Homage to Archimedes

The Antikythera device: you’ve probably heard of this marvel. I’ve seen earlier articles about it and have just read another (in Scientific American January 7 weekly news email, “An Ancient Greek Astronomical Calculation Machine Reveals New Secrets,” by Tony Freeth, titled “Wonder of the Ancient World” in the January magazine).

I’m stunned. I protest against that lazy cliché, but sometimes the brain finds itself confronted by a block of information that seems to say: “Fists up, I’m your match!”

Off the southernmost tip of Greece is an island called Kythera (Cythera in our latinized spelling; pronounced Kithira in modern Greek). It was the birthplace of Aphrodite, goddess of love, as shown on the cover of our book about her. South again, in the strait between this and Crete, is a smaller island, Antikythera.

Places like this, where storms and currents rush between rocky headlands, are perilous for ships.

In 1900, on the sea floor off Antikythera, a Greek diver for sponges came upon the wreckage of a ship loaded with what he took for “naked dead bodies.” They were marble and bronze sculptures, including a statue now known as the Antikythera Ephebe. The ship had perhaps been transporting looted Greek art to Rome, around 70 BC.

This find became a founding event for marine archaeology. A less obviously beautiful object brought up and taken to the national museum in Athens was a sort of muddy fossil, about the size of a small suitcase, a bit more than foot high and half as wide and a few inches thick.

It fell apart, eventually into 82 fragments.

They have been painstakingly pieced together. Some bear dense inscriptions.

And, showing through the encrustation of dirt, there were bronze gear wheels!

Generations of scholars have worked to reconstruct and analyze the Antikythera Mechanism –  archaeologists, linguists, computer scientists, materials scientists, astronomers. The latest team has used X-ray tomography to get at hidden internal workings. Encased in a wooden box, which was mostly of course lost, was the machine, with a front face with a large gear wheel and a back face with two, and these were linked to smaller gears on these faces or inside.

This diagram through several internal planes gives an idea of the mind-boggling complexity.

What was it all about?

A user turning one of the large dials could set pointers to the positions, for dates in the past and future, of the Sun, Moon, and the five known wandering stars – Mercury, Venus, Mars, Jupiter, Saturn – in relation to the fixed stars along the ecliptic. The machine could also indicate the apparent events of the moving bodies, such as their moments of becoming stationary and reversing direction; it predicted the dates and types of solar and lunar eclipses (by means of the Babylonian discovery of the saros periodicity). There was a shutter-like representation of the phases of the Moon. There were dials for the four-year Olympiad calendar and the 19-year Metonic cycle which brings the Moon back into sync with the Sun.

It was an Astronomical Calendar or a Zodiac Chart of its time, and its ingenuity puts to shame the computer-powered ease with which we can spin out such modern equivalents!

That Greek technology was so advanced was a profound surprise. Freeth remarks that we shouldn’t be surprised, because the Greeks had built the Parthenon and the Lighthouse of Alexandria. But the engineering of megastructures seems almost easy compared with the microengineering of this gadget.

How would you, without electric tools or a computer, fashion a perfect bronze disk or spiral, then mark its perimeter at 223 exactly equal intervals, then at each of these cut exactly similar teeth about a millimeter long, then mount this wheel so as to mesh perfectly with the teeth of another with a different number of teeth? There are ball bearings that move to the positions of planets; there are pins in moving parts that engage with slots in others.

The Greeks had numbers for the periods of the planets; they did not have our Copernican Sun-centered model to explain why the planets go into reverse or our Keplerian model of elliptical orbits; they used an epicycle system – a small rotating circle on the circumference of a larger one – and the device was able to reproduce this – rather like drawing an ellipse with pencil, string, and two pins – by superimposed gear wheels with off-center spindles!

Greek numerals were without a decimal place system: 1 to 9 were the first nine letters of the alphabet, then 10, 50, 100 and so on were other single letters. Less clumsy than the Roman VII, IX, XVIII… but how, using it, would you figure out that 63 shares the prime factors 3 and 7 with 462 and therefore two planets could share a gear train containing a 63-tooth gear turning in a D-shaped space and this would substitute two smaller gears for one that would have been too large to fit inside the little box? I know I haven’t got that exactly right, because I don’t understand it.

The Antikythera mechanism is like no other known. But it surely was not the only one. Such sophistication had to have evolved. Why have no others survived? Bronze was scarce and valuable, and when one of these things broke or wore out it probably was melted down for re-use.

There are a few references in classical literature to mechanisms that showed astronomical positions; chiefly an attempt by Cicero (around 50 BC) to describe two “spheres” that had been brought to Rome by a Roman general after the siege of Syracuse in 212 BC and had been made by Archimedes.

Archimedes. His name, “supremely cunning,” is so blatantly appropriate that one wonders whether it was his real name. Indeed, because the only ancient biography of him is lost, almost nothing is known about his life except the ending of it. He was born about 287 BC in Syracuse, the most important of the Greek cities in Sicily. Among his many inventions were machines for defending a besieged city. Important for Syracuse: its repulse of a siege by the Athenians in 415 BC was a turning event in Greek history, and then it had fought off four sieges by the Carthaginians. When the Romans besieged it in 212, their commander, revering Archimedes, gave orders that he should not be harmed, but a soldier killed him.

Enough of his writings survive to prove his towering genius. He invented the mathematical processes of approximation that calculate the areas and volumes of all sorts of curved shapes, and his insights on the motion of bodies in space anticipate those of the Renaissance and the seventeenth century. The spiral dials in the Antikythera mechanism are of the kind we call Archimedean as opposed to logarithmic (as is my spiral library).

Archimedes may not have built something exactly like the Antikythera machine, but it very likely developed out of things he did build.

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