Archimedes: Accelerator Reveals Ancient Text

good evening and thank you very much for coming please join me for a journey

which we find fascinating and which in fact from our point of view here at

Stanford has just begun if you could

have read the New York Times on July 16 1907 you would have found on the front

page the headlines of a big literary find in Constantinople the Danish

scholar Johann Ludwig Heiberg had discovered an ancient a series of

ancient writings inside a 12th century prayer book and it is this book whether

it's our journey today is concerned about but let us go back another 2,500

years what might look to you like the Sierra Foothills on a early summer day

is in fact a location where on September 11 490 BC the fate of Western

civilization was hanging on a very thin thread a huge Persian army led by King

Darius had landed on the Greek shore in the bay of Marathon estimates about the

size range from twenty to sixty thousand men strong after several days of

discussion and consultation the Athenians decided to go to face the

enemy and they sent into the valley of Marathon an army of 10,000 Athenians

with the help of a thousand Plataea being about sixteen hundred yards from

the front line of the Persian archers the Athenians did the usual thing they

organized their troops into a large balance where they protected themselves basically like a turtle with all their

shields and started to march it took about ten minutes when they reached the

range of the Persian archers - about 200 yards at that point something happened

which hadn't happened in the history of warfare before rather than continuing the march and being exposed to the hell

of art of arrows they started to rush in a almost sprint into the front and did

such a surprise attack avoiding the arrows they got immediately into an in fight and it took only part of a day

before the stronger equipped

Greek Athenian soldiers had beaten the Persians at the end of the battle 6,400

Persian soldiers were killed and only 192 Greek fighters upon which the

Persians decided to flee one of the fighters by D pedis after fighting all

day had to run 26 miles to Athens to deliver the message of victory upon

which he dropped dead there might be some people amongst you who regret that

Athens is actually that far away from the bay of Marathon the Battle of

Marathon was the first victory of a new form of government it was the first

victory of the Occident over the Orient and it is considered as one of the most

important events marking the birth of Western culture and the beginning of the

age of classics the UNAM and slave and

Norman subject was said about the Athenians they are proud the Athenians the victorious Democrats self-confident

and ambitious approaching arrogance sounds familiar

they have a mentality that leads them to enormous accomplishments in politics arts philosophy and architecture there

was a great Greek philosophers Socrates born only 20 years after the Battle of

Marathon the questioner his most famous phrase all I know is I know nothing his

student Plato the idealist who wrote among many important works the Republic

and his student Aristotle the taxonomist

who was amongst many alikom accomplishments the educator of a

thirteen-year-old boy who turned out later to be known as Alexander the Great and there were the mathematicians Euclid

of Alexandria his concept of space in

fact of three-dimensional space has survived 2200 years until a former

patent clerk of the name Albert Einstein discovered that in fact space is not

three-dimensional there is a fourth dimension time multiplied with a

constant the speed of light which is perpendicular to the three dimensions he

later also realized that this four-dimensional space-time is actually

not straight but it's curved under the influence of gravity and this resulted in the general rarity of relativity

still valid and confirmed many times it

will be seen how long Einstein's concept of our universe will hold there are strong doubts it'll will survive 2,200

years certainly string theorists don't hope so and then there was the greatest

of them all Archimedes of Syracuse born in the city-state of Syracuse on the

island of Sicily and an unfortunate

event killed at the age of 74 by a Roman soldier who didn't follow his orders

Archimedes was famous at the time the Romans had all her to kept him alive he

was such a valuable person but supposedly deep into thoughts about

mathematical problems he didn't follow the orders and was killed Archimedes as

a student was sent to Alexandra to learn the teachings of Euclid and actually

also of Aristotle he amongst his many

accomplishments in mathematics engineering warfare and science is the

famous pulley a means with which you can pull a weight many times heavier than

yourself the famous Archimedes screw a pumping system still used in many places

around the world with which you can pump water from a lower level to a higher

level during the siege of Syracuse Archimedes employed a combination of

hooks and levers and the Roman

battleships which were anchored at the K these hooks were brought underneath and they were shaken some some of them

tipped over and the soldiers were scared to death the most famous story about

Archimedes however is his Eureka moment

the king of Syracuse had asked the Goldsmith to make him a wreath and he

had suspected that the Goldsmith had mixed some lesser noble metal within the

gold and which is also lighter he asked Archimedes to help him solve the problem at the time of Archimedes is

it was relatively easy to weigh a an object however in order to determine

that's cold or not you needed to know the density and for that you need to

know not only the weight but also the volume how could you ever determine the volume of such a complex object like a

wreath a camellias supposedly taking a bath all of a sudden got a great idea

the water in his bathtub which he moved

away with his body was exact had exactly the same volume of his own body no matter how complicated and irregular his

own body was and by knowing that you had a way to measure the volume now all you

had to do measure the weight so and a possible experiment how to do this is

you put a balance beam you put the amount of code equal to the amount in

the wreath and then you dip them balls into the water if the wreath has a

larger volume it'll be it'll get a stronger lift and the balance will get out of out of balance in that matter the

King actually realized that the Goldsmith wasn't this honest man he had put some lesser noble metal into the

wreath Archimedes also invented the law of the lever and everyone who has played

with their children on a teeter-totter knows how valuable that is it tells you

that the mass a and the disk times the

distance a of the center on a balance equals the mass the distance B times the mass B are on the same balance in order

to stay in equilibrium and I will show you now in a short version how

Archimedes did the proof of this important concept I'll show it in

Reverse how he did it but I think it's it's better for the illustrations imagine you have two objects of equal

mass at an equal distance your balance beam will be perfectly straight now of

course you could replace them by four objects as similarly spaced

or without disturbing anything you could place these four objects close to the middle and put them in one large as long

as they're always at the exact same distance from the balance now imagine you take 16 8 on either side you take

four of them and replace them with one which is four times as heavy you will not bring the balance you will not

disturb disturb the balance you take the other ones and do the same thing in this

case it's 12 and you pray you place them by 12 all you have to do now is remind

yourself at which place these objects wear and you know that because the this

object is exactly at this school location and the object of 12 is exactly in between the six on either side you

can measure that and you have the law of the lever this law has dramatic

consequences of course because it tells you that in principle you could lift

something extremely heavy as long as your beam is long enough and that late led to the famous saying give me where

to stand and I will move the earth which is of course not to be taken literally but Archimedes was well aware of the

power of the other law of the lever in fact Archimedes was so famous at its time that as his fame grew his

challenges grew grew as well at one point the king of searchers asked him or

and at one point Archimedes took a combination of other levers and pulleys

and pulled a ship all by himself on land the king was so impressed and said from

now on we have to believe what Archimedes is saying scientists sometimes hope that the

reigning bodies today would have the same respect for them

archimedes most one of his most famous mathematical accomplishments was the

determination of the number pi it is compared to the mathematical invention

of the wheel pi is the ratio of the diameter and the circumference of a

circle and Archimedes used the following estimate he said he knew how to

calculate the lengths of the three sides of a triangle and he said well I know

that the triangle is that lengths has to be shorter than the sphere because all

of it is inside the sphere then he said why not divide these through three sides

and create an hexagon and then he knew also how to calculate the side of each

hexagon and if you add up all the six sides you will still get a number which

is smaller than the circle because it's it's still inside the circle however it is already much closer he continued that

through through 12 sides 24 48 until 96

at that point he had a very good lower limit of the circumference and then he

said let's do the same thing from the outside so he started from the outside and also went to 96 by those two methods

he had an upper limit and a lower limit and he got the value to a precision of 3.14

a value which is still used by many of who work in the construction that's good

enough Archimedes had a friend Eratosthenes he was 11 years younger and

Archimedes was kind of a mentor for him our tostones is famous because he was the first person to measure the size of

the earth how did he do it

the city of Aswan lies directly on the Tropic of Cancer that means on June 21st

at noon there is no shadow the Sun is directly overhead and here I'll show you

the situation of the earth this is the equator this is the north-south and the

Tropic of Cancer would be this line basically this is the race from the Sun

at noon our toastiness who came from Alexandria also knew that at the same

time on the same day there was in fact a small shadow and he could measure it it

was about a seven degree angle of the Sun he knew the distance between the two

cities from the Cavor Caravan traveling's it was about 5000 stadia and

one stadium is about 185 metres all he

had to do now take that distance multiplied by 360 divided by seven and

he got the estimate of the earth his number was falling and it's partly to

the uncertainty of its angle partly to the uncertainty of what exactly one stadium is it is believed to be have

fallen with between 39 and 46 thousand kilometers and the exact value is 40

thousand kilometers it's a remarkable achievement for that time before the war

we know that Archimedes wrote a letter to his friend Eratosthenes greetings since I know you

are diligent an excellent teacher of philosophy and greatly interested in any mathematical investigation that may come

your way I thought it might be appropriate to write down and set forth for you a certain special method he

later continued I presume there will be some among the present as well as future

generations who by means of the method explained will be enabled to find other

theorems which have not yet fallen to our share only through a miracle if you want or

through a series of fortunate circumstances that this letter actually

survived until today and in fact the method which our Archimedes describes in

here is of greatest significance which I will show you in a second in Archimedes time his work was written

on papyrus it was then copied also on papyrus go here you have a drawing of

Archimedes writing on papyrus growth in the fourth century the scribes changed

their method they started to use parchment made out of mostly goat and

sheep skin and they used an iron gall ink for their writings and the

Archimedes text or the Archimedes letter in this case was then written on a

parchment it is believed that the last time these texts were written was in the

10th century in the second half of the 10th century probably in Constantinople

however in the 12th century the 4th 4th crusade sacked Constantinople and his

parchment book was taken apart and in a

common practice at the time reused for other mostly religious writings we are

now in the deep part of the Dark Ages there was no interest in mathematics and

it was very hard to get by parchment so this was an early method of recycling

and here's how a palimpsest then expel

him says staining first raped again is made you take the original book which

you find with the parchment you use a acid made out of lemon juice and try to

wipe it out as perfect you can then you cut the two pages apart

turn them 90 degrees and write overwrite them with your own writings rebind them

and you have your little prayer book polemicist it was this palimpsest which

Johan Ludvig Heiberg had discovered in Constantinople in 1907 it did not only

contain seven of Archimedes three disease two of them had been previously

unknown one of them the method of mechanical theorems the letter of Archimedes to his friend Eratosthenes

it also contained the only Greek version of Archimedes famous treatise on

floating bodies hi Burke tried to get the manuscript out of Constantinople to

Copenhagen but they didn't let him do it so all he could do is travel to Constantinople and equipped with a

magnifying glass that was that all the technical help he had at the day each

strata started to transcribe the manuscript we know now that in his

transcription of the method there are significant gaps after World War one the

Archimedes palimpsest disappeared in fact Constantine / was looted to a large

extent and was believed that it had gone forever and then oh I'm sorry I'm going ahead

let me say the importance or the significance of the method and this is according to reveal nets who is the one

of the leading scholars a Stanford professor on Archimedes and he knows the method very well in fact we work

together with him in the method

Archimedes combines pure mathematics with physical considerations for example

by putting segments of a geometric of geometrical objects on a balance as a similar to what I just showed you at the

law of the lever he manages to measure the area and volume of geometrical objects basically

he is deriving geometrical discoveries by a physical thought experiment

the second extremely important point is Archimedes is able to perform infinite

sums he takes a fear for example and calculates its volume as the infinite

sum of circles from which it is made this is a breakthrough comparable to the

modern integral calculus and most of you if not in high school you had to deal

with that probably in college both findings are essential features of

modern science in fact and it is no exaggeration to say that Archimedes

method was 2,000 years ahead of its time

Galileo for example was considered the first physicist who used mathematics to

describe physical experiments Newton is considered the person who invented

calculus and it is one can only speculate how people like Galileo Newton

or da Vinci would have developed if they

would have known about the method from Archimedes on October 29 1998 shortly

after the Archimedes palimpsest what resurfaced in Paris it was auctioned at

Christie's New York and sold to an unknown investor important to note here

is that the person pledged not to limit access to an ancient manuscript and the

owner was contacted by will know from the Walters Art Museum shortly after the

auction and agreed to lend the manuscript for an integrated effort of

conservation and imaging in fact since 1998 there has been

significant progress in understanding the method because now other than a

magnifying glass one could use modern technology such as UV light or

multispectral imaging to better bring out the different texts however there

was a problem first of all the palimpsest was in

horrible conditions in fact since Heiberg had read it until between

haibach's 1907 and 1998 it had was

attacked by mold and many of the pages have been have really deteriorated since

then furthermore curiously four of the pages had medieval paintings on them

Heiberg never reported about medieval paintings they could have been they

could have been real but it was suspected immediately that there's something wrong with that and indeed

when looking at the manuscript rexella be able to take national in France

published in 1929 you can see a drawing which is almost identical to the one

which was found on the Archimedes palimpsest in fact it had the identical

size which suggests very much that this was just copied from someone onto the

parchment we know now in fact only since

about about two months that this

painting was done after 1939 from the composition of the different colors in

the painting we do not know who did it and we certainly do not know whether the

person who did it knew what he was actually doing whether he had any idea that the

was text by Archimedes underneath this is when I learned for the first time

about the Archimedes palimpsest in fact now comes Neil's introduction I was at a

photosynthesis meeting in Germany in November 2003 and I stayed home for one

night with my parents and my mother as many mothers too gave me a stack of

journals and little cop little snips of papers to read and that's when I heard

about the Archimedes palimpsest what struck me was the fact that the writings

were done with an iron-based ink I just had come from a conference

where for three days we were talking about nothing else then spinach and in

that spinach and now comes the question to you what a spinach have in common with the Archimedes palimpsest

we all know that spinach has a lot of iron in fact generations or one

generation at least mine had been forced to eat a lot of spinach because of a scientific error at one point it was

thought it has ten times more than the other green leaves it's not true there's not that much iron in spinach in fact

though so don't worry about it if you don't eat it every day does it have more

or less than than the Archimedes palimpsest III was sure it has less than

the Archimedes palimpsest in fact the experiments we do on spinach

show that this is really a trace element and I could not believe that even the

faintest text in the Archimedes palimpsest wouldn't have some traces of spinach similar some trace excuse me of

iron similar then to an our spinach now what else do you need to look through

meta for example through a painting it's x-rays and we all know that

because we have taken we have gotten our chest x-rays done and of course the

inventor of x-rays hood and the invention just celebrated the 100th birthday is billion cannot Welkin and

the first really x-ray image is supposedly that of his wife's hand which

also shows that the jewelry in that time was actually pretty big would you be

able to do would you be able to image the Archimedes palimpsest with such a

device and the answer is no because this

image is produced from a contrast so what you do is you shine the x-rays

through and the the part in this case the bones or this ring absorb much more

and so it stays darker if you have something extremely thin or something of

very dilute extremely dilute that contrast doesn't come out at all it is

like looking at the stars in bright daylight the light of the stars is there

but we won't see it why because the sunlight is so much stronger so what do

we do we look at the stars at night of course and that is very similar to the technique I'm going to describe you now

so please bear with me we are now traveling to the inside of an atom and I

will show you here a schematic setup how an atom is built it has a nucleus made

out of protons and neutrons and it has a whole array of electrons zipping around

the nucleus what determines an element

is only given by the number of protons you have in the nucleus if you have if

the nucleus has 26 protons it is iron and nothing else it doesn't matter how

many neutrons it has those are different isotopes but they are all iron if it has

another amount like six it is carbon etc etc now it also has

the same amount of electrons to balance this positive charge so iron has typically 26 electrons zipping around

imagine now as we know that the positive protons attract the negative electrons

imagine now you have a charge of 26 plus 26 putting a force on the inner

electrons you can you can believe that that is a very strong force much stronger than for example a carbon

nucleus which has only six electrons six protons and the way how the electrons

experience such a strong force is that they are much tighter bound to the nucleus in order now to remove one of

those electrons you need four iron a lot of energy and four carbon you need you

need less energy and in both cases you need x-rays to do that and I'm showing

you now how it is done and then I'm showing you as well what we are using for the imaging an x-ray comes in it

knocks out the inner electron that hole is immediately filled from the outer

electron and sends out a second x-ray with a different color now I use the

word color in a larger sense because obviously x-rays do not have any color

for our eyes but what the important point is that by looking at the color of

the x-rays send out you can unambiguously determine what element you

are looking at because that color strongly depends on how much energy you

need to knock out the inner one and then it the energy difference between those two gives you that particular color if

you let me show it to you one more time this is another example in this case we are looking at this one and it might be

a closer shell it falls in and sends out a different color the imaging the x-ray

imaging of the Archimedes palimpsest of the iron in the

we dispel insist relies exactly on that method you look at a particular color of

x-rays how do you do it first you need the palimpsest obviously you need a

detector and then very intense x-ray beam and now all you have to do is you

move your palimpsest through the x-ray beam each time when you hit an atom or a

series of atoms of iron it'll send out the little fluorescence you're done with one line you go down and move to the

next line in that order you basically scan your book back and

forth and record each time when you get this signal you record it in your

detector and you can make a map of an iron map in that case or of any element

you want of what you can see now what you need for this is an extremely

intense x-ray beam as you can imagine and you need a very small x-ray beam because the size of your actual beamed

tells you how well you will be able to see the text later on so let me finish

where can you find such an x-ray beam well we are at the Stanford Linear

Accelerator Center and there are powerful beams here of course the most

famous is our two my long linic but we also have if you if you go into this

little corner here not far from here as a matter of fact the Stanford Synchrotron Radiation Laboratory which

is a an oval or almost round shaped device which produces very intense

x-rays in fact s srl has been one of the

first in the first multi-user multi GeV

that is a very high energy lab of this kind it started in the 1970s since then

there has been a revolution with these machines there are now more than 50 operating around the world at places like

hurry-mart Japan this is the largest one in the world one-mile circumference is

so big you will not find a one-mile straight area in Japan so what did they

do they build it around the hill the Advanced Photon Source in Illinois one

kilometer circumference almost the sister lab beautifully located below the

mountains where the 1968 Olympic Games took place in Grenoble the European

Synchrotron radiation facility across the bay from us with a beautiful view on

the Golden Gate Bridge the advanced light source in Berkeley and its sister lab Bessie Berlin how does such a

synchrotron radiation laboratory look on the inside basically what you do is you

store an electron beam in a vacuum tube

which is surrounded by series of magnets when you force the electron when you

force the charge to go around to be bend around it'll send out this very intense

x-rays and you have in principle two or three different sources of x-rays one of

them is called bending magnet radiation it comes out like a fan similar to when you have your bicycle tire wet and you

spin it fast the water comes out like a fan and it's annoying because if your back gets always dirty the other one our

so-called wigglers or under laters and they in fact force the electrons on a

little slalom racetrack and by doing that you can actually collimate the

x-ray beam coming out even further and you get even more intense x-rays x-rays

from synchrotron are between a million and a billion times brighter than the Sun and

you can imagine when I told that to the curator of the Walters Art Museum I'm

going to use a beam which is a billion times brighter than the Sun to put it on

your Archimedes palimpsest he was very happy in fact he of course didn't give me the

time sis right away we had to do several tests before and I'll show you that in a

second this is the inside of a ring just to impress you a little bit the series

of magnets they are remarkable machines and this are some snapshots on the

experimental floor these are where the users like myself use these x-rays you

can see a control station here of a hard active beam line you see someone putting a sample into the x-ray beam you see a

complicated diffractometer device and this is kind of an overview where you see there it's an amazing activity going

on our left for example has up to 2000 users a year coming from around the

world doing different research in our laboratory I just told you they wouldn't

give me the palimpsest however Abigail quant was kind enough to

lend me from her own private collection a 19th century parchment an English will

and you're welcome to come by after the talk and have it and have can feel how

how wonderful it is it this one is made out of sheepskin very similar to the

Archimedes palimpsest and the first test we did is we wanted to see can we really

image something and I'm just holding it up right here this is the world or from this text and this is our x-ray iron

image from that particular word the resolution is something like of order 600 dpi some of

might be familiar with these terms in order to protect the Archimedes

palimpsest from this very intense x-ray beam we had to come up with a mechanism that each time when the beam was at the

end of a line we inserted a shutter to close the beam so that the X so that the

palimpsest was not exposed to the beam it would then move up to the next line started to move open the shut again and

go back and forth by doing that we guaranteed that any given point of the

palimpsest was no longer than about 10 to 20 milliseconds exposed to this

intense beam we also had a mechanism in case something fails the shutter is just

closed right away in addition we need it to come up with a air-conditioned and

humidifier system because the conservator from the Art Museum avigal

quand asked me to keep the document always at a 50% humidity level at about

70 degrees Fahrenheit I got a lot of help from a student Jessica Lee she's

now she has now joined Stanford as a freshman and we basically built a we

modified a commercial humidifier for your house into one which requires the

string more stringent levels of for the Archimedes palimpsest

let me now finally show you the

palimpsest arrived in May and here you see Paige with the gold forgery this is

Abigail who is she and she is basically was the only person who was allowed to

handle these pages and she is now inside our experimental hatch and we are take

we have taken this photos through the lead window during exposure during

measurements no one is allowed to be inside there is an interlock system which keeps you out of out of that

what you see in the back is kind of a plastic tent this was our very sophisticated construction for the

humidification system it was hidden underneath there but it worked

I'll show you a little and another view every girl has now left the hutch and we

are able to put the beam inside the hutch here basically you you see a set

of filters and slits those were these very fast pneumatic slits which could

drop in at an instant in case there was a problem with the x-rays and here this

is a different page now you see a view of a little bit closer look the x-rays

came through here there was a very tiny slit and created this x-ray beam which is about 40

microns that's just about the size of your hair a little bit smaller than the size of your hair and that's what that's

how how small the x-ray beam was and schematically I show you again here how

we basically then raster scanned this document back and forth you can think of

it as the world's most expensive coffee machine if you let me show you now our

results the first I'll show you this corner and this is the normal view you

have and it is really hard if not impossible to imagine if or that there

is any text and this is how the x-ray image looks like and I'm blowing it up right now this is what came out right of

the computer the horizontal writing is from Archimedes the vertically writing

is from the that is the biblical writings both of them contain iron so

both of them show up also unfortunately in the drawing itself some part of the

drawing also contain iron and so these parts will be a little bit harder to

read in fact we are thinking about a ways where we look at different elements in order to read these parts but

certainly these parts you can start to find letters Forex

you can find at all you can find a theta you can find maybe maybe like a five

year if you're an expert of ancient Greek it might help you but you can imagine as well that it is not easy to

read the text partly because of the quality of the image but also partly

because of the fact that when you when the column says de try to to wipe out

the old text what he really did is he distributed the ayran all over the place

that's what we do when we take an array signed and and take out the some of the

things so so you can see actually there's iron all over the place and it is not typically in a parchment that

there is iron this is this was distributed let me show you another

image this is now an the x-ray image of folio 163 V stands for versa it's the

front side and I'm showing you this I'm showing a part of it here you see again

Archimedes text in the horizontal and the text above in the vertical and I

would like to point out a remarkable feature about the x-rays

again you see some characters in this direction these are Archimedes characters and this is the this is the prayer-book text the

x-rays for the x-rays the parchment

itself is actually transparent but of course if you have two texts on top of each other the amount of iron adds up

you have the iron from the top layer and you have the iron from the layer beneath and you can see that here you can see

that at the parts where these characters overlap you actually get more signals so in our case more signal means like a

bright like a more white look of this and this might help you to actually read

underneath text which is above because you can still see it with an optical

imaging if something is above it completes he blocks it out and you will never be able to read it so that can be very

helpful there is one difficulty with using

x-rays because they because the parchment is transparent you will see actually both sides so it would be like

looking looking for example at this page which is written on both sides looking against a light and you will see the

writing from both sides so you have to somehow try to find a way to disentangle

the front side from the back side and in fact by using images from both sides so

what we did is we image from that side and then turn around image from that side and then through a smart trick of

one of our collaborators you can then take these data and and crunch them as we say and you will get out the front

and the back side with different colors and here I just show you an example of that the front side writings would be in

red and the back side would be in kya now I would say you can take on your

glasses and I have to take mine as well

actually okay so please remember the blue goes to

the right eye that's the most important thing otherwise you see six-dimensional

one of our colleagues Bob Martin he had the idea why don't we do some

stereographic imaging and we did that all you have to do is you come in front

to different angles just about the same angles as your two eyes are and then you can print them in two different colors

and here's what you see this is now a 3d image of folio 163 with the text of

Archimedes on it the first thing which you observe is that the parchment is

actually waved and you can see that very clear I hope you can see that very clearly

second of all with this 3d effect you can actually get an idea of which of the

writings is on the front side and which of the writings are is actually on the backside

and for example here on that right corner you see clearly that this text seems to be like it is floating above

the text underneath so this is clearly from the front side and then this text is clear from the back side and I'll

show you another example now you are zooming in really to a size that is kind

of the size the scholars like to look at these characters at they want to have them as big as they're as big as their

computer screen basically and again you can you can get a very good idea about how the different layers of text are at

different components so this method so you can take off your your glasses again

this method of using the three-dimensional way of looking at it

or the stair as they call it stereographic way might help in some cases for the imaging let me now finish

with the outlook we have just started the Archimedes imaging and the museum

will come back in March with the other forgery pages in particular of a

particular important importance is page 2 of the introduction of the method that

is underneath a fortress and we hope we can read as much as we can of that page it is basically the continuation of the

letter of Archimedes to his friend Eratosthenes the palimpsest er was a

busy person there was not they did not only find Archimedes in this column says

there is text by a possibly unknown author and we haven't been able we don't

even know yet which elements are in the ink we know there is no iron in the ink we hope we might be able to help what I

was told is it is enough to read something like three to five words of

any book in the world and using supercomputers you can then deduce

whether that is a new text or whether there is in it listing text so if we could if we would

be able to read let's say one line of this unknown writer we might be able to come to new text hyper riotous was a

contemporary of Plato and he is seems to be rather important for some of the

scholars as well by within the next

three years at the latest there will be a hopefully a full translation made

available to the public of the Archimedes palimpsest with all the treatises particular the method and and

the other three disease as well and the palimpsest will be again on display and

it's not completely decided yet exactly where it is but there's a chance it will be at the Field Museum in Chicago and by

showing a couple of impressions of my collaborators and myself at work I would

like to finish with a thought what would

Archimedes think if he would be seeing us here using a huge machine to try to

find the last words and characters of some of his work I think he would say

something like that you foods of the 21st century I like the fact that you use these large

round beautiful objects to study my work but I wish you could have recovered my

treatise on flying objects that would have helped you probably a couple of

centuries thank you very much

so we've a thank you very much for a fantastic talk we have time for just a

couple of questions I don't know food can you answer any questions absolutely yeah let's try it anybody got any questions

attacks

so the question is whether there are other texts that I believe there are

many texts very many texts where this technique should be useful in fact in

England some similar work is actually going on on some texts and I'm not a

scholar but from what I heard from from my colleagues that there could be many texts where this would be very helpful

how much time does it take to scan one page so that's actually a very good

question and it's it is surprising how long it actually takes because what you have to

what what you have to keep in mind is that if you have a page let's say off of this size and you can very easily

calculate how many of those small 40 micron pixels actually corresponding to

the 600 dpi on it and it turns out to be something about a 10 10 million and so

you can then you can then estimate how short you have to stay on each of them

in order not to make the scanning take a year and in our case it took us about 30

hours for a half page and that seems like a very long time but but you have

to compare it to about a several month for the scholars to read to read it then

so in that sense actually we are our time is not that long there was another

question because even is it only besides that

there is we know that this for example also sulfur in the ink there is

potassium in the not in the Archimedes ink but in the ink of the prayer-book so

the thought is if you use basically like a subtraction method you can image the

potassium and the iron and then subtract out the other texts the problem really is that as I showed in this example of

how to how this x-ray florescence how this x-ray glow works if you go to lighter elements like sulfur the x-rays

do not penetrate as much anymore and it is very difficult to look at this

lighter elements but we are making an effort in fact what we would have to do is put the Archimedes palimpsest inside

a helium atmosphere and we are currently thinking about how to do that one could humidified for example a little bit so

the waves on the page which I showed was basically a a cartoon picture of an

x-ray photon which we call a photon a part of an x-ray beam coming in and

hitting the hitting the atom and knocking out the electron and and then

basically creating this the secondary glow now you might say how in the world

is it possible to hit anything as small as an atom and atoms are indeed extremely small the the good news is

there are lots of them and so basically if you have lots of them you you will

hit you will hit one you will never be able to tell exactly which one but you will hit one of them so that that was

are you asking about what kinds of concentrations are well our detector is

basically what we call it's a single photon counting detector so in other words it really counts every event

coming in okay and the in order to get an image that you can that you can

really that is useful that you can see you you need several thousand probably

and and so that gives you kind of the the limit if you get to lower numbers it

starts to get grainy very similar to a photo photographic exposure when you go

to when when you take a photo ed when it's very dark you get graininess and that lets just

due to the fact that the signal gets slower but but but the sensitivity I would say you know the the way to

characterizes would be as a function of kind of how much concentration or how they loot you can be and and and so I

you know I could give you more details on that that's an excellent question in

fact we did so what we did is we took the we took this parchment there's

British parchment and we went put it in the beam and we did different times of

exposure okay and then after that I actually sent these different these

parts which have different long exposure times to Ottawa to the conservatory

Institute and they looked at the fragility of the fibers in there so they

did a very stringent test in fact much better than you would see for example with a microscope and we came up with

the dose of 10 to the 10 per pixel and if you cut if you go back to the number

we used we used about one hundredth of that for our current imaging so in

principle we would be allowed to scan another hundred times over that same area and if some places in fact we might

need to scan longer because if if the iron it gets very diluted as as the previous question was you need to stay

on a little bit longer in order to get a good picture it's like you exposure time in your camera busy do

you have to match the energy of the well

in order to knock out the photon in excuse me in order to knock out the electron you all you need to do is go

above the threshold to knock it out so so in fact what you do is you don't want to go you don't want to go too close to

the edge because then your detector might see a lot of of those unwanted

x-rays which are just scattering and not doing a glow also so what so what we did is we went to an energy which was about

30 percent higher than than the energy of the fluorescence and that and that gave us a nice clean signal from the

iron maybe maybe two more questions people hold pens differently okay at

different angles is does your technique allow you to discern like a blaze angle

one that is a preferred reflection or vector for such a thing so that you

could distinguish between one set of writing and another yeah and and it's a

very good point you you bring up when we inspected the irony of the text you

could actually see that from which angle the pen was pushed because when you then

try to wipe it out there is always more iron left in that corner where it is pushed in and and in some in some cases

optical imaging or UV imaging also brings that out but in other cases with

it with the x-ray images it becomes extremely clear from which side that the pen was unfortunately not it's the

original well obviously we are looking at a 10th century document so the original it's actually 1200 years older

than the original writing however the scholars have very good idea of how often it was

copied and it is believed that the Archimedes text was not copied no more

than about five times when it made it into the prayer book so the fact that is

in ancient Greek and the fact that it is such a young copy in the sense of number of repetition make makes it actually

extremely valuable so early movie is

gonna hang around so those of you who have more questions I'm sure he's very happy to answer those for you

for a look at the bits of parchment that's our last lecture of the year we start again a new series in 2006 bigger

and better I'd like to say the opportunity to wish you all very happy holidays our cafeteria is open if you

want a drink after all of this so once again will they thank you very much indeed

well obviously the we are looking at a 10th century document so the original it's actually 1200 years older than the

original writing however the scholars have a very good idea of how often it

was copied and it is believed that the Archimedes text was not copied no more

than about five times when it made it into the prayer book so the fact that is

in ancient Greek and the fact that it is such a young copy in the sense of number of repetition make makes it actually

extremely valuable so early movie is

gonna hang around so those of you who have more questions I'm sure he's very happy to answer those for you or a look

at the bits of parchment that's the last lecture of the year we start again a new

series in 2006 bigger and better I'd like to take the opportunity to wish you

all very happy holidays our cafeteria is open if you want a drink after all of this so once again over thank you very

much indeed

SLAC National Accelerator Laboratory