Chanukah candles in War and Peace



This article demonstrates an extraordinary convergence of words related to the Candles of Chanukah, hidden in the Hebrew translation of War and Peace. Using the methods established by Doron Witztum, we calculate a significance level of 1 in 4 million.


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 picture is 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.

Mr Witztum is fond of the following analogy: "What I show are genuine $100 notes, but the skeptics have only produced counterfeit $100 notes". On the contrary, what has been clear for a long time is that Mr Witztum can't produce any genuine $100 notes or even a particularly good fake. The real dialogue runs like this:

Please enjoy the following 100% genuine fake $19 note.

The Rules

The form of the experiment is that there are one or more central words and a list of related words. The experiment measures the degree of closeness of each of the related words to the central words. This structure is explained in detail in [WRR3], where it is called a "header sample set". 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 various experiments of Witztum, Rips, and others sometimes seek words as Equidistant Letter Sequences (ELSs) and sometimes as sequential words (strings of letters forwards or backwards in the text with no gap between them). Invariably those experiments "work" in the form they are presented and don't work in the other form. We will avoid this freedom of choice by seeking all words both as ELSs and as sequential words. We will also restrict ourselves further by admitting only those ELSs which are minimal in the whole of the text, not merely in part of the text as Witztum et al permit. These stronger rules were previously used by us in the informal experiment described in [Ch1], so we also have the virtue of consistency.
  3. The spelling rules of [WRR1-3] will be used. Where it is not possible to choose one spelling by these rules, we will use all reasonable possibilities. Articles and prepositions will not be used, because it has been demonstrated they lead to excessive freedom of choice. (Who can forget Witztum's concoctions like "for the Menorah" and "to Sadat"?)
  4. The distance measure of [WRR1] will be used when both words are represented by ELSs, except that to enforce Rule 2 only ELSs minimal in the whole of the text will be used. For measuring the distance between a sequential word and an ELS, the distance measure of [WRR2] will be used, again restricted to minimal ELSs only.
  5. The significance level will be computed according to the method given for "header sample sets" in [WRR3]. (An outline of the method is given below.) The statistic P2 will be used, as in [WRR2].

Collecting the data

As every Jewish child knows, the Chanukah candles are central to this Holiday of Lights, so choosing them as the central theme was a natural thing to do. On Chanukah, Jews are commanded to light one candle a day, though it is a custom to light more than one. Thus, we chose as our central words "Chanukah candle" in both its singular form and its plural form .

Note that is the correct spelling by Rule 3, as appears in the Tanach but does not.

We began our exploration of the candles of Chanukah by consulting the famous authority on Jewish law, the Shulchan Aruch, on the subject of lighting the Chanukah candle. In article 675 of the section Orech Chaim, we found the statement (the lighting fulfils the commandment), and so selected the words and . (The verb is a common word with no particular relevance to our subject.)

Before a candle is lit, the (blessing) is said. We selected that word also.

The candles are lit in a special lamp called a Chanukiya, which recalls the Menorah (Temple lamp) involved in the famous Miracle of Chanukah. Thus, we included both Chanukiya and Menorah. According to the spelling rules, we were forced to include two spellings of Menorah, and , as both are used in the Torah. In the case of Chanukiya, the word does not appear in the Masoretic Text at all, so the spelling rules do not select any single spelling. Therefore, we took the two spellings which appear in the standard Even-Shoshan dictionary, and .

In summary, we have the following:
Central words: ,
Related words: , , , , , , .

The Significance Level

According to Rule 2, we looked for each word as both a sequential string of letters and as a minimal ELS.

First, we considered our central words. Neither was found as a sequential word, and did not appear as an ELS either. We were left with as our only central word, to be investigated as an ELS. The singular form is quite appropriate, as "candle" appears in the singular in the blessing.

Second, of the related words only and appear sequentially. Words shorter than five letters are excluded from being tested as ELSs by the rules of [WRR1-3]. Thus, we are left with testing and as sequential words, and , , and as ELSs.

The method of calculation according to [WRR3] is to compute the P2 score from all the word pairs. This gives a single overall closeness score. Then the similar score is computed when the letters of each of the related words are permuted at random. For example, the related word can be permuted to , , and so on. However, since both positive and negative skips are used, and are regarded as the same. See [WRR3] for more details.

The result: 1 in 4 million

We conclude that this convergence does not appear in War and Peace by chance.

By way of comparison, exactly the same experiment performed in the Book of Genesis produces a result even worse than average: 964 in 1000.

Supporting evidence

After completing this experiment, we were amazed to discover some other very relevant expressions also appearing near . The minimal ELS of (miracle of God) passes right through the centre of . The of that expression is the second of (night), which appears with skip 1. Of course, night is the time when Jews are commanded to light a candle.

The theme of hidden supernatural codes is supported by the nearby appearance of the unique minimal ELS of (hidden code) just above the phrase (supernatural) in the plain text.

The name of the famous family central to the Chanukah story is also there in minimal skip, using the form (Hashmani) that appears in the well-known song that is sung on all eight days of Chanukah while the candles are burning, and a macabre reference to their victory over the Greek army appears in the expression (Greek blood).

In the text with skip 1 or -1, we also found (oil) and (miracle on the 25th). We also found the expression (in those days), which is part of the second blessing said on Chanukah.

Finally, the phrase (as the consequence of trust) in the surface text reflects the victory of this small group of people over their powerful enemy, which could not have been achieved without trusting in God.


Astounding Discoveries in War and Peace, (1997).
D. Witztum, E. Rips and Y. Rosenberg, Equidistant Letter Sequences in the Book of Genesis, Statistical Science, 9 (1994) 429-438.
ibid, Equidistant Letter Sequences in the Book of Genesis, II. The relation to the text, preprint ca 1995.
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.


Technical comments

The description of the method in [WRR3] has a missing detail. Since words are sought as ELSs with both positive and negative skip, a word and its reverse are basically the same. However, the distance measure is not precisely symmetric, and sometimes gives a different result for a word and its reverse. The rules in [WRR3] do not specify which to use in the case of words with their letters permuted. We have adopted the following rule consistently: if the unpermuted word comes before its reverse in Hebrew dictionary order, we use only permutations of it that come before their reverses. If the unpermuted word comes after its reverse, we use only permutations of it that come after their reverses.

The choice of rule matters quite a lot. Our first, less systematic, calculation produced a result of 1 in 14 million. It would be no problem at all to devise an alternative definition that appears just as objective as the one above but produces 1 in 14 million as the "correct" answer.

Another unsatisfactory aspect of [WRR3] is its practice of removing words that do not appear. For example, we removed the word because we were following [WRR3]. However, some permuted versions of it do appear. Removing the word entirely because of the nonappearance of its unpermuted version artifically separates the permuted from the unpermuted and violates the tenet that they should have equal footing. In other words, there is a mathematical error in [WRR3].

Correcting this error by not removing improves the result from 1 in 4 million to 1 in 6 million.

A pretty picture

The picture below shows the minimal ELS for and some of the other words we found nearby. All the ELSs have skip which is minimal over the entire text. The number of 100% minimal ELSs in this picture is twice as many as Doron Witztum ever showed in a picture this size.

Note: 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 checked the computations and produced the text on this page, with much help from his friends.

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