This is a copy of an article that Doron Witztum published as a PDF file. The Hebrew has been transliterated using the Michigan-Clairmont encoding scheme. No claims of accuracy are made.
A reply to this article is available.
This is a response to an article "Astounding Discoveries in War and Peace", published on the internet in May '97. Did They Really Find Codes in War and Peace? FULL VERSION Doron Witztum, '97 SUMMARY Recently on Channel One Television in Israel, on the show "Popolitika", as well as in other places, psychologist Professor Maya Bar Hillel claimed that she and her colleagues found "hidden codes" in the Hebrew translation of Tolstoy's War and Peace. They claim that this finding is the same type of code that is found by code researchers in the Torah. The first example they brought was on the subject of Chanukah. There is a fundamental difference between the serious scientific research that has been done on codes in the Torah, and the "War and Peace" example presented by this group. It is possible to distinguish between them like distinguishing counterfeit money from the real thing. INTRODUCTION Scientific research into ELSs (Equidistant Letter Sequences) in the book of Genesis has been proceeding for some twelve years. The researchers have focused on two phenomena: 1. The close proximity of one minimal ELS to another, where there is a conceptual relationship between them (e.g., an ELS of "hammer" near an ELS of "anvil"). 2. The close proximity of a minimal ELS to a conceptually related expression in the text, as it is read consecutively (e.g., an ELS of "hammer" near the appearance of "anvil" in the text as a string of consecutive letters). Please note that the researchers do not measure the probability for the appearance of any individual expression as an ELS. Rather, given two expressions appearing as ELSs, we measure whether their proximity is closer than may be expected to occur by chance. METHODOLOGY After defining the phenomena to be investigated, the researchers then determined a rigorous method to measure the level of success: determining what was to be considered "in close proximity" and what was not. After establishing this methodology, the researchers were now able to conduct experiments to investigate the phenomena; to check if the proximities of such ELSs occur much more frequently in the text of Genesis than would be expected to by chance. An "experiment" in this instance means examining the proximities between paired words of a specified set. For every "topic" there is a pool of expressions which are conceptually related. These can be represented schematically in the form of a pyramid: At the top of the pyramid are just a relatively small number of the most important words and expressions: These comprise the top of the hierarchy. As one descends the hierarchy, there are many more expressions related to the topic. A method must be found to select appropriate pairs of expressions upon which to carry out the experiments. This must be done in such a way that the set of expressions will be an objectively "closed sample." This can be accomplished in two ways: A. If the expressions chosen are those at the top of the hierarchy. This is feasible only with regard to those topics or subtopics where it is clear which expressions deserve to be at the top of the hierarchy. B. If the expressions are not those at the top of the hierarchy, then one can make use of an objective outside source (even, for example, an encyclopedia or an impartial expert) to determine the sample. Of course, this could be done for option A as well. Experiments Conducted Ten samples of word pairs, selected according to the methodology outlined above, have been described thus far in scientific papers, and have been used as the basis for experiments: Two of these samples are described in the paper, "Equidistant Letter Sequences in the Book of Genesis," by Doron Witztum, Eliyahu Rips and Yoav Rosenberg, published in Statistical Science (1994). A third sample is described in a paper by Harold Gans: "Coincidence of Equidistant Letter Sequence Pairs in the Book of Genesis." (preprint) Three further samples are described in another article by Doron Witztum, Eliyahu Rips and Yoav Rosenberg: "Equidistant Letter Sequences in the Book of Genesis II: The Relationship to the Text", (regarding proximities of ELSs with expressions found in the consecutive text). Four additional samples are described by these same authors in the article, "A Hidden Code in the Book of Genesis: The Statistical Significance of the Phenomenon" (Hebrew), which was presented as a guest lecture before the Israeli National Academy of the Sciences on Mar. 19, '96. In 8 out of 10 of these experiments the results were statistically significant in the extreme. Of the remaining two, one gave results which were statistically significant, and one was recorded as a failure. Additional samples, prepared under the same guidelines, served as the basis for other similar experiments, the details of which will be described in full in Doron Witztum's forthcoming book. A few partial examples from this collection are presented publicly in lectures given by, among others, "Arachim" and Aish HaTorah. The results of these experiments indicate that the convergences between the ELSs themselves, as well as between the ELSs and the text are not chance occurrences. A CASE STUDY- THE HOLIDAY OF CHANUKAH I will describe here a brief experiment that was carried out on the topic of "Chanukah." This topic can be spelled in one of two ways in Hebrew: "XNKH" or "XNWKH". Furthermore, each of these spellings can be written with or without the prefix "H" (the definite article): "HXNKH" and "HXNWKH". The source for spelling "XNWKH" appears, for example, in the legal work which is considered the final authority in our day, the Mishna Brurah, (670:1): WYMYM )RW HW HNQR)YM XNWKH, RWCH LWMR: XNW K"H, $BYWM K"H XNW M)WYBYHM "And these days are called Chanukah, that is they rested ("Chanu") 25th ("k"h", the 25th), since on the 25th (of Kislev) they rested from their enemies" I used precisely the language which appears in this source. In the first stage I searched for proximities of XNW (they rested) and M)WYBYHM (from their enemies). The proximity of these ELSs was significant. I then marked the minimal ELS of the word XNW which participated in this convergence, and checked whether it was also convergent with the phrase $BYWM K"H (since on the 25th). I also checked whether it was proximal to the words XNWKH and HXNWKH. Investigation showed that each of these four convergences was significant, and the combined probability of occurring by chance is about one in a thousand. It also became clear from this experiment that the form HXNWKH was by far the most successful, so I chose to use it for the continuation of the experiment. In the second stage I decided to use an expression taken from the very top of the hierarchy of expressions related to Chanukah. The first expression which came to mind was the name of Judah the Maccabee, of the Hasmonean family. For example, in the Encyclopedia Hebraica, under the entry for "Chanukah", he is the only member of the Jewish forces mentioned as the hero (as YHWDH HMKBY and as YHWDH HX$MWN)Y; Judah the Maccabee and Judah the Hasmonean). He is mentioned there not only as the chief military leader, leading the victory over the Greeks, but also as the one responsible for establishing the holiday of Chanukah. Not only are his name and appellations mentioned in the encyclopedia, they are on the lips of every Israeli toddler. Using his name and appelations from this entry in the Encyclopedia Hebraica, I listed all of the possibilities for his appellations: 1. Judah the Hasmonean - YHWDH HX$MWN)Y 2. Hasmonean - X$MWN)Y 3. The Hasmonean - HX$MWN)Y 4. Judah the Maccabee - YHWDH HMKBY 5. Maccabee - MKBY 6. The Maccabee - HMKBY 7. Judah- YHWDH Of this list, only the following occur as ELS's in the text of Genesis: 1. Hasmonean - X$MWN)Y 2. Maccabee - MKBY 3. The Maccabee - HMKBY 4. Judah - YHWDH The name YHWDH is exceptional in this sample in that it is a common Jewish first name. If you were to mention the name "Yehudah" on a Jewish street, no one would have the faintest idea that you were referring to the star of the Chanukah story. This is not the case with the other appellations. We decided therefore to investigate the three word pairs: 1. HXNWKH - X$MWN)Y 2. HXNWKH - MKBY 3. HXNWKH - HMKBY THE RESULTS An experiment was performed searching for ELSs of these pairs. The combined probability for these three pairs (as calculated according to the procedures described in the above articles) is 1/700,000. It is important to emphasize that the decision whether or not to utilize the word YHWDH was not a difficult one. There are, after all, only two choices. The critical reader is at liberty to double the probability to 1 in 350,000. "CHANUKAH CODES" IN WAR AND PEACE Research into hidden codes in Genesis has attracted the attention of two different groups of people, who have consequently become involved in the field. There are those who want to make money and/or to promote their own interests through the codes. This group is uninterested in the credibility or the scientific basis of the phenomenon. There is a second group, who would like to undermine the credibility of the phenomenon. This group is opposed to it for reasons of their own, not the least of which are ideological. The common denominator between the two groups is that they make the exact same mistakes, using flawed and misleading examples when it suits their purposes. This is similar to counterfeiting-- some people counterfeit money simply to make money. Others do it (e.g. in times of war) to undermine confidence in the enemy's currency. For example: In May 1997 it was publicized through the Internet that amazing codes had been "discovered" in the book War and Peace. The authors of the document, who signed their names as codes in the segment of War and Peace which accompanied their report, were Professor Brendan McKay of the Australian National University, Dr. Dror Bar Natan from the Hebrew University of Jerusalem, Alec Gindis and Aryeh Levitan of Jerusalem. This is the group that Professor Maya Bar Hillel works with as well. These authors report that they examined a text of 78,064 letters (the same length as Genesis), taken from the Hebrew translation of War and Peace (from the beginning of the book). They investigated how the topic of Chanukah appears in this text. By their account, they discovered that in one section of the text no less than 59 expressions related to Chanukah appear, each one of which is the minimal appearance of the word in the entire text, or else it appears in consecutive letters. The authors claim that they calculated the probability of this occurring by chance and discovered that it came to less than 0.0000000000000000000000001. In the document which they publicized, the authors try to create the impression that what they are presenting is similar to the codes which have been discovered in the book of Genesis. (See the internet site at http://www.math.gatech.edu/~jkatz/religions/numerics/chanukah.html). The truth is that there is an enormous difference between this attempt and the genuine discoveries which have been made. Let us consider the following analogy: Imagine that a certain bomb manufacturer, the "Alpha Company," is trying to persuade a Congressional subcommittee that the U.S. army should be supplied with bombs of their making. The company's scientists claim that they have developed "smart" bombs, which are incomparably more accurate than any other bomb. However, they themselves admit that not every "smart" bomb strikes exactly on target: Mainly because the guidance system still does not take into consideration every single factor affecting the trajectory (because the factors are numerous and complicated). Yet, the developers of the bomb assert that tests have shown that the accuracy of these "smart" bombs is much greater than would be expected without a guidance system. They provide the members of the subcommittee with photographs and diagrams documenting their tests. On these photographs and diagrams one sees impressive strikes on or near the target, and all within a 10 metre radius of the target. The chairperson of the subcommittee consults with the neutral experts whom he has invited to attend the meeting. They agree that the strikes seem to have been extremely accurate. However, they note that one important piece of data is lacking: How many bombs struck outside the target area? "That's a very good question," comments the chairman to the scientists of "Alpha," "What do you have to answer?" They explain that the bombs were manufactured under the supervision of the governmental agency in charge of military testing, an objective institution, who can verify just how many bombs were supplied for each test, how many of them struck within 10 metres of the target, and how many landed outside the target area. And indeed, the documentation which has been made available is sufficient for the experts to make their own calculations and to see for themselves just how impressive the test results are. At this point, lobbyists from the other bomb manufacturers try to intervene. They claim that ordinary bombs can achieve just as good results. To prove their claim they present a document reporting tests which were run using ordinary bombs. They lay before the members of the subcommittee a large photograph with an accompdiagram on which many strikes have been indicated. "Here!" say the lobbyists for the ordinary bomb makers, "You see that the ordinary bombs were no less accurate than the "smart" bombs! There are no less than 59 bombs that landed near the target!" The members of the subcommittee examine the photographs and the accompanying diagram, and compare them with the documents presented by the manufacturers of the "smart" bomb. They notice immediately that there is a big difference between the two presentations: In the tests done by "Alpha" the strikes were within a 10 meter radius of the target. On the other hand, the documents of the other lobby cover a much larger area, with a radius of a 1000 meters, in which there are a number of individual targets, but the strikes are not particularly close to these targets. The members of the subcommittee request one additional piece of critical information: How many bombs struck outside of the target area? The lobbyists hem and haw, and reply that they do not have that information. "If so," says the chairman of the subcommittee, "What claim do you have at all? - Of course when you have such a large target area some of the bombs are going to fall inside of it! The comparison you have made is nothing but a fraud!" As we have seen above, the researchers working on the hidden codes in the book of Genesis have proceeded like the scientists of the "Alpha Company." The number of expressions in the experiment, corresponds to the number of "bombs" in our analogy. The parallel to having the bombs manufactured under objective supervision consists of choosing a set of word pairs which forms an objectively closed sample. We have already discussed the ways in which this can be accomplished. We now proceed to the regular "bombs" manufactured by the competition. A. HUGE AREA OF THE TARGET Dr. McKay et.al. proceeded in the same manner as the "lobbyists" of our analogy. In contrast to the compactness of the proximities which we presented relating to the topic of "Chanukah", McKay et al. used an enormous array consisting of 14,719 letters, which comprises about 20% of the entire text! Of course, it is only to be expected that about 20% of the expressions tested for should land within such an enormous area. B. LAXNESS IN THE LIST OF EXPRESSIONS A close examination of the list of expressions which these researchers report having found reveals certain peculiarities. (We will use the following convention: We will rank the ELS's of a particular expression according to the size of the skips between letters. The ELS with the shortest skip in the entire text will be termed the "most minimum." The next smallest ELS will be called the "second most minimum" and the one after - the "third most minimum," etc.): 1. McKay et al.'s claim to have found 41 different expressions, each at its most minimal appearance or as consecutive letters. Some of these appear more than once, yielding 59 total hits. 2. The word list they supply in English. When one tries to deduce what words they correspond to in the Hebrew text, one runs into difficulties, as we discovered when we tried to replicate their experiment. For example: * They list the expression "Greek army." The Hebrew equivalent, CB) YWNY, does not appear in the target segment. They seem to have had in mind the expression CB) YWN, which does appear in its most minimum form in the segment. * The expression "Hashmonai," which is written in Hebrew X$MWN)Y, does not appear in the segment at all. * "Modiin" is written MWDY(YN in Hebrew. This word does not appear in the segment. We thought perhaps they had used the nonstandard spelling, MWDY(YM, but this form also does not appear in the segment. * "Pure oil" (as it relates to the topic of "Chanukah") translates as $MN +HWR. This expression does not appear in the segment. * "Maccabees" is written in Hebrew MKBYM. The minimum of MKBYM does not appear here. This expression appears in the segment only in its eighth most minimum form! After additional investigation, we guessed that they were referring to the expression HMKBYM (the Maccabees), with the definite article. And indeed, the minimum form of this word does appear. * "Praise" is the translation of the word HLL. This short word appears in its most minimum form 76 times in the text, 14 of which are in this segment, just as one would expect to occur by chance. Therefore we thought that perhaps they had in mind the expression HHLL (the praise) with the definite article. However, this form appears 6 times in the text, only one of which is in this segment. * Of course, the most fundamental expression related to this topic is the word "Chanukah" itself. The minimum of XNKH does not appear here. We looked for the word XNKH in the segment, and it appears only in its seventh most minimum form. By now our experience had taught us to try adding the definite article, but written this way we found the word only in its 13th most minimum form! It then occurred to us that perhaps they were referring to an appearance of the word as XNKH consecutive letters in the text. And indeed, XNKH does appear in its consecutive form. If we spell the word "Chanukah" in its alternative form, XNWKH, we find that it does appear as a minimum. (The spelling XNWKH appears in the segment in its fifth most minimum form). "Chanukiya" is written in Hebrew either XNKYH or XNWKYH. Since on the table which they supplied it appears that they used both forms, we looked for both forms. XNWKYH appears only in its second most minimum form, as does the spelling XNKYH. With the addition of the definite article, HXNWKYH does indeed appear in its most minimum form, but HXNKYH only appears in its third most minimum form. * "Torah" appears in this segment only in its 15th most minimum form. As consecutive letters in the text only one of its three appearances landed in the target segment. With the definite article it appears only in its 13th most minimum form. * "Miracles" translates into NSYM in Hebrew. We were only able to find it in its seventh most minimum form. We thought that here too they had used the definite article, but NSYM only appears in its ninth most minimum form. We thought of looking for the word in its consecutive form, and indeed we did find one such appearance, but unfortunately it was outside of the target segment. Only afterwards, when we consulted their own table did we discover that they had spelled the word - "NYSYM" (the addition of the first "Y" is a convention to facilitate reading without diacritical marks)! * A "spinning top" is a SBYDWN in Hebrew. This word does not appear at all in the segment. It was later discovered that they had used the word "dreidel", which isn't even Hebrew, it's Yiddish! Let us summarize what we have learned in the preceding section: McKay et al. must have investigated at least the following possibilities for each of their 59 words: * The word as it is written in its "full" form, i.e. with the inclusion of the vowels "W" and "Y" * The word as it is written using it's vowelized spelling form ('ktiv dikduki'). * With the definite article ("H") * Without the definite article ("H") * Non-Hebrew forms of the word (e.g. "dreidel"). Each of these possibilities was searched for twice: once as an ELS and then again as consecutive letters in the text. In all, 10 different possibilities for each word. Even if their list really represented an a priori list of expressions relating to the topic of Chanukah (which we will soon see it does not), and even if there were only five different possibilities for each word instead of 10, we would still expect to receive result similar to the ones they observed purely as a result of chance, because the probability of hitting within such a large target area, comprising a fifth of the text, is of course one in five. Moreover, we have learned that the report which was publicized contained inaccuracies, and that some of the words reported are not to be found at all! THE REAL RESULTS In order to demonstrate just how critical the size of the target segment is, and just how critical it is to use a precise methodology for measuring proximites, we ran the following test. Our measurements were made using the methodology outlined in the above-mentioned papers. McKay et al. are familiar with it, and they know how to use it: We mentioned in section 2 that within the enormous area of the table used by the researchers there were two possible "targets" - the two occurrences of the main topic, "Chanukah." The spelling XNWKH appears as an ELS, and the spelling XNKH appears as consecutive letters in the text. If the associations are genuine, then the related words should converge around these two targets. We carried out two test "bombings," where the arsenal of "bombs" consisted of exactly the words the researchers had marked off on their table. In one test we "bombed" the word "XNWKH." The combined results were just what one would expect to happen by chance. In the second test we "bombed" the word "XNKH" with the same bombs. Once again the results were totally random. The proximities they show around the word XNKH or XNWKH, are expected to occur by chance on every other page of your local newspaper. C. FURTHER ERRORS By all rights, we could end our critique here. But if we examine the way they chose their expressions, we can see that the situation is even more grave: McKay et al. quoted translations from (primarily) three Hebrew sources. They indicated with bold face type the words which they considered to be the most important ones. One can see right away that they chose to mark off only a small selection of words. Among those which they have ignored are some of the most central ones related to Chanukah. For example the name Matthias (MTTYHW). Even more surprising is the fact that they did not even use all of the expressions which they themselves marked off! They seem to have "forgotten" the words: "priests", "king", "Greek kings", "High Priest", and others. On the other hand, among the list of words which they marked off in the segment of the text, there are more than 10 which are not marked in the sources. The explanation is simple: the expressions which they "forgot" are the ones which failed to show up in the target segment! But that is not all: The innocent reader is lead to believe that the expressions which they did find in the segment are the same as those which appear in the original Hebrew sources from which the word list was compiled. This is in fact not true. They retranslated the words back into Hebrew arbitrarily to fit the words found in the target segment! In one instance, they went even one step further. They actually changed an original text of the Talmud. Instead of the phrase "..and only found but one vessel of oil", they changed the source to read "..and they found but one small pure vessel of oil." Why the change? Very simple--they needed the expression 'pure vessel', because they knew that it appeared in their segment of the text! Naturally, we would like to believe that all of this happened as the result of innocent errors, but the document proby McKay et al. should at least serve as warning to all to be wary of charlatans. What is clear from our analysis is that one has to check any claimed results carefully: scientific analysis allows us to distinguish between what is real and what is counterfeit.