Oldtidens store skrifter er ikke tilgængelige i deres oprindelige form. De er tilgængelige, fordi middelalderens skrivere kopierede dem, igen og igen. Således er det også med Arkimedes, den store græske matematiker.
The great texts of the ancient world don't survive to us in their original form. They survive because medieval scribes copied them and copied them and copied them. And so it is with Archimedes, the great Greek mathematician.
Alt som vi ved om Arkimedes som matematiker, ved vi fra blot tre bøger, som hedder A, B og C. A blev smidt væk af en italiensk humanist i 1564. B hørte man sidst om i pavens bibliotek cirka 160 kilometer nord for Rom i Viterbo i 1311. Kodeks C blev først fundet i 1906, og det havnede på mit skrivebord i Baltimore den 19. januar 1999. Dette er Kodeks C.
Everything we know about Archimedes as a mathematician we know about because of just three books, and they're called A, B and C. And A was lost by an Italian humanist in 1564. And B was last heard of in the Pope's Library about a hundred miles north of Rome in Viterbo in 1311. Now Codex C was only discovered in 1906, and it landed on my desk in Baltimore on the 19th of January, 1999. And this is Codex C here.
Kodeks C er faktisk gemt i denne bog. Det er en gemt skat. Denne bog er nemlig faktisk en bønnebog. Den blev afsluttet af en fyr ved navn Ioannes Myronas den 14. april 1229. For at lave sin bønnebog brugte han pergament. Men han brugte ikke nyt pergament, han brugte pergament, som var genbrugt fra tidligere manuskripter, som der var syv af. Arkimedes' kodeks C var blot et af disse syv. Han skilte Arkimedes' og de syv andre manuskripter ad. Han slettede al skriften, hvorefter han skar arkene over på midten, han blandede dem, og han roterede dem 90 grader, og han skrev bønner på dem. Disse syv manuskripter forsvandt nu i 700 år, og vi har en bønnebog.
Now Codex C is actually buried in this book. It's buried treasure. Because this book is actually a prayer book. It was finished by a guy called Johannes Myrones on the 14th of April, 1229. And to make his prayer book he used parchment. But he didn't use new parchment, he used parchment recycled from earlier manuscripts, and there were seven of them. And Archimedes Codex C was just one of those seven. He took apart the Archimedes manuscript and the other seven manuscripts. He erased all of their texts, and then he cut the sheets down in the middle, he shuffled them up, and he rotated them 90 degrees, and he wrote prayers on top of these books. And essentially these seven manuscripts disappeared for 700 years, and we have a prayer book.
Bønnebogen blev fundet af denne fyr, Johan Ludvig Heiberg, i 1906. Kun ved hjælp af en lup tydede han så meget af teksten, som han kunne. Sagen er, at han fandt to tekster i dette manuskript, som var unikke. De fandtes slet ikke i A og B; De var helt nye tekster af Arkimedes, og de hedder "Metoden" og "Stomachion". Manuskriptet blev verdensberømt.
The prayer book was discovered by this guy, Johan Ludvig Heiberg, in 1906. And with just a magnifying glass, he transcribed as much of the text as he could. And the thing is that he found two texts in this manuscript that were unique texts. They weren't in A and B at all; they were completely new texts by Archimedes, and they were called "The Method" and "The Stomachion." And it became a world famous manuscript.
På dette tidspunkt skal det forstås, at denne bog er i dårlig stand. Dens stand forværredes i det 20. århundrede, efter Heiberg så den. Falsknerier blev malet i den, og den led frygteligt af mug. Denne bog er selve definitionen af skrammel. Det er den slags bog, som burde være på en institution. Men den er ikke på en institution, den blev købt af en privat ejer i 1998.
Now it should be clear by now that this book is in bad condition. It got in worse condition in the 20th century after Heiberg saw it. Forgeries were painted over it, and it suffered very badly from mold. This book is the definition of a write-off. It's the sort of book that you thought would be in an institution. But it's not in an institution, it was bought by a private owner in 1998.
Hvorfor købte han bogen? Fordi han ville redde det skrøbelige. Han ville gøre det unikke universelt tilgængeligt. Han ville gøre det dyre gratis. Dette gjorde han som en principsag. Fordi mange mennesker ville aldrig læse Arkimedes på oldgræsk, men de burde have muligheden for det.
Why did he buy this book? Because he wanted to make that which was fragile safe. He wanted to make that which was unique ubiquitous. He wanted to make that which was expensive free. And he wanted to do this as a matter of principle. Because not many people are really going to read Archimedes in ancient Greek, but they should have the chance to do it.
Så han samlede Arkimedes' venner, og lovede at han ville betale for alt arbejdet. Det var et dyrt arbejde, men det kom ikke til at koste så meget, som man kunne tro, da disse folk ikke kom for pengene, de kom for Arkimedes. Og de havde alle mulige baggrunde. De kom fra partikelfysikken, de kom fra klassisk filologi, de kom fra bog-konservering, de kom fra oldtidens matematik, de kom fra data-styring, de kom fra videnskabelig billedbehandling og program-styring. De fandt sammen for at arbejde på dette manuskript.
So he gathered around himself the friends of Archimedes, and he promised to pay for all the work. And it was an expensive job, but actually it wouldn't be as much as you think because these people, they didn't come from money, they came from Archimedes. And they came from all sorts of different backgrounds. They came from particle physics, they came from classical philology, they came from book conservation, they came from ancient mathematics, they came from data management, they came from scientific imaging and program management. And they got together to work on this manuscript.
Det første problem var konserveringen. Dette er et eksempel på hvad vi havde at gøre med: Der var lim på bogens ryg. Hvis I ser nøje efter på billedet, er den nederste halvdel af bogen ganske brun. Limen er udvundet af dyrehud. Hvis man er konservator, kan man relativt nemt fjerne denne slags lim. På den øverste del har man brugt trælim. Det er en emulsion af polyvinylacetat, som ikke kan opløses i vand, når den først er tør. Den er meget sejere, end pergamentet den blev brugt på. Så før vi kunne begynde at scanne Arkimedes, var vi nødt til at skille bogen ad. Det tog fire år at skille bogen ad. Dette, mine damer og herrer, er et sjældent billede af processen.
The first problem was a conservation problem. And this is the sort of thing that we had to deal with: There was glue on the spine of the book. And if you look at this photograph carefully, the bottom half of this is rather brown. And that glue is hide glue. Now if you're a conservator, you can take off this glue reasonably easily. The top half is Elmer's wood glue. It's polyvinyl acetate emulsion that doesn't dissolve in water once it's dry. And it's much tougher than the parchment that it was written on. And so before we could start imaging Archimedes, we had to take this book apart. So it took four years to take apart. And this is a rare action shot, ladies and gentlemen.
(Latter)
(Laughter)
Derefter måtte vi fjerne al voksen, da man brugte det under gudstjenesterne i den græsk-ortodokse kirke; og man brugte voks fra lys. Voksen fra lysene var beskidt, og vi kunne ikke scanne igennem voksen. Så med den største forsigtighed måtte vi mekanisk skrabe al voksen af.
Another thing is that we had to get rid of all the wax, because this was used in the liturgical services of the Greek Orthodox Church and they'd used candle wax. And the candle wax was dirty, and we couldn't image through the wax. So very carefully we had to mechanically scrape off all the wax.
Det er svært at beskrive præcist, hvor dårlig en stand bogen er i, men ofte kom den i små stykker. Under normale forhold ville man ikke bruge energi på de små stykker, men disse små stykker kunne indeholde unik tekst af Arkimedes. Så det lykkedes os faktisk, at sætte bittesmå fragmenter på plads.
It's hard to tell you exactly how bad this condition of this book is, but it came out in little bits very often. And normally in a book, you wouldn't worry about the little bits, but these little bits might contain unique Archimedes text. So, tiny fragments we actually managed to put back in the right place.
Da vi havde gjort det, kunne vi begynde scanningen af manuskriptet. Vi scannede manuskriptet under 14 forskellige lysfrekvenser. Fordi hvis man ser på noget under forskellige lysfrekvenser, ser man forskellige ting. Her er et billede af en side scannet under 14 forskellige lysfrekvenser.
Then, having done that, we started to image the manuscript. And we imaged the manuscript in 14 different wavebands of light. Because if you look at something in different wavebands of light, you see different things. And here is an image of a page imaged in 14 different wavebands of light.
Men ingen af dem virkede. Så vi gjorde det, at vi scannede billederne sammen, og vi satte to billeder sammen på en blank skærm. Her er to forskellige billeder af Arkimedes' manuskript. Billedet til venstre er det normale røde billede. Billedet til højre er et ultraviolet billede. På billedet til højre kan I måske se noget af Arkimedes' skrift. Hvis man samler dem på et digitalt lærred, er pergamentet lyst på begge billeder, og det fremstår som lyst. Bønnebogen er mørk på begge billeder, og den fremstår som mørk. Arkimedes' skrift er mørk på et billede og lyst på et andet. Den fremstår som mørkerød, og så kan man begynde at læse den ret klart. Sådan ser det ud.
But none of them worked. So what we did was we processed the images together, and we put two images into one blank screen. And here are two different images of the Archimedes manuscript. And the image on the left is the normal red image. And the image on the right is an ultraviolet image. And in the image on the right you might be able to see some of the Archimedes writing. If you merge them together into one digital canvas, the parchment is bright in both images and it comes out bright. The prayer book is dark in both images and it comes out dark. The Archimedes text is dark in one image and bright in another. And it'll come out dark but red, and then you can start to read it rather clearly. And that's what it looks like.
Dette er et før og efter-billede, men sådan læser man det ikke på skærmen. Man zoomer ind, igen og igen, og nu kan man bare læse det.
Now that's a before and after image, but you don't read the image on the screen like that. You zoom in and you zoom in and you zoom in and you zoom in, and you can just read it now.
(Bifald)
(Applause)
Hvis man fremkalder de samme to billeder på en anden måde, kan man faktisk slippe af med bønnebogens skrift. Dette er meget vigtigt, fordi diagrammerne i manuskriptet er eneste kilde for diagrammerne, som Arkimedes tegnede i sandet i det 4. århundrede før vor tidsregning. Her er de, jeg viser dem til jer.
If you process the same two images in a different way, you can actually get rid of the prayer book text. And this is terribly important, because the diagrams in the manuscript are the unique source for the diagrams that Archimedes drew in the sand in the fourth century B.C. And there we are, I can give them to you.
Med denne type scanning -- denne slags infrarøde, ultraviolette, usynligt lys-scanning -- kunne vi aldrig scanne igennem de guld-baserede falsknerier. Hvordan skulle vi kunne gøre det? Vi tog manuskriptet, og vi besluttede at scanne det ved hjælp af røntgenfluorescens. En røntgen-stråle kommer ind på diagrammet til venstre, og det banker en elektron løs fra et atoms inderste bane. Denne elektron forsvinder. Som den forsvinder, hopper en elektron fra en ydre bane, ind og tager dens plads. Når den tager dens plads, giver den elektromagnetisk stråling fra sig. Den afgiver en røntgenstråle. Denne røntgenstråle har en særlig frekvens for det atom, som den rammer.
With this kind of imaging -- this kind of infrared, ultraviolet, invisible light imaging -- we were never going to image through the gold ground forgeries. How were we going to do that? Well we took the manuscript, and we decided to image it in X-ray fluorescence imaging. So an X-ray comes in in the diagram on the left and it knocks out an electron from the inner shell of an atom. And that electron disappears. And as it disappears, an electron from a shell farther out jumps in and takes its place. And when it takes its place, it sheds electromagnetic radiation. It sheds an X-ray. And this X-ray is specific in its wavelength to the atom that it hits.
Det som vi sigtede efter var jern. Fordi blækket var lavet af jern. Hvis vi kan kortlægge, hvor denne røntgenstråle kommer fra, kan vi kortlægge alt jernet på siden, og så kan vi, teoretisk set, læse billedet.
And what we wanted to get was the iron. Because the ink was written in iron. And if we can map where this X-ray that comes out, where it comes from, we can map all the iron on the page, then theoretically we can read the image.
Sagen er, at man skal bruge en meget kraftig lyskilde for at kunne gøre det. Så vi bragte manuskriptet til Stanfords SSRL i Californien, som er en partikel-accelerator. Elektroner kommer fra den ene side, og positroner kommer fra den anden. De mødes på midten, hvor de skaber sub-atomare partikler som charm-kvarken og tau-leptonen. Vi ville ikke lægge manuskriptet ind i strålen. Men når elektronerne bevæger sig rundt med lysets hastighed, afgiver de røntgenstråler. Dette er den stærkeste lyskilde i solsystemet. Det kaldes synkrotron-stråling, og man bruger det normalt til at se på ting som proteiner og den slags. Men vi ville bruge den til at se på atomer, på jern-atomer, så vi kunne læse siden fra før og efter. Og se nu her, vi opdagede at det var muligt. Hver side tog 17 minutter at fuldføre.
The thing is that you need a very powerful light source to do this. So we took it to the Stanford Synchrotron Radiation Laboratory in California, which is a particle accelerator. Electrons go around one way, positrons go around the other. They meet in the middle, and they create subatomic particles like the charm quark and the tau lepton. Now we weren't actually going to put Archimedes in that beam. But as the electrons go round at the speed of light, they shed X-rays. And this is the most powerful light source in the solar system. This is called synchrotron radiation, and it's normally used to look at things like proteins and that sort of thing. But we wanted it to look at atoms, at iron atoms, so that we could read the page from before and after. And lo and behold, we found that we could do it. It took about 17 minutes to do a single page.
Så, hvad fandt vi ud af? En af de unikke skrifter i manuskriptet hedder "Stomachion" Denne fandtes ikke i kodeks A og B. Vi vidste, at den havde at gøre med denne firkant. Det er et perfekt kvadrat, og det er opdelt i 14 stykker. Men ingen vidste hvad Arkimedes lavede med disse 14 stykker. Men nu tror vi, at vi ved det. Han prøvede at finde ud af, hvor mange måder man kunne sætte disse 14 stykker sammen på og stadig have et perfekt kvadrat. Kan I gætte svaret? Det er 17.152 fordelt på 536 familier. Det vigtige med det her er, at det er det tidligste studie i kombinatorik i matematikken. Kombinatorik er en vidunderlig og interessant matematisk disciplin.
So what did we discover? Well one of the unique texts in Archimedes is called "The Stomachion." And this didn't exist in Codices A and B. And we knew that it involved this square. And this is a perfect square, and it's divided into 14 bits. But no one knew what Archimedes was doing with these 14 bits. And now we think we know. He was trying to work out how many ways you can recombine those 14 bits and still make a perfect square. Anyone want to guess the answer? It's 17,152 divided into 536 families. And the important point about this is that it's the earliest study in combinatorics in mathematics. And combinatorics is a wonderful and interesting branch of mathematics.
Det virkeligt forbløffende ved dette manuskript er, at vi så på de andre manuskripter, som palimpsest-mageren havde lavet, som skriveren havde lavet denne bog af, og et af dem var et manuskript indeholdende tekst af Hypereides. Hypereides var en taler fra Athen i det 4. århundrede f.v.t. Han levede på samme tid som Demosthenes. I 338 f.v.t. bestemte han og Demosthenes sig for at gøre modstand mod Filip 2. af Makedoniens militære magt. Så Athen og Theben gik i krig mod Filip 2. af Makedonien. Det var en dårlig idé, for Filip 2. af Makedonien havde en søn ved navn Alexander den Store, og de tabte slaget ved Chaeronea.
The really astonishing thing though about this manuscript is that we looked at the other manuscripts that the palimpsester had made, the scribe had made his book out of, and one of them was a manuscript containing text by Hyperides. Now Hyperides was an Athenian orator from the fourth century B.C. He was an exact contemporary of Demosthenes. And in 338 B.C. he and Demosthenes together decided that they wanted to stand up to the military might of Philip of Macedon. So Athens and Thebes went out to fight Philip of Macedon. This was a bad idea, because Philip of Macedon had a son called Alexander the Great, and they lost the battle of Chaeronea.
Alexander den Store endte med at erobre den kendte verden; Hypereides blev retsforfulgt for forræderi. Dette er hans forvarstale fra retssagen -- og det er en stor tale: "Det bedste," siger han, "er at vinde. Men hvis man ikke kan vinde, bør man kæmpe for en ædel sag, for så vil man blive husket. Tag spartanerne som eksempel. De vandt utallige sejre, men ingen husker dem, fordi de alle blev udkæmpet af egoistiske grunde. Det eneste slag, som spartanerne deltog i, som alle kan huske, er slaget ved Thermopylæ, hvor de alle blev slagtet, men kæmpede for Grækenlands frihed." Talen var så god, at retten i Athen lod ham slippe uden straf. Han levede i 10 år til, før den makedonske hær fangede ham. De skar hans tunge af for at spotte hans tale, og ingen ved, hvad de gjorde med liget. Så dette er opdagelsen af en glemt stemme fra antikken, som taler til os, ikke fra graven, fordi hans grav findes ikke, men fra retten i Athen.
Alexander the Great went on to conquer the known world; Hyperides found himself on trial for treason. And this is the speech that he gave when he was on trial -- and it's a great speech: "Best of all," he says, "is to win. But if you can't win, then you should fight for a noble cause, because then you'll be remembered. Consider the Spartans. They won enumerable victories, but no one remembers what they are because they were all fought for selfish ends. The one battle that the Spartans fought that everybody remembers is the the battle of Thermopylae where they were butchered to a man, but fought for the freedom of Greece." It was such a great speech that the Athenian law courts let him off. He lived for another 10 years, then the Macedonian faction caught up with him. They cut out his tongue in mockery of his oratory, and no one knows what they did with his body. So this is the discovery of a lost voice from antiquity, speaking to us, not from the grave, because his grave doesn't exist, but from the Athenian law courts.
På dette tidspunkt bør jeg nævne, at man normalt ikke, når man ser på manuskripter fra middelalderen, som er blevet skrabet, finder unikke skrifter. Så at finde to i ét manuskript er noget særligt. At finde tre er fuldstændig mærkeligt. Vi fandt tre.
Now I should say at this point that normally when you're looking at medieval manuscripts that have been scraped off, you don't find unique texts. And to find two in one manuscript is really something. To find three is completely weird. And we found three.
Aristoteles' "Kategorier" er en af de grundlæggende skrifter i den vestlige verdens filosofi. Vi fandt en kommentar om den fra det 3. århundrede. Muligvis af Galén og sandsynligvis af Porfyr.
Aristotle's "Categories" is one of the foundational texts of Western philosophy. And we found a third century A.D. commentary on it, possibly by Galen and probably by Porphyry.
Al det data som vi har samlet, alle billederne, alle de rå billeder, alle transskriptionerne, som vi lavede, og den slags er lagt på nettet under en Creative Commons licens, så det kan bruges af alle til ethvert kommercielt formål.
Now all this data that we collected, all the images, all the raw images, all the transcriptions that we made and that sort of thing have been put online under a Creative Commons license for anyone to use for any commercial purpose.
(Bifald)
(Applause)
Hvorfor gjorde manuskriptets ejer dette? Det gjorde han, fordi han forstår data såvel som bøger. Det man skal gøre med bøger, hvis man vil sikre deres langvarige brug, er at gemme dem i skabe, og lade meget få mennesker se dem. Det man skal gøre med data, hvis man vil have det til at overleve, er at slippe det fri og lade alle få det med så lidt kontrol af dataene som muligt. Og det er, hvad han gjorde.
Why did the owner of the manuscript do this? He did this because he understands data as well as books. Now the thing to do with books, if you want to ensure their long-term utility, is to hide them away in closets and let very few people look at them. The thing to do with data, if you want it to survive, is to let it out and have everybody have it with as little control on that data as possible. And that's what he did.
Og institutioner kan lære af dette. For i øjeblikket indskrænker institutioner deres data med ophavsretsrestriktioner og den slags. Hvis man vil se på manuskripter fra middelalderen på nettet, er man nødt til at gå til Nationalbiblioteket Y's hjemmeside eller Universitetsbiblioteket X's hjemmeside, som er den mest kedelige måde, man kan behandle digitale data på. Det man skal gøre er, at samle det hele.
And institutions can learn from this. Because institutions at the moment confine their data with copyright restrictions and that sort of thing. And if you want to look at medieval manuscripts on the Web, at the moment you have to go to the National Library of Y's site or the University Library of X's site, which is about the most boring way in which you can deal with digital data. What you want to do is to aggregate it all together.
Fordi fremtidens net af oldtidens manuskripter vil ikke blive bygget af institutioner. Det vil blive bygget af brugere, af folk som samler disse data, af folk som vil samle alle mulige slags kort fra det sted de kommer fra, alle mulige slags romaner fra middelalderen fra det sted de kommer fra, folk som blot vil lave deres egen pragtfulde samling af smukke ting. Det er nettets fremtid. Det er en tiltrækkende og smuk fremtid, hvis vi blot kan bringe den til udfoldelse.
Because the Web of the ancient manuscripts of the future isn't going to be built by institutions. It's going to be built by users, by people who get this data together, by people who want to aggregate all sorts of maps from wherever they come from, all sorts of medieval romances from wherever they come from, people who just want to curate their own glorious selection of beautiful things. And that is the future of the Web. And it's an attractive and beautiful future, if only we can make it happen.
Vi, på Walters Art Museum, har fulgt dette eksempel, og vi har lagt alle vore manuskripter ud på nettet, så folk kan nyde dem -- al råmaterialet, alle beskrivelserne, alle metadata -- under en Creative Commons licens. Walters Art Museum er et lille museum, og det har smukke manuskripter, men dataene er fantastiske. Resultatet af dette er, at hvis du søger på googles billede-søgning nu og for eksempel skriver "Illuminated manuscript Koran", vil 24, ud af de 28 billeder du finder, være fra min institution.
Now we at the Walters Art Museum have followed this example, and we have put up all our manuscripts on the Web for people to enjoy -- all the raw data, all the descriptions, all the metadata. under a Creative Commons license. Now the Walters Art Museum is a small museum and it has beautiful manuscripts, but the data is fantastic. And the result of this is that if you do a Google search on images right now and you type in "Illuminated manuscript Koran" for example, 24 of the 28 images you'll find come from my institution.
(Bifald)
(Applause)
Lad os tænke over dette. Hvad får institutionen ud af det? Institutionen får en masse ud af det. Man kan nævne humaniora og den slags, men lad os tale om egennyttige emner. Fordi det, som institutionen i virkeligheden får ud af det, er dette: Hvorfor besøger folk Louvre? For at se Mona Lisa. Hvorfor vil de se Mona Lisa? Fordi de allerede ved, hvordan hun ser ud. Og de ved, hvordan hun ser ud fordi de har set billeder af hende alle vegne.
Now, let's think about this for a minute. What's in it for the institution? There are all sorts of things that are in it for the institution. You can talk about the Humanities and that sort of thing, but let's talk about selfish things. Because what's really in it for the institution is this: Now why do people go to the Louvre? They go to see the Mona Lisa. Why do they go to see the Mona Lisa? Because they already know what she looks like. And they know what she looks like because they've seen pictures of her absolutely everywhere.
Der er slet ikke brug for disse begrænsninger. Jeg synes, at institutioner burde frigive alle deres data under ubegrænsede licenser, og det ville være til alles fordel. Hvorfor lader vi ikke bare alle have adgang til disse data og lave deres egen samling af oldtidens viden og vidunderlige og smukke ting og derved øge skønheden og den kulturelle betydning af internettet?
Now, there is no need for these restrictions at all. And I think that institutions should stand up and release all their data under unrestricted licenses, and it would be a great benefit to everybody. Why don't we just let everybody have access to this data and curate their own collection of ancient knowledge and wonderful and beautiful things and increase the beauty and the cultural significance of the Internet.
Mange tak.
Thank you very much indeed.
(Bifald)
(Applause)