System A and System B

SIS-tem AY and SIS-tem BEE

babylonian: System A / System B (modern designations; no native Akkadian term)

Definition

System A and System B are the two arithmetical schemes of Late Babylonian mathematical astronomy that compute solar, lunar, and planetary positions and phenomena. System A holds a quantity constant within ecliptic zones (step function); System B varies it linearly between fixed maximum and minimum values (linear zigzag function). Both schemes are sidereally fixed — norming the cardinal points at 10° Aries (A) and 8° Aries (B) — and were used simultaneously in Babylon and Uruk c. 250-50 BCE.

In Tradition

Neugebauer, Hunger-Pingree, and Rochberg concur in treating the two as parallel computational frameworks built on the same arithmetical primitives. Kugler showed System A is the more primitive and therefore older; subsequent study confirms this. Rochberg formalizes the contrast as longitude-as-function-of-longitude (A: λ = f(λ)) versus longitude-as-function-of-sequence-number (B: λ = f(n)).

In Practice

A reader of the ACT corpus identifies a tablet's system by inspecting its column structure. System A tablets carry a step-function solar-velocity column (solar speed 30°/synodic month on one ecliptic arc, 28;7,30°/synodic month on the complementary arc, with jumping points at Virgo 13°/Pisces 27° or Pisces 13°/Virgo 27°); System B tablets carry a linear zigzag function in the corresponding solar-velocity column. The same dichotomy applies to lunar theory and to each planetary theory: Mercury, Mars, Saturn, and Jupiter all received System A and System B treatments. The mean values of the two systems agree closely — for Jupiter, System B's μ = 33;8,45° versus System A's mean synodic arc 33;8,44,48°. Neither system uses geometric modelling; both proceed purely arithmetically.

Historical Origin

Attested across the ACT corpus from Babylon and Uruk in the Seleucid period (c. 250-50 BCE); procedure-text colophons name Kidinnu (System B, via teršītu attribution) and Nabû-rimannu (System A, on Schnabel's hypothesis). Modern critical treatments: Neugebauer, *Astronomical Cuneiform Texts* (1955) and *The Exact Sciences in Antiquity* (1957) Ch. V; Rochberg, *The Heavenly Writing* (2004) §§4.2.4 and 7.4.2; Hunger-Pingree, *Astral Sciences in Mesopotamia* (1999) §C4.

Further Reading

  • Otto Neugebauer, The Exact Sciences in Antiquity
  • Francesca Rochberg, The Heavenly Writing
  • Hermann Hunger & David Pingree, Astral Sciences in Mesopotamia
  • Otto Neugebauer, Astronomy and History: Selected Essays