don't survive to us in their original form.

我們看到的偉大古文字

They survive because medieval scribes copied them

並不是它們的原件。

and copied them and copied them.

由於中世紀抄寫員的不斷抄寫，

And so it is with Archimedes,

反覆抄寫，所以它們仍然存在。

the great Greek mathematician.

阿基米德，

Everything we know about Archimedes as a mathematician

他是個偉大的希臘數學家，

we know about because of just three books,

這就是我們所知有關他的東西。

and they're called A, B and C.

我們從三本書知道他是這樣的一個人，

And A was lost by an Italian humanist in 1564.

分別是A，B和C。

And B was last heard of in the Pope's Library

在1564年，一個意大利人道主義者遺失了A書；

about a hundred miles north of Rome in Viterbo in 1311.

在1311年，人們最後一次在維泰博羅馬

Now Codex C was only discovered in 1906,

北面約一百里的教皇的圖書館聽到B書；

and it landed on my desk in Baltimore

在1906，C的抄本被發現，

on the 19th of January, 1999.

並運到我在巴爾的摩的辦公桌上。

And this is Codex C here.

那是1999年1月19日的事。

Now Codex C is actually buried in this book.

而這就是C書的抄本

It's buried treasure.

事實上，C的抄本是埋在這本書內。

Because this book is actually a prayer book.

這是被埋藏的寶藏，

It was finished by a guy called Johannes Myrones

因為這是一本禱告書。

on the 14th of April, 1229.

約翰內斯在1229年4月14日，

And to make his prayer book he used parchment.

完成了此書。

But he didn't use new parchment,

他用了羊皮紙去釘裝成他的禱告書，

he used parchment recycled from earlier manuscripts,

但他沒有用新的羊皮紙。

and there were seven of them.

他用早期的手稿循環再造的羊皮紙，

And Archimedes Codex C was just one of those seven.

而那些羊皮紙內有七份手稿，

He took apart the Archimedes manuscript and the other seven manuscripts.

阿基米德的C手抄本只是其中一份而已。

He erased all of their texts,

他把阿基米德的手稿和其他七份拆開，

and then he cut the sheets down in the middle,

抹去上面的所有文字，

he shuffled them up,

然後把羊皮只從中間切開。

and he rotated them 90 degrees,

他把它們洗了牌，

and he wrote prayers on top of these books.

旋轉90度變成橫向，

And essentially these seven manuscripts

最後把禱文寫在那些舊書上。

disappeared for 700 years, and we have a prayer book.

基本上，這七份手稿都已經消失700年了，

The prayer book was discovered by this guy,

而幸好我們有這本禱告書。

Johan Ludvig Heiberg, in 1906.

在1906年，一名叫約翰•海伯格的男人

And with just a magnifying glass,

發現了這本禱告書。

he transcribed as much of the text as he could.

他僅用了放大鏡，

And the thing is that he found two texts in this manuscript

盡可能抄寫了那些文字下來。

that were unique texts.

他在整份手稿中

They weren't in A and B at all;

發現了兩份獨特的文本。

they were completely new texts by Archimedes,

它們不是A書或B書，

and they were called "The Method" and "The Stomachion."

而是阿基米德所寫的新文本---

And it became a world famous manuscript.

《阿基米德方法》和《胃痛》。

Now it should be clear by now

它從此成為世界著名的手稿。

that this book is in bad condition.

所以，現在你們應該很清楚

It got in worse condition in the 20th century

這本書的保養情況十分惡劣。

after Heiberg saw it.

在二十世紀經海伯格看完以後，

Forgeries were painted over it,

它的情況更強差人意。

and it suffered very badly from mold.

偽造的文字曾被塗在上面，

This book is the definition of a write-off.

黴菌更長滿此書。

It's the sort of book

這本書肯定會被報銷，

that you thought would be in an institution.

它的情況好像

But it's not in an institution,

你在機構裡見到的舊書一般。

it was bought by a private owner in 1998.

但它不在機構內，

Why did he buy this book?

而被一個人在1998年賣下來。

Because he wanted to make that which was fragile safe.

為什麼他會買此書呢？

He wanted to make that which was unique ubiquitous.

因為他想令脆弱得東西得以安全，

He wanted to make that which was expensive free.

令獨一無二的東西普及，

And he wanted to do this as a matter of principle.

令昂貴的東西變得免費。

Because not many people are really going to read Archimedes in ancient Greek,

當然，這也是根據他一貫的原則---

but they should have the chance to do it.

即使只有少數人真的會閱讀阿基米德的古希臘文本，

So he gathered around himself the friends of Archimedes,

所有人都應有機會閱讀它。

and he promised to pay for all the work.

所以，他召集了一群阿基米德的支持者，

And it was an expensive job,

並承諾負擔一切的費用。

but actually it wouldn't be as much as you think

預料之內，這是十分昂貴的工作，

because these people, they didn't come from money,

但你絕對意想不到

they came from Archimedes.

那些人不是為錢而來，

And they came from all sorts of different backgrounds.

而是為阿基米德而來。

They came from particle physics,

他們來自不同背景，

they came from classical philology,

包括粒子物理、

they came from book conservation,

古典哲學、

they came from ancient mathematics,

書本保養、

they came from data management,

古代數學、

they came from scientific imaging and program management.

數據管理、

And they got together to work on this manuscript.

科技成像和程序管理。

The first problem was a conservation problem.

他們一起開始工作，

And this is the sort of thing that we had to deal with:

而首個難題是關於書本保養。

There was glue on the spine of the book.

這是我們無可避免要處理的難題：

And if you look at this photograph carefully,

書脊上有膠水。

the bottom half of this is rather brown.

如果你仔細看看這張照片，

And that glue is hide glue.

你會發現底下的一半是偏啡色的。

Now if you're a conservator,

那是隱藏膠水。

you can take off this glue reasonably easily.

假如你是一個管理員，

The top half is Elmer's wood glue.

你會頗容易地把這些膠水剝下來。

It's polyvinyl acetate emulsion

但上面的那一半是牛頭牌木膠，

that doesn't dissolve in water once it's dry.

一種乾後不溶於水的

And it's much tougher than the parchment that it was written on.

聚醋酸乙烯乳液。

And so before we could start imaging Archimedes,

它的質地遠遠比那張羊皮紙硬。

we had to take this book apart.

故此，在開始進行影像掃描之前，

So it took four years to take apart.

我們要把這本書拆開。

And this is a rare action shot, ladies and gentlemen.

我們用了四年才完成。

(Laughter)

先生小姐，這可是很不平常的事。

Another thing is that we had to get rid of all the wax,

（笑）

because this was used in the liturgical services

另外，我們還要弄走那些臘，

of the Greek Orthodox Church

那是希臘東正教教堂

and they'd used candle wax.

的禮拜儀式滴留在書上的。

And the candle wax was dirty,

而且，那些是臘燭的臘，

and we couldn't image through the wax.

那些臘是很髒的，

So very carefully we had to mechanically scrape off all the wax.

而我們更不能透過那些臘進行影像掃描。

It's hard to tell you exactly

所以，我們得小心翼翼地動手刮去所有的臘。

how bad this condition of this book is,

我很難確實地告訴你

but it came out in little bits very often.

這本書有多殘舊，

And normally in a book, you wouldn't worry about the little bits,

只能說它的碎片不時的跌出來。

but these little bits might contain unique Archimedes text.

通常，這種大小的碎片你跟本不會在意，

So, tiny fragments

但是這些碎片都可能有獨一無二的阿基米德字跡。

we actually managed to put back in the right place.

所以，這些小碎片，

Then, having done that, we started to image the manuscript.

我們還是要仔細的放回原頁。

And we imaged the manuscript

然後，我們開始影像掃描。

in 14 different wavebands of light.

我們用了14種光波的波段

Because if you look at something in different wavebands of light,

來掃描。

you see different things.

當你在不同波段看同一樣東西的時候，

And here is an image of a page

你看到不同的東西。

imaged in 14 different wavebands of light.

這一頁上有14種

But none of them worked.

不同波段的各個映像。

So what we did was we processed the images together,

但是，沒有一個可用。

and we put two images into one blank screen.

所以我們把那些映像一起處理，

And here are two different images of the Archimedes manuscript.

把兩個映像疊在同一頁。

And the image on the left

這是阿基米德的兩個不同的綜合手稿。

is the normal red image.

左邊的映像

And the image on the right is an ultraviolet image.

是普通的紅色圖像；

And in the image on the right

右邊的映像則是紫外光的圖像。

you might be able to see some of the Archimedes writing.

右邊的映像

If you merge them together into one digital canvas,

有比較清晰的阿基米德字跡。

the parchment is bright in both images

當你把這兩個圖像合併成同一個數碼影像，

and it comes out bright.

羊皮紙在原本兩個圖像都是亮色的，

The prayer book is dark in both images

所以它現在是亮色的。

and it comes out dark.

禱告書在兩個圖像都是暗色的，

The Archimedes text is dark in one image and bright in another.

所以它結果也是暗色的

And it'll come out dark but red,

阿基米德文字在一張是暗的，在另一張是亮的，

and then you can start to read it rather clearly.

所以它結果是暗紅色的。

And that's what it looks like.

現在你可以清楚的看到了，

Now that's a before and after image,

就在這裡。

but you don't read the image on the screen like that.

這是處理前和處理後的圖像，

You zoom in and you zoom in

但是你不會在這種背景去閱讀的。

and you zoom in and you zoom in,

你把它放大，放大，

and you can just read it now.

放大，然後再放大，

(Applause)

然後再去讀。

If you process the same two images in a different way,

（掌聲）

you can actually get rid of the prayer book text.

如果你把同樣的圖像用不同的方法處理，

And this is terribly important,

你甚至可以弄走禱告書本身的文字。

because the diagrams in the manuscript

這是非常重要的，

are the unique source for the diagrams

因為手稿上的影像

that Archimedes drew in the sand in the fourth century B.C.

是所有其他合成影像的唯一來源。

And there we are, I can give them to you.

阿基米德在公元前四世紀時在沙子上畫的

With this kind of imaging --

這裡，我會給你看到，

this kind of infrared, ultraviolet, invisible light imaging --

在影像掃描之下的

we were never going to image through the gold ground forgeries.

紅外線影像，紫外線影像，和透明光影像。

How were we going to do that?

但是，我們還是無法對有金色底稿的偽書進行掃描。

Well we took the manuscript,

我們怎麼辦呢？

and we decided to image it in X-ray fluorescence imaging.

我們拿了那些手稿，

So an X-ray comes in in the diagram on the left

放在螢光X射線下掃描。

and it knocks out an electron from the inner shell of an atom.

所以，一束X射線在圖像左面射進來，

And that electron disappears.

從原子的電子內殼層撞了一顆電子出來，

And as it disappears, an electron from a shell farther out

然後這顆電子消失了。

jumps in and takes its place.

當它消失的同時，外一層得電子外殼中，

And when it takes its place,

一顆電子跳進內層，取代原本的位置。

it sheds electromagnetic radiation.

同時，那顆電子

It sheds an X-ray.

釋出一束電磁輻射。

And this X-ray is specific in its wavelength

它釋出的便是X射線。

to the atom that it hits.

這種X-射線有獨特的波長，

And what we wanted to get

專門為這種原子調校。

was the iron.

我們想要拿到的

Because the ink was written in iron.

是鐵，

And if we can map

因為原手稿的墨水含有鐵的成份。

where this X-ray that comes out, where it comes from,

如果我們可以

we can map all the iron on the page,

把X射線從哪裡射入、那裡射出的地方標記，

then theoretically we can read the image.

我們就可以標示出整頁有鐵成份的地方。

The thing is that you need a very powerful light source to do this.

理論上，我們可借此閱讀圖像。

So we took it to the Stanford Synchrotron Radiation Laboratory

實際上，我們則需要用一個強大的光源去做這件事。

in California,

所以我們把手稿拿去史丹佛的同步輔射實驗室，

which is a particle accelerator.

坐落於加州的

Electrons go around one way,

一部粒子加速器。

positrons go around the other.

電子從一邊走，

They meet in the middle,

正電子則往另一邊，

and they create subatomic particles

然後在中間相遇，

like the charm quark and the tau lepton.

合成亞原子粒子，

Now we weren't actually going to put Archimedes in that beam.

就好像夸克和τ子。

But as the electrons go round at the speed of light,

我們本來沒有打算把阿基米德的手搞放進那光束裡，

they shed X-rays.

但是當電子以光束打圈時，

And this is the most powerful light source in the solar system.

它們會釋出X射線。

This is called synchrotron radiation,

這是太陽系內最強的光源---

and it's normally used to look at things

同步輻射，

like proteins and that sort of thing.

而我們平常看東西也會用它，

But we wanted it to look at atoms, at iron atoms,

例如蛋白質那類東西。

so that we could read the page from before and after.

但現在我們想看到原子，鐵原子，

And lo and behold, we found that we could do it.

然後讓我們看到的是處理前和處理後的影像。

It took about 17 minutes to do a single page.

你看，我們的確可以做到的。

So what did we discover?

它用大約17分鐘去完成一頁的掃描。

Well one of the unique texts in Archimedes

我們發現什麼了？

is called "The Stomachion."

一份獨特的阿基米德手稿

And this didn't exist in Codices A and B.

《胃痛》，

And we knew that it involved this square.

這並不存在於抄本A和抄本B內。

And this is a perfect square,

我們知到它談到這個正方形，

and it's divided into 14 bits.

這是一個完美的正方形，

But no one knew what Archimedes was doing with these 14 bits.

然後分成14塊。

And now we think we know.

沒有人會知道阿基米德用這十四塊做什麼，

He was trying to work out

而現在，我們認為我們知道了。

how many ways you can recombine those 14 bits

他試圖找出

and still make a perfect square.

不同方法重新組合這 14 塊

Anyone want to guess the answer?

成一個完美的正方形。

It's 17,152 divided into 536 families.

有人要猜猜看嗎？

And the important point about this

總數是 17,152， 分為 536 類別。

is that it's the earliest study in combinatorics in mathematics.

最重要的是，

And combinatorics is a wonderful and interesting branch of mathematics.

它是組合數學的最早研究，

The really astonishing thing though about this manuscript

組合數學是數學中精彩而有趣的分支。

is that we looked at the other manuscripts

這份手稿令人驚異的事情

that the palimpsester had made,

是當我們看著再生羊皮紙卷上的其他的手稿

the scribe had made his book out of,

其他手稿時，

and one of them was a manuscript containing text by Hyperides.

在抄寫員釘裝成它那本禱告書時，

Now Hyperides was an Athenian orator from the fourth century B.C.

其中一份是包含海柏維特的文字，

He was an exact contemporary of Demosthenes.

海柏維特是西元前四世紀雅典的演說家，

And in 338 B.C. he and Demosthenes together

堪稱當代的狄摩西尼。

decided that they wanted to stand up

在西元前 338 年，他和狄摩西尼一起

to the military might of Philip of Macedon.

決定反抗

So Athens and Thebes went out to fight Philip of Macedon.

馬其頓菲力浦的軍隊，

This was a bad idea,

所以雅典人和底比斯人去抵抗馬其頓菲力浦的軍隊。

because Philip of Macedon had a son called Alexander the Great,

這是一個糟糕的主意，

and they lost the battle of Chaeronea.

因為馬其頓菲力蒲的兒子是亞歷山大大帝，

Alexander the Great went on to conquer the known world;

所以他們在海羅尼亞的戰鬥落敗了。

Hyperides found himself on trial for treason.

亞歷山大大帝繼續征服那時的世界 ；

And this is the speech that he gave when he was on trial --

海柏維特則因叛國罪受審。

and it's a great speech:

這是他在判刑時的演說，

"Best of all," he says, "is to win.

一個偉大的演講全文：

But if you can't win,

"最好的結果，"他說："是勝利。

then you should fight for a noble cause,

但如果你贏不了，

because then you'll be remembered.

你應該為一個崇高的理想去打那場仗，

Consider the Spartans.

因為你會名留青史。

They won enumerable victories,

試想想斯巴達，

but no one remembers what they are

他們贏得不可枚舉的勝利，

because they were all fought for selfish ends.

但沒有人記得它們是哪些戰場，

The one battle that the Spartans fought that everybody remembers

因為他們為一己之私而戰。

is the the battle of Thermopylae

我們唯一記得斯巴達的

where they were butchered to a man,

是溫泉關的戰役，

but fought for the freedom of Greece."

他們完全被宰殺了，戰敗了，

It was such a great speech

但為希臘的自由而戰鬥。"

that the Athenian law courts let him off.

這是一個偉大的演講

He lived for another 10 years,