Friday, January 8, 2010

The Archimedes Palimpsest

I have not forgotten my promise to explain the topology of function spaces.  Part II is coming soon!  Meanwhile....

Some may remember our friend Mr. Walker and his marvelously reductive and tendentious rendering of something he called "The Christian Dark Ages," by which he meant what regular historians call the Middle Ages.  In a curmudgeonly mood, I commented on it with The Age of Unreason.  Eventually, someone kindly informed him of this -- his own site makes no provision for contrary voices thinking freely contrary to his dogma -- and he responded with Mike Flynn Discovers the Dark Ages, where he declared that he he was "not a Middle Age scholar" and then he set about proving it.  This led to a riposte of my own Return of the Age of Unreason Part I and II, before I got bored.  This sort of thing is like goat barbecue.  The more you chew it, the bigger it gets.  Walker makes a one sentence ejaculation of faith; the response is a paragraph or two; but then Walker's next antiphon is a series of paragraphs to each statement, sometimes even to a word or two, each of which garners another paragraph in the harvest, and soon we have something very much like the expansion of the early universe a la Alan Guth's gloss on the Big Bing.  There is a lot of dark energy here, if there is any at all. 

In any case, in the True Spirit of the Web, some dude named Richard Carrier has now weighed in with Flynns Pile of Boners.  Now, first, I am astonished that anyone still uses the term "boner," but aside from that Mr. Carrier really is an historian - at least he has a Ph.D., which is no small potatoes - but he is no less tendentious.  His degree is in ancient history, and so he owns a lot more factoids from that era; but not necessarily of the medieval period.  His tendentiousness takes a novel twist.  He agrees that Walker was full of it.  The Christians, he admits, did not deliberately destroy ancient learning etc.  They simply neglected it because they did not care.  Presumably, they were busy thumping their Bibles and shouting "Do Jesus!" or something. 

In any case, like Walker, he looks for causes in spiritual matters rather than in material things - like mice, rot, mold, age, flood, and fire. Calling Prof. Ockham! Do we really need to multiply entities like "indifference" [let alone "supression"] to account for lost manuscripts?  Why not just suppose that they were ordinary schmoes like the rest of us, and embodied the usual range of human behaviors? Every major city in the ancient world went up in flames at least once. Already by the time of Domitian, we read of the emperor trying to replenish libraries destroyed by fire, "seeking everywhere for copies of the lost works."(*) How many did his agents find? How many were already lost forever?

At any rate, I think our disagreements are more epistemological than factual. 'Tisn't the facts but the construal of the facts that breed contention. If one approaches them with an a priori Theory, why then one will see that Theory confirmed everywhere. "A man sees what he expects to see" and confuses conclusions with the echo of his own assumptions. (I started my research into the Middle Ages with expectations similar to our interlocutors, though not nearly so histrionic and tendentious. What I learned over the three years following caused me to change my opinion.)

Now the basic problem with Dr. Carrier's reponsorial is that he knocks over a bunch of straw men: things he claims I claimed that I did not claim. [I may comment on them later, if I feel like it.]  He equivocates on the meaning of the term "science," expanding it in order to gather in the favored ones (Greeks and Romans) and contracting it to exclude the disfavored ones (medievals). He calls an acorn an oak when it suits, and dismisses the work of others as mere acorns.  He includes mathematics, medicine, and engineering / tinkering as "science." At times, he seems to regard science as little more than a closet full of curious facts about nature and takes the Whiggish view that what matters is "who got the fact first."  (Newton versus Leibnitz writ large.)  In fact, it may matter more who did it last!  He starts the Renaissance in 1300 in order to claim that medieval accomplishments were actually Renaissance accomplishments. In one passage he even starts the Renaissance in "the 13th century," which is 1200, possibly to claim the human dissections and medical schools for the Renaissance; but at this point he is not only inconsistent but disturbing the shade of Huizinga unduly. 

History is continuous more so than discontinuous. The roots of the Renaissance lie in the High Middle Ages. The roots of the medieval world lie in late antiquity. The man who makes the beer owes much to the man who grew the hops. But hop-growing isn't brewing. And there is an important distinction between science as an accumulation of facts about the world (a la China), science as a spinning of grand theories (a la some ancient Greek philosophers) and science as a machine grinding theories through the facts in a systematic and rigorous way. If the Greeks planted seeds and the 17th century revolutionaries saw them blossom, then someone along the way nurtured the first tender shoots.

But we digress.  Let's get to the topic of tonight's symposium.  Namely

The Archimedes Palimpsest

Carrier writes:
[The Christians] just showed little to no interest in [ancient writings], and thus let them rot and vanish, sometimes even scraping them off and writing over them with hymns to God, as happened to the Archimedes Codex. This was not because of any hatred at Archimedes or desire to suppress his work. It was just because of a complete disinterest in that work, and a greater preference for preserving hymns to God instead. Such represents the pervasive attitude of medieval Christianity, even in the East, where this terrible "deliberate" destruction of the work of Archimedes occurred.

I respond:

One of the oldest Bibles we have is a ghost text on a palimpsest overwritten with perfectly ordinary sermons.  Unless Carrier is prepared to argue that they had a complete disinterest in the Bible, it may well be that their motives in overwriting a text were not what he wants them to have been. 

Of course, over-writing was what "scratch paper" was for.  You rough-drafted it on the parchment, then fine-copied it to the paper, then "scratched" off the parchment for re-use.  Remember, this stuff was expensive, and you re-used it as much as possible.  That's why scholars - including Ockham - had razors.  From which, our word "eraser." 

+ + +
Now, I had written in response to Walker that
At the time that parchment was reused, as we know from references, the complete works of Archimedes were in circulation and so there was no big deal in re-using a scratch copy.

To which Carrier responded:

There is actually no good evidence for this assertion. The evidence we have actually suggests the contrary. As discussed in The Archimedes Codex, at the time this palimpsest was made (in the 13th century), his works were so rare there may have been only two other codices in the world with Archimedean works in them, neither of which contained all the works erased in this one (much less all the works of Archimedes).

...the text wasn't erased by an attempt to 'suppress calculus', but neither was it erased in the belief that the text wouldn't be lost. It was erased quite simply because no one cared anymore.

I was unclear. At the time of the erasure in the 13th century, the Archimedian corpus was copied and translated, probably in Sicily; that means there was at least one Greek copy which resulted in at least one Latin copy.  Some of the Greek mss avaialable at the time are no longer extant, and we have only the Latin translations.  We now know that at least two Greek mss were not available in Sicily; but that was far more likely due to Bacon's "shipwrecks of time" than because "no one cared anymore."  If no one cared, why did Billy Moerbeke copy all the Archimedian treatises he could find?  In Sicily.

The Archimedes Palimpsest Project states that the undertext was written in the 10th century, which means the Byzantine Christians cared enough to copy it. The Project believes that the 10th century copy goes back to Leo the the Geometer, a cousin of John VII Morocharzianus, who was Patriarch in Constantinople between 837 and 843. It is unlikely the copy he worked from was an original, so the work had already been copied and preserved by the Byzantine Christians for several centuries.  No one cared anymore?  Forsooth.

Now Archimedes is hard. He was far better known as an engineer than as a geometer, and his practical works were well known. In fact, most of the works on the Archimedes Palimpsest were works already known. Two were unknown. One is the prize: he describes a method using infinitesimals which he regarded as illegitimate but useful. In determining areas and volumes he used his infinitesimals as a kind of intellectual scaffolding to discover the answer; then he went back and "proved" that answer the "right" way, by the method of exhaustion and did not publish the scaffolding. One reason why this treatise was not more widely known is that Archimedes did not widely use it. Certainly, no one else in antiquity seems to have used to it, which argues against many copies in wide circulation.

Anyone desiring a flavor of Archimedes, one of his popularization is The Sand Reckoner.  This is our only source for Aristarchus of Samos and his heliocentrism. (Archimedes himself did not hold this.)

In the 13th century, when the monks at Mar Saba in the Jordanian desert were overwriting their copy of a collection of Archimedes, William of Moerbeke, a Fleming who had become bishop of Corinth in Greece, was asked by Aquinas to find some better translations of Aristotle than the ones then circulating in the West. In the course of this, William also translated the Archimedian corpus directly from Greek copies available in Byzantium. (William did most of his work in Sicily,) In any event, it indicates that copies of Archimedes best work were readily available in Greek in the 13th century.

It so happened that two of the treatises in the Mar Saba codex are now the only surviving copies of them. That does not mean that they were the only surviving copies in the 13th century. There may have been oodles in Constantinople; but Constantinople would be sacked, twice, in the intervening centuries, as would most other eastern cities. Several of Archimedes' works that William of Moerbeke translated from Greek to Latin now exist only in his translated Latin ms. (One of these showed up in the Mar Saba codex in Greek.) The other Greek mss. he translated from were lost after his time.  Not because "no one cared any more," but because of the shipwrecks of time.  Try the Sack of Constantinople by the "fourth" crusade?   

In sum: if the Christians were so indifferent to Archimedes-the-mathematician, then why did Leo the Geometer, cousin of the Patriarch, copy it?  Why did Bishop William try to translate into Latin the entire Archimedian corpus in the same era when the famous palimpsest was overwritten?  (BTW, Billy Moerbeke's translations are still there in the Vatican library!  Unless some of them have been lost.  Rome has been sacked a time or two in the interim.) 
(*) Domitian and the burnt libraries (pl.)  The complete passage in Suetonius' Domitianus 20 reads:
Liberalia studia imperii initio neglexit, quanquam bibliothecas incendio absumptas impensissime reparare curasset, exemplaribus undique petitis missisque Alexandream qui describerent emendarentque.


  1. In one passage he even starts the Renaissance in "the 13th century," which is 1200

    Forgive the pedantry, but the first year of the 13th century was 1201. Which is obviously when the Renaissance started: Jan 1, 1201, 9:00 am Greenwich Mean Time.

  2. Call it shorthand for "the 1200s," which is what I meant to type.


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