Ratio 3:2 (Babylonian longest-to-shortest daylight)

Definition

The 3:2 ratio is the Babylonian canonical norm for the ratio of the longest to the shortest daylight of the year — the empirical-schematic latitude parameter for Babylon (32.5° N) that underlies every Babylonian length-of-daylight scheme. Neugebauer records that the Babylonian schemes for the length of daylight are always based on this 3:2 ratio, i.e. on the extrema M = 216° = 14;24 hours (longest day) and m = 144° = 9;36 hours (shortest day), the figures expressed in degrees of time (360° = 24 hours) and equivalently in sexagesimal hours.

In Tradition

Neugebauer, with Hunger-Pingree concurring, treats the 3:2 ratio as the single Babylonian norm: Babylonian astronomy never introduced any element of geographical variation but used this one ratio throughout, treating it as a fixed empirical parameter of the schematic-latitude apparatus rather than as a latitude-dependent variable to be recomputed for other localities.

In Practice

For the reader of a Babylonian length-of-daylight scheme, the 3:2 ratio is the canonical input from which the System-A linear and System-B doubled-zigzag schemes derive their extrema. In the MUL.APIN shadow scheme the ratio appears as 7;12 bēru (longest day at Babylon) to 4;48 bēru (shortest day) in 3:2 proportion. Greek geography took the Babylonian 3:2 norm — labelled in the Greek tradition as characteristic for "Syria" — and expanded it into the seven climata, each with its own M differing from the next by 4° = 0;16 hours; the computations for each clima followed Babylonian System B (or, in the Alexandria-centred variant, System A). The same 2:3 (shortest:longest) ratio of the Seleucid astronomical cuneiform texts is identified by Neugebauer as the parameter transmitted to Indian astronomy, alongside the Greek-geographical error that placed Babylon at 35° instead of the correct 32.5°.

Historical Origin

Attested as a canonical input parameter across the Babylonian astronomical corpus from MUL.APIN (~1000 BCE) through the Late-Babylonian ACT lunar procedure texts (c. 250-50 BCE), and transmitted to Greek mathematical geography and to Indian astronomy via the Seleucid cuneiform corpus. Modern critical treatments: Neugebauer, *Astronomy and History: Selected Essays* (1983), essay [4] §IV.13 vol. p. 64 and essay [31] vol. p. 365; Hunger-Pingree, *Astral Sciences in Mesopotamia* (1999), Ch. II §C4.

Further Reading

• Otto Neugebauer, Astronomy and History: Selected Essays
• Hermann Hunger & David Pingree, Astral Sciences in Mesopotamia