The Archimedes Palimpsest: a correction

Some time ago I wrote about the Archimedes Palimpsest.  It's an incredibly ancient book written by Archimedes, that was thought to be totally lost for two thousand years.  Then a copy of it was found underneath a bunch of Christian writings.  A mediaeval monk had re-used the parchment, you see.

Researchers used some very clever imaging systems to recover the original text, at which point they not only discovered a lost ancient book, but they also discovered that Archimedes had been well on the way to discovering calculus, one thousand eight hundred years(!) before Newton and Leibniz got it.

Two days ago a correction appeared in the comments of that post I wrote.  I'd said that the monk who covered over the text was unknown.   Someone named Roger Easton, a newcomer to the blog, wrote to say that the name of the monk was indeed known, and that he's credited with (inadvertently) saving the book.  

I get random comments on older posts all the time, so I didn't give it a lot of thought.

Then the next day it suddenly hit me...the name of the imaging guru who recovered the Archimedes Palimpsest was none other than... Professor Roger Easton.

I think we can take this comment as coming ex cathedra.  Here's what Professor Easton had to say:

The comment that we do not know the name of the monk who erased the original Archimedes text is incorrect -- it is Ioannes Myronas, as discovered in 2006 when the manuscript was imaged using X-ray fluorescence. Dr. William Noel, Director of the Archimedes Palimpsest project, has said that he believes that Myronas may be credited with SAVING the writings rather than destroying them, since he provided a camouflage that actually preserved them.

2013

Welcome to 2013!   It's the first year to consist of four digits that can be arranged consecutively (0,1,2,3), since the year 1432!

We live at a privileged time, because like the people in the 1400s, we'll see this unusual phenomenon twice.  Next stop: 2031.

Aristarchus: a bright lad

Some time in the third century BC, a fellow by the name of Aristarchus of Samos wrote a book in which he said the earth moved around the sun. The book's lost. We know about it because Archimedes quoted it with approval in a book of his own called The Sand Reckoner.

Aristarchus of Samos brought out a book in which the universe is many times greater than that now so called. His hypothesis is that the fixed stars and the sun remain unmoved, that the earth revolves about the sun in the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same center as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface.

That beats Copernicus by about 1,700 years.  It's when you read things like this that you realize how much was lost when the classical world collapsed.

Archimedes clearly bought into the theory. He wrote The Sand Reckoner to work out how many grains of sand it would take to fill up the universe, assuming Aristarchus was right. The numbers were so huge that to do it, Archimedes had to invent a whole new number system. The number of he got, in modern notation, was 8 x 10⁶³ grains of sand, which is amazingly close to modern estimates for the number of known particles (though obviously we now know about massive amounts of vacuum too).

Archimedes finishes:

I conceive that these things will appear incredible to the great majority of people who have not studied mathematics, but that to those who are conversant therewith and have given thought to the question of the distances and sizes of the earth, the sun and moon and the whole universe, the proof will carry conviction. And it was for this reason that I thought the subject would not be inappropriate for your consideration.

The Classical Athenian Calendar

Since we're starting a new year, this would be a good time to talk about the classical Greek calendar, or rather, the classical Athenian calendar, because every city ran its own version and the only one we really know anything about is the Athenian.

Mental health warning: this is long, complex, and confusing! Do not proceed if you value your sanity.

Let's start with year numbering.

There wasn't any. In Athens each year was named in honor of the city Mayor-cum-CEO who held office that year, called the Eponymous Archon, meaning archon who names [the year]. Eponymous is a word in English to this day, btw, and its meaning hasn't changed much in 2,500 years. So my first book, The Pericles Commission, opens in the Year of Conon, which we call 461BC.

Named years have caused historians to put a lot of effort into working out the correct and complete archon list. Without it, you can't work out what happened when. It's all very well for X to happen in the Year of Fred and Y to happen in the year of Jane, but which came first?

It gets worse, because every city named their years after their own officials, and no one ever kept a list of corresponding years between cities. The cities also kept different months, as we're about to see, and began their years on different days.

So unless two events happened within shouting distance of each other, no one could ever know which happened first. This is reflected in the words of Thucydides, Herodotus et al., who frequently use terms like, "X happened at about the same time as Y." They're not being deliberately vague; they genuinely have no idea which happened first or how much time separated. They can easily be out by many months. In fact, to compare two distant events, the smallest safe unit of resolution is probably the season.

Greek months are lunar. Every Greek month starts with the sighting of the next new moon. In fact, they called the first day of each month noumenia which means (surprise!) new moon. Every noumenia was considered a particularly holy day. Officials went out of their way to never schedule anything for a noumenia. So if you ever catch my characters attending an official function on a noumenia you can validly beat me up. I did, in fact, in my short story The Pasion Contract have a contract killing arranged for noumenia, but I figure that's acceptable since hired thugs probably aren't all that pious.

There are 29 days, 12 hours, 44 minutes and 3 seconds in an astronomical lunar month. So Greek months were either 29 or 30 days long. Since the new month was defined as starting on the sight of the new moon, there was never much doubt when a new month began.

The definition of "day" was a bit odd. For the Greeks, the old day ended and the new one began at dusk. This makes perfect sense for people working to a lunar calendar. Their day begins with the moon telling them what day of the month it is. But it creates a terminology problem for me. Nicolaos could say at midday, "I'll meet you early tomorrow," and mean that night, leaving you the reader totally confused. I solved this problem by completely ignoring it and sticking to modern convention.

The Athenian months in order were:

Hekatombion
Metageitnion
Boedromion
Pyanepsion
Maimakterion
Poseidon
Gamelion
Anthesterion
Elaphebolion
Munychion
Thargelion
Skirophorion

No, I can never remember them either (and can barely pronounce them!) but the exotic names are great for atmosphere. I can say things like, "He died on the noumenia of Hekatombion," as if it made sense.

Every city had a different set of names for their months. Just to make it more fun, they started their years at different times too. All the Hellene cities fell (broadly) into two very ancient tribal lineages: the Dorians and the Ionians. I have a feeling, which I've never been able to confirm, that it was mostly Dorian cities which started their year at winter solstice, and mostly Ionian starting at summer. But don't quote me on that. The Athenians, as good Ionians, began theirs on the first new moon after the summer solstice, putting them as out of synch with the modern calendar as you can get.

The lunar month does not divide evenly into 365.2423 days. (Nor does any other sensible number, for that matter. When God created the universe, he really screwed up on this point big time.)

The Greeks tried to fit a lunar calendar into a solar year, so that the months had a fighting chance of being consistent with the seasons. Such calendars are called lunisolar.

Twelve lunar months fall short of a solar year by about 11 days. The Athenians handled this by inventing an extra month every two years. And not just inventing, but duplicating the previous month. It is said, but I've never seen the proof, that the month they usually duplicated was Poseidon, so every second year there'd be Poseidon I followed by Poseidon II. Or not, if they decided to duplicate a different month instead. The guy who got to decide was the Eponymous Archon.

This still didn't fix the problem completely since twice 11 does not equal 29. Not to worry...the archons invented extra days at random to pad things out. This was a useful trick for buying extra rehearsal time before important festivals if people weren't ready. I'm not kidding...this actually happened! Once, the calendar was frozen for 4 days before a Great Dionysia.

Since the noumenia of Hekatombion is the first new moon after the summer solstice, it acts like a reboot for the calendar. No matter how screwed up the calendar had become, there was always a clean reboot in the future.

They couldn't even manage to number the days in a month consecutively. Every month was broken into three sections: moon waxing, full, and waning. After noumenia, the next day was called 2nd Waxing, then 3rd Waxing, and so on to 10th Waxing. Then the system changes to 11th, 12th, 13th...19th, and then earlier 10th! 10 doesn't normally come after 19, but that's how it worked! The earlier is very important because the following day was later 10th. Yes, they had two 10ths in a row: earlier and later. After later 10th it counted down: 9th Waning, 8th Waning, ..., 2nd Waning, and ending with hena kai nea, meaning old and new. On a 29 day month 2nd Waning was dropped.

If you're getting the impression the Greek calendar was insanely chaotic, you're right. A modern astronomer confronted with the Greek calendar would probably be driven to self-harm, or more sensibly, Greco-harm.

The only thing common across every calendar in every city was...the Olympics. They happened every 4 years at a more or less consistent time, fixed by the leaders of the city of Elis, who were always the hosts. That's why some ancient authors might refer to an event as happening in the year of the 74th Olympiad, or whatever. It's their attempt to make dating sensible across all of Hellas, but that's the closest they ever got to unity.

The Archimedes Palimpsest is now on Google Books!

Back in 1229 A.D., someone, probably in Jerusalem, probably a monk, wanted to write a prayer book. He had no clean sheets of parchment, so he did what people used to do in those days: he looked for some existing parchment, intending to scrape it clean and re-use it.

As this fellow searched about for pre-loved parchment, his hand fell upon the last remaining copy of Archimedes' treatise called The Method of Mechanical Theorems. It wasn't a religious text so obviously no one would want it; he erased it. He picked up the only remaining copy of On Floating Bodies written in the original Greek. He erased that too. He erased sections of the Stomachion which have not survived anywhere else. He tossed in four other books by Archimedes which at least have survived elsewhere in other versions. For good measure he threw in ten pages of oratory from Hyperides, whose words appear nowhere else, the 4th century legal eagle who was the defender of Phryne the Hetaera, the man who made legal history in a way described in another of my articles.

This monk is lucky we don't know his name, because he may hold the record for the greatest single-handed destruction of knowledge ever. The burning of the Library of Alexandria would obviously have destroyed far more, but it took lots of men to do that. It was this fellow's bad luck to pick up one unique text after another.

Our monk erased all these unique books, and wrote over them a bunch of prayers of no particular interest whatsoever. The resulting palimpset passed from place to place until, 723 years later in 1906, the underlying text, barely visible through the overlying ink and mostly illegible, was recognized for what it was. Scholars took some photos, as best they could in 1906, and then...you're not going to believe this, it reads like a thriller...the Archimedes Palimpsest went missing, probably stolen.

As far as anyone knew, that was the end of the story, the lost works of Archimedes lost once more.

Cut to 1998. Christies Auction House is selling a palimpsest that has been in a private collection since the 1930s. Upon inspection it turns out to be...the Archimedes Palimpsest.

Modern digital imaging technology was applied to the parchment before anyone else had a chance to lift it, and the Archimedes Palimpsest appears for the first time on Google Books. How cool is that?

This book is seriously out of copyright, so everyone is free to download it and at least gaze at ancient texts that went missing for centuries.

The most amazing thing for me about what's been discovered is that, in The Method of Mechanical Theorems, Archimedes describes a mathematical technique which is the next best thing to calculus! Now calculus was worked out independently by Isaac Newton and Gottfried Leibniz in the 17th century, and its development opened up new ways to analyze the world and vastly sped up scientific discovery. It seems Archimedes got there first, but we didn't know it until now. How smart would a guy have to be to make such a discovery 1,600 years before the next person to work it out? And how much more advanced might the world be today if that monk had published Archimedes instead of wiping him out?