Dr. Bergmann's Talk

All images of the Archimedes Palimpsest are
copyright to the owner of the ‘Archimedes Palimpsest’
X-ray images of the Archimedes Palimpsest taken at SLAC
Photos and multi spectral images of Archimedes Palimpsest
taken at Rochester Institute of Technology
TO REQUEST PPT SLIDES OF THIS TALK PLEASE
SEND E-MAIL TO:
BERGMANN@SLAC.STANFORD.EDU

Physics Colloquium, Ohio State University, May 1 st , 2007
Secrets in the Ancient
Goatskin:
Archimedes Manuscript
under X-ray Vision
Uwe Bergmann
Stanford Linear
Accelerator Center

July 16, 1907
Hagia Sophia

Prelude

Miltiades
- huge Persian army lead by King Darius had landed on the Greek shore
- Greek army of 10,000 Athenians and 1,000 Plataeans
- after 10 min march at 200 yards distance suddenly a surprise attack by Greek Phalanx
- at the end of battle 6400 Persian soldiers killed but only 192 Greek fighters
- legend has it that Pheidippides ran 26 miles to Athens
- first victory of a new form of government
- first victory of Occident over Orient
- considered one of the most important events marking the birth of
Western culture, beginning of age of Classics

Greek Philosophers
Socrates 470 – 399 B.C.
‘The Questioner’
Plato 427 – 347 B.C.
‘The Idealist’
Aristotle 384 – 322 B.C.
‘The Taxonomist’
Educator “All I know “The of 13 is Republic" Year I know old nothing" Alexander

Euclid of Alexandria
ca. 325 – 265 B.C.
Archimedes of Syracuse
287 – 212 B.C.

Archimedes screw
pulley
Siege of Syracuse

Law of the Lever
A
a
A ·a = B ·b
b
B

4
4
4
4 ·6 = 12 ·2
6 2
12

Approximating the value of π
3.14090 < π < 3.14282

palimpsest =
‘scraped again‘
Archimedes wrote out his theories on
papyrus scrolls. Succeeding generations
preserved his works by copying and
recopying them onto other scrolls.
In the fourth century A.D., scribes began to
copy the writings onto parchment, then
bind them between wooden boards. This
was the earliest version of what is known
today as the "book". The writings were
done with iron gall ink on goat or sheep skin
parchment.
In the 13th century parchment was scarce
and it was common practice to re-use old
manuscripts for religious writings.
Apparently, the Archimedes text was taken
apart, most likely in Constantinople, for this
purpose.

Making of a Palimpsest

Heiberg had discovered the oldest surviving
manuscript containing seven treatises of
Archimedes including the only Greek version of
‘On Floating Bodies’
and two previously unknown treatises
‘The Stomachion’
‘The Method of Mechanical Thoerems’
relying only on a magnifying glass,
Heiberg transcribed the faint
Archimedes script in the Palimpsest

Eratosthenes
(276 - 194 BC)
on the summer solstice at local noon on the Tropic of Cancer, the
Sun would appear at directly overhead in the town of Aswan
in his hometown of Alexandria, north of Aswan, the angle of elevation
of the Sun would be 7.2° south of the zenith at the same time.
the distance between the cities was known from caravan
travellings to be about 5,000 stadia (1 stadium ~ 180 m)
Eratosthenes' value corresponds to ~ 39,690 km
(exact value: 40,008 km) N
equator
S
7.2 o

‘Archimedes to 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….
I presume there will be some among the
present as well as future generations who by
means of the method here explained will be
enabled to find other theorems which have not
yet fallen to our share.’

Volume of Paraboloid by Archimedes’ Method
BD2 /OS2 = AD/AS
MS2 /OS2 = AD/AS
AS * MS2 = AD * OS2 AS * (π MS2 ) = AD * (π OS2 )
M
O
A S
D
A
H S K
B
D
Sherman Stein:
‘Archimedes What did He Do Besides Cry Eureka ’

AK = 1/2 AH = 1/2 AD
H K
H
A
D

Significance of The Method
1) Archimedes combines pure mathematics and physical considerations.
By putting segments of geometrical objects on a balance, he manages
to measure the area and volume of the geometrical objects.
geometrical discoveries by a physical thought-experiment
2) Archimedes is able to perform infinite sums: he takes a sphere,
for instance, and calculates its volume as the infinite sum of he circles
from which it is made.
breakthrough, comparable to the modern integral calculus
Both findings are essential features of modern science!
The Method was two thousand years ahead of its time.

October 28, 1998 - Christie's of New York

Owner was contacted by
The Walters Art Museum
He agreed to lend manuscript for an
integrated effort of conservation and
imaging
Henry Walters
original “Art Gallery“

St. Luke St. Mark
folio 21r
On Floating Bodies
folio 81r
On Floating Bodies
Equilibrium of Planes

St. Matthew St. John
bifolio 64r - 57v
Method of Mechanical Theorems

Wilhelm Conrad
Röntgen 1845-1923
X-ray Vision
first X-ray Image
1895

Horowitz and Howell
Science, 178, 608, 1972

the inside of
an atom
nucleus
electron
orbit

X-ray Fluorescence Imaging
detector
X-ray beam

Stanford Linear Accelerator Center
Stanford Synchrotron
Radiation Laboratory

Synchrotron Sources around the World
SPring-8, Harima, Japan
Advanced Photon Source
Argonne, Illinois, USA
Advanced Light Source (ALS), Berkeley, USA
European Synchrotron Radiation
Facility , Grenoble, France
BESSY, Berlin, Germany

Synchrotron Radiation
schematics of a
synchrotron lab

Brighter than a Million Suns
-short pulses
-very bright
- polarization
-tunable

Inside the SPEAR3 Ring

Experimental Floor at SSRL

First test on 1870 English parchment
40 μm pixel size ~ 600 dpi

Inside the Hutch

Experimental Setup
top view

‘By the hand of presbyter Ionnes Myronasdo’

visual appearance
multispectral
pseudocolor
image
x-ray fluorescence
image

Diagram on ‘The Method’
Folio 159V-158R Science, 313, 744 (2006)

‘The ‘kai’ at the end is very safe, because while
the alpha is almost entirely gone, and the iota
entirely gone, *the grave on that putative iota is
clearly visible*. There are very few alternatives
therefore to the reading kai which in context is
also quite likely’ Reviel Netz

finding is significant for debate of Archimedes’ concept of infinity
from Heiberg transcript:
‘is true for any’
‘if any, therefore all’
based on x-ray image Netz suggests:
‘however many lines are taken’
[therefore infinitely many]

Stereo View Imaging

Conclusions and Outlook
- x-ray images add significant information
- continuation planned later this year
- the full translation will be available
- Palimpsest will be on display
- new book by Netz and Noel:
‘The Archimedes Codex’
- idea of instute for imaging of human heritage
- work has inspired other x-ray imaging projects

THANK
Martin George
YOU
SSRL
Alex Garachtchenko
William Noel Walters Art Museum
Abigail Quandt
Jennifer Giaccai
see also:
Mike Toth Toth Associates
Reviel Netz Stanford
(for history, background, images)
Collaborators
Jessica Lee Stanford (Castilleja alumni)
http://www.archimedespalimpsest.org
Isabella Griffin Norfolk
Manisha Turner
(for archived live coverage)
Keith Knox Consultant for Rochester
Institute of Technology
http://www.exploratorium.org/archimedes/index.html
(for 2006 media coverage)
Gene Hall Rutgers
Bob Morton Children of the Middle Waters
http://today.slac.stanford.edu/feature/archimedes-media.asp
Roger Easton Rochester Institute of Technology
thanks to The Owner, DOE, SSRL, SLAC