On Archimedes and Palimpsests

Take a piece of paper and a pencil with medium-hard and dark lead. Now write something on the paper with that pencil. Anything will do--just write.

Now, erase. Yes, I said, erase. But don't obliterate. Just make the appearance of writing go away.

Now turn the paper sideways and write something else.

You have just created a palimpsest. "A what?" You say.

A palimpsest: writing material with something erased and used again. That simple.

That is just what happened to a text written by Archimedes. Or better, several texts by Archimedes, one by Hyperides and some other parchment texts.

This is not anything new: there are plenty of palimpsests out there.

But the science, mathematics, history and classics fields are all abuzz with the revelation of the text of the Syracusan, Archimedes.

The texts, found beneath the text of a 13th century Byzantine set of Greek prayers provides these fields with the only Greek texts of Archimedes' The Method of Mechanical Theorems and Stomachion (a game played with polygons arranged to form a square (see Stomachion: Introduction) from which the player would attempt to create interesting shapes), and the only Greek text of one: On Floating Bodies.

The other parchment used also contains a text from 4th century BC orator, Hyperides. This is the most complete text of his; the rest survive only in small fragments.

And there is much more to the palimpsest: there are Neoplatonic texts, more liturgical works and some, as of yet, undeciphered texts.

Simply put the Archimedes Palimpsest is an incredible find. The prayer book was identified as a palimpsest containing Archimedes as early as 1899 but it was not until 1998 that the book made it into the public sphere where it could be properly examined and deciphered. See more at NPR: A Prayer Book's Secret: Archimedes Lies Beneath.

Now imagine that you are baking some tasting cookies or other item requiring butter. For some reason you cannot measure the amount of butter you need (let's say, 1 cup). But you then remember something your mother told you. Take a large measuring cup (say, 4 cups), fill it with cold water to 3 cups and then slowly drop in chunks of butter. When the water level reaches the 4 cup mark you know you have 1 cup of butter. You might say "Eureka!"

This is just what Archimedes is reported to have said when he discovered the principle of buoyancy. As the story goes, King Hiero of Syracuse was suspicious of a metalworker charged with designing a pure gold crown, thinking that he might have taken some of the gold provided him and replaced it with silver. Hiero asked Archimedes to investigate but he was not allowed to damage the crown in anyway.

Supposedly, as one does, Archimedes took a bath when faced with a seemingly unsolvable problem. But this solved it for him. As he gingerly sat himself in the water (or maybe he just jumped in), he noticed the overflow. He didn't freak as some of us might as seeing so much water spill everywhere.

Instead, he realized that his body--of a certain density--displaced a measurable amount of water. Knowing that gold is denser than silver, he realized that he could give the crown a bath and solve the problem. Running naked through the streets, he shouted, "Eureka!" (Greek for "I found (the solution)".)

Perhaps the poor scribe (whose name we know (an interesting fact in itself): Johannes Myronas) was only trying to clothe the crazy Greek before setting down his sacred tracts!

In any case, we now have a tremendous cultural artifact.

Tom