Antikythera mechanism UCLDH seminar

1
This animation shows slices through a false-colour X-ray volume of the
main surviving fragment of the Antikythera Mechanism, going from the
back to the front. You can see all the gears, plates, arbors, pins,
bearings etc. It was made in ancient Greece and is one of the true
wonders of the ancient world. It is also a work of genius.
Thanks very much to Digital Humanities for asking me to give this
presentation. Many thanks also to Lindsay MacDonald, who originally
suggested it.
©2015 Tony Freeth.
All rights in this presentation are reserved.
Please respect copyright.

2
Lindsay asked me how I had become so involved in the Antikythera
Mechanism and I had replied that it was the product of a mis-spent
middle age! So he suggested that I give a personal account of my life
with the Mechanism. So that’s why I changed the title.
I have never really looked at this history from a purely personal
perspective before and I am somewhat apprehensive. In many ways, it
goes against the grain for a scientist to give a personal account—
particularly if they have worked with a research team. We normally say
“we”, not “I”. But looking back on this history from a personal
perspective has been very interesting. For me, it is an amazing, unlikely
and almost surreal history. I hope that it doesn’t come across as being
too egotistical but I thought that I should embrace the idea of a personal
account.
Lindsay isn’t here. He’s done a runner! He fled to France—no doubt to
avoid the monster he had spawned! Anyway, if it all goes wrong, I shall
blame it all on Lindsay, since he is conveniently not here!

3
I am not going to give an account of all the discoveries that I have been
involved with, since there is nothing like enough time. I am going to
concentrate on the most extraordinary discovery, which is how the
Mechanism tracks the Moon—the so-called lunar anomaly.
In the words of Douglas Adams, What is the answer to the Gears, the
Moon and the Antikythera Mechanism? The answer will appear later!

4
First, the relevant background.
I had a mis-spent childhood, playing with Meccano. I must have done
other stuff—like eating and being hit by my elder brother—but I don’t
remember much of it. This is a differential gear, which I must have
made when I was around 12 years old. I was fascinated by it. It uses
epicyclic gears, which are gears where the axle of the gear is mounted
on the face of another gear and moves round with it. Epicyclic gearing
is a subtle and extraordinary type of gearing system, with particular
relevance to the Antikythera Mechanism.

5
It’s not really as difficult as Quantum Mechanics—but it is very
surprising and hard to understand.

6
I had a mis-spent childhood and early adulthood studying mathematics.
Mathematics was always my favorite subject at school. I became far too
narrowly focused at much too early an age. First Cambridge: pure
mathematics for my first degree and a postgraduate degree in
mathematical logic and algebraic topology (Part III of the Maths Tripos,
now MMath). Then Bristol: an MSc and PhD in mathematical logic,
specializing in Set Theory.
So what has all this advanced modern mathematics got to do with the
Antikythera Mechanism? The answer is, nothing. So what has
mathematics got to do with the Antikythera Mechanism, the answer is,
everything. Every aspect of the design is informed by mathematics. The
maths is simple, but it’s used in a way that amounts to genius. It is an
astonishing design, which was clearly designed by a mathematician. I
recognized the mathematical way of thinking that is embodied in every
aspect of its design. A long immersion in mathematics gave me the
background needed to understand it.

7
Then, being a perpetual student, I went to the National Film School and
mis-spent my time training as a Director and Cameraman, followed by a
25-year mis-spent career in the film and television industry as a Director
and Producer, making documentary films.
So why is this background relevant? As regards filmmaking, the hugely
difficult task of data gathering stretched all the skills that I had learned
over 25 years producing and directing films. All the skills dealing with
people and expensive projects. All the diplomatic skills needed to
persuade people in institutions to do things they normally don’t do.
So that’s the first 53 years dealt with! And 53 is a very significant
number for the Antikythera Mechanism, as we shall see! If only I had
realized the significance of my age at the time, I could have saved
many years of research—as we shall see!

8
Now the jokes are over! It’s a serious account from now on. So, no
laughing please!
I first heard about the Antikythera Mechanism as a TV producer. I was
approached one day in 2000 by someone I knew well, Professor Mike
Edmunds, a distinguished astronomer at Cardiff University. He asked
me if I had ever heard of the Antikythera Mechanism. He wanted to
make a TV program about it. Little did I know the life-changing
consequences of that conversation.
I had never heard about the Antikythera Mechanism. So Mike told me
the story of its discovery.

9
The story starts with a man called Fotis Lindiakos, seen here with his
family in the 1890s.

10
He was a boat-owner running sponge fishers from the small island of
Symi in the Eastern Mediterranean.
This is the sort of equipment they used—large brass helmets and
canvas suits, pumped air. It was very, very dangerous and many divers
were killed or incapacitated.

11
The sponge divers set off from Symi. When they reached the small
island of Antikythera, between Crete and mainland Greece, they were
caught in a violent storm.

12
When the storm subsided, the captain, Demetrios Kondos...

13
... ...sent down one of the younger divers, Elias Stadiatis, to look for
sponges. He soon emerged from the sea, trembling in fear and shouting
that he had seen “a heap of dead naked people under the water”.

14
These turned out to be marble sculptures, lying on the seafloor along
with many other ancient artefacts. He had discovered an ancient wreck,
full of Greek treasure.

15
Then the captain went down and emerged from the sea carrying a
larger-than-life bronze arm.

16
They continued with their sponge fishing expedition and returned to
Symi. They debated what to do about their discovery, Should they
return and plunder the site after their sponge-fishing trip? Or should
they tell the authorities?
To cut a long story short, they told the authorities.

17
The response some months later was the first major underwater
archaeology in history. A navy gunboat, the Mykali, stood by to deter
looters. The sponge divers (top right) were employed to carry out the
dive. It was very dangerous—one diver died and two were permanently
disabled. It took months to bring everything to the surface.

18
It was a stunning find. They had uncovered a treasure trove of ancient
Greek objects: beautiful bronzes, jewellery, superb glassware,
amphorae, tableware and many other objects.

19
No-one at the time was electrified by another object they found—a
corroded lump, which almost certainly came out of the sea in one piece.
Like all the other finds, it was taken to the National Archaeological
Museum in Athens. It was left in an open-air cage to be examined at a
later date. Then a former Minister, Valerios Staïs, visited the Museum
and noticed that it had split apart. This changed everything!

20
Inside the object they discovered the remains of some gearwheels.
These were not the crude mechanical gears you might find in a
watermill or windmill, these were precision gearwheels—mathematical
gearing as it is sometimes called—with teeth about a millimetre long. It
was a truly shocking discovery for ancient Greece. Such gearwheels
simply should not have been there. There was huge excitement and
much controversy.

21
It is the most extraordinary artifact ever found from the ancient world.
Finding out what it was has been an extraordinary voyage of discovery:
for me personally, it has been an absolutely amazing journey. It has
involved a 100-year trail of clues; mysteries; confusions; missed
opportunities; and breakthroughs.
At each stage of research, new generations of scientists have brought
“new eyes” to this stunning object—not only new technology but new
ideas and new ways of understanding the device.

22
To give an overview, I am going to sketch in the four major stages of
research on the mechanical structure of the Mechanism.
Albert Rehm was the first person to understand its essence as an
astronomical calculating machine as well as crucial features of the
inscriptions that cover its external plates. He got everything wrong
mechanically but his ideas were extraordinarily prescient.
Derek de Solla Price made major advances. He was the first to carry
out X-rays, together with Charalambos Karakalos. This established the
astonishing complexity of the gearing. He determined the basic
architecture of the Mechanism. Crucially, he identified the 19-year
Metonic Cycle in the gearing of the device.
Michael Wright, initially with Professor Allan Bromley, carried out the
second X-ray study— using stereo pairs and an early form of 3D
tomography. He has made a sequence of major advances.
Together with the Antikythera Mechanism Research Project, I organized
new investigations of the Mechanism and determined a number of
crucial features of its mechanical structure—including eclipse
prediction. I am going to talk about the first lunar anomaly: it is the most
important and astonishing feature of the Antikythera Mechanism,
involving all four generations of research. First I am going to wind
forwards to the results of this research to show you where we are going.

23
This is the back of the main surviving fragment of the Antikythera
Mechanism. It is evidence for all of these gears at the back of the
Mechanism.
These fragments witness the back dials of the Mechanism, with an
upper calendar and lower eclipse prediction dial.
We now come round to the front of the Mechanism, which shows the
Main Drive Wheel, with its mysterious pillars, which we believe are part
of the evidence for planetary mechanisms, based on the epicyclic
theories of Apollonios of Perga—though much of the evidence is
missing. The basic architecture of this planetarium, mounted on this
large four-spoked, wheel, was proposed by Michael Wright. These
conjectural coaxial pointers indicate the positions of the Sun, Moon and
planets in a display that portrayed the ancient Greek cosmos.
This is Fragment C, part of which shows in the centre the Moon phase
device discovered by Michael Wright. These fragments are evidence of
the Parapegma—the star calendar discovered by Albert Rehm—on the
front plate of the Mechanism.
This extraordinary mechanism was contained in a wooden box, with an
input at the side.

24
This is the final result. It is a wonder machine of genius, designed on
mathematical principles. An astronomical compendium, incorporating
the whole predictive power of ancient Greek astronomy. It is a “Theory
of Nearly Everything in a Box”!

25
Mike Edmunds and I did not manage to set up a TV programme. The
TV commissioners told us it was an old story. The main research had
been published in 1974. So, at that stage, we failed to get the project off
the ground.
But we were still deeply interested and Mike started to set up an Anglo-
Greek Academic team of interested people—with myself, Professor
John Seiradakis, one of Greece’s leading astronomers, Professor
Xenophon Moussas, an astrophysicist, who recruited physicist Yanis
Bitsakis and later philologist Dr Agamemnon Tselikas.

26
I became completely fascinated with the Mechanism. Our main problem
was that we had no good data—not even a good set of still
photographs. I started to look at previous research.

27
In the early years after its discovery, there was much speculation. Some
maintained that it was a navigation device (after all it had come from a
ship); some that it was an astrolabe—a device for tracking the stars.
This was closer, but neither hypothesis was right. There were fierce
academic disputes, where both sides were wrong. (Nothing surprising
there then!) There was much confusion but there was some significant
progress.

28
The one person, who really understood it was a German philologist,
Albert Rehm. He claimed that it was an astronomical calculating
machine.
Albert Rehm was an extraordinary man. Later in life in the early 1930s,
he became Rector of Munich University. He was strongly anti-Nazi and
this caused him to lose his job and he was forced into "internal exile".
He was rehabilitated after the war and once again became Rector of the
University.

29
Albert Rehm was an expert on ancient inscriptions and in 1905 he
started by examining the text that was visible on the surfaces of the
fragments. He is seen here with Fragment C.

30
On this fragment, he found many inscriptions, which you can see faintly
in the pictures. Rehm identified an Egyptian calendar and he
determined that the text on the face of Fragment C was a star calendar,
called a Parapegma. He transcribed the text.

31
We owe the preservation of some of this text to Rehm, since the original
material is now lost. Parapegmata were common in the ancient world.
They were essentially star almanacs, which set out the risings and
settings of prominent stars in the annual cycle. Often these were linked
to weather predictions and sometimes medical advice. On the
Antikythera Mechanism, it is purely astronomic.
Rehm's published a couple of papers, but they are not of huge interest.
It's his notebooks, where he expresses many speculative ideas, which
are a goldmine.

32
Here is another page from Rehm’s notebooks. I’ve highlighted a note
that he wrote in the margin. In this note we can see the numbers 76 and
19 and further down he mentions the Kallippic Cycle and the Metonic
Cycle.

33
Here is another page from Rehm’s notebooks. I’ve highlighted the
number 223.
Where did Rehm get these numbers—76, 19 and 223? What are they
all about?

34
This is Fragment 19. It is part of the Back Cover of the Mechanism,
which is covered in inscriptions. It has been described as a sort of User
Manual for the Mechanism. It describes the basic principles on which
the Mechanism is based.

35
I want to look at this fragment, using a brilliant technique devised by
Tom Malzbender of Hewlett-Packard, which I will come back to later. It
highlights details on surfaces. It makes the text stand out very clearly.

36
Here we find exactly the numbers mentioned by Rehm. He must have
seen this fragment and copied them. The 19-year Metonic cycle, named
after a Greek astronomer, Meton of Athens, but known earlier in
Babylonian astronomy. The Kallippic Cycle, an improvement on the
Metonic Cycle, where Kallippos took four Metonic Cycles and removed
a single day—making a 76-year cycle. And the 223-month Saros
eclipse prediction cycle from 7th century BC Babylon.
If you want to make a geared mechanism for tracking the astronomical
bodies, these are the sorts of astronomical cycles that you need.

37
When the ancient astronomers looked at the night sky, they saw the
great dome of stars rotating from East to West every night, centred on
the Pole Star—as the Earth rotated in the opposite direction.
But there is another movement of the astronomical bodies that are
close to us—the Sun, Moon and planets. They move predominantly in
the opposite direction, relative to the fixed stars, from West to East. And
they all move in much the same plane, called the ecliptic, through the
band of stars called the zodiac.
These movements of the Sun, Moon and planets in the ecliptic plane
were the primary subject matter of ancient astronomy. We call it the
Solar System, but in ancient Greece their viewpoint was primarily
geocentric—Earth-centred. The positions of the astronomical bodies
were expressed in terms of their position in the zodiac—in other words
their ecliptic longitude.

38
The Metonic Cycle is a 19-year cycle of the Moon. It comes in two
parts. The first part identifies 19 years with 254 sidereal months: that’s
the basic orbital cycle of the Moon from one star back to the same star.
The second identifies 19 years with 235 lunar months: that’s the phase
cycle of the Moon from New Moon back to New Moon.
If we observe the Moon near a particular star at a particular phase and
then we look at it 19 years later. It will be near the same star and at the
same phase.

39
The Saros eclipse prediction cycle works like this. If you have an
eclipse of the Moon or the Sun in one month and you look 223 lunar
months later—just over 18 years—then you will get a very similar
eclipse. And the repeat goes on for 12 – 15 centuries.

40
Rehm explored the basic architecture of the Mechanism, but he didn’t
really understand how it was put together.

41
Rehm also started to explore possible mechanical arrangements. He
got everything wrong. The thing about Rehm is that he got all the details
of the mechanical structure wrong, but he had incredible insights. Rehm
did publish some articles about the Antikythera Mechanism, but they are
far less interesting than his unpublished research notes, which can now
be found in the Bayerische Staatsbibliothek in Munich.

42
This is another remarkable page from Rehm’s notebooks.

43
Incredibly, he wrote about eccentrics and epicycles. Epicyclic gearing
involves gears whose axes are mounted on other gears. It is a difficult
and sophisticated concept and it is utterly astonishing to suggest this for
ancient Greece. Again Rehm proved to be right—but in ways that he
never dreamed of.
Some of his notes are in an early German shorthand, called
Gabelsberger. He is clearly struggling here to understand the
mechanical structure, without enough data. Rehm was a genius. If his
insights had been combined with our X-ray data, we could probably
have saved a hundred years of research and I would have been
deprived of my passionate journey of discovery!
Rehm left a fascinating but unresolved legacy.

44
Half a century after Rehm had started on this Mechanism— a period in
which nothing much happened—his legacy was taken up by the great
Derek de Solla Price He was a British physicist, turned historian of
science, originally at Cambridge, then at Yale. Like Rehm, he got much
wrong, but what he got right was absolutely crucial. Price is the reason
we are all here.
1959, Scientific American: brought the extraordinary device to a much
wider audience. In his work, themes began to emerge: “At least 20 gear
wheels… have been preserved... a sort of epicyclic or differential
system.” Again epicyclic gears, probably following Rehm: a shockingly
bold claim for ancient Greece. It has great significance for the history of
technology. Price’s Differential became his most celebrated discovery.
Price wrote, “…from all we know of science and technology in the
Hellenistic Age we should have felt that such a device could not exist.”
All of us, who have studied this Mechanism in depth, would heartily
agree with Price.

45
In around 1970, Price teamed up with Greek radiologist, Charalambos
Karakalos, to carry out the first X-ray study. It was a critical step. These
X-rays showed the true complexity of the gearing. To their
astonishment, they found 27 gears in Fragment A—all overlapping in a
very confusing puzzle.
In order to understand what a geared mechanism does, you need to
count the numbers of teeth on the gears. This will tell you what
astronomical cycles it embodies.
In the right-hand picture, the teeth are marked for counting. This was
done by Charalambos and his wife Emily. They would then estimate the
total number of teeth on each gear—nearly all the gears are damaged
and partial. They would then give these tooth counts to Price. By this
time, Price was beginning to develop his own ideas about how the
Mechanism worked and he began to argue with the Karakalos family
about the tooth count—much to their annoyance apparently! They had
done the scientific process of estimating tooth counts and Price was
challenging them without any good evidence!
Let me show you an example.

46
The gear here, which fills the square, was counted by the Karakalos
family as having 128 teeth.

47
But Price said he thought that it has 127 teeth. Well, what’s a single
tooth between friends!

48
Let me show you a modern X-ray CT of this same gear. You can see
the huge advantage of modern X-ray technology. Nearly all the teeth
are visible and we can with confidence say that it has 127 teeth. Price
may not have been very scientific, but he was right!
This was extremely significant...

49
...because 127 is the large prime factor in 254, which is the number of
sidereal months in the 19-year Metonic cycle.
Rehm had found the ancient Babylonian Metonic Cycle in the
inscriptions; Price found it embedded in the gearing. It was a discovery
of historic importance.

50
I want to show you how Price incorporated this gear into the
Mechanism. It gives insights into how the whole Mechanism works.

51
At the back of the Main Drive Wheel is attached a small gear, b2, with
64 teeth. All the gearing behind the Main Drive Wheel is driven from this
gear. I am going to build Price’s Metonic gear train from this. At the
same time, I will show what is being calculated. The two gears on axis b
rotate at 1 revolution per year.

52
Add another gear, c1, with 38 teeth. As you can see this brings the
prime number 19 from the Metonic cycle into the calculation. The minus
sign simply means that the gear rotates counter-clockwise when seen
from the front.

53
c2, with 48 teeth, is riveted to c1 and they turn together on a fixed axle,
attached to the Main Plate.

54
Adding d1, with 24 teeth means a simple doubling of the ratio.

55
Now we add a large gear d2 with 127 teeth, which you will recognize as
Price’s gear.

56
This meshes with e2, with 32 teeth, to give the simple ratio 254/19. This
represents the sidereal form of the Metonic cycle. This was a great
discovery by Price: the Metonic cycle is embedded in the gearing of the
Mechanism.

57
This is the output of this gear train. As you can see it is on an unusual
axis with a small pentagonal section, which has a hole through it: it is
the end of a tube. This output, which is the mean sidereal month, is a
mystery that I will return to. Price thought wrongly that it went directly to
the front of the Mechanism to show the mean position of the Moon in
the zodiac on the large front dial. Why the axle had a pentagonal
section is something I don’t completely understand—though I do have
an idea. Later I will show you why there is a hole in the middle of the
axle.

58
Price went on to examine the gears at the back of the Mechanism.
Famously, he proposed that this system was a Differential, using
epicyclic gears. It was a revolutionary idea—pre-empted by Rehm.
The Differential subtracts (“differences”) the rotation of the Sun from the
rotation of the Moon to give the phase cycle of the Moon. It was a
brilliant and revolutionary idea for ancient Greece. It became his most
celebrated discovery. But unfortunately, it was wrong. A beautiful idea
that is wrong is hard to abandon and this in my view set back Price’s
research significantly. He got stuck with his brilliant but wrong idea.

59
As it turned out, it was the right idea in the wrong place (again!) and it
was far too complicated. And he could find no role for the largest gear in
the system, E4.
Gears from the Greeks includes much scientific presentation, with
measurements to a tenth of a millimeter, complicated diagrams and
confident assertions. At first, I didn’t question it. Then I started to get
sceptical.

60
After 20 years work, Price put together all his ideas in what he believed
was a complete model of the Mechanism. It’s complicated and hard to
understand at first glance. I don’t want to explain it in detail. You can
see his Metonic gear train in blue in the centre of the diagram.

61
I just want to say one thing: apart from his Metonic gear train, Price got
everything else wrong! All of the rest of the gear trains are wrong!
His “Sunwheel” was impossible. His “four-year dial” for the Upper Back
Dial was wrong. His famous Differential was wrong.

62
This is where I came in terms of research. I wrote a paper called
Challenging the Classic Research, which essentially said that Price’s
model was very complicated but it did rather simple things. It was much
too complicated for its outputs: a clear violation of the principle, often
known as Occam’s Razor: that you should keep everything as simple as
possible. I have spent the last fifteen years dismantling Price’s model.

63
But Price also got much of the Mechanism right. He was the first person
to propose the basic architecture of the device, which we follow today. It
is basically a box with an input handle and pointers that go round dials
to show astronomical parameters, driven by complex gearwork inside.

64
Price did 20 years of research on the Mechanism. By 1974, Price was
Avalon professor of the History of Science at Yale University and he
wrote up all his results in his masterwork, Gears from the Greeks.
Though much of the details are wrong, it is a truly great paper and we
are all here because of Price. I revere Price: Gears from the Greeks is
the ‘Bible’ for later researchers. But, just like the Bible, you do not have
to literally believe all its details! In scientific research, you don’t have to
get everything right to make very significant progress. And much of his
work has not stood the test of time.

65
Gears from the Greeks drew me into a fascination with the Antikythera
Mechanism. I became passionate about it—or obsessed as my wife
describes it… But you don’t make any serious progress without total
focus, total concentration. I studied every bit of literature that I could
find.
Having dismantled Price’s model, I wanted to find out how it actually
worked.
We had no good data—not even a good set of still photographs. None
of our Greek colleagues could find the X-rays that Karakalos had done.
So I started to look around for new techniques to gather new data.

66
Then I saw an article in New Scientist called Tricks of the Light about a
technique for looking at surfaces, which enhanced detail. An example
given was a Babylonian tablet, where the details of the carving and the
text stood out with astonishing clarity. The external surfaces of the
Antikythera Mechanism are covered in tiny inscriptions, literally
thousands of text characters.
Polynomial Texture Mapping (PTM) was invented by a brilliant scientist
at Hewlett-Packard, called Tom Malzbender.

67
I met Tom at the National Gallery in London, where he was using his
technique to study paintings—revealing such things as the fingerprints
of the artists. We got on really well and Tom was keen to bring his
equipment to Athens to study the Antikythera Mechanism.

69
...the excellent Hewlett-Packard team to our growing research project.

70
I also wanted to look inside the fragments with 3D X-rays. One day I
saw a false-colour X-ray image of a goldfish, with all the bones and fins
visible. I wondered if this might work on the Antikythera Mechanism. I
contacted the researcher, Steve Wilkins from Australia, who had made
the X-ray images. I asked him if we could use his technique on the
Antikythera Mechanism. He said, no: his technique of phase contrast X-
rays needed thin slices of the sample. (I didn’t think that the Museum in
Athens would be very keen on us slicing up the Mechanism into thin
slices!) What I needed was Microfocus X-ray Computed tomography. To
cut a long story short, via the Welding Institute...

71
...I found X-Tek Systems. They were world leaders in Microfocus X-ray
Computed Tompgraphy (X-ray CT)—high-resolution 3D X-rays. In film-
making, much of your time is spent persuading people to take part in
your project—sometimes reluctantly. So my background in film-making
kicked in and I managed to get the interest of the company. And then I
had to keep them interested for four years, while we got all the
necessary permissions from the Greek authorities. It was a nightmare.
After a couple of years, they were going to ditch the project because
they didn’t think that their equipment was powerful enough. So I wrote
an email to the company founder, Roger Hadland and we arranged to
meet.

72
I got on really well with Roger and I got his attention. Afterwards, he told
me that he expected that the meeting would be a short one where he
would say no. But he started to get interested in the Antikythera
Mechanism—really interested! After the meeting, he decided that he
would do the project. This would mean building a special prototype X-
ray machine with much more power. It would be the most powerful X-
ray CT machine in the world. It was an extraordinary decision. Later, I
would learn that the company was failing at the time, with 60 employees
and almost no orders for their machines. It was a huge risk and it cost
Roger a furious row with his Finance Director. It was an incredibly
courageous decision. But he was fascinated with the Mechanism and
he had the instinct that, if he formed a team around making a uniquely
powerful X-ray machine, it would have far-reaching commercial
advantages.

73
So the X-Tek team joined the project. They were a superb team. But we
didn’t have permission from the Greek authorities to carry out the new
investigations. They had turned us down in 2001 because they said that
the fragments are very fragile—a good reason—and that the previous
set of X-rays had not yet been fully researched. This was a bad reason,
since they had been done 12 years previously.

74
The previous set of X-rays had been taken by Michael Wright (on the
right), a former curator of Mechanical Engineering at the Science
Museum in London and Professor Alan Bromley, a professor of
computer science at Sydney University and an expert on Babbage. You
can see a reconstruction of one of Babbage’s engines in front of him.

75
They had wanted to get the 3D information that the Karakalos X-rays
lacked and they had used an early form of tomography called linear
tomography. It was a technique that delivered data, which was very
hard to interpret. Sadly Bromley and Wright fell out and then Bromley
died.

76
But Michael Wright was very persistent and made a series of important
discoveries—some of which I will describe.

77
I am going to look now at one important part of Michael Wright’s work. I
want to describe his work on the Metonic Calendar Dial.

78
Price had suggested that the Upper Back Dial might be a Metonic
Calendar, with 47 months on each of its five rings—making a total of
235 months. But he threw the idea away in favour of his simplistic Four-
Year Dial—again an idea that would find a role on one of the subsidiary
dials (the Olympiad Dial). Right idea, wrong place... yet again!
Wright revived Price’s idea of a Metonic Calendar and he showed how it
could be turned by the surviving gears.

79
Let me strip off the plate to reveal the gearing. This is the Main Drive
Wheel. On average it goes round once a year, driven by the small
crown gear at the side. The gearing system that I am going to show you
was proposed by Michael Wright. It is so bizarre that at first I thought
that it was incomprehensible.

80
Fixed to this large wheel is a smaller wheel with 64 teeth. Much of the
Mechanism is driven from this wheel.

81
I am going to build up the gear train that leads to the Upper Back dials.
l1 meshes with b2 and brings the prime factor 19 into the ratio—the
Metonic cycle. The minus sign simply means that l1 turns in the
opposite direction. This is a gear train that was proposed by Michael
Wright.

82
l2 is fixed to the same axle as l1 and they turn together. It brings the
strange prime number 53 to the ratio...

83
And here is an X-ray of the actual gear. It really does have 53 teeth.
I couldn’t understand what it was doing there when I first read Michael
Wright’s paper.

84
And on axis m we get this ratio, with no apparent astronomical
meaning, and with the bizarre prime number 53.

85
Now we can complete the gear train. We get exactly the ratio we need
for a 19-year 5-turn Saros Dial. But notice, we have had to introduce
another conjectural gear to get rid of the damn prime number, 53. It
doesn’t seem to make sense. Why introduce 53 and then cancel it out
like this? What on earth is going on?

86
I should say that I was so concerned about Wright’s 53-tooth gear that I
changed 53...

87
...to 54 in my model. This turned out to be a big mistake!

88
This is Michael Wright with the version of his model, which he published
in 2005.

89
It included a pioneering planetarium at the front, which is conjectural
because the evidence is missing. At the back is the Metonic Calendar
that Price had suggested and then thrown away, and which was then
revived by Wright. Also he introduced a dial that showed the draconitic
month, the latitude cycle of the Moon that is important for eclipses, over
a scale of 218 half days. Immediately I read about it, I knew that it was
wrong.
This was the latest model that was published before our new
investigations...

90
...which only happened because of the extraordinary persistence of one
of our Greek professors, Xenophon Moussas, in getting the necessary
permissions. Xenophon would not take “no” for an answer. He called
the Ministry of Culture between 40 and 60 times and got the same
negative answer each time, until one day they gave him an appointment
with the Deputy Minister of Culture, Petros Tatoulis. Xenophon went to
the meeting, expecting 15 minutes at best. Tatoulis was there with his
wife who worked with him in his office. It turned out that they were both
really keen on ancient Greek astronomy! After more than an hour,
Tatoulis told Xenophon that he wanted to do the new investigations. He
called the Director of the Museum, Dr Nikolaos Kaltsas. Kaltsas, who
said no, he didn’t want to do it. But Tatoulis was very persuasive and
finally persuaded Kaltsas to do the new investigations. Without
Xenophon’s persistence, the project would not have happened.

91
At last we had the full team. At the National Archaeological Museum in
Athens we would be looked after by senior archaeologist, Mary
Zapheiropoulou, and Head of Chemistry, Eleni Mangou.
Everything was set and then the Museum suddenly asked us how we
proposed to insure the fragments! Our hearts sank. Were they worth a
$1m or $100m or maybe $1bn?!! We had to persuade them that all the
handling would be done by the Museum staff: we would never touch the
fragments. Diplomacy is not really my strong suit—but when it is
necessary, you have no choice. (And it was often necessary.) My
experience making films helped a lot, since you often have to deal with
difficult situations. Finally they agreed.

92
Before 2005, these were the main fragments that we knew about—with
some additional small pieces that Price mentioned.

93
Then in 2005, Mary Zapheriopoulou called one of our team to say that
she had discovered some trays of bits in the store room, labelled
“Antikythera”. Were we interested? Of course, we were!

94
To cut a long story short, we ended up with 82 fragments. We would
use both our new techniques on all the fragments, as well as taking a
new set of still photos, which you can see here.

95
First Tom Malzbender came to Athens with his excellent team—Dan
Gelb and Bill Ambrisco—and set up his PTM dome. This is covered in
flashlights and takes a sequence of still photos with lighting from
different directions. These images are then integrated by a computer
into an interactive image.

96
This is Fragment C, where Rehm found the Egyptian calendar and the
Parapegma. This image can be re-lit on the computer from any
direction. Also a number of filters help with deciphering details...

97
...for example, specular enhancement is particularly powerful, yielding
great clarity in the surface details. It is a wonderful tool for deciphering
text characters.

98
It can be re-lit from any direction...

99
...enabling different details to be enhanced. And different text characters
to be read.
A week later, we had a superb data set.

100
But we didn’t yet have our X-ray machine. The Bladerunner—as they
would call it because it was destined to be used on turbine blades—was
far from being ready. It was in pieces: that’s the trouble with prototype
technology. All the delays in getting permission had worked in our
favour, but it still wasn’t ready.
With days to go before it was due to be picked up, they had a nine-inch
spark, which equates to several hundred thousand volts. Luckily it didn’t
kill anyone but it destroyed three computers and other vital equipment.
So they had to rebuild much of the machine. I was filming all of this with
cinematographer, Stephen Macmillan. Then the Greek lorry driver
turned up to pick it up. Stephen and I knew that our job was to keep the
driver happy while they finished the machine.

101
We discovered that his favorite food was fish and chips! So we took him
for fish-and-chips and we talked for hours about his family and the
corrupt police that he would meet on the way to Athens. Apparently lorry
drivers have to pay many small bribes to police to continue on their
journeys.
He was very good natured and patient. At around 2.00 am the next
morning…

102
…we saw off the Bladerunner en route for Athens. Some days later, it
arrived at the National Archaeological Museum in Athens with a police
escort and was maneuvered into the Museum basement with a forklift.

103
It was pushed and shoved into the basement of the Museum and
everything was set up by a superbly professional team.

104
It was a complex operation. Each day we would arrive at 7.00 am and
work through the day, with lunch on the job, until around 7.00 pm. We
had told the Museum that we might work some long days but this turned
out to be every day. The Museum was not really used to this: they went
into culture shock!
There was a lot of tension around the project. I was used to that as a
filmmaker but at times it got extreme.

105
One issue was the safety of the fragments. They were carried on flimsy
stands down a winding stairs and through a door, past security guards
and to the X-ray machine, where a dozen or more people were milling
around. I became extremely anxious and had sleepless nights worrying.
I tried to get proper protocols in place to ensure the safety of the
fragments. Mary and I had some vigorous conversations about the
safety of the fragments.

106
I think that Mary was as anxious as I was, but she didn’t really know
how to deal with it. The conservators were fantastic with a very secure
touch—you would entrust them with brain surgery—but we worried
about the system for transporting the fragments. In the end nothing bad
happened and we survived.

107
After two weeks, we had four days to go and we still hadn’t done all the
small fragments. Then Mary and Eleni told us that we had to stop work.
It was a bombshell!

108
We discovered what had happened. There had been a staff meeting
with the Director. The women had told him that we worked these crazy
hours and they had to be there the whole time. Could they have some
time off in lieu when we had left? The Director said, no. So they had
been forced to withdraw their services.
Solving this problem took all of my filmmaking skills and some very
skilled diplomacy from our Greek professors.
Nietzsche wrote that, whatever does not kill you makes you stronger.
This only goes to prove that Nietzsche never worked with the National
Archaeological Museum in Athens!
Talking of Nietzsche, I recently spoke in Basel. Two very congenial
academics took me a tour of Basel, with its old 14th century houses, its
cathedral and a plaque celebrating the Bernouilli brothers. But the
highlight of the tour came when they showed me the street where
Nietzsche caught syphilis!

109
We got stunning results with nearly a terabyte of data. These are tiny
details—for example the teeth of the gears are about 1mm long and
most of the text is less than 2 mm high, typically 1.6mm high. All of this
detail preserved despite 2,000 years under water.
We expected that the surface imaging would show us the inscriptions
and the X-rays would show us the structure of the gears. So we were
astonished when the X-rays also revealed many thousands of new text
characters, hidden inside the fragments and unread for 2,000 years.

110
So we got all our data back home. I was charged with trying to sort out
the mechanical structure. There was a severe technical problem with
the X-ray CT data of Fragment A.

111
So I started with Fragment F—one of the fragments found by Mary in
the Museum store.
On the surface, it looks just like beach pebble, with the green perhaps
indicating bronze. It is full of fascinating information.

112
This is a slice through our 3D X-ray data. To start with there is nothing
of interest.
I am going to go down through a sequence of parallel slices through the
data.

113
Here maybe there is a hint of structure.

114
Here we begin to see some scales. This is the great power of X-ray
CT—you can isolate a single slice.

115
Now we can see clearly defined scales...

116
...with beautiful definition.

117
Now we start to see scale divisions…

118
...and more scale divisions… Fragment F is rich in information.
I developed a very simple strategy: focus on scale divisions. If you want
to know what a scale does, you should try to find out how many scale
divisions there were round the whole dial. It may seem an obvious
strategy—but it had not been applied very well by previous researchers.
These scale divisions...

119
...look very similar to those in Fragment A...

120
...which Price had recorded. They are visible on the surface and are
part of the Lower Back Dial.

121
We can transfer these scale divisions onto the four-turn spiral scale.

122
And put them together with the divisions from Fragment F and from
another small fragment, Fragment E.
Now we have enough divisions to make a very good estimate of the
total number of divisions round the whole dial.

123
You’ve probably guessed it! It is the remarkable answer, 223. The
number on Fragment 19 that Rehm had seen a hundred years earlier.
It is the Saros eclipse prediction cycle. The Lower Back Dial is an
eclipse prediction dial. It was our first major breakthrough from our new
data.
The Saros cycle works like this. If you have an eclipse of either the
Moon or Sun in one month and you look 223 months later, then you will
get a very similar eclipse. This repeat goes on for 12 to 15 centuries. It
really is a very good cycle.

124
But there was more to discover from Fragment F.

125
Between divisions I found blocks of text and symbols.

126
Here are some close-up X-ray slices. What did these mean?

127
And surrounding the dial there were dense inscriptions.

128
Remember that In Fragment A, Price had found similar blocks of text
and symbols.

129
These are on the surface and can be viewed using HP’s beautiful
surface imaging. I called them ‘glyphs’ and I am going to explain what
they mean.

130
There were also similar inscriptions round the dial.

131
These glyphs occur at either six-month or five-month intervals or are
adjacent—just like actual eclipses. They must surely be the eclipse
predictions.
The Saros Dial is a 223-lunar month dial over a four-turn spiral. The
eclipses are indicated by glyphs, which indicate the type and time of the
eclipse. Each glyph includes an index letter, which references
inscriptions around the dial, with more information about the eclipses. It
is a very ambitious and sophisticated eclipse prediction scheme, though
far from being entirely accurate. I have been doing some research on
this recently, which you can find by googling “Antikythera Plos One”. It’s
an open-access online journal, which is free to all.

132
Let me just summarize here. This is the Saros Dial, with the glyphs,
which indicate the eclipses around the four-turn spiral.
We don’t yet know how the pointer for the Saros Dial was turned.

133
Let’s strip off the Back Plate to reveal the gears. The gears at the top
are for the Metonic Dial, which we looked at already. I want to add those
for the Saros Dial.
The large cross-spoked gear is the Main Drive Wheel. It is turned by the
small crown gear at the side, which was probably turned by a knob or a
crank.

134
I want to show how the gear trains branch at axis m—the branch that
we’ve seen to the Upper Back Dials and another branch to the Lower
Back Dials. Axis m is really the only plausible axis from which to turn the
Saros Dial. It goes through the Main Plate, which I have suppressed
here so that you can see the gears.
What I am going to show you is a complete departure from Price’s
model and Wright’s later modification of Price.

135
For the 223-month cycle, I needed a gear with 223 teeth. 223 is a prime
number, so it can’t be broken down into smaller gears.

136
This is the back of Fragment A. We want a gear with 223 teeth

137
There is really only one good candidate. e3 is the largest gear at the
back of the fragment.
It is not the ring gear which just a bit smaller and has 188 teeth; it’s the
gear outside that, which is fixed to it.

138
The teeth can be seen more clearly in our X-ray CT. There are enough
teeth to make a confident estimate that there were in fact 223 teeth.
The Karakalos family estimated that it had 222 teeth and Price had
explicitly rejected any idea that it might have 223 teeth. He wrote that
the ratio “went the wrong way”. This was essentially because of his
wrong Differential.

139
This is a computer model of these gears—the gear e3 with 223 teeth
and the ring gear e4 with 188 teeth.
At the moment, it is an orphan, detached from the rest of the
Mechanism. How shall we turn e3?

140
Again, there really is no choice. It must be powered by a conjectural
gear m3 and we give this a tooth count of 27 to make the ratios work. It
also fits exactly into the space with this number of teeth.

141
As we saw before, axis m turns at this rate.

142
This means that the gear pair e3-e4 turns at this rate.
This will turn out to be a very significant ratio, as we shall see later.

143
The next gear is f1, with 53 teeth, giving this ratio. Again, the
mysterious prime number 53 is cancelled out.

144
We have gear f1 and there are sufficient teeth to be confident that it has
53 teeth. We are going to have to solve this mystery.

145
Now I will add the rest of the gearing. This is exactly what we need for a
4-turn dial, showing the 223 months of the Saros cycle.
e3 had found no role in any previous model of the Mechanism.

146
Now I had a nice story: I knew that the Lower Back Dial was a Saros
eclipse prediction dial; I knew how it was turned via a 223-tooth gear;
and I and my colleagues had decoded much of the information in the
glyphs.
But I also had a huge problem, which took me months to sort out!

147
We can see the large gear pair e3, with e3 having 223 teeth. You will
notice some fittings on this gear.

148
This is the back of Fragment A, which is the evidence we have for e3.

149
Stuck on the back of e3 are a couple of other gears and I want to
highlight this system.

150
In close-up we see two gears. These were part of Price’s famous but
wrong Differential.

151
This is an X-ray CT slice through this system. But these are not the
gears that you see on the right: they are behind them. You will notice
the pentagonal hub at the centre of e5.

152
If we take an X-ray CT slice one millimetre towards us, we see another
pair of gears. These are the gears on the right. There are four gears in
the system. It is to Price’s great credit that he saw this.

153
After months of puzzling and a fog of confusions, I got onto the plane
from London to Athens.

154
I took my research notes with me.

155
I couldn’t work out what these four gears were doing there. They were
part of Price’s Differential, but I knew that was wrong. They were part of
Wright’s modification of Price, which generated the draconitic month by
subtle choice of the gear counts of the four gears. I was sure that was
wrong as well.
I had taken months agonizing about this gearing system.

156
I took a huge spreadsheet with me with thousands of entries. This
shows a small part of it. I was following Michael Wright’s paradigm by
looking at all the possible gear counts for these gears, which you can
see on the left. Could subtle choices of the tooth counts within the
accepted possible ranges produce the right result? There were many
possibilities of types of month. There was one output with a period of
26,000 years. Epicyclic gearing really is extraordinary. Could this be the
precession of the equinoxes?! I couldn’t really make any headway.
There were thousands of possibilities, most without any meaning.

157
I had also taken a paper on quasi-periodic motion by Giovanni
Gallavotti.

158
This included a diagram showing the ancient Greek epicyclic theory of
the Moon according to Hipparchus, which explained its variable motion
through the zodiac.

159
Then I remembered a brief remark in a paper by Michael Wright about
an observation that he had made, which he didn’t regard as important. It
was in a throwaway paragraph in one of his papers.

160
I want to concentrate on the bottom gears. These are epicyclic gears,
which are attached to e3.

161
You will see that there is a slot at the bottom of this gear. This was
noticed in 1902 by Rados, but not understood. Price thought that it was
evidence of a repair to a broken tooth that had subsequently dropped
out. But Michael Wright made a far more astute observation.

162
He noticed that there is a pin on the gear k1, behind k2.

163
And this engages in the slot on k2. A tooth has broken off at this point.
What on earth is that all about? Most people would think that this
arrangement was useless. The gears would turn at the same rate and
you might as well just fix them together.

164
Wright made another crucial observation. He said that the two gears k1
and k2 turn on eccentric axes. K1, the gear at the back, turns on the
blue axle and k2, in front of it, turns on the pink axle. This induces a
variable motion in the gear k2.
I am going to show you how this works with an animation. Forget for the
moment that these are epicylcic gears—I will come back to that later.
The animation shows what happens when the eccentric axes are fixed.

165
This is the gear with the pin that sits on one of the eccentric axes. On
top of it is the gear with the slot that sits on the other offset axis. When
the pin is further out from the slot, the driven gear moves slower and
lags behind the driving gear; when the pin is closer to the centre, it
drives the gear faster and the driven gear moves ahead. This is how the
system induces the variable motion.

166
Wright discarded this idea because it didn’t work in his model, where e3
turned much too fast for it to work. In our model it doesn't—recall that in
our model e3 turns very slowly to drive the Saros pointer. I came to
believe that this system must model the variable motion of the Moon.
And that to do this, all four gears in the system should have equal tooth
counts. Without the pin-and-slot, this would mean that the system didn’t
change the rotation at all—completely useless. So Wright’s paradigm
had to change. First I need to tell you about the orbit of the Moon.

167
This is my contribution to Shakespeare scholarship! You will all recall
how Romeo swears his love for Juliet by the Moon. Juliet, “O swear not
by the Moon...” We don’t know what sort of variability in the Moon she
was talking about. Probably the phase cycle of the Moon. My own belief
is that, if she knew the full picture, she would have walked away there
and then—and saved herself a lot of grief! So—in case you find
yourselves in the same position, where your partner swears their love
by the Moon—I am going to give you the full picture!

168
In modern terms, the orbit of the Moon is an ellipse, with the Earth at
one of the foci. This diagram exaggerates the eccentricity of the ellipse.
The point when the Moon is closest to the Earth is called Perigee.
That’s when the Moon is moving fastest relative to the zodiac. The point
when the Moon is furthest from the Earth is called Apogee. That’s when
the Moon is moving slowest relative to the zodiac.
If we follow the Moon from a prominent star back to the same star,
that’s called the sidereal month and is on average 27.32 days. If the
Moon starts at Apogee at a prominent star and goes round through its
orbit back to the same star—its sidereal cycle—you might think that it
will return to its Apogee.

169
But in fact the Line of Apsides, which is the long axis of the elliptical
orbit, has moved round by around 3°. So the Moon must catch up with
the Line of Apsides to get back to Apogee—to its slowest motion. This
cycle of the Moon, from its slowest motion back to its slowest motion, is
called the anomalistic month and it is just a bit longer than the sidereal
month—only about 5½ hours longer. The ancient Greeks knew about
this cycle, as did the ancient Babylonians before them. And all this
knowledge is built into the Antikythera Mechanism.

170
We need to understand the ancient Greek theory of the Moon’s variable
motion. This is known as the lunar anomaly. This theory explains the
variable motion of the Moon as the addition of two simple circular
motions. A constant rotation on the so-called Deferent, with period of
the sidereal month.

171
Plus a second circular motion in the form of a small epicycle, carried by
the deferent, which models the variable motion of the Moon.
The epicycle turns in the opposite direction to the deferent with the
period of anomalistic month relative to the deferent. I am going to play
an animation, which shows the resultant orbit generated by this theory.

172
The epicycle is turning backwards relative to the deferent almost as fast
as the deferent is turning forwards. This means that the pink pin
representing the Moon turns anticlockwise very slowly – in parallel with
the Line of Apsides.
The result is an orbit that looks very much like an off-centre circle. In
fact it’s very subtly different and each time the Moon orbits, it follows a
slightly different path.
The blue arrow shows the direction of the Mean Moon – the Moon’s
average position. The pink arrow shows the actual Moon according to
the theory. Sometimes it lags behind the Mean Moon, and sometimes it
is ahead. Notice at the end that the blue arrow is horizontal, but the pink
arrow has not yet got back to apogee. It needs to travel onwards until it
reaches the red Line of Apsides. A key idea in this theory is that the
period of the Moon’s variable motion is the anomalistic month, which is
just slightly longer than the sidereal month.

173
The idea is that this system models the ancient Greek epicyclic theory
of the Moon. This is the addition of two circular motions with the
deferent turning at the rate of the mean sidereal month and the deferent
at the rate of the anomalistic month—in other words, the orbit of the
Moon from apogee back to apogee.
The crucial question is: how fast must e3 rotate in order for it to model
this theory?

174
The answer is the difference between the rotations of the sidereal and
the anomalistic months. We can calculate this from a combination of the
Metonic and Saros cycles. (I will leave you to do the arithmetic.) This
results in a very familiar ratio. This is the rotation that we have already
calculated for the rotation of e3. We can calculate this and the result is
0.112579655 to nine places of decimals.
So now we understand the 53 tooth gears. The first ensures that e3
turns at the rate of the Line of Apsides of the Moon and the other two
cancel out the 53 where it is not wanted.

175
When I was on the plane, I knew what the target was for the rotation of
the large 223-tooth gear, e3. But this gear already has a rotation to turn
the Saros Dial. There was some choice on the input gear m3 that
turned e3.

176
I thought that it had 27 teeth. So I tried this. Too big!

177
Then I tried 26 teeth. Too small!
Mathematicians are strange people, as I am sure you know. Sometimes
they do crazy, impossible things.

178
So I tried the impossible 26.5 teeth for m3. It was exactly the right
answer, to nine places of decimals. I sat bolt upright in my seat. It
couldn’t be a coincidence! I immediately realized that twice 26.5 is 53:
Michael Wright’s 53-tooth gear that I had changed to 54 teeth.
Then everything fell into place! There was a cascade of consequences.

179
Let me show you how this works. The inputs to this system are the
rotation of e3 that we encountered earlier, with the bizarre prime 53,
which we now understand.

180
The other input is the rotation of the mean sidereal month that resulted
from Price’s Metonic gear train.

181
You will notice the pentagon on the hub that carries the mean sidereal
month rotation and the hole through the middle of it.

182
e5 with 50 teeth sits on the pentagonal hub and carries the mean
sidereal month rotation. Notice that there are two offset axes on the
right. Their separation is about a millimetre.

183
k1, also with 50 teeth, is the gear with the pin and it sits on the larger of
the two eccentric axes. (An important insight was that all four gears in
the system have the same number of teeth. Without the pin-and-slot,
this would be a useless arrangement, which would give a unity ratio.)

184
And the slot on k2 engages with this pin. What is the point of this
arrangement? As we have seen, the answer lies in the eccentric axes
on which the gears turn. As they turn, sometimes the pin is closer to the
outside of the slot, when k2 turns more slowly, and sometimes to the
inside, when k2 turns faster. This induces a variable rotation in k2.

185
This variable motion outputs at e6. With equal gears, the whole point of
the system is to introduce the variable motion.

186
This is not at all the obvious way to model the epicyclic theory of the
Moon.

187
Mounting the Pin & Slot epicyclically changes its period of variation from
the sidereal to the anomalistic month. It was an incredible idea by the
designer. It is a work of genius.
But there was still an outstanding problem. What I had found was that
the rotation of e6 modelled the variable motion of the Moon. But where
did this output end up? It had always been assumed that the epicyclic
system at the back outputs to the Back Dials. I couldn’t work it out.

188
Here is a profile view of the same gearing.
A couple of weeks later I got a call from Mike Edmunds in the Canary
Islands. Could the output go back through the large gear e3 and up to
the back dials? I told him that I thought not and put down the ‘phone. I
immediately realized that he was right and I called him back.

189
I want to concentrate on this area.

190
If I now add the output at e6, it goes back through the hole in the
pentagon that we noticed earlier, then to e1 with 32 teeth.

191
e1 then engages with an equal sized gear, b3, that reverses its direction
of rotation. From there it goes up to the front dials.
It was obviously insane to attempt to do this in the 2nd century BC. You
would have thought that was enough and you would then simply add a
pointer to show the variable position of the Moon in the zodiac.

192
But they had a special kind of insanity. They added a device to display
the phase of the Moon.

193
Here is another angle. You can see the semi-silvered ball that displays
the phase of the Moon as well as the lunar pointer that shows the
position of the Moon in the zodiac. The Moon phase device was
identified by Michael Wright. It occurs much later in history on many
medieval astronomical clocks.

194
Strip off the cover and you can see the gears. It is an exquisite
differential device, with an epicyclic crown gear, carried round by the
casing of the lunar phase mechanism, which engages with an equal-
toothed gear on the Sun output. This differential device that subtracts
the solar rotation from the lunar rotation to get the phase. It does
exactly the same as Price’s Differential in his old model in Gears from
the Greeks. Price had the right idea in the wrong place and made it
much too complicated.

195
The gear in the centre is the 53-tooth gear. It turns the large gear pair,
e3-e4, at the correct rate, so that the period of variability of the output of
the pin-and-slot device is the anomalistic month. The diagram shows
how this is geometrically equivalent to the ancient Greek theory of
variable lunar motion. The output then goes up through the hole in the
pentagon to the Moon phase mechanism and the lunar pointer, to show
the variable motion of the Moon through the zodiac.

196
This is a gear diagram of the whole Mechanism, except the planets at
the front. It’s not easy to understand at first glance! You can see the 53-
tooth gear, which Michael Wright identified. And how this turns e3. You
can see the pin-and slot that generates the variable motion and how its
output goes up to the front dials. I hope that I have given you some
insights into the research that created this model.

197
This entirely new model of the Antikythera Mechanism became part of
our first publication in the prestigious science journal, Nature, which
gave us huge worldwide publicity. It was a heady experience.
As a research team, we had clung on by our fingernails through years
of frustrations and setbacks. There were many times when we were
sure that the project would fail. I found a persistence and focus in doing
this project, which I never knew I had. Maybe Nietzsche was right: it
didn’t kill me and in many ways I became stronger! I was extremely
privileged to be in the right place at the right time with the right skills to
make a contribution to this research.

198
What is the answer to the Gears, the Moon and the Antikythera
Mechanism? The answer is 53 !!

199
It really is incredible that sponge divers in 1901 should recover a
corroded lump that contains two gears with 53 teeth and evidence of a
lost technological revolution. We should never forget that this device is
from ancient Greece. It re-writes the rules on the history of ancient
technology. It challenges us to re-think this history and to question all
the assumptions about it.
I would like to end on a quote from Derek de Solla Price’s 1959
Scientific American article.
“It is a bit frightening to know that just before the fall of their great
civilization the ancient Greeks had come so close to our age, not only in
their thought, but also in their scientific technology.”
So that is how I spent much of my mis-spent middle age!

Antikythera mechanism UCLDH seminar

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