua Hakhali, or
Yeshua Hou Khali. Moreover, while one of the meanings of the word Khali (in
Hebrew three characters Khet, Lamed, Yud) is embellishment (any bauble,
not only a polished jewel) its other, quite common meaning is disease.
So, why did Rambsel choose the meaning fitting his purpose, but chose to ignore
another, quite common meaning, which obviously would be working against his
contentions? I am curious, how many more words similar to disease,
situated close to Yeshua, Mr. Rambsel did not care to report about?
But the most important fact is that, whatever those expressions may
mean, there is no proof whatsoever that any of them have been deliberately
encoded rather then appear by chance. Indeed, similar phrases occur in
non-biblical texts as well, as I have demonstrated above.
The claim that those ELS have been deliberately encoded in the Torah
has no more validity than the claim that John Doe had won big in the California
lottery not by chance but because he was deliberately chosen (by God? By
extra-terrestrials? By the lottery's management?) Reportedly, some people who
had won in the lottery believe indeed that they had been personally chosen by
God for a reward. Well, if you believe in God who encourages gambling, then you
have to believe that Las Vegas and Monte-Carlo are his holiest cities, casinos
are his temples, and roulette tables are his altars.
In conclusion of this section, let me state that I have not
proven in this article the absence of codes in the Torah, nor did I try to
do so. What I did, though, was to show that the alleged proofs of the validity
of their views, as presented by Rambsel, Jeffrey, and others, actually do not
prove anything. Maybe there are codes in the Torah. Maybe some of them say
something about Jesus of Nazareth. However, to prove that, Rambsel,
Jeffrey, etc, would need to do much better than they did so far.
G. Jeffrey and Y. Rambsel have recently published more books, in
which they give more examples of ELS they found in the Bible, supposedly
confirming their previous assertions. Likewise, there are additional, more
recent postings on the Web, also providing more examples of "discoveries" about
Yeshua, or about some "predictions" of future events, etc. All of it makes use
of the same argumentation, which I have addressed in this article. None of it
adds a shred of real evidence as to the authenticity of the alleged "codes" but
appeals quite strongly to the gullibility of its readers. There is no point to
continue addressing time and time again each of these "new discoveries," as this
would be an open end game without a winner.
In this article, I have not discussed the question as to whether the
ELS found by the "code" proponents in the Bible do necessarily spell indeed what
they have been claimed to spell. This question is addressed in my paper at Do the ELS in the Bible indeed spell what they have been claimed to spell?
where I have shown that the very spelling of the ELS in question, more
often than not, is quite ambiguous and is often interpreted in an arbitrary
My criticisms have nothing to do with any religious beliefs, or with
the question as to whether the Bible has been inspired by God, or with the
question whether or not Jesus of Nazareth was Son of God and the Messiah. The
scope of this article is much narrower. It deals only with the question whether
or not the arguments by Rambsel, Jeffrey, etc, prove the authenticity of the
alleged codes in the Bible. My conclusion is that they do not. I am not claiming
though that some better proofs of the alleged codes' authenticity cannot be
found one day. Such proof, if offered, must necessarily include a convincing
explanation as to what is the difference between ELS found in the Bible and the
same ELS found in non-biblical texts.
In his book Michael Drosnin claims to have made amazing discoveries
in the Bible. In particular, he claims to have found a prediction, encoded in
the form of an array of ELS, of Yitzhak Rabin's assassination. The array of ELS
in question, reproduced as a tableau in Drosnin's book, comprises the name of
the late Israeli Prime Minister (found with a very large skip of over 4000
characters) as well as the phrase Rotzeakh SheIrtzakh, meaning killer
who will kill, the set of letters denoting the year (in the Hebrew calendar)
when Rabin was assassinated, and also the name of the killer, Amir.
Looking at the tableau in question reveals that of those words only
the name Yitzhak Rabin is an ELS (with a very large skip). All the rest of the
words in the set are just parts of the regular not-coded text, so are not codes
at all. Hence, Drosnin feels free to combine both ELS and parts of the Bible's
"open" text while interpreting the meaning of his finds. Since many people
remained skeptical in regard to Drosnin's claims, that author, in an interview,
had said that if somebody found a prediction of a Prime Minister's assassination
in Moby Dick, then he would admit being wrong. I assume that by saying
Moby Dick Mr. Drosnin actually meant any book other than the Bible. As to
the prediction of the Rabin's assassination, I assume he would allow us to look
for such a "prediction" in the form similar to what he did, as a set of ELS that
appear in some book close to each other and spell words such as Rabin,
murderer, and the like.
Out of curiosity, I turned again to the book by Dahn Ben-Amotz,
mentioned earlier in this article and titled, as I said before, Screwing is
not Everything. As mentioned before, I found in that book, without
using any computer program, ELS spelling Yeshua Shmi etc. Now I decided to look
for some ELS related to Rabin. Again, I did not use any computer program, so I
limited myself to relatively short skips. My intention was to see if I could
find relevant ELS rather easily. Following Drosnin's practice, I counted only
the letters, ignoring the spaces between the words, commas, periods, etc.
A copy of the pertinent paragraphs in Ben Amotz's book, described
below, can be viewed at rabin.cfm.
The word RABIN popped up on page 33, in the uppermost paragraph on
that page, with a skip of -35. Then I looked around that word to determine if
there are some other ELS related by meaning to Rabin. What I found in that
search was as follows. In the 2 uppermost paragraphs, consisting of only about
600 characters, the following ELS appeared, in a chain formation, one following
the other: 1) An ELS consisting of four Hebrew letters, with a skip of only -2,
YUD-RESH-TZADE-KHET, which reads IRTZAKH (meaning (he) will kill). 2) Three
Hebrew characters, with a skip of -15, RESH, HEY, MEM, which is the Hebrew
abbreviation for ROSH HA MEMSHALA, meaning PRIME MINISTER (this abbreviation is
commonly used in Hebrew, and is also used as such by Drosnin). 3) The following
Hebrew characters with a skip of -7, GIMEL, BET, RESH, which is normally read as
GEVER (meaning MAN) but is interpreted, for example, by Satinover as GIBOR
(meaning HERO or MIGHTY MAN). 4) As mentioned before, word RABIN with a skip of
So, in just two short paragraphs in a randomly opened page, in a
randomly chosen Hebrew book, that has nothing to do with the Bible, without
employing any rearrangement of the text like those usually performed by Drosnin,
set of 4 ELS, with small skips between the letters of each word, all
words appearing in one chain, one after the other, in a very close proximity,
reads: (he) will kill, Prime Minister, hero, Rabin.
Now, what about the name of the killer, Amir? To relate to this
question, let us consider the idea of a code. Obviously, if some entity planned
to encode certain information, then this entity was not confined to the use of
ELS. The code may be more complex, and the only requirement is that the code
follows certain rule. If myself and my friends, as 12 year old boys, used a
"code" in which the skips either increased or decreased in a regular manner from
letter to letter, why could not such a "code" be employed anywhere else as well?
So, I looked for any occurrence of such a "code". In the same chain of words,
mentioned above, I found the following 4 Hebrew letters: Ain, Mem, Yud, Resh,
which read AMIR, with the skip between the first and the second letter being -8,
between the second and the third letter being -9, and between the third and the
fourth letter being -10. What a nice regularity, and what a beautiful code,
isn't it? Now all "encoded" words, all within the same two paragraphs, with
small skips, in a chain, read Amir Will Kill Prime Minister Hero
Following Drosnin, one may say, What an amazing discovery! Obviously,
the probability of those words appearing in the same one third of a page, in a
chain formation, must be so small that it could not happen other than by a
conscious design! Hence, we must conclude that in a book published in 1979 a
message was deliberately encoded predicting the assassination or Prime Minister,
the hero, Rabin, by Amir, some 16 years before it actually happened.! Such a
prediction could've been made only by God or by extraterrestrials who possessed
an intelligence much exceeding that of humans!
Indeed? Regarding the probability of those ELS appearing in the
paragraph in questions, I can only repeat what I have said earlier in this
article in regard to Cramer&Eldridge statements. If the concept of
probability is properly interpreted, as explained above, there is nothing
amazing in the appearance of the cited ELS in the paragraph in question. Neither
is it amazing in the Bible.
Since Mr. M. Drosnin has challenged anybody to find a "code"
predicting the assassination of Rabin in a book other than the Bible, I would in
return challenge him to admit that his condition has been fulfilled herewith.
Now he is expected to retract the extraordinary claims made in his best-selling
(and certainly very profitable) book. Of course, he is free to verify my claim
by checking the book by Dahn Ben-Amotz. I hold my breath.
The unavoidable conclusion is that the claims by M. Drosnin asserting
that the ELS in the Bible are deliberately inserted codes, many of which predict
the future, have no reliable proof. Most likely those ELS are just random
coincidences, which could be found in any text of sufficient size. If the codes
in the Bible are real indeed (which, of course is not impossible) Mr. Drosnin
would need to look for a more believable proof for his claims.
It is worth to mention that M. Drosnin, unlike Dr. J. Satinover (see
below) has not used anywhere in his examples the concept of the "minimal" or
"nearly minimal" skips. Therefore he hardly can resort to the argument about the
skips being not minimal in the Ben-Amotzís book. The skips I found there are all
very short anyway, none of them being anywhere close to sometimes very
long skips in M. Drosninís book.
The book by J. Satinover contains some interesting pieces of history,
popular explanations of certain aspects of cryptology etc. Unfortunately, also
in Dr. Satinover's book there are examples of alleged amazing finds in the
Bible. Although Dr. Satinover uses an additional criterion of nearly minimal
skips, his finds still are most likely results of a random chance.
Here is one example. In chapter ten of his book Dr. Satinover
presents a number of "arrays" of ELS found in the Bible by himself as well as by
Doron Witztum, by Eliahu Rips, and by Moshe Katz. These arrays supposedly
contain encoded information about Dr. Satinoverís ancestor, Rabbi Abraham
nicknamed Angel, as well as about Emperor Franz Joseph of Austria, about
diabetes, about AIDS epidemics, and about the assassination of Anwar Sadat.
I decided to look if any similar "arrays" can be found in a text
other than the Bible. For my test I chose the array described by Dr. Satinover
on page 164 of his book. According to Dr. Satinover, it was found by D. Witztum.
It deals with the AIDS epidemic.
As Dr. Satinover reported, the array in question contains ELS
which spell the following words: AIDS (Aleph-Yud-Dalet-Samekh), MaVeT
(Mem-Vav-Tet, meaning death), BeDaM (Bet-Dalet-Mem, meaning "in(the)
blood"), The HIV (Hey-Hey-Yud-Vav) etc.
Again, I leafed randomly through the book by Ben-Amotz, mentioned
before. I did not use any computer program and did not rearrange the text like
Dr. Satinover, D. Witztum, and other explorers of the Bible code do routinely.
My goal was to see if the "arrays" in question could be discovered easily.
On page 67 of Ben-Amotzís book, I found the following ELS, all
situated within the two uppermost paragraphs which contained the total of about
600 characters ( The paragraphs in Dahn Ben-Amotz's book that contain the
"array" of ELS related to AIDS, which is described below, can be viewed at aids.cfm).
The ELS I found on page 67 are as follows: BeDaM (Bet-Dalet-Mem,
meaning in (the) blood) with the skip of 15. MaVeT (Mem-Vav-Tet, meaning
death) with the skip of Ė10. HIV (Hey-Yud-Vav) with a skip of 18.
Additionally, in the same paragraphs there was word KHaLi (Khet-Lamed-Yud,
meaning disease). Now, what about word AIDS? Again, remembering the codes
I used as a kid, and realizing that the "code" must not necessarily be limited
to ELS, I looked for word AIDS (Aleph-Yud-Vav-Samekh) "encoded" with a regularly
increasing or decreasing skip. I found that word in the same paragraphs, the
skips being Ė18 between the first and the second letter, -17 between the second
and the third one, and Ė16 between the third and the fourth letters. How small
is expected to be the probability of the described occurrences?
There remains little doubt that by using a computer, and rearranging
the matrixes of text, every single ELS of Witztumís and Satinoverís arrays, as
well as tight clusters of ELS related by meaning could be located in the
Ben-Amotzís book, as well as in any text of sufficient length.
M. Drosnin is a journalist. J. Satinover and D. Witztum, however,
supposedly are scientists. Therefore they are expected to provide a convincing
explanation as to what is the difference between the "arrays" in the Bible they
have described and similar occurrences in the non-biblical texts. Using the
trivial argument about the "minimal" skips would be not convincing. The skips I
found in Ben-Amotzís book are so small as to make the question of "minimal" or
"nearly minimal" skips irrelevant. As I did not use a computer, I automatically
limited myself to only very short skips. All arrays of ELS I found in
Ben-Amotz's book were situated within very short segments of text.
Furthermore, in Dr. Satinover's book there are strange errors, which
make one take the rest of the book with caution.
Here is one example. On page 237 of the book in question, Dr.
Satinover indicated that Max Planck developed his theory (which was the
beginning of the quantum physics) in 1912, and that he was at that time 19 years
old. Not true. Max Carl Ernst Planck was born on April 23, 1858. So, in 1912 he
was much older than 19. Moreover, he developed his theory not in 1912, but in
November - December of 1900. At that time he was 42.
Another example. In the chapter dealing with the information
allegedly encoded in the Torah about Dr. Satinover's ancestor nicknamed Angel, Dr. Satinover
consistently refers to the town where his ancestor lived, as Fostov. There is no
such town in the Ukraine. There is in that country though a town named Fastov.
Not a very serious error, but such errors hardly enhance the credibility of the
rest of the book in question.
In the article by D. Witztum, E. Rips, and Y. Rosenberg (WRR) its
authors have reported on some results which, although quite extraordinary, are
often touted as products of a scientific approach.
G. Jeffrey, M. Drosnin, J. Satinover, and D. Mechanic all refer to
that paper with the utmost esteem. As one of the arguments in favor of "codes"
reality, these writers indicate that Witztum, Rips and Rosenberg are genuine
scientists, that their paper was published in a prestigious refereed magazine,
and that no skeptical scientists could so far find any errors in WRR's
Drosnin and Satinover also bestow on some people whose views they
like, including WRR, the ranks of what they call "world-class" mathematicians,
probabilists etc. It reminds me of the mores in the scientific community of the
former USSR. Scientist had there ranks like officers in the army. According to
that system, a full professor was meant to be automatically smarter than an
associate professor ("docent"), a Doctor of Science automatically smarter than a
Candidate of Science, etc. No assistant would dare to utter an opinion
contradicting that of a professor, etc. Now we have a funny picture of
journalist Drosnin awarding ranks of "word-class" scientists. So, now we may
have a table where scientists would be ranked as "world-class",
"continent-class", "country-class", "city-class", "village-class" and "no-class"
experts, and the ranking would be performed by writers of sensational books who,
apparently, themselves would be counted among "galaxy-class" judges.
I understand that the three authors contributed different components
to their paper. In particular, the mathematical calculation was reportedly the
contribution by E. Rips. Y. Rosenberg developed the computer program, while D.
Witztum has been characterized as the foremost researcher of the Bible
codes per se. I also understand that E. Rips is an expert in Group
Theory rather than in Statistical science. I am not at all an expert in Group
Theory so I can't judge Dr. Rips' scientific achievements and credentials. I am
prepared to happily accept the assertion that E. Rips is a brilliant
mathematician, highly qualified in his field, as well as a very nice and a
perfectly honest person. Does it mean that we have to take uncritically
everything WRR claim?
There had been many brilliant scientists who goofed, sometimes in a
most bizarre way. One of the most outstanding Russian scientists of the last
century Dmitry Mendeleev is deservedly revered for one of the most important
discoveries in the history of science, namely the Periodic System of elements.
Until the last days of his life he vigorously fought against the theory of
electrolytic dissociation developed by Svante Arrhenius. In that, the famous
Russian chemist was wrong. A brilliant Russian physicist N. S. Akulov produced
in the late thirties a very elegant and powerful theory of magnetic behavior of
solids based on the concept of symmetry. Later in his life, though, Akulov wrote
a book on the Theory of dislocations which had become a laughingstock among
scientists. Professor Fleishman, a respected electrochemist, once a President of
the International Society of Electrochemistry, who authored a considerable
number of good quality research papers, in the late eighties published (together
with Pons) an article claiming the discovery of the "cold fusion" which turned
out to be a non-existent phenomenon. There are many more such examples.
Therefore an argument which makes use of a scientist's reputation as a proof
that his claims are correct, be it E. Rips or anybody else, is irrelevant with
all due respect for E. Rips scientific achievements.
On the other hand, if one wishes to use the argument based on the
credentials of WRR, then one has to account for the opinion of many prominent
mathematicians and experts in Mathematical statistics who expressed an
unequivocal rebuttal of WRR's paper (see the letter of over 50 mathematicians at
One more argument often offered in favor of WRR paper is that so far
no scientist had found errors in WRR calculations. This statement is not true.
There are several publications on the Web in which serious doubts have been
offered in regard to WRR's calculational procedure. A very serious rebuttal of
the entire approach by WRR , from the standpoint of Mathematical Statistics and
Probability Theory has been proposed by a prominent expert in Mathematical
Statistics, Dr. A. M. Hasofer. The paper by A.M. Hasofer is available in this
Web site - see A statistical critique of Witztum et al paper.
Another prominent mathematician, Dr. B. Simon of Caltech has also
unequivocally rebutted WRR's method (see http://wopr.com/biblecodes/TheCase.htm).
I've also read the calculations in WRR's paper in question. There is
one statement in the paper by WRR, at the end of section A.1 of that paper,
related to the calculation of the
expected number of ELS with shortest skips, that number chosen by WRR to be
10. I believe that statement is in error. It had though no
substantial effect on the final result of WRR's calculation (see Appendix 2,
added on December 6, 1998). What is more important, though, is that I found in
WRR's paper serious deviations from the established rules of Probability Theory
and Math. Statistics, which I discuss in my other article at Some remarks in regard to D. Witztum's writings concerning the "code" in the book of Genesis. Finally, as mentioned earlier in this article, over 50 experts in Math.
Statistics have signed a petition in which they denounce WRR's paper from the
standpoint of Math. Science. There is no such document in existence signed by
any mathematicians which would support WRR's method and conclusions.
Another argument by Drosnin, Satinover, Jeffrey, etc, is that the
paper by WRR was published in a prestigious scientific journal where it was
subjected to a rigorous review by experts.
I had been, for a number of years, on the Editorial board of an
international scientific journal devoted to surface science. Besides, I also
served as a reviewer for a number of other scientific publications. I can state
with confidence that the mere fact of publication of a paper in even the most
prestigious journal by no means assures the truth of the paper's claims. While
papers containing obvious errors are usually rejected, in many cases an honest
reviewer would not consider himself/herself the ultimate judge of the
credibility of the paper's results. On several occasions, I, as a reviewer,
recommended to publish some articles despite having doubts in regard to their
contents. I know for fact that I was not alone with such an attitude. In 1978,
an anonymous reviewer of a paper I submitted to Surface Science magazine,
wrote in his (or her) review that he (or she) had doubts in regard to the
physical meaning of certain kinetic coefficients in my formula. Nevertheless,
that reviewer recommended the article for publication, because, as that reviewer
indicated, this was a matter for discussion between the author and the readers,
rather than for the reviewer's discretion. (The paper was published, and
initiated some discussion in which my view finally won acceptance). The reasons
for such an attitude are that most reviewers realize, first, that they can be
wrong, and second, that even a paper containing errors may also contain some
interesting results, some provoking ideas and some stimulating challenges.
Hence, the publication of WRR's paper in Statistical Science magazine is
not at all a certificate of infallibility.
The paper by WRR has already met a number of critical comments. Dr.
Gil Kalai in his paper had pointed out certain features in the paper by WRR,
which seem to suggest that the three authors may have used, consciously or
subconsciously, certain optimization procedure that led to the desirable outcome
of their experiment. In some other publications it has been shown that the data
set used by WRR may not be entirely correct, etc. Those are worthy pursuits and
their outcomes may serve to debunk the unfounded hypotheses in regard to the
alleged "code." On the other hand, I believe that the questions, whether or not
the data set used by WRR was correct or not, or whether an optimization took
place or not, are not the most crucial points.
Let us assume that the data set chosen by WRR was faultless, and that
their mathematical and statistical treatment was impeccable. I believe it does
not matter because the paper by WRR is based, in principle, on a premise, which,
in my view, is unsubstantiated.
WRR have used in their article an artificially constructed criterion
of the authenticity of the codes in the form of a quantity they named
proximity. I believe that the final conclusion in the paper in
question, stating that (I am quoting) "the proximity of ELS with related meaning
in the Book of Genesis is not due to chance" is actually an
interpretation of their result by the three authors. Even if the data set
used by the three authors contained no errors or arbitrary choices (this has not
yet been established beyond doubts and is being disputed by a number of
scientists) the only scientific conclusion could be that the quantity
they introduced under the name of proximity reaches an almost extreme
value when a data set chosen as the "correct" one by WRR, as well as the
actual text of Genesis, are used, as compared with scrambled data sets and
control texts. Anything more than that would be an interpretation open for a
In a scientific approach, the factual statement of result must be
clearly separated from its interpretation. The authors may offer an
interpretation but must not substitute it for the conclusion.
The justification WRR offered for the use of the "proximity" to
distinguish between the deliberately placed "code", and coincidental ELS, is
characterized by an unfounded logical jump. In the beginning of their paper, WRR
discuss a situation when a text written in an unknown language is to be
analyzed. They suggest that in such a text pairs of words conceptually related,
for example hammer and anvil, are expected to tend to appear in
"close proximity." As far as it relates to a text, with a meaningful
contents, their hypothesis may seem to be fairly plausible (even if still open
to rebuttal). Then, however, WRR extend their hypothesis to arrays of ELS
in the Bible.
Since the words in a pair are supposed to be connected via
their meaning, the described hypothesis by WRR is valid only for a) logically
organized texts, and b) only if such a text is not very short.
Indeed, if the text in question comprises only a few tens of letters, related
words such as anvil and hammer simply may have no opportunity,
spacewise, to display their tendency to appear in proximity.
Obviously neither of the above two conditions holds for ELS. All of
ELS demonstrated so far do not form even simple grammatically ordered sentences,
not to mention paragraphs of any length or any semantically ordered chunks of a
continuos meaningful text. Even when found in "arrays" and meeting the condition
of "minimal" skips, they are usually still just individual words. They appear as
separate one-word islands within the framework of the grammatically ordered
text. They are not connected to each other by any grammatical links. They are
not arranged in any sequences that constitute segments of a continuous
Hence there is no reason whatsoever to assume that if ELS are
products of a conscious design, then pairs of conceptually related ELS
must tend to appear in a closer "proximity" than if they happen just by a
random chance. Therefore, even if WRR's data set and calculations are faultless,
there is no clear logical relationship between the extreme values of "proximity"
and the assertion that the "codes" have been deliberately inserted into the
Genesis' text by a conscious design.
By interpreting their result as they did, WRR actually attempted
nothing less than to have read the mind of the alleged creator of the
"code." On what grounds have WRR believed that the alleged creator of "codes"
has arranged the distribution of the ELS in the text in such a way as to make
their "proximity" have an extreme value? The alleged author of "codes" could
have chosen any number of various ways to make his authorship recognizable, or
maybe, to the contrary, to conceal it. The almost extreme values of the
"proximity" found by WRR, even if they are correct, may have any number of
explanations not related to any conscious design of the pattern in question.
(see Some remarks in regard to D. Witztum's writings concerning the "code" in the book of Genesis).
Indeed, why should the alleged creator of codes have placed the ELS
in close proximity to each other but failed to provide any grammatical link
between them? Equally plausible (or, better, not more implausible) is the
assumption that the alleged creator of "codes" would rather create ELS with as
little "proximity" among them as possible. Indeed, as we have seen in previous
sections of this article, a human mind is capable of creating arrays of ELS in
any text. However, this task is relatively easy for a human mind only if the
skips are relatively short. Likewise, it is easy to manually find the ELS in the
text as long as one limits the search to short skips. For skips exceeding the
length of one page, the task becomes rather difficult. It becomes much easier if
using a computer. The lengths of skips contribute to the overall value of
"proximity" calculated by WRR. Hence, would it be not more reasonable to guess
that, if the alleged superhuman creator of codes wished to make his authorship
recognizable (i.e. distinctive from what could be placed in the text by human
writers) or if he wanted to delay the discovery of codes until the computer age,
he would rather opt for creating ELS with very long skips? The
requirement of "minimal skips," which is one of the components of "proximity,"
appears to be an arbitrary speculative choice without a logical or factual
There may be many ways in which the state of mind of the alleged
creator of "codes" could be surmised. None of such guesses could though either
be based on a factual evidence or logically bridged to any well-established
Since there is no way to figure out the way of thinking of the
alleged creator of "codes", there is no way to reasonably choose a reliable
criterion of the code's authorship. Therefore even the most sophisticated
mathematical calculation would not solve the controversy. On the other hand,
given the ease the "code" quite similar to that in the Bible can be located also
in other texts, the most likely explanation of the phenomenon remains so far
that the ELS happen in the texts by chance rather than by design.
One feature of the alleged code is that all those arrays of ELS do
not reveal any information that is not available without those arrays. So, what
could be the possible motivation for the alleged creator of "codes" to play such
a game with the Bible text?
I can envisage an argument in favor of the "proximity" being a valid
criterion, as follows: does not the mere fact that the "proximity" has the
extreme (actually it is an almost extreme) value for the text of the
Genesis and for the "correct" data set, as compared with control texts and
scrambled data sets, prove by itself that that quantity is indeed a meaningful
criterion? I have a detailed discussion of that question provided in my paper at
Some remarks in regard to D. Witztum's writings concerning the "code" in the book of Genesis. I may say here, that of course the "proximity" may be a meaningful
criterion of something. The question is what is the meaning of that
criterion. To that question there is so far no good answer.
I have not discussed here one more, quite crucial point, namely the
very strange behavior of the cumulative criteria of "proximity" suggested by
WRR. I discuss this behavior in my other article at Additional critical remarks in regard to D. Witztum, E. Rips, and Y. Rosenberg "code" related publications. I show in that other article that the four criteria P of "proximity"
which WRR refer to as four "statistics" behave in an erratic and contradictory
way, indicative of some profound fault in WRR's approach. This haphazard
behavior of the four "statistics" alone negates the validity of their
The primitive search for single ELS in the Bible, or
for short phrasal constructions made up of two or three ELS (Rambsel, Jeffrey,
etc) as well as the more sophisticated method of forming matrixes that contain
arrays of ELS related by meaning (Witztum, Drosnin, Satinover etc) so far have
not produced anything that definitely extends beyond coincidences which
happen in any text of sufficient length. Neither is sufficiently convincing the
alleged scientific analysis of the "code" by WRR. Of course, if some,
better-substantiated proof could be found of the "code" being real, it would
change the landscape of the field of the controversy in question. So far,
though, it did not seem to happen.
(Discussion of "simple" calculations of
In this Appendix, the "simple" calculation of probabilty of a word to
occur in a text as an ELS, employed by many a code defenders, is being
discussed. The following discussion will show that such
calculations ignore certain basic rules of the Probability Theory and therefore
produce meaningless numbers.
Let's say some word is a sequence of n characters
x1, x2, x3.....xn.. What
is the probability that this word appears, as an ELS, in a given text? The code
proponents usually calculate the probability Pi of each of the
characters in the word in question to be found at any arbitrarily chosen site in
the text. They do it by dividing Ni - the number of times character
xi is found in the entire text in question, by N - the total number
of all characters in that text.
This operation implicitly assumes that the occurrences of the
character in question are distributed uniformly over the text. In other words,
they calculate the average probability of finding the character in
question at any arbitrary site.
Unfortunately using average quantities in an improper way may often
distort the results. The very concept of an average quantity is ambiguous. This
quantity depends on the procedure chosen for its calculation. (A detailed
analysis, including examples, of the effect the calculation procedure may have
on the average values, has been given, for example, in my paper published in
1976 in Surface Technology, vol. 4, pages 538-564). In many cases, there
are several average quantities for the same set of random quantities, each
having different value and meaning. (This does not relate to the mean
value, which is unambiguously defined in the Integral Calculus and in the
Mathematical Statistics. The average value used by Cramer et al does not
meet the definition of that mean value).
Let us illustrate the effect of the above implicit assumption.
Imagine that we have a text describing tastes and properties of fruits. We
choose a portion of that text, of a certain length, to see if there are some ELS
in it. Suppose we discover that one half of the selected text discusses apples,
while the other half of it deals with oranges. Obviously, in the first half word
apple will be encountered more often than in the second half, while word
orange will be met more often in the second half. Hence, the first half
of the text will contain a larger number of consonants p and l
(per unit of text) than the text as a whole, while the second half will contain
more consonants r, n, and g per unit of text than the text
as a whole.
Now we want to look for an ELS which spells, for example, word
play. Obviously, we will find ELS for this word more often in the first
half than in the second one. On the other hand, if we are looking for an ELS
spelling word grain it will be found more often in the second half of the
text in question. Finally, if we are looking for an ELS which spells, for
example, word grapple, its occurrences in both halves of the text will be
found with about the same frequency. Therefore, ELS for words grain and
play, read both right to left and left to right, will be found more often
with such skips' lengths that the corresponding ELS would cover not more than
the length of a half of the text in question. On the other hand, ELS for word
grapple, which require characters from both apple and orange,
will typically have such skips' lengths that these ELS would extend over
more than half of the text in question. Making a note of that fact, let us
postpone the discussion of its consequences for probabilities' calculation until
some later paragraph of this Appendix.
Having calculated Pi for every xi, thecode
proponents usually assign value of 1 to P1 and multiply all other
average probabilities Pi. Thus they supposedly calculate the average
probability Pw of the word in question to appear as ELS, starting
from any arbitrarily chosen site containing letter x1 ,
that ELS having an arbitrarily chosen particular skip.
Here we encounter another, much more profound fault in
the calculation. The probability of a combination of consecutive events is
calculated as a product of individual probabilities of those events. This is a
common procedure in the Theory of Probability. Unfortunately, such a calculation
ignores a crucial point. Multiplication of the "initial" individual
probabilities is valid only if two conditions are met. These conditions are as
- Each "test" must be performed under the same conditions, exactly
reproduced for each test.
- All consecutive tests must be independent. This means that the
results of each consecutive test must not depend on the results of the
Condition 2 must be met always. Condition 1 must be met
if one multiplies "initial' probabilities which existed before any test has been
performed. If, though, one recalculates the probabilities for every test
after the first one, then condition 1 may be waved, and the recalculated
probabilities may be multiplied, as will become clear from the further
As we shall see, the "simple" calculation does not meet
either of the above conditions.
Let us consider an example. Imagine that there are
three balls in a box, one white, one black, and one red. Balls are pulled from
the box in a random fashion. Obviously, each of the three balls has the same
chance to be pulled from the box in the first test. The probability of that
outcome is 1/3.
Now, for the second test we first restore the initial
conditions, namely, put the ball, that was pulled out, back into the box. Then
condition 1 will be met. Now, again, the probability for any of the three balls
to be pulled out in the second tests is again 1/3. The result of the second test
is independent of the result of the first test, so condition 2 is also met. Now
the probability that after two tests any two specified balls have been
pulled is indeed the product of 1/3 and 1/3, which is 1/9, and it is the same
for all 9 possible combinations of consecutive results (white+black, white+red,
black+red, black+white, red+white, red+black, white+white, black+black,
Now let us change the procedure. Namely, after each test, make sure
that the ball, which happened to be pulled from the box in the first test, is
somehow prohibited from taking part in the second test. (For example, that ball
can be glued to the bottom of the box). It means that condition 1 is not met any
longer. Under the new rules, again, in the first test, when all three balls are
available for removal from the box, the probability for any one of the three
balls to be pulled out is still the same as before, that is 1/3. However, for
the second test, when only 2 balls out of three can be subjected to the test,
the probability of any of those two balls to get out is 1/2 rather than 1/3. In
Statistical Physics it is called "to impose constraints on the system." Now the
probability of any combination of balls to wind up out of the box after two
tests is 1/3 times 1/2 that is 1/6 instead of 1/9, and is the same for all 6
possible "events" (white+black, white+red, black+red, black+white,
red+white, red+black). In this case we have recalculated the individual
probabilities for the second test, thus making it possible to multiply these
recalculated probabilities even though condition 1 is not met any longer.
This example illustrates the following rule: each time condition 1
is not met in the manner described, the probability of a combination of events
to occur increases as compared with the situation when condition 1 is
Before discussing the effect of condition 2, let us see
if condition 1 was met in code proponents "simple" calculation. Obviously
it was not, nevertheless they erroneously multiplied initial probabilities
rather than the recalculated ones.
Indeed, as soon as the first letter x1 of the ELS has been
chosen, all the sites in the text which are occupied by x1, are
rendered unavailable for the next character in the word. The reason for that is
that as soon as the identity of the first letter in the word has been chosen,
this replaces some of the probabilities with a certainty. Namely, we are now
certain that letter #2 can not occupy N1 sites, which are
occupied by letter #1. We do not know which sites are occupied by letter #1, but
we know how many! That number of sites become inaccessible
for letter # 2.< Hence, the number of
sites in the text that are accessible for the second letter x2
decreases from N to N-N1 . Consequently the
average probability of the second letter to be found becomes
N2/(N-N1) instead of N2/N. For the third
character in the ELS in question the number of accessible sites decreases again
etc. (There can be a rare exception when a certain character happens in a word
twice in a row. In that case the number of accessible sites for character
xi+1 decreases by 1 instead of Ni. Most of the time,
though, it decreases by Ni in each step whose number is [i+1]).
Hence, the probabilities must be first recalculated in order to
multiply them. Cramer et al did not recalculate probabilities, and
therefore their calculation had, already on that stage, generated underestimated
values of probabilities.
This effect accumulates rapidly with every letter added
to the ELS. In the example with the balls, rendering a ball, that had wound up
outside the box, unavailable for the consequent tests, led to the increase of
the probability of a given combination of balls to get out. Similarly, in the
calculationwe discuss, the fact isignored that choosing a specific letter of the
ELS necessarily imposed constraints on the number of accessible sites for every
next letter. This oversight resulted in an underestimated probability of
a certain ELS to be found in the Bible by chance. The longer is the ELS, the
larger is the underestimation.
Now we shall discuss the effect of condition 2, which is much more
profound than that of condition 1.
Let us consider a modified example with balls. Imagine that there are
six balls in a box, one white, two black, and three red. The probability of any
one of the balls to be pulled out in the first test is 1/6 for each of them.
Since, though, there are different numbers of balls of each color, the
probabilities of each of the three colors to show up in the first test
are different, being 1/6 for white, 2/6 = 1/3 for black and 3/6 = 1/2 for red.
(Colors in this example are analogs of various letters in a
Now let us see what happens if in the first test a white ball has
been pulled out. As we want to model the "simple" calculation by code
proponents, where condition 1 has not been met, we will discuss now a situation
where that condition is not met either. It means that after the first test the
white ball must be rendered unavailable for the second test. Then in the second
test there are no more white balls. There are now two black and three red balls
available, the total of 5 balls. Now the probability of any of the balls, either
black or red, to get out in the second test becomes 1/5 instead of 1/6. Since
the numbers of black and of red balls are 2 and 3 respectively, the probability
that in the second test a black ball is chosen is now 2/5, while for red balls
it is now 3/5.
Now let us see what happens if in the first test a black ball was
pulled out. Note, again, that different colors in our example are analogs of
different characters in the code proponents' calculation. According to the rules
we agreed upon, and which reflect what code proponents routinely had done in
their calculation, we must now make both black balls unavailable for the
second test. Now there are only four balls (one white and three red) available
for the second test. Then the probability of a white ball to be chosen in the
second test becomes 1/4 (in the previous example it was 0), while the
probability of a red ball to get out becomes 3/4.
Hence, we see that the probability of a red ball to be pulled out in
the second test depends on the outcome of the first test. If the first ball out
was white, the probability of a red one to be out in the second test is
3/5. If the first ball out was black, then the probability of a red one
to be out in the second test becomes 3/4. It is an example of tests, which
are not independent: outcome of every next test depends on the
outcomes of the previous tests!
Now imagine a box containing thousands of balls, having 22 different
colors (there are 22 characters in the Hebrew alphabet). It will be a model of a
text for which the probabilities are calculated. The picture becomes much more
complex, but its main features remain the same: if after each test the balls of
a certain color that got out, are rendered unavailable for he next test, the
tests are not independent, and the probabilities of various outcomes now form a
tangled web of multiple variations. Multiplying individual probabilities in this
case generates meaningless numbers as the probability of a combination of
outcomes is not a single valued quantity any more, but is different for each
possible sequence of results of the consecutive tests.
That is what happens in the code proponents' calculation. Indeed, the
values of Ni (numbers of times a given characters happens in the
text) are different for each character. (This is analogous to different numbers
of balls of each color, in the box.). Therefore, depending on the outcome of a
test number i, the number of sites accessible for character number (i+1)
decreases in each case by a different number Ni . Therefore
the probability of character number (i+1) to be encountered in the text varies
depending on which characters were preceding it. Hence, the code proponents
multiply probabilities, which are not independent! This is an elementary and
quite crude error. There is usually a warning against such an error in
introductory courses of Theory of Probabilities.
Let us reiterate our conclusion for this part. For each character the
frequency of its occurrence (the value of Ni ) in the text is
different. Hence the probability of each subsequent character to be encountered
in the text depends on the order in which the characters follow each other in
the specific word. In other words, the probabilities of different characters to
occur in a text, in sequences, which constitute various words, are not
independent. One of the basics of the theory of probability is that
multiplying probabilities, which are interdependent, without first recalculating
them, is meaningless. (The Probability theory has certain ways to handle the
situation with interdependent probabilities. It is usually handled as the
so called "conditional probabilities". Another way to cope with the problem of
interdependent probabilities is to use Theory of Games. However, the simple
multiplication of initial probabilities is a wrong way to go).
Having multiplied probabilities, which are not independent, the code
proponents continue their manipulation of numbers, which at this stage of their
calculation have already lost any meaning. Their next step is multiplying
Pw (see its definition above) by the number N1 of
occurrences of character x1 in the text. This way they supposedly
calculate the average probability PA of finding the word in question
in the entire text, that ELS having an arbitrarily chosen particular skip.
In the next step the code proponents multiply PA by the
number z of skips they wish to explore (on different occasions they chose
different z between 2 and 1000).
Now let us recall our conclusion that different words tend to form
ELS with different lengths of skips. We had established earlier in this article
that some words in a given text are more likely to form ELS with
shorter skips (in our example those words were play and grain)
while some other are more likely to have longer skips (in our example it was
word grapple). Therefore simply multiplying PA by the number
of skips z means one more averaging, this time again without
accounting for the actual distribution of ELS over skip lengths (which of course
is not known).
The last step of the "simple" calculation is multiplying the number
calculated so far, by 2, since ELS can be read both from left to right and from
right to left.
Once more, this operation would be valid only if the text in question
were a chaotic conglomerate of characters. Actually it is a highly organized
meaningful text. In such texts the probabilities of a certain sequence of
letters to happen when reading from right to left is different from that when
reading from left to right. Here is a simple example: in any meaningful English
text, if read normally, from left to right, the sequence the will be met
very often. When reading from right to left, the same sequence would be quite
rare. In other words, by multiplying their number by 2, one more implicit
averaging is performed, again without accounting for the actual
distribution of the ELS, this time over the direction of reading.
Thus they arrive at a number which, the code proponents
say, is the alleged total probability to find the word in question in the text
in question, as ELS with skips ranging from 2 to z.
Besides the use of uncertain average values, piled upon each other at
least three times, and besides the most egregious error of multiplying the
interdependent probabilities, the above calculation also ignores some other
factors. For example, it ignores the edge effect (which is the
limitations on the possible skip values for sites that are close to both the end
and the beginning of the text). It ignores different frequencies of occurrences
of different characters = pairs or
characters = triplets, etc.
The inevitable conclusion is that the values of probabilities often
suggested by the code proponents are meaningless numbers. Generally speaking,
they are, as a rule, grossly below the actual probabilities of various ELS to
appear in the text of the Bible.
About WRR's formula for calculation of the expected number of ELS
(Added on December 6, 1998)
As I have mentioned,
I found WRR's calculation of the expected number of ELS to be flawed, but not
substantially affecting their final result. I did not though elaborate as
such an elaboration must necessarily involve certain concepts of mathematical
statistics not commonly familiar to laymen. I have received though some
e-mail messages whose senders requested an explanation what was WRR's error that
I had in mind. Therefore I am adding now this Appendix 2, to elaborate on my
assertion, with a warning that its understanding requires some, at least a
minimal one, background in mathematical statistics.
In their paper WRR wrote (I am quoting): "This expected number
equals the product of the relative frequencies (within Genesis) of the letters
constituting w multiplied by the total number of all equidistant letter
sequences with 2<=d<=D."
This statement means WRR assumed the numbers of letters in the tested
text to be independent variables, because in sufficiently long texts the
relative frequencies of letters actually equal the probabilities of encountering
a specific letter at a site in the text, and probabilities can be legitimately
multiplied only if they are independent. WRR's assumption would be
correct only for a perfectly random conglomerate of letters but it was wrong for
a meaningful text and it was equally wrong for any permutation of that
meaningful text. In the meaningful text and in all of its permutations
the letters are not independent since the stock of letters available to fill a
site is limited to the factual letter set of the text (in the case of Genesis
this set comprises 78064 letters). As soon as a specific letter
x has been used to fill a site, the stock of available letters loses
that x. This situation meets the condition of what is called in
Math. Statistics "test without replacement," and the pertinent distribution of
letters in this case is hypergeometric. WRR have implicitly used instead a
multinomial distribution which pertains to a case of "tests with
replacement." Their approach was principally wrong. However, the
quantitative difference between the results obtained using the correct,
hypergeometric distribution and those obtained using the faulty, multinomial
distribution, in the case in point would be very small. One of the reasons
for that is that the words' lengths are very small as compared with the total
text's length. One more reason making WRR's error practically inconsequential is
that their choice of the number of ELS to be 10 was completely arbitrary, and
therefore if their faulty calculation led actually to a number different from 10
they chose, for example making it 11 or 9, it would hardly matter for the
further treatment by WRR. I made my
comment in order to dispute the assertion that, first, no scientists have
found any errors in WRR's work, and, second, to show that an argument making use
of WRR's reputation is irrelevant, as neither Rips, nor Witztum nor Rosenberg is
an expert in mathematical statistics. (Neither am I, but noticing the described
faulty assumption by WRR did no require one to be a real expert in math.
statistics, as the error was both obvious and elementary).
After the first version of this article had been
posted on the Internet, I received several replies. Some of them supported my
conclusions, while some other opposed them. Notably, the negative responses came
mainly from people who claimed to have religious faith. (It does not mean
that all the positive responses came only from atheists or agnostics). One of
those religious respondents asserted that she is a believer because there
are so many codes in the Bible obviously inserted there by God.
In my view, religious people have no more reason to believe that God
inserted the codes into the Bible, than the atheists or agnostics have, and may
be even less. Indeed, anybody who, like Rambsel, Jeffrey, Cramer & Eldridge,
etc, believes that God had deliberately created the codes in question, actually
believes in a very strange God. God, who, as they are supposed to believe, gave
Moses the commandments, who created galaxies, supernovas, black holes, quarks,
neutrinos, etc, who is omnipresent, omnipotent, and perfect in every sense of
the word, this God, if we believe Rambsel's attribution of "codes" to him, has not even mastered the grammar
of Hebrew! Rambsel's and Jeffrey's
"God" appears to be rather tongue-tied, and even
half-witted, as all this strange "God" managed to produce was a number of
ambiguous phrases with obscure meaning, allegedly encoded in a manner
much less sophisticated than a variety of human-generated ciphers and
Comments are welcome ( firstname.lastname@example.org)
M. Perakhís personal page: http://members.cox.net/marperak/
The readers who wish to explore the alleged "code" in the Bible
themselves may order a computer program for that purpose, for example at http://members.xoom.com/codefinder/index.htm. I have not tested these programs myself and therefore cannot provide a
judgement as to their quality, but at the above site there are posted comments
of some people who had tried the programs in question.
Originally posted to Mark Perakh's B-Codes page.