The Brain and the Tomb

A Large Hole, Geometric Figures, Medieval Prayer, Obscured Mathematical Texts, Christie’s in New York, The Anti-Scribe, Time along a Parabola, Construction of a New Overtext, Invisibility, Potential Properties of Books, The Circumscribing Sphere, Mind v. World, The Shortcomings of Diagrams, Writing as Writing Over, Approaching Infinity, Innumerable Layers
by Avi Davis
A page of the Archimedes Palimpsest. The Archimedes text is faintly visible beneath the prayers. Copyright the owner of the Archimedes Palimpsest.

The Brain and the Tomb

Avi Davis
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Quid in tanta lacuna dictum, non expunto. So wrote the German classicist Jo­han Ludwig Hei­berg in 1906, after peering at a particularly inscrutable section of the medieval manuscript he had just uncovered in a Constantinople library. “What in such a large hole could have been said, I will not guess.” Heiberg was attempting to translate the words of Archimedes, arguably the most important thinker in the history of science. His frustration arose from the fact that, sometime in the thirteenth century, the Archimedes text had been scraped off, cut up, rebound, and written over to make a Greek Orthodox prayer book, rendering the ancient mathematics nearly impossible to read.

It might seem incongruous for a German professor to be translating ancient Greek into Latin in Turkey in the twentieth century. But this is the least remarkable of the book’s oddities. The text Heiberg faced had been written in the ninth or tenth century CE—a copy of innumerable previous copies stretching back to the original treatise Archimedes wrote in the third century BCE. And almost immediately after Hei­berg’s discovery, the book disappeared for ninety years. The Archi­medes Palimpsest, as it is now known, is indeed like a pit into which we can peer forever and never see the end.

We begin, as always, with a copy. The long pages of animal hide bear twin columns of dense script—an antique hand already obsolete—interrupted occasionally by geometric figures. Triangles and squares bisect one another; rectangles nestle in circles, as stray line segments float alongside. The document is instantly baffling, its authority suspect. The scribe, raising his knife, pauses to consider the text before his eyes. But it remains unreadable. Ghosts of their original selves, the words and shapes retreat from his gaze, lost within layers of impenetrable meaning. The work of the blade is quick enough, though never complete.

Now scraped nearly clean, the manuscript leaves are cut in two and refolded in preparation for the new text. In a priest’s practiced hand, he writes his prayers perpendicular to the faded lines below. Soon only traces of the older script and the elegant diagrams can be seen under the newest text. And, in the words of the freshly obscured treatise, “Though many worthy eyes will see it, they all will not know it, and none will perceive it.”1 On the first page of his new book, the scribe writes: “This was written by the hand of presbyter Ionnes Myronas on the 14th day of the month of April, a Saturday, of the year 1229.”2

This was the creation of the Archimedes Palimpsest—a book formed by the erasure of other books. The word palimpsest comes from the Greek palimpsestos, “to scrape again.”3 The book’s modern name derives from the fact that the majority of the folios—manuscript leaves—My­ro­nas used for his prayer book came from a tenth-century copy of the treatises of Archimedes, which now comprises the oldest existing transcription of the ancient mathematician’s writings.

Yet like the words Myronas wrote, this name obscures the many texts hidden in the Palimpsest. Two folios come from a ­late-tenth-century liturgical book containing Ro­man hymns for the third of May and a canon for an abbot in Constantinople. Three more come from a philosophical treatise, and were only identified in 2007 as copies of a second- or ­third-century commentary on Aristotle’s Categories. Five folios contain speeches of Hyperides, a fourth-century Athenian orator, copied in the eleventh century, and which up to now were thought to have been lost. Six more folios are yet to be identified; the only thing we know is that they come from two different texts.4 The remaining one-hundred-and-forty-odd leaves contain the Archimedes treatises. Over these disparate pages, My­ronas wrote the prayers of the Greek Orthodox church. Re­searchers have not yet been able to establish ex­actly where he created the Palimpsest.

For the past hundred years, re­searchers have been patiently un­doing the work of Ionnes My­ronas. When Heiberg traveled to Constantinople, all understanding of the ancient mathematician’s writing was based on only two manuscripts. Heiberg realized he had just discovered a third. Using only his naked eye, he became the first person to read the treatises in nine hundred years. Despite his re­markable translations, so much of the mathematical work remained veiled behind the intervening lit­urgy, or buried in the creases of the prayer-book pages, that the treat­ises begged for a more technologically advanced reading. Before it could be further studied, though, the Palimp­­sest mysteriously disappeared from Turkey sometime between the world wars. For ­ninety years it remained a phantom, a palpable absence—the most im­portant nonexistent book in science.

In 1998 it resurfaced inexplicably at a Christie’s auction in New York. The Palimpsest sold for $2.2 million to a private bidder, who then deposited it for study at the Walters Art Museum in Baltimore. Here it would be conserved, im­aged, and transcribed.

Abigail Quandt is in charge of preserving the Archimedes Palimp­sest at the Walters. Her first task was to undo the work of Ionnes My­ronas, becoming, in effect, the anti­scribe. To aid the work of modern scholarship, she would have to reverse the efforts of her medieval counterpart, carefully taking apart what he had put to­gether. Yet her task, in many ways, ran parallel to his. Although seven hundred years had passed, it began with no less of a copy. The pages were the same, though the words were different. The antiscribe, knife raised, might have paused to consider the book in front of her. But she would have found it no more readable than did the medi­eval writer whose creation she was about to disassemble. The time of his legibility had passed—the pages had to be cut and cleaned to make room for a new, digital text to take the place of the existing layers. So in an act mirrored across the centuries, the book went under the knife once again.

Quandt was not just trying to undo Myronas. After the Palimpsest was created, it was used as a working prayer book for four hundred years at Mar Saba, a monastery near the Dead Sea, before being taken back to Constantinople sometime in the nineteenth century. When Heiberg found it, flood marks, charring, and candle wax, as well as the medieval prayers, all stood between him and Archimedes’s words; ironically, over the next ninety years, it seemed to age far more than during its first seven hundred. From Constantinople, the Palimpsest may have traveled to Los Angeles before winding up in the hands of an antiques dealer in Paris, who had to pass it off to a friend before fleeing the Nazis. At some point, forged paintings of Greek saints were added to four of its pages to increase its value.

Burnt, ripped, twice rebound, vandalized: an impossible accumulation of historical layers burdened the Palimpsest when it arrived at the Walters. The experience of the Palimpsest suggests a kind of quickening of history. We can imagine that for some objects, time does not progress along a straight line, as we normally imagine it, but along a parabola—one of Archimedes’s conic sections. The Palimp­sest suffered more, and traveled farther, in the twentieth century than at any other point. Even natural processes seemed to speed up—it decayed the most during its ninety years of invisibility. As we gaze back­ward at history, events seem to pile atop one another as time progresses, the most recent period always appearing the most ­crowded. The Palimpsest is a witness to this hastening crush. As we see history racing toward us, so that it seems to approach even the speed of our everyday life, threatening to engulf the present, we grow increasingly anxious to secure the past—to put it out of the reach of time, to preserve it in a stable, unified, unchanging state, beyond history’s grasp.

Quandt’s purported task was to uncover Archimedes’s words, but in fact she was charged with countering history. In order to uncover a particular (imagined) moment in the past, she had to undo hundreds of years of very real history. Over more than four years, she painstakingly unbound, unfolded, cleaned, and repaired the Palimpsest’s folios to make the undertext legible. The book became an illustration of its own discontinuity—a lesson in disintegration. William Noel, its curator, calls it Archimedes’s tomb; Reviel Netz, its translator, calls the book Archimedes’s brain. Yet, with an irony we may never fully grasp, the Palimpsest forces us to take it apart before we can make it into any sort of whole. It obliges us to ac­knowledge the disunity of the text. Its multiple authors never saw it whole, and its owners can never read it whole. Noel calls it the greatest manuscript ever, but it may instead be the greatest book—the one that most fully achieves the potential properties of the book.

Once the work of Ionnes My­ronas was undone, the imaging could begin. Strangely, the method of creating readable images of the Palimpsest was itself palimpsestic. By stitching together ten separate, overlapping digital photographs, a single image was created of each page. Each of the ten individual shots was taken using three dif­ferent light sources. And of those, the red, green, and blue color channels could be adjusted independently. Thus, in an echo of the palimpsest’s creation, a new overtext was sewn together. With it, modern scholars like Netz could finally read the ancient words behind the medieval prayers.

Yet the Archimedes Palimpsest is a book whose form seems to du­plicate itself in everything it ­touches, within the text and without: just as the entire book has multiple authors, the underlying Archi­medes text, we learn, was copied by two scribes—one for the words, one for the diagrams. Simon Finch, a London book dealer, won the book at the Christie’s auction. No one knows on whose behalf he was acting. Finch’s client remains anon­ymous, referred to publicly only as “Mr. B.” In fact, Finch’s patron was in attendance, unrecognized by the rest of the audience, as hidden as the ancient text for which he would pay so much money. An invisible text, bought by an invisible author.

On yet another plane, Archi­medes’s writing itself symbolizes the nature of the book. Netz tells us that Archimedes’s ancient dia­grams were schematic, as op­posed to the illustrative diagrams of modern science. Where contemporary mathematicians insist on draw­ings that exactly reproduce the figure being discussed, ancient dia­grams are merely representational thought aids. Archimedes might write: “Let there be two isosceles cones, ABÃ, ÄEZ, and let the base of ABÃ be equal to the surface of ÄEZ, and let the height AH be equal to the perpendicular KÈ5 and the corresponding figure would look like this:

Triangles are shown, instead of cones, and the line AH appears much longer than the line KÈ, where they should be equal—this is not an accurate illustration, only a schematic one. The diagram is not the object itself, merely a proxy—yet the idea prevails over the shortcomings of the diagrams. Just so, the text of the book persists through the centuries, despite the near destruction of the book that transmits it. The book and the diagram are poor approximations of the ideas they embody, yet the idea survives; the imaginary conquers the merely visual.

The essential task of Archi­medes’s treatises was the squaring of the circle. He begins with a curved object—a circle, a parabola, a section of a sphere—and derives the straight-edged equivalent—a square, a triangle, a prism—whose size can be measured easily. His work then consists of finding the measurable, the readable, that is inscribed within the unmeasurable, though never equal to it:

So there will be a certain figure inscribed in the sphere, contained… whose surfaces will be smaller than the surface of the sphere.6

A figure inscribing another figure, circumscribed by a sphere—this provides an apt metaphor for the book: an object containing the inscribed words, within the perfect fullness of the text that circumscribes it. How can we measure the one without but by the one within? The circumscribing sphere is too perfect—without edges, without points. Like the text that is never fully realized, we can imagine it, but it gives us no limits by which we can get its actual measure. We must resort to the cruder figure within it, the smaller figure. Its lines are finite, readable, familiar. Yet it never quite reaches the full capacity of the text—the sphere—that surrounds it, though we may reduce the difference between the two to a size smaller than a grain of sand, so approaching infinity.

Like the persistence of the text despite the book that carried it, and like Archimedes’s schematic diagrams, which are only poor likenesses of the forms for which they stand in, Archimedes’s entire science depended on the application of pure mathematics to the physical world—on the ability of the nonphysical to conquer the physical, the mental to outdo the visual. Plutarch tells us that when Archimedes “was occasionally carried by absolute violence to bathe or have his body anointed, he used to trace geometrical figures in the ashes of the fire, and diagrams in the oil on his body,”7 so great was his ability to overcome the vulgarities of the physical world with the power of his mind.

Much time and money have been spent making the copied words of Archimedes legible. But no matter how visible imagers have made the letters behind the prayers, Archi­medes still recedes under the accumulated layers of redactions and copies. “The hidden rhetoric is that nothing can be more beautiful than this unadorned mathematical text,”8 wrote the anonymous Byzan­tine scribe when he had com­pleted copying book one of Archimedes’s treatises onto a page that would later end up in the Palimp­sest. Yet the ancient mathematician’s work was already more than a thousand years old by the time this scribe—the earliest one we know—set it down. Heiberg, Netz, and other translators inherit not an unadorned text but one riddled with insertions and revisions. They will add their own, and more will surely follow. Clearly we have not arrived at the final word on Archi­medes, but we can be equally sure we will never arrive at the original word, either. It lies forever beyond our sight, lost beneath the blackness Heiberg could not penetrate, blotted out by the interceding generations. And like the medieval priest whose prayers covered the works of the ancient writers, every writer who puts pen to paper commits not just an act of writing but an act of writing over. No writer, in effect, begins with a blank page, but always writes over the entire ­history of the written word, using a language itself formed of innumerable historical layers. Whether made with quill on parchment, or with pixels on a screen, to write is to create a palimpsest, though what is covered might never be seen.

Perhaps it is appropriate that the only text in the Archimedes Palim­p­sest now legible with the naked eye is the only one I will probably never read a word of—at least not anytime soon. Netz published the first volume of his English translation of the complete works of Archimedes, based on the new readings, in 2004. The rest are forthcoming. Natalie Tchernetska, at Cambridge University, has published a portion of the Hyperides text in English. A fragment of the commentary on Aristotle, pertaining to the philosopher’s system of classification and nomenclature, appeared in English in an April BBC article. Yet, as Will Noel informed me, there is little chance of Ionnes Myronas’s prayer book being transcribed or translated anytime soon. It’s of too little importance to the academic world compared to the texts it covers. The only writing done on the Palimp­sest’s overtext ap­peared in an Italian academic journal in 2005, and the only library in New York that lists the journal in its collection is Columbia’s. In August I walked into the domed building with huge letters on the front spelling out THE LIBRARY OF COLUMBIA UNIVERSITY and asked a woman at the in­formation desk where I could find the Bollettino della Badia Greca di Grottaferrata. “Oh, this isn’t the library, dear,” she said. “It used to be. The library’s on the other side of campus.” But the journal wasn’t available there, either. It is in preparation to be bound.

1. Archimedes. On the Sphere and the Cylinder I, from Reviel Netz, The Works of Archimedes, Vol. I (2004).
2. William Noel and Reviel Netz. The Archimedes Codex (2007). Most of my understanding of the Archimedes Palimpsest’s history comes from this book. In fact, the inscription read “of the year 6737.” According to the Greek Orthodox calendar at the time, the world was created in our year 5509 BCE, making 6737 equivalent to our 1229 CE.
3. Abigail Quandt. “The Archimedes Palimpsest: Conservation, Treatment, Digital Imaging and Transcription of a Rare Medieval Manuscript,” in Works of Art on Paper: Books, Documents and Photographs (2002).
4. Nigel Wilson. “The Archimedes Palimpsest: A Progress Report,” in A Catalogue of Greek Manuscripts at The Walters Art Museum and Essays in honor of Gary Vikan (Journal of the Walters Art Museum, 2004).
5. Archimedes. On the Sphere and Cylinder, I.17, from Reviel Netz.
6. Ibid.
7. Plutarch. Lives. Translated by John Dryden (1979).
8. Netz, p. 183.
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