With Java animations by Bill Casselman
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Update: Technology available to Tony Freeth and his collaborators, including computed X-ray tomography (like a high-resolution CAT-scan), has allowed a much better understanding of the structure of the mechanism and has shown that earlier work by Price, while correctly assessing the intellectual scale of the Greek's achievement, was dead wrong on many of the details. Read about some of the discoveries made in 2009 here.
General plan of all gearing, composite diagram
from De Solla Price, Transactions of the American Philosophical
Society Vol 64 No 7 (1974). Reproduced with permission.
It is hard to exaggerate the singularity of this device, or
its importance in forcing a complete re-evaluation of what had
been believed about technology in the ancient world. For this box
contained some 32 gears, assembled into a mechanism that accurately
reproduced the motion of the sun and the moon against the
background of fixed stars, with a differential giving
their relative position and hence the phases of the moon. It is
enough to know that there is no trace of anything like it until
around 1000 A.D., and that when it was first published there were
serious suggestions that it had been dropped into the wreck at
a much later date or even that it was the
work of alien astronauts.
The general plan of the gearing could only be drawn after 1971 when, on De Solla Price's instigation, the remnants of the mechanism were viewed with gamma rays, which could penetrate the calcareous block in which the gears were embedded. Then careful counting of teeth, and examination of the way the gears meshed, showed that "the gear ratios could be associated with well-known astronomical and calendrical parameters" (Price) and allowed the almost complete description of how the device must have functioned.
This is the first of two columns on the Antikythera Mechanism. In each we will examine one part of the mechanism that has special mathematical interest. This month it is the Sun-Moon assembly, next month: the Differential Gear.
SUNY at Stony Brook