Uruk Scheme

OO-rook SKEEM

babylonian: Uruk Scheme / Uruk solstice scheme (modern Assyriological label; the Babylonian scribes give arithmetical tables of cycle-year vs cardinal-point dates without a name)

Definition

The Uruk Scheme is the Late-Babylonian arithmetical scheme for computing the dates of the four cardinal solar phenomena — summer solstice, autumn equinox, winter solstice, vernal equinox — within a fixed 19-year intercalation cycle of the Babylonian luni-solar calendar. Reconstructed by Neugebauer in 1948 from joined Uruk fragments (Istanbul tablets), it records year-numbers, lunar months, and day-numbers with sexagesimal fractions whose successive entries differ by a constant 11;3,10 tithis modulo 30 — an excellent approximation to the 19-year Metonic relation. The scheme is the primary calendrical-astronomy machinery underwriting the Seleucid-period horoscopes and the so-called ‘observation texts.’

In Tradition

Neugebauer, Sachs, Hunger-Pingree, and Rochberg concur in treating the Uruk Scheme as a computed-not-observed scheme: Neugebauer and Sachs showed that every recorded solstice and equinox date in the Seleucid ‘observation texts’ is derived from it by truncating the scheme’s tithi-dates to civil-calendar dates, with no genuine observational input. Rochberg uses it throughout her Babylonian Horoscopes editions to fix or verify the calendar dating of horoscope tablets, citing cycle-and-year coordinates (e.g. ‘cycle 9 year 2’) for individual cardinal points.

In Practice

A reader of a Late Babylonian horoscope identifies the cardinal point (vernal equinox / summer solstice / autumn equinox / winter solstice) closest to the birthdate and resolves its calendar date against the Uruk Scheme’s 19-year cycle. Rochberg notes the convention that the horoscope records whichever cardinal point falls nearest birth as the astrologically significant one. The scheme places the vernal equinox in Nisannu only in years 7, 15, and 18 of the cycle; in other years the equinox falls in Addaru or the intercalary Month XII. Sachs also extended the matrix from 4×19 cardinal-point entries to 7×19 by adding the rising, setting, and acronychal rising of Sirius, all derived arithmetically from the same Uruk pattern. Hunger-Pingree note an equivalent tithi-interval form (autumn-equinox + 3 months 3 ‘days’ = winter solstice; winter solstice + 3 months 3 ‘days’ = vernal equinox) on a related tablet from Uruk.

Historical Origin

Attested continuously from -330 (Seleucid Era year 1); BM 36810+ reverse covers Artaxerxes III years 2-12 (-356/-345); Sachs dated its introduction to "less than a century after -380." Modern critical treatments: Neugebauer, *A History of Ancient Mathematical Astronomy* (1975) pp. 360-363 + *Selected Essays* (1983) essays [16] p. 251 and [17] §3 pp. 258-259; Hunger-Pingree, *Astral Sciences* (1999) pp. 169-170; Rochberg, *Babylonian Horoscopes* (1998) pp. 43-139.

Definition

In Tradition

In Practice

Historical Origin

Further Reading