Analyzing shell structure from Babylonian and modern times

We investigate ``shell structure'' from Babylonian times: periodicities and beats in computer-simulated lunar data corresponding to those observed by Babylonian scribes some 2500 years ago. We discuss the mathematical similarity between the Babylonians' recently reconstructed method of determining one of the periods of the moon with modern Fourier analysis and the interpretation of shell structure in finite fermion systems (nuclei, metal clusters, quantum dots) in terms of classical closed or periodic orbits.Comment: LaTeX2e, 13pp, 8 figs; contribution to 10th Nuclear Physics Workshop "Marie and Pierre Curie", 24 - 28 Sept. 2003, Kazimierz Dolny (Poland); final version accepted for J. Mod. Phys.

Babylonian House Numbers and Squares of Zodiacal Signs: The Origin of the Quadruplicities, Part I

BM 47762 is the rest of a circular tablet, which was divided into 12 sectors by lines from the center to the rim. Each sector was labelled by a zodiacal sign. Our tablet consists in part of the sectors IX, X, XI, and XII, which are concerned with the zodiacal signs of Sagittarius (month IX), Capricorn (month X), Aquarius (month XI), and Pisces (month XII). In lines 2 to 5 of each sector, some four numbers are written, which in pairs can be understood as a date (month, day) or as a position (sign, degree)—just as in the Dodecatemoria and its inverse, the Calendar Texts (Kalendertexte). The combination of number pairs on BM 47762 do not appear in those schemes. However, the difference between the pairs in lines 3, 4, and 5 is always equal to 277, a very special number which is known from the Calendar Texts. Evidently, our number pairs must somehow be connected to those number schemes. This paper investigates and finds a very interesting connection. It shows that all number pairs stand for dates, for which the Dodecatemoria scheme will give the position of the schematic Moon in its four important phases. The second number pairs refer to the months of the section, while the first pairs give the dates of the four important lunar phases three months earlier. The two dates on each line correspond to lunar positions taking place at almost the same position in the zodiac. The zodiacal signs of the lunar phases on days 7, 14, 21, and 28 join to squares which are mostly known from Greek astrology. For example, for month XI, the signs of the Moon have the numbers 2, 5, 8, and 11, i.e., the zodiacal square with 11 as one of the corners. Maybe we here have found the origin of the quadruplicities of the zodiacal signs

The Babylonian Dodecatemoria and Calendar Texts: Inverse Schemes for Determining Position and Times for the Schematic Sun and Moon

The Dodecatemoria may be understood as a very simple reproduction of the Moon’s movement: for each day in the schematic year, the Dodecatemoria-scheme gives the position of the schematic Moon in the zodiacal circle. The Moon’s angular velocity was calculated as 13°/day and the Sun’s, as 1°/day. The scheme of the Calendar Texts may also be interpreted astronomically: for each position in the zodiacal circle, it gives the date at which the schematic Moon was in that position. We know that the schemes are inverse. A closer analysis of the texts accompanying the Calendar Text (LBAT 1586+1587) shows that the Babylonians also knew and utilized that fact as well