Archimedes, Far More than the Eureka Man

In his book, Is God a Mathematician?, Mario Livio calls Archimedes one of the greatest mathematicians of all time. He calculated the “areas of the circle, segments of a parabola and of a spiral, and volumes of segments of cylinders, cones and other figures”. He proved that pi lies between 3¹⁰/₇₁ and 3¹/₇. In physics, he discovered the laws of floating bodies and the laws of levers.

 

Then, of course, there’s the famous Eureka story. But was that real? This podcast points out that Archimedes never mentions it in his own books, and the first mention of this incident occurs 200 years after his death. Centuries later, Galileo pointed out that while the idea of relative displacement was correct in theory, the difference in case of a crown would be too small to be detected using the measuring instruments of the time.

 

Most interestingly, Archimedes has a parallel with Alan Turing, the man who cracked the Enigma code in World War II. While both men were great mathematicians, it’s their war time contributions that they are best known for!

 

And it’s these war time contributions of Archimedes that the podcast focuses on next. Archimedes lived in city of Syracuse. A rising Rome attacked Syracuse and thus started the Siege of Syracuse. The king of Syracuse asked Archimedes to help in the war against Rome.

 

Archimedes designed adjustable catapults to rain rocks at the Roman ships coming from the sea. The next layer of defense was the Scorpion: It consisted of holes in the city walls, from which smaller catapults would rain iron darts at Roman ships. Both machines definitely hurt the Romans and prolonged the Siege of Syracuse. These war machines are mentioned by multiple historians of the age, and they sound well within the capabilities of the age, so they’re probably true.

 

Next, let’s move onto the more awesome machines that Archimedes is supposed to have built. First up, the Archimedes Claw. The Claw could grab a ship, lift it into the air, shake it up, and toss it back into the water. The historian Plutarch called the Claw a “dreadful thing to behold”. But did it exist? Well, Archimedes never left any designs of it, but given his mathematical and mechanical knowledge, it is conceivable that he could have built it. Modern experiments show that the Claw would have been effective even if it couldn’t lift the ship. Just shaking ships and slamming one into a neighboring ship would be enough. So the Claw may have existed, even if the lift-and-throw part is probably mythology.

 

Saved for the last is the famous Death Ray, a device that could focus the sun’s rays onto a ship and set it ablaze. Sounds awesome, right? Also a bit too far-fetched? On this one, the data and science don’t stack up well. In theory, yes it’s possible. A group of students at MIT arranged mirrors in a parabola and focused them on a replica of a Roman ship and set it ablaze. But it required perfect conditions: no clouds, and most problematically, a stationary target. The Roman ships were surely moving. Plus, even if a spot on the ship began to singe, all it would take was for the Romans to pour some sea water, and the fire could never really get started. Lastly, no contemporary historian of Archimedes ever mentioned it. So this is almost certainly a myth started centuries later.

 

Even if the Death Ray didn’t exist, Archimedes’ contribution to the Syracuse war effort was recognized even by the head of the Roman fleet, Marcellus, who wanted Archimedes captured alive so he could be made to work for the Romans! But that was not to be: Archimedes was killed, not captured. And yes, there are many stories on how that happened, and we’ll never if they are fake like the Eureka and Death Ray stories? Or if they’re real like the catapults and the Scorpion?