This article demonstrates an extraordinary convergence of words related to the Jewish New Year, Rosh Hashana, hidden in the Hebrew translation of War and Peace. Using methods inspired by Doron Witztum, we calculate an astonishing significance level of one in a billion.

## Summary

This experiment is a parody of the experiments presented by Doron Witztum and others. Although those experiments are presented as serious science, we don't believe they are. We offer this example just to show that we can do it, too. The data and the calculations are correct, and the pictures are genuine. In fact, everything that can be verified is correct. The story of how we decided what data to present and how to analyse it is another matter. We will merely express our belief that our story is no less true than those of Doron Witztum, and that our experiment is no more ridiculous.

While our previous demonstration experiments have been primarily produced by careful data selection, this one was produced mainly by playing with the mathematics of the anaylsis method. Our inspiration was the "Seal of God" experiment of Doron Witztum, whose apparent significance is almost entirely due to an analysis method which is mathematical gibberish. As before, our point is "we can do it too".

## The Rules

This experiment demonstrates a new kind of ELS phenomenon. We will take a natural collection of words all related to the same theme, and find that their average closeness to each other as ELS's in War and Peace is remarkably small. The rules of our experiment were as follows:
1. The text will be the first 78064 letters of the Hebrew translation of War and Peace, exactly as used as a control text in [WRR1].
2. The distance function c(w,w') defined by Witztum, Rips, and Rosenberg [WRR1-3] will be used to measure the closeness of two words. WRR's aggregate statistic P2 will be used to measure the overall closeness of sets of word pairs.
3. The spelling rules called ktiv dikduki, determined in [WRR1] to be the correct rules, will be used.
4. Following the frequent example of Doron Witztum, we will consider words both with and without the definite article. However, unlike Wiztzum, who sometimes places articles where they are rarely used (such as in HaChanukah), we will use an objective test to eliminate them. We will count the number of times a word or phrase appears in the Responsa database, with and without the definite article. If one of the two forms appears more than 10 times as often as the other, we will drop the rarer form.
5. The significance level will gauge the overall closeness of all the words to each other. Since this idea has not been used by WRR to our knowledge, we must devise a new method of analysis. Our choice has similar mathematical soundness to several methods used by Doron Witztum, and is described in detail below.

## Collecting the data

According to the rules in [WRR1-3], we reject all words that are less than 5 letters long or more than 8 letters long.

Our experiment on Rosh Hashana must, of course, include the phrase "Rosh Hashana", and the other common names by which the Jewish New Year is known. Refering to Rabbi Joseph Grossman's book Otzar Erchei Hayahadut (Jerusalem, 1990), and adding articles in legal places, we find these names: , , , , , , , and .

Above we listed all the forms with 5-8 letters having the definite article in legal places. However, some of those uses of articles are very rare and our rules require us to remove them. Accordingly, we remove , which appears in Responsa hundreds of times less often than does . We also remove , which doesn't appear in Responsa at all, and , which appears 15 times less often than the form with a definite article. (The latter form is too long for inclusion.) For the additional words we list below, this test does not eliminate any of the legal article usages.

The essential mitzvah [commandment to Jews] of Rosh Hashana is to hear the sounding of the shofar. A shofar is a trumpet usually made from a ram's horn (though our picture shows one made from an antelope horn). The spelling of "shofar" without the definite article is too short, so we can only use , in accordance with the rules. The shofar can be sounded in three manners, called Shevarim (, ), Tekiah (, ), and Teruah (, ).

The prayers of Rosh Hashana include three special blessings which have existed for at least 2000 years. After they are said, the shofar is blown. The names of the blessings are Malchiot (, ), Zichronot (, ), and Shofrot (, ).

In summary, we have 18 of the most important words and phrases associated with the holiday of Rosh Hashana. Further information on these words can be found in Aish HaTorah's introduction to Rosh Hashana.

## The Significance Level

As far as we are aware, none of the many analysis methods used by Doron Witztum can be used to analyse all pairs of words in a sample. This forces us to invent a new method of analysis. Our method will be as mathematically valid as some of Witztum's methods.

From our 18 words, we can form 153 pairs of words.

We start by making a large table of distances, with 153 rows and 100 columns. There is one row for each word pair. In the first column, we put the distance for each word pair in War and Peace. To form each of the remaining 99 columns, we do exactly the same thing except that first we randomly permute the letters of each of the 18 words. In each case, the distances are defined according to the method defined by Witztum, Rips and Rosenberg [WRR1].

Let us call this table T, and denote by T[i,j] the value in the i-th row and j-th column. We know that T[i,1] is the true distance for the i-th word-pair, and T[i,j] (for j not equal to 1) is a randomised version of the same distance.

WRR's statistic P2 takes a collection of distances and turns them into a single number. Using the 153 distances in the first column of T gives us the "true" P2 value, which is approximately 0.0000006. To see how unlikely such a small value is, we take another 153 distances from T by choosing one distance at random from each row. Those 153 new distances give a "randomised" P2 value, which we compare to the "true" P2 value. Then we do the same again for another randomly chosen 153 distances, and so on many times. We regard the "true" P2 value to be remarkably small if very few of the randomised P2 values are smaller.

## The results

We compared the true P2 value against one million randomised P2 values, and found that the true P2 value was the best (i.e. the smallest). Then we tried one billion randomised P2 values and still the true P2 value was the best. Finally, we tried 10 billion randomised P2 values, and only then started to see some better than the true P2 value.

The significance level is estimated to be 10 in 10,000,000,000 !!

By way of comparison, exactly the same experiment using the Book of Genesis produced the completely uninteresting result of 139 in 1000.

## References

[WRR1]
D. Witztum, E. Rips and Y. Rosenberg, Equidistant Letter Sequences in the Book of Genesis, Statistical Science, 9 (1994) 429-438.
[WRR2]
ibid, Equidistant Letter Sequences in the Book of Genesis, II. The relation to the text, preprint ca 1995.
[WRR3]
ibid, Hidden Codes in Equidistant Letter Sequences in the Book of Genesis, The Statistical Significance of the Phenomenon, Hebrew preprint accompanying a lecture given by E. Rips in the Israeli Academy of Sciences, 1996.

## Some pictures

The statistical analysis above does not rely on pictorial evidence, but on the complex calculations designed by Witztum and Rips. Nevertheless, our data of course contains some remarkable geometric convergences. Here we present two of them.

## Technical comment

The reader should note that we only promised an analysis method as good as Doron Witztum's. This is a particularly easy criterion to meet, as some of Witztum's methods are mathematically absurd. Nevertheless, the flaws are quite subtle, and have to do with stochastic dependencies between some of the distances. The same flaw, to a lesser extent, effects the famous rabbis experiment. A much worse flaw, our inspiration, appears in Witztum's "Seal of God" experiment.

## Notes

1. The phenomenon in War and Peace demonstrated on this page was discovered by a person whose name has not been publically mentioned in relation to codes. He/She wishes to remain anonymous. Brendan McKay performed all the computations and produced the text on this page, with much help from his friends.
2. We have been asked what the effect was of our decision to remove the words that use the definite article in a rare manner. The answer is that the result rises to 83/billion, or about 1 in 12 million. In other words, the result is still very strong, but naturally weakened by the use of less satisfactory data.