The Rips and Levitt cluster study
In 2006 Eliyahu Rips and Art Levitt published a cluster study built on the words of one newspaper's headlines about the attacks of September 11, 2001. We show it for one reason: the authors account for their choices in the open. It is a good case for learning how that accounting works.
What was done
Rips and Levitt set out to make a cluster experiment simple and explicit. Instead of choosing key words themselves, they took the nouns in the headlines of one Hebrew daily, Maariv, on September 12, 2001. They sorted them into groups: primary nouns printed large, proper nouns, secondary nouns and all others. They searched for tight clusters of equally spaced sequences of those words in the Torah.
They used two simple measures of tightness: the area of the smallest rectangle holding the sequences, and the length of the shortest stretch of text. Their control was ELS random placement, which slides each sequence to a random start and measures again.
Four of six primary nouns formed a tight cluster in the Book of Numbers. Ten rectangles in 100 million control runs were smaller, for a raw value of 1.05 × 10⁻⁷. Five of the six secondary nouns also clustered at the same spot, with a raw value of 1.105 × 10⁻⁵. The proper nouns gave nothing.
The choice factors
The paper's most useful feature is that it lists the choices and pays for them. Rips and Levitt treat each one as a multiplier, using the Bonferroni bound.
| Choice | Factor |
|---|---|
| Which of three major newspapers | 3 |
| Which book, or the whole Torah | 6 |
| Which of six primary nouns to include | 64 |
| Which of six secondary nouns to include | 64 |
| One-dimensional or two-dimensional measure | 2, in each experiment |
| Which of the three experiments to include | 8 |
They multiply the two raw values by their own factors, combine those with Fisher's method, and then apply the remaining factors. Their final figure is 5.14 × 10⁻⁵.
What the accounting leaves out
Listing choices is much better than hiding them. It is still fair to ask whether the list is complete. A reader can name others.
- Which event to study. The paper studies one. The world had many, and nobody can say how many were looked at before this one was picked.
- Which nouns count as primary, and which grammatical form to use.
- Which spelling to use: the authors followed the newspaper's, which fixes the choice. The article was deleted where possible, and kept in one case for grammar.
- The settings for rows and columns. The authors report their choice and two others, which give values of the same order.
- ELS random placement takes the found sequences as given. It does not test how the set was picked.
The authors say plainly that the second cluster was tied to the first location. To keep to one spot they included one word from the first set in the second search. They also tried the case where a proper noun is promoted to the primary list, and report 9.84 × 10⁻⁵.
How to read it
Please read this entry as an example of method. The paper was published at a pattern recognition conference, and we know of no independent replication or reply in a statistics journal. Its authors state a conclusion about Torah codes. We state none. No matrix is shown here, because a picture of this kind invites the reader to treat it as the event's own record, and that is a step no measurement can take.
The lesson is one you can apply today. List your choices. Multiply them. Use a control that does not depend on how you chose your set. Lock what you can in advance. If the number survives all that, you have something to discuss. If it does not, you have saved yourself from a mistake.
The attacks took thousands of lives, and we keep this entry to one page of method out of respect for that. Nothing here speaks about their causes or meaning.
Sources
Checked against its sources on 2026-10-31.