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This is the first article in a series about a discovery I made while researching Tserouf in the writings of the Kabbalist Abraham Aboulafia (1240 – after 1291). Tserouf is the Kabbalistic art of permuting the letters — and, in plain mathematical terms, it is the enumeration of all the permutations of an n -letter word.

In Or ha-Sekhel (“The Light of the Intellect”), Aboulafia prescribes a systematic method for enumerating all the possible arrangements of an n -letter word. The method is conceived inside a frame of spiritual practice — and yet it carries a mathematical structure of remarkable rigour.

For a three-letter word, Aboulafia gives the Tserouf — the ordering of all six permutations — explicitly:

The words fall into three groups, by their first letter:

Aboulafia explicitly mentions two rules for the Tserouf of 3 letters:

Rule 1 — the mirror. The whole sequence must end on the reverse of where it began . Aboulafia says it plainly: “the last utterance is the reverse of the first.” The first word is abc ; the last must be cba , its end-to-end reversal.