בהרד at skip 42 in Genesis

What Rabbeinu Bachya wrote

Rabbeinu Bachya ben Asher lived in Saragossa in Spain and began his commentary on the Torah in 1291. On Genesis 1:2 he talks at length about בהר"ד. That is the traditional sign for the moment of the first new moon in the Jewish calendar: the second day, five hours and 204 parts of an hour.

After a discussion of the Name of 42 letters and the opening of the Torah, he adds a remark. If you look with care, he says, you will find בהר"ד marked in this passage, with 42 letters between each of its four letters. He says a person of understanding can tell that this is no chance matter, and he goes on to tie it to a teaching about creation.

בין כל אות ואות מ"ב אותיות

Rabbeinu Bachya on Genesis 1:2: between each letter, 42 letters

This is the oldest clear written statement of a letter interval that we can find and check ourselves. The passage is cited more often than it is quoted. It is in his comment on Genesis 1:2, and you can read it there.

The check

Start from the first letter of the Torah, the ב of בראשית, and take every 42nd letter.

They spell בהרד. The fit to his description is exact, with one point of counting to note. In our terms the skip is 42: each letter stands 42 places after the one before. Read strictly, "42 letters between" could mean a skip of 43, but skip 43 from the same start gives ב, ו, ל, ל, which is not the word. His count is the one that includes the far letter. This is the same "49 or 50" question that comes up with Rabbi Weissmandl's sequence.

The span is only 127 letters, all in the first four verses of the Torah, so there is little room here for the differences between editions that trouble longer sequences.

The measurement

At this skip the whole book has this one sequence. Chance alone gives about half of one. Across skips 2 to 1,000 forward, Genesis has 517 sequences of בהרד, and chance alone gives 496. It is a very ordinary string of letters.

The start is less ordinary. From the first letter of the Torah, three skips between 2 and 5,000 spell the word: 42, 1,260 and 4,594. Chance alone gives about 0.6 over that range. Skip 42 is by far the smallest, and it was named by a commentator who had a reason for that number in the Name of 42 letters. A reader should weigh that, and should also recall that nobody fixed the question in advance.

Within the first chapter of Genesis, forward at skips 2 to 500, the string appears 3 times, and chance alone gives 2.6. So it is not rare there either.

How to read it

This entry is here for history as much as for measurement. Rabbeinu Bachya was not running a test. He noticed something, or received it, and he read it as a teacher. We do not know how he found it or what else he looked at. The number he gives is correct, and that alone is a remarkable thing to be able to say about a remark from the 13th century.

It also shows how old the temptation is. In one sentence he already says the thing everyone has said since: a thoughtful person will see this is no accident. That is the claim a chance figure exists to examine. We print the figure, we print his words, and you can weigh them together.