In 1994, Doron Witztum, Eliyahu Rips, and Yoav Rosenberg published a study in the peer-reviewed mathematical journal Statistical Science titled "Equidistant Letter Sequences in the Book of Genesis". The authors argued that conceptually related words can be found encoded closer together in the Torah than would be expected by chance. This argument was supported by an experiment, and a below is a brief summary of their experiment as they present it in their paper.

1. The authors selected all 32 rabbis contained in the Encyclopedia of Great Men in Israel who had entries containing between 1.5 and 3 columns of text.
2. Shlomo Havlin compiled the appellations for each of these rabbis (that is, the various names and spellings used to refer to these rabbis).
3. The authors measured the closeness of the appellations to the birth or death dates of each of these rabbis using four different methods: P1, P2, P3, and P4. Each of these methods returned a value, and each of these values were compared with the values returned for 1,000,000 randomly shuffled lists of rabbis and dates.
4. The P4 rank had the highest rank of 4/1,000,000. This rank was multiplied by the number of tests run to reach a final probability of 16/1,000,000. In other words, the probability that the result occurred by chance is 1 in 62,500.

In 1999, Brendan McKay, Dror Bar-Natan, Maya Bar-Hillel, and Gil Kalai presented the results of a thorough analysis of the study of Witztum et al (1994). In their paper titled "Solving the Bible Code Puzzle" and published in Statistical Science, the authors concluded that the experiment is "fatally defective, indeed that their result merely reflects on the choices made in designing their experiment and collecting data for it." The authors presented a considerable amount of evidence to support this view, including (but not limited to) the following.

1. The authors show that in early descriptions of the experiment, Witztum et al never claimed that the appellations were compiled independently by Shlomo Havlin.
2. By replacing some of the appellations used by Witztum et al with other equally valid appellations, McKay et al were able to find hidden codes in the Hebrew translation of War and Peace.
3. The authors show that Witztum et al tended to choose options more favorable to their results when a choice was available. The same was found in numerous other experiments by Witztum et al, such as their 70 nations experiment.
4. The P2 value, a measurement used by Witztum et al, was closer to each other for the two lists of rabbis than what would be expected by chance. Having them close together makes it appear that the results are consistent. However, McKay et al found that when shuffling the two lists of rabbis together and splitting them in half, the results were only equal around 1% of the time. The same analysis was performed on the rabbis in Gans' cities experiment and found similar results.
5. McKay et al conducted several of their own independent studies using data collected by specialist Simcha Emanuel and found no traces of hidden codes in Genesis.

In short, McKay et al have demonstrated that Witztum et al were indeed correct that their their result did not occur by chance. Yet they were incorrect in attributing this result to remarkable properties in Genesis; rather, the result was caused by inappropriate manipulation of the experiment's data and design.

These findings, as well as subsequent findings that undermine the reliability of Witztum et al's results are discussed later in this index.
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After some aspects of the great rabbis experiment of Witztum et al were criticized, Witztum et al presented a new experiment which they claimed could not have been biased as the original experiment could have been. This new experiment appeared to show a tendency for the Seventy Nations of Humanity (according to Jewish tradition) to be encoded close to the actual names of these nations in Genesis chapter 10. Below is a brief summary of this experiment, as it is described in their paper.

1. The authors selected the names of the seventy descendents of Noah listed in Genesis chapter 10. According to Jewish tradition, these individuals are the ancestors of the Seventy Nations of Humanity.
2. The authors added the prefixes "the nation of," "the country of," "the language of," and "the script of" to each of these nations. In some cases, the original name of the nation was replaced with a more recent name derived from another Jewish source.
3. The authors used a method to compare the closeness of each ELS of a nation's name with an added prefix to the actual text mentioning the nation's name in Genesis 10.
4. The authors found that the ELS's of each nation with a prefix added tended to be closer to the nation's name in Genesis 10 than would be expected by chance. They concluded that the probability that the result was obtained by chance was 0.000000004.

After studying this experiment, Bar-Natan, McKay, and Sternberg demonstrated that like the original great rabbis experiment, the remarkable results of the Nations experiment were caused by choices made in conducting the experiment. That is, despite the claims of the experimenters that the experiment had little to no room for tuning, the analysis of Bar-Natan et al unambiguously demonstrates that room for tuning the results was available and was used. In short, below is a list of the evidence presented by Bar-Natan et al:

1. To support their choice of prefixes, Witztum et al cite the Vilna Gaon's commentary on Job in which he lists the four characteristics that define nations: name, country, dialect, and script. However, instead of using the Hebrew word for dialect Witztum et al actually used a different Hebrew word that translates as language. They also used the Hebrew world for nation as a prefix instead of the Hebrew word for name. Correcting these errors make the results considerably less remarkable.
2. In his commentary on Isaiah, the Vilna Gaon lists different characterists of nations than he does in his commentary on Job. Yet if these characteristics are used as prefixes the results are much less remarkable.
3. The prefix "the people of" was added some nations and not others. Yet there are several equally valid ways to spell "the people of," and the spelling used by Witztum et al achieves the most remarkable results.
4. At least 136 reasonable prefixes exist, but the three that perform the best are among the four Witztum et al chose to use.
5. By modifying the experiment using alternate prefixes, Bar-Natan et al achieved remarkable results in the Hebrew text of War and Peace and mundane results in Genesis. (As evidenced below, this does not take advantage of the full flexibility available in the experiment.)
6. After Bar-Natan et al fixed several grammatical errors, the results became much less remarkable in Genesis.
7. Many arbitrary choices were made in the decision process of replacing the names of nations. When almost any other equally valid choices were made in this decision process, the result were weakened.
8. Witztum et al used the edition of Targum Yonatan by Ginsburger to update the names of the nations. Yet among the many different editions of Targum Yonatan, the Ginsburger edition is one of the poorer ones. When other editions were used, the results became much less impressive.

The items above are an incomplete summary of the findings by Bar-Natan et al. Perhaps the most appropriate way to conclude their findings is by quoting a caption from the paper:

"King Midas of Phrygia ... Helenic tradition tells us that anything that King Midas touched turned into gold ... Do Witztum, Rips, and Rosenberg have similar powers over significance levels?"

Doron Witztum, Eliyahu Rips, and Shlomo Havlin have claimed that Havlin compiled the appellations independently, and that Witztum and Rips used this data without making any changes. The available historical evidence does not support this conclusion, however:

1. In the 1986 and 1987 preprints of the Great Rabbis experiments, Shlomo Havlin is thanked for "valuable advices," and there is no claim that he compiled the appellations independently. The same is true for Witztum's 1989 book.
2. In 1985 Eliyahu Rips described the appellation collection process of a similar experiment as using "every possible variation we could think of ... If any additional variation comes to mind, we must include it. We simply took every possible variant that we considered reasonable."
3. Witztum and Havlin do not agree on who compiled the dates. Witztum has written that "Havlin's job was to prepare lists of names and appellations and nothing else ... I explicitly wrote that I amended the dates myself ..." Yet Havlin claims that he was responsible for the dates. Therefore, either Witztum or Havlin is making at least one false claim concerning the data collection.

Harold Gans has made the claim that the arguments of the skeptics imply an elaborate conspiracy:

As we shall see, if there is a conspiracy here the number of people necessarily involved in it will stretch the credulity of any reasonable person.

In this scenario, the conspiracy has grown to include Witztum, Rips, Havlin, Rav Deutch, Rav Fisher, and Zvi Inbal, who provided the list of cities to Gans, as well as Gans and Bombach who verified the authenticity and accuracy of the protocol and list.

This claim is unfounded, however. Nowhere in the literature on the Torah Codes do the skeptics claim such a remarkable conspiracy. There are far more plausible explanations for the outcome of the Torah Codes experiments than such a conspiracy.

Most likely, Witztum consulted with Havlin for "valuable advices" during the preparation of the lists for the Great Rabbis experiment, and that Havlin only later repeated Witztum's claim that Havlin prepared the lists independently to avoid destroying Witztum's credibility (and hence the experiments).

Gans' Cities experiment does not indicate the existence of an elaborate conspiracy either. Upon Gans' request, Zvi Inbal produced a list of guidelines that he claims he used to obtain the data for the Cities experiment. Many people agreed that these guidelines made historical and linguistic sense, and were specific enough to reproduce the same data. Therefore, argues Gans, if the skeptics are correct that the data was manipulated, all these people must be involved in a conspiracy. A more likely explanation, however, is that the rules do make historical and linguistic sense, but that they are arbitrary. In other words, when two equally valid choices were available, the choice that improved the result was selected.

This reduces the necessary people involved in the "conspiracy" to Doron Witztum and Zvi Inbal. (And, most likely, a few other individuals are withholding information, presumably with good intentions. This, however, does not constitute a conspiracy.)
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