  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.
