תורה at skip 50 in Exodus

The observation

Exodus opens ואלה שמות. The first ת of the book is the last letter of שמות, the eighth letter of Exodus. Every 50th letter from there reads ת, ו, ר, ה. The final ה stands in the word ההוא in Exodus 1:6. So Genesis and Exodus both give תורה at skip 50 from the first ת of the book.

Two matches at the same skip from the same kind of start is the point of the story. It is told in the name of Rabbi Michael Dov Weissmandl, and both reproduce in the Leningrad text.

The measurement

Eight is a lot. Chance alone expects about 2.3, and only 6 of 1,000 shuffled copies of Exodus got there. The eight start in Exodus 1:1, 12:11, 12:46, 14:5, 14:12, 28:14, 33:17 and 39:8. Skip 50 is also the highest count of any skip from 2 to 100 in this book. The next highest is 7.

One of the eight is worth a second look. The sequence that starts at Exodus 12:11 is the same תורה that appears in the משנה and תורה entry, so these entries are not independent facts.

Before you get excited

This is the number in our gallery most worth learning from, because it looks strong and has to be read with its history.

1. It is one skip of many. Across skips 2 to 100 in Exodus the counts run from 0 to 8, with an average of 2.4. Among 99 skips, you expect a high one. A chance of 0.003 at one skip becomes about 1 in 4 across 99.
2. It is one book of five. Across all five books the same search has more chances still. Forward at skip 50, the counts are 3, 8, 3, 3 and 4.
3. The skip came from the start-of-book pattern and not from this count, so nobody went hunting for the highest skip. That helps a little. It does not make this a fixed test, since nobody set it before seeing the text.
4. Other terms exist. Thousands of words could have done this in some book at some skip.

Letters in real text also stand in patterns that a shuffle destroys. A rhythm in the language or in repeated passages, such as the instructions for the Tabernacle in Exodus, may raise a count at one skip. Letter shuffles do not catch that. We would want a text-level control before reading much into it, such as a comparison with other books at the same skip.

So the honest statement is short. Exodus has more sequences of תורה at skip 50 than chance alone would give, and that is unusual if you take this one skip as a single fixed question. Nobody tested it as one. Try the same search yourself and see how the figure changes when you allow for the range.

Try it

Open this entry in the laboratory and switch to the Spectrum view. You will see skip 50 stand above its neighbors in Exodus. Run 25 shuffles and look at the histogram. Then set the skip range to 2 to 100 and see how many other skips rise above the curve.

If you want a fair test of the five-book pattern, write down what would count as a success before you run anything: the skip, the direction, the start letter in each book, and the term. Lock it. Then compare it with the same rule applied to a different word.