MERLIN SCIENCE — Sexagesimal Reciprocals: Cuneiform Mathematics Without Zero — E8 Intelligence Research

Today's finding: the sexagesimal reciprocal tables of Old Babylonian mathematics constitute a closed multiplicative lattice under the primes 2, 3, and 5, and that structure, not any abstract algebra, is what let scribes compute square roots to six decimal places a thousand years before Pythagoras. Here is the problem this touches. We tend to treat mathematical notation as neutral scaffolding around the real content. But early cuneiform had no true zero, only a placeholder gap, and no symbolic manipulation at all. Operations ran through tables. If the mathematics still worked, and it did, then the representational substrate was doing more than we usually credit. The mechanism is concrete. Sixty factors as two squared times three times five. Any number of the form two-to-the-a, three-to-the-b, five-to-the-c has a reciprocal that terminates exactly in base sixty. One half is thirty. One third is twenty. One eighth is seven and thirty sixtieths. One twenty-seventh is two, thirteen, twent Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com