A 13th-Century Enumeration Algorithm, Ignored for 700 Years
6 hours ago
- #Recursive Algorithms
- #Kabbalah
- #Historical Mathematics
- Aboulafia's Tserouf is a Kabbalistic method for enumerating all permutations of n-letter words with a spiritual yet mathematically rigorous structure.
- For three letters, two rules define the order: 'the mirror' (first and last words reverse) and 'hold the head' (exhaust permutations starting with one letter before moving to the next), leaving a specific ordering question (e.g., bca before bac) unresolved.
- A recursive rule (rotate first letter to end) generates permutations for any n, creating nested groups and forming an efficient algorithm that Aboulafia described as simple, infinite in output, yet finite.
- Aboulafia's 13th-century method was historically unique until 17th-century English change-ringers independently devised a similar permutation order, highlighting its early significance.
- The ordering matches a 1984 algorithm by Shimon Zaks, linked to Bill Gates's only scientific paper, promising further exploration in subsequent articles.