One of the highlights of my visit to Athens last year was to see the Antikythera Mechanism in the Archaeological Museum there. This artifact does not look like much in the flesh and my wife was slightly non-plussed about my excitement on seeing it (picture and article). It was found in an ancient Greek shipwreck over a hundred years ago and consists of a large number of gear wheels mealded together by rust.
The mechanism is a fine technical achievement. It uses an arrangement of gears to model the movements of the planets. It is hard to say how accurate it was, but scientists who have studied it seem to be impressed. It was not a computer in the modern sense of the world, although it was a calculating machine of sorts. It's purpose was almost certainly to fascilitate astrological predictions and horoscopes. These were big business in ancient Greece and no other profession could have afforded the enormous cost of such an artifact. An astrologer needed to know the precise positions of the planets on a given date and it was a laborious process to look them all up. The Antikythera Mechanism probably did the job for him.
The tradition of clockwork machines lasted through the Christian era. We have a description of a Byzantine automaton that featured birds, lions and a flying throne that dates from the 9th century AD. Although we tend to call this kind of technology clockwork, the Greeks never invented the mechanical clock. The reason for this was that they lacked a usable escapement mechanism to keep time. This was not invented until the thirteenth century when medieval craftsmen discovered it (although predictably there are claims the Chinese got there earlier and then let the idea drop).
The Antikythera Mechanism does not tell us that the Greeks were more scientifically advanced than we thought. But we can certainly admire their technical skill in producing this complex machine. It is unlikely that it was unique and perhaps more surprises are in store.
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