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, there has been huge progress in understanding this geared astronomical calculating Ever Ever since its discovery by Greek sponge divers in 1901, the Antikythera Mechanism Speaker 15 15 June 2012

- mail: -

From Antikythera to the Kilometre Array:Square Lessons from the Ancients Kerastari, 12

10 Hereford Road, South Ealing, London 4SE, W54 UnitedKingdom E Building Building the Cosmos in the MechanismAntikythera Freeth Tony Antikythera

1 history and one of the true wonders of the includes ancient a world. mechanical representation The of latest the model the back cover of the . instrument. We believe that we are now has inspired fascination and fierce debate. In the early years no result of a hundred years of research, particularly by Albert Michael Rehm, Derek Wright de and, Sol most recently, by members of the Project machine. With its astonishing lunar anomaly mechanism, it emerges as Abstract Copyright owned by the author(s) under the terms of the Creative Commons the ofCommons author(s) the terms the Creative owned by Copyright under

 PoS(Antikythera & SKA)018

9

— and and such

- t was called called - . I and - tory tory and it

Tony FreethTony anomalistic anomalistic and furthest and furthest

basic basic orbital Metonic

sidereal sidereal

Cosmos Cosmos in the its 1 The .

are are built into the — : the the the (27.21 (27.21 days) is the perigee . Remarkably, Moon. Remarkably, —

stem stem that from come Sophocles

. They saw them as is is the phase cycle of the — Earth sy an an early form of astrology

- — ng ng as simple as possible! As all Earth system . In this geocentric Cosmos, the line line of apsides. -

Moon Solar Solar System that that could be used for thesemaking - node. It is shorter than the sidereal draconitic draconitic month a fundamental step in the history of lunar Moon - Cosmos —

Earth system Earth - 2 such a time period. I would like to give two

- not not straightforward, with their prograde and

and

- Moon are was was named after the Greek astronomer, Meton of -

hat hat we call the Century Century BC Babylonian : 19 years = 235 also also called the

h follow follow regular, if complex cycles. Some t —

o astronomers astronomers on the cycles of the Moon. The - a new model of this device that includes ronomy ronomy about the they they d

Metonic joins these two points. The

are the points where the Moon’s crosses the plane of the Earth’s of the the Earth’s plane crosses orbit Moon’s the where points are the (29.53 (29.53 days)

ining ining these two points is called the

The

based on joint research by myself and Alexander Jones and Alexander myself by research joint on based

Over the best part of the first millennium BC, the ancient Babylonians

It It is the longest recorded set of scientific observations in his present , 2

as well as three different types of calendar month 2 . nodes — want to The line jo line line of nodes

. . synodic synodic month the the bodies near to the Earth t — (27.55 (27.55 days) is the cycle of the Moon from apogee back to apogee. It is longer than the Astronomy? Impossible to understand and madness to investigate... to madness and understand to Impossible Astronomy? cycles

apogee

There are period two ofrelations fundamental the Sun First some definitions for non The Antikythera Mechanism is Greek but its roots lie in the previous great era of Since Since astronomy is so difficult, I will try to keep everythi ncient Astronomy ncient Babylonian period relations of the Sun of relations period Babylonian Cycles of the Moon the of Cycles Babylonian

A

Babylonian Babylonian astronomy. , but it was known earlier in 5 synodic = 254 sidereal months. In ancient times, this identity of lunar months and years all of these months Mechanism. Antikythera 1.3 is its month sidereal because month the line of apsides precesses from away the Moon in a period of about years. The Moon relative to the Sun from new Moon because Moonmonth the up catch the must toSun to return again with back new to new Moon. It is longer than the sidereal (27.32 days) is the cycle of the Moon from The Moon’s period. one star back to the same star orbit and the month from one of the Moon’s nodes back month to because the the line of same nodes precesses round towards the Moon in a period years. The Moon’s orbit is elliptical: the Moon’s closest ofto point earth is its about 18.6 an astronomical cycle was repeated after such examples from Babylonian ast Saros 1.2 daily daily watched the skies and recorded their in observations the tabletscuneiform of the so Astronomical Diaries was an extraordinary enterprise. It was driven by omen telling which required predictions to be made of the positions of the astronomical bodies. Much of the project concerned became with repeating identifying cycles such that form had the typically which relations, on period This was based predictions. technology. technology. I Mechanism Antikythera 1.1 Babylonian astronomy. manifestations of gods and goddesses. This was their movements of such bodies as the retrograde motions. However, planets genius conceived the idea that you possible to could construct mechanize a these machine cycles to with predict the gearwheels future 1. astronomers know well, the stars are fixed! When the ancients looked number of astronomical bodies at that moved relative the to the stars. sky, These were they the Sun, Moon saw and a Building the Cosmos in the Mechanism Antikythera PoS(Antikythera & SKA)018

in the in the

surviving surviving Tony FreethTony Century Century BC

Cosmos

th . . It is an

Polynomial Texture in all two great cycles. cycles. great two

it it really is an excellent was was that all the so there will be a repeat Karl Jung

concerned concerned researchers for

— 3 came came from 7 —

—

imaged with

w Moon (enabling a ) a w (enabling Moon solar eclipse) 239 anomalistic months Saros cycle = 82 surviving fragments

3 The The

re are

The

peat peat eclipse will be very similar, since the Moon will be at solar calendars. - of the Antikythera Mechanism

242 draconitic months

cular enhancement.

with spe

hera Mechanism Research Project Mechanism Research hera What What is the “secret order” jigsaw in this thatpuzzle wrecked the reveals (PTM)

Fragments A, B and C 3 . acies acies in the cycle means that the repeat no longer happens

| ) In all chaos there is a cosmos, in all disorder a secret order... secret a disorder in all is cosmos, a there chaos all In Antikyt

What What about the planets in the Antikythera Mechanism? These were the other main 1 1 The Planets

2005 Fig. Fig. Fig. Mapping © ( Mechanism? Antikythera components components of the ancient Greek Cosmos. It is a question more that than has a hundred years. There are 82 surviving fragments of the Antikythera Mechanism generates generates repeat for a period between twelve inaccur and fifteen centuries before the slight eclipse cycle. One of the main results of our paper in in 2006 these by be explained can Mechanism Antikythera in the one) (except 2. Babylon: Babylon: 223 lunar months = cycle, which works because of the identity of a whole number ofnumber the If months. draconitic isMoon near of a node at ne lunar months with a whole then it will be back near the eclipse. same Similarly node for after lunar eclipses. this The eclipse identity period in the Saros anomalistic months means that the re cycle with a whole number of the same distance from the Earth and hence the same size relative to the Sun. The Saros cycle Building the Cosmos in the Mechanism Antikythera was used primarily to build luni PoS(Antikythera & SKA)018

more more

. Most of 5 turn spiral , , are which - Tony FreethTony

4 ) We We are now

2 unich Fig. Fig. ( M

It is the Bible for us is us the for Bible It

6 in .

ient ient times. He He did much research on So Rehm was completely

8 , 7 , 6

. as as is having the right idea and then

— Staatsbibliothek in 1905

he

4 Gears from the from Gears ing ing the right idea and then putting it in the

a German philologist, who was the first person to

. What did the early researchers suppose about the ) sighted sighted ideas was that the Mechanism included a 2 e... just under the front dial plate.” plate.” dial the front under just e... - Cosmos being shown on the front face of the Mechanism the of face shown on the front being Cosmos

ice came to the subject of the planets, he wrote: planets, the of subject to the came ice m m was Fig. Fig. ( of the Mechanism with the Sun, Moon and all five planets is planets is and all five with the Sun, Moon Mechanism of the

this Dr HermannDr Dannheimer

— © , unich one ring for each of the planets known in anc Albert Albert Reh of the AntikytheraMechanism

M One One of his far

—

in all the mechanical details wrong but he got the essence right. essence the but he got wrong details mechanical the all

month month calendar following the Metonic Cycle. - Much Much of Rehm’s work consisted of speculation in the face of very limited are aiming for aiming are

tes tes that are now kept in the Bayerisc

. He thought this that was displayed on the scales in B Fragment axial display at the front axial display particularly particularly Fragment C year year 235 - - Staatsbibliothek — he device it would be most appropriat be most would it device “...there is a possibility that... a gearing system, now totally vanished... served to exhibit the rotations of all of the planets... If such gearing was to be part of the | Fragments A, B,| C A co A This time, he didn’t get the idea in the wrong place, he simply threw it away and didn’t Derek Derek de Solla Price is the next great name in Antikythera research. He undertook twenty For more than a hundred years, there has been controversy about the planets in the The The Antikythera fragments in 1905 were similar to today but have considerably

2 Overall Design of the Mechanism the of Design Overall Derek de Solla Price de Solla Derek Albert Rehm Albert

the model that we we that the model develop the idea at all. This is exactly what we now believe. now what we is exactly This all. atidea the develop 2.3 years of research before publishing his great paper, paper, his great publishing before of research years all. However, like his predecessor, Albert Rehm, Price When Pr ideas. of his best got some away a lot wrong, as well as throwing wrong wrong about where the planets were shown. Hav wrong place is a recurring feature of Antikythera research throwing it away! got often He evidence. 2.2 his ideas about the gearing unbelievably and architecture prescient. of the Mechanism are wrong, but very often in the form of five rings sure that the scales in Fragment B form part of the Upper Back dial, which is a five with a 19 Fig. Antikythera Mechanism. realize that the Mechanism was an astronomical calculating machine. the Mechanism but published very little. We only know how advanced his ideas were because of his research no Bayerisc material these fragments? from the planets of presence Building the Cosmos in the Mechanism Antikythera 2.1 PoS(Antikythera & SKA)018

al al so so

06 - with with — . We Tony FreethTony exactly exactly what Some Some of his and

—

5 Michael Michael Wright

lunar lunar anomaly e believe that these The The first person to

Saros 3 W , which kably, kably, Rehm in 1905

) the called 4 - e! e! — Fig. Fig. e input. Another set of outputs Remar (

the so Some Some of these pointers indicate

—

5

idea in the wrong plac wrong in the idea

ight rate rate relative to the turn of th

constant rate rate are those involved in eclipse prediction

b1, which rotates once a year at the rate of the mean Sun. This in

ther ther pointers on the Mechanism showed the longitude of the rch rch notes concern the feature in Fragment C , coupled with pin and slotted follower devices. follower slotted and pin with coupled gearing, epicyclic

constant a Moon phase mechanism a hundred years later.

epicyclic epicyclic gearing for the Moon with a fixed on the central axis

All the o as The Mechanism The was Mechanism driven an by input on the side via a crown gear engages that

using

3 1 . ) — | | Back and Front views of a reconstruction of our latest model of the Antikythera

A A key example of variable motion is that of the Moon 3 3 Mean Mean Sun Wheel The Lunar Anomaly The Lunar

2012 Ltd First Tony Freeth, Images Fig. Fig. Rehm had got it wrong. Again it was the r the it was Again it had got wrong. Rehm know know that this anomaly is represented consider in that the Antikythera the Mechanism. lunar unpublished resea anomaly might be identified represented was Albert Rehm. considered would a emerge hundred years later for the planets. For inferior the Moon, it does not work Fig. Mechanism. 3. © bodies the turn drives gear trains that turn calendars and rotate the at a pointers on the dials. that turn at a pointers. astronomical bodies on the scale at the front of the Mechanism. pointers all turned at a variable speed in order to follow the variable speed of the astronomic Building the Cosmos in the Mechanism Antikythera ( PoS(Antikythera & SKA)018

a yet yet the the

—

— Price’s

Tony FreethTony silvered ball - brilliant idea, brilliant idea, Right:

a years years before they

the the Moon in the y do? y was was nonetheless very (PTM) with specular

1,500 oon. It oon. was It ization ization of that the gearing system at

discovery discovery The American Philosophical Society ThePhilosophical American asserted

that that calculated the difference between the

1974 from from Gears from the Greeks (Price 1974)

6 ©

Right Right idea by Price, but in the wrong place Right:

(PTM) of the back of Fragment A. 9 Polynomial Texture Mapping

Differential Differential

ar at the back of the Mechanism, which was part of his one one gear is carried round on the face of another gear

He He studied the fragments in depth and thought that he had

6 was was a

seen with )

5 Fig. Fig. ( on the large ge

. The Mechanism does include a differential device to calculate the phase of the the phase of the calculate to device a differential does include . The Mechanism , , riding He He got the of the gears wrong, but this Polynomial Texture Mapping The Moon phase mechanism runs from the centre of the circular feature in the

6 . ack of Fragment C Antikythera Mechanism Research Project. Antikythera Mechanism wrong

system mechanism mechanism discovered by Wright. B Left:

| a | In In epicyclic gearing, the axle of on of the 10 o’clock position. The small circular feature at the end was a semi

Antikythera Mechanism Research Project Antikythera Mechanism Research

2005

Price Price was the next to publish theories on the mechan ! 4 5 © 2005 Fig. reconstruction of the epicyclic system as a Left: Left: were supposed to have been invented. What did these epicyclic gears actuall gears epicyclic these did What invented. been have to were supposed again very advanced and subtle form of gearing. Rehm suggested epicyclic gears in the Antikythera an in identifying a critical discovery made Price place. but not However, in the right Mechanism epicyclic Differential significant. It was toastonishing find epicyclic gears in , Mechanism, Mechanism, nearly 70 years later. solved the mechanical structure of the Mechanism. He back of the Mechanism Moon’s rotation and the Sun’s to rotation theproduce phase of the M but was it Moon: © Fig. enhancement. directi that displayed the Moon’s phase. Building the Cosmos in the Mechanism Antikythera PoS(Antikythera & SKA)018

— ray ray Ray Ray was was - This This

-

of the of the linear linear 3

. second second 10 for the r X

quashed quashed

Tony FreethTony (PTM) very very similar in anomaly

The pin gear k1 . Michael Wright —

) 3 Microfocus Microfocus X 6 called - Fig. Fig. ray ray study using it as irrelevant ; and ( -

the the so — (AMRP) (AMRP) in association with the

actually actually do? This was the most The The effect of the eccentric axes is n noticed that there is a slot in k2. . Tek Tek Systems (UK), led by Roger ) — - The ancient Greeks had a geometric 6

Fig. Fig. ( so so he dismissed

7

— Polynomial Polynomial Texture Mapping

Differential

is h It It is said that they first thought that the Moon

—

. 2 ) 6 , by a team from X creating creating an epicyclic motion. The subtlety was that, with Packard, Packard, led by Tom Malzbender

11 should should have a perfect circular orbit, because gods and - — ahead, ahead, when the pin is near the inside of the slot. If the gears Fig. Fig. — (

an absolutely useless device, since the gears will simply turn at simply the the will since useless gears device, an absolutely ray ray CT) nt of the other. These mesh with two gears at the centre of e3 to - the first The The resulting orbit is an epicycle. It looks like a slightly s resolution 3D. resolution

-

(X

Antikythera Antikythera Mechanism Research Project hours hours longer than the sidereal month.

Slot ray ray “slices” just a millimetre apart reveal the four gears: in one slice, e5 and ½ - - discarded observation discarded and fect fect of the eccentric mounting of the gears is highly significant. - , led to an absolutely crucial observation by Michael Wright. Since the early days by by a team from Hewlett

was was the first fruit of new scientific investigations of the Antikythera Mechanism, carried l the Moon’s correctly: anomaly the period of variation must be the anomalistic month. So The ef Study Study of the epicyclic gears k1 and k2, with an earlier X The The gearing system at the back of the Mechanism consists of a large gear e3 with 223 What did Price’s epicyclic system In In terms of modern astronomy we know that the Moon has an elliptical orbit and this The Pin The Wright’s Wright’s The Epicyclic System Epicyclic The centre centre circle, whose axis precesses around in a period of about nine years

- period, period, namely the sidereal month. The designer of the Mechanism knew mode that this would not 3.3 turns at a constant rotation and drives k2 via the slot that the driven slot gear k2 sometimes lags behind the outside of pin the slot and sometimes gear k1, when the pin is near the were not mounted then epicyclically, the period of this variation would be the as same the input might might say this that like looks same rate but Michael Wright made another fine observation. eccentric He axes: this makes a saw critical difference that to the resulting the motion gears turn on had no idea what again! away thrown idea, Right Mechanism. Antikythera this device was doing there after the discovery of the Antikythera Mechanism, it had bee Price thought that it was evidence that the gear had been repaired, but Wright had a much more important insight. He saw that k1 had a pin on it and this engages with the slot on k2. You gears gears k1 and k2, one in fro complete the epicyclic system. At first glance, it appears that there are only two small gears in the system. It is to Price’s great credit that he identified four gears, as we can see in ou CT data. Two X k2 e6 and slice, second in the k1; 3.2 undertaken Computed Tomography Hadland. The first technique revealed fine in high them inside looked surface details in the fragments and the teeth, to which is attached a ring gear e4 with 188 teeth. On the face of e3 are two epicyclic extraordinary extraordinary result of the research that we published paper in our paper in Nature in 2006 out in 2005 by the National Archaeological Museum in Athens. correct correct parameters, the period of the second circular motion relative to the first longer is the anomalistic slightly month. off theory. beautiful a was It ellipse. precessing as a orbit Moon’s the of picture to today’s form 3.1 causes causes a in variation the velocity of the Moon as seen from Earth Moon. This creates a variation in the Moon’s with velocity the period of the month, anomalistic which is about 5 theory to explain this variable representing motion. the goddess Selene goddesses were perfect. But this didn’t agree with the second reality circular rotation of to the Moon. So they added a Building the Cosmos in the Mechanism Antikythera PoS(Antikythera & SKA)018

3 .

, with an Tony FreethTony

complexity.

echanism echanism to be turned at just four gears its . A work of genius. of work . A ) — slot mechanism induced a - 7

Epicyclic Theory of the Moon of the Theory Epicyclic and - Fig. Fig. (

slot, epicyclicallymounted on e3. slot epicyclically to subtly change its - - and and

- - 8

economic economic solution

he ancient Greek Greek ancient he

the pin

very Tony Freeth, Images First Ltd Images Tony Freeth, a with

is

year year period. In this way, the pin - this extraordinary conception. is this It extraordinary not the ofdirect way the modelling

the difference between the sidereal month rotation and the anomalistic — devised tiful tiful and elegant solution to the lunar anomaly. It is very hard to understand the Moon on the Zodiac dial at the front. the at dial Zodiac the Moon on the

mall gearsmall of the epicyclic system, S Tony Freeth, Images First Ltd First Tony Freeth, Images | Schematic gear| diagram of the Antikythera Mechanism, showing |

It It is a beau

7 6 2012 © Fig. epicyclic pin gear and an epicyclic slot gear on eccentric axes eccentric on gear slot an epicyclic and gear pin epicyclic ©2005 Antikythera Mechanism Research Project / Antikythera Mechanism©2005 Research Fig. how the designer model, but it period period of variation. He forarranged the large gear at the back of the M exactly the right rate month rotation, with a 9 to t equivalent geometrically is which variation, Following the output up through the Mechanism of motion results in a pointer following the variable Building the Cosmos in the Mechanism Antikythera he took an extraordinary step: he mounted the pin PoS(Antikythera & SKA)018

ar ar two two

In 212 BC, 212 BC, In Tony FreethTony

6 so Price was particularly particularly the — —

hand account, since the -

es was killed by a Roman es a by was killed Roman sms sms were around in ancient though though I think that it is very nothing else out of the great ray CT we can read many text can CT read we ray many , took home with him —

- "... hera hera Mechanism

this... this... globe... on which were

hand hand account. was a student of with our X with our - year year Metonic calendar dial with 235 lun

-

9 (Price 1959) wrote: 1959) (Price

was was seen around 70 years later in the house of .. .. might well present information on the

lawyer, politician and orator, Cicero. politician and lawyer,

globes globes

this this is a first

51 BC 51 BC

–

Derek de Solla Price de Solla Derek

y constructed by our friend Posidonios, which at each 12 One One of these ,

6

recentl ately ately by a single device for turning the globe those various and

ere is an inscription on the Mechanism that exactly fits Price’s description. slot device in the lunar anomaly mechanism creates a precedent for looking at creates for looking precedent a slotmechanism in the anomaly lunar device -

these these quotes give us a strong historical background for believing that all five and

- . The inscriptions on this dial are month names and year numbers 8 , sighting sighting was around a century before Cicero wrote about it. Cicero also writes about 7 , 6 “...the “...the risings risings and settings, stations and retrogradations Saturn).” of and Mars, , (, Greeks the planets known to the “On the upper (back) dial the inscriptions. that take place in the heavens every day and night...” and day every the heavens in place take that 45 BC deorum, natura De Cicero, revolution reproduces the same motions of the sun, the moon and the five planets divergent movements with their different rates of speed...” of rates their different with movements divergent 54 publica, re De Cicero, “... the famous Sicilian had been endowed with greater imagine it genius possible than for a one human would being to possess... delineated the motions of the sun and moon called and wanderers... of (the those five five planets)... stars ... which had are thought out represent a accur way to We now know that the Upper Back dial is a 19 In In In In this case, it is probable that This inscription sounds exactly like the Antikythera Mechanism. Cicero mentions that the First some remarkable evidence from the from evidence remarkable First some The The pin Inscriptions Classical quotations Classical

Evidence for the Planets the for Evidence

Fragment Fragment G was part of However, because is G the so worn. surface theFragment Front Cover. Price could only read a few text characters on months wrong. However, th planets. Both Mechanism. Antikythera the in included planets were 4.2 Posidonios, Posidonios, who was head of the Stoic scientist. So school it is of very likely philosophy that in Cicero did actually see and this device. a Again it included considerable all the times times and included all five planets. However, it is obviously a second reported machine: another device device was made from bronze but he doesn’t say that it had gears likely that it did. It is our first piece of evidence that such mechani the grandson of Marcellus. of the grandson the Romans finally succeeded in their siege of Syracuse in and of succeeded their siege Syracuse theArchimed finally Romans soldier. Cicero writes that astronomical “globes” that had been made by Archimedes and the victorious general, store of Marcellus booty captured." the mechanization of other variable motions in the Antikyt planets. The evidence that the planets turn.in be examined were will four which sources, from comes It overwhelming. included in the Antikythera Mechanism is now 4.1 Building the Cosmos in the Mechanism Antikythera 4. PoS(Antikythera & SKA)018

are are

Again, Again, (not the (not the as little

) ”. 8 Tony FreethTony Cosmos Fig. Fig. (

progress progress and will be unar unar theory, based on - in - in a schematic way

in particular, part of the Back work lf is included in the inscription. He has found traces of the names the names of has found He traces —

1 itse

Cosmos 10

!

century century BC were, like the l

nd

ray CT slices through Fragment B, showing the Back Cover - sings sings and settings, stations and retrogradations Indeed Indeed the word ri

that this is a description of the front of the Antikythera

over over describes the synodic periods of the planets and the Back In In general, what we read in the inscriptions is reflected in the gears

We believe

Recently Recently we have read even more. This is

3 so we can be very confident that the planets were displayed on the Mechanism. the on were displayed the planets that confident be very can so we — als Antikythera Mechanism Research Project / Jones Antikythera MechanismAlexander Research | A | composite image of several X

So how would the planets have been mechanized in the Antikythera Mechanism? The In In summary, the Front C

Recently, Recently, Jones Alexander has looked again at the Cover Back inscription 8 Astronomical Theory Astronomical

2005 prevailing prevailing theories of the planets in the 2 Cover Cover is a description of how they were Greek displayed geocentric Cosmos. on the Front Dials in an ordered and di ancient 4.3 © Fig. inscription. Planetary names (some incomplete) highlighted in red. for all five planets and the word Mechanism Mechanism as a geocentric Cosmos with the circles. concentric through moving spheres planets displayed Cover that survives in mirror text imprinted onto Fragment B. Fragment onto imprinted text in mirror survives that Cover of all five planets in this inscription. They are mentioned ancient Greek in geocentric Cosmos. a specific order that reflects the The inscription describes how each moves in a “circle” which is above the circle for the previous planet and each planet appears to have be represented by a “little sphere” that moved through the circle. our new data. published in a forthcoming series of papers about the inscriptions, Jones, so I coordinated will not comment by in detail about theAlexander inscription. However I can say that the content is about the planets and their “... place wrong the in idea the right exactly had Price Front Cover inscription described in the previous paragraph) Building the Cosmos in the Mechanism Antikythera characters. Yanis Bitsakis and Agamemnon Tselikas read more than 900 new characters from PoS(Antikythera & SKA)018

d. on As As

1 Wright Wright use the with with all

, we are n reality centuries centuries I

in in a very There is a this this sort of Tony FreethTony

nd research 15

, 14 , again again 13 Mean Mean Sun Wheel — saw saw model his and early 2

, though Wright prefers rd These theories had been

modelling modelling the Babylonian 2 first way 03 on how the planets could — ). ). A final criticism is that all

sm. sm. These models also seem 20 5.3 – gear

(publication (publication forthcoming)

pproach pproach has been to try to find an complex

Section Section ric ric model of the Solar System. he places their axes between the spokes. hand side, where the input crown wheel is

- — spoked spoked gear b1, called the - 11

particularly for the superior planets. superior the for particularly available at the time. the at available

— was impossible, but I have since changed my min my changed since have but I impossible, was

On On the right

In all of the versions of Wright’s model that includes the the includes that ofmodel all Wright’s In of the versions large large box at theprotruding front. Because of

a esearch esearch in the period 2000

All of these papers included interesting ideas, but the work

15 lso lso built physical models. When I , 14 , 13 The inferior planets are not placed directly on the spokes of the echanism. an an example. A large circle rotates at the rate of the Mean Sun. as would seem natural ) inscription on the Front Plate

a lot of r 15 —

At At the centre is a squared thatboss is tofixed suitable gears, carry like axial pointers on the front dials, I was astonished. I thought

- Mean Sun Wheel Sun Mean 16

the accommodated in accommodated

I I believe that the evidence from the surviving data strongly suggests that the

he whole arrangement is unnecessarily cumbersome and not in the spirit of parapegma ow, but no better theory was theory better no but ow, T eight eight co

the Planets the

1 at the front way way with seven or eight gears for each planet, powered by an awkward auxiliary and

On On the spokes of this wheel are a number of evident holes and flattened areas. ). icated Let me take Venus as 9 The front of Fragment A shows the large four Though Though Wright’s models are groundbreaking, I don’t believe that they are plausible For an inferior planet like Venus, this theory can easily be mechanized.

is gearwork is is gearwork planets 2

Evidence from Evidence Wright’s Models Wright’s Modelling

Mechanical Evidence & Models Evidence Mechanical

Fig. Fig. mounted on mounted this wheel. the fixed gear of the Venus m elegant mathematical solution to the problem to solution elegant mathematical 5.3 ( Wright has proposed, these are surely the traces of an extensive epicyclic system of gears to abandon the surviving evidence of the pillars on b1 ( of th the star calendar ( confident that the front was flatof the Mechanism to so include these Wright’s box inscriptions, cannot be correct. Mechanism was designed by a mathematician. My own a large large wheel b What is the a point ofwheel withmaking spokes, if thenyou have to fill in the gaps to the carry bearings of several gears? Wright has compl also included the superior planets axle at the side. economy and elegance that we know from the rest of the Mechani 5.2 Mechanism. models of the Antikythera planets, they are mechanized in essentially the same very the description “extensive”. Using Using these ideas, there was be included in the Mechanism. of Michael Wright was for the most part the most advanced and I want to focus on this. not only published his result, but a five Greece ancient in sophistication mechanical fixed fixed gear at the centre with 50 teeth which and is carried round this at the rate meshes of the mean with Sun by another an epicyclic gear with period for Thererelation is Venus. a pin this on 80 which withgear, engages a follower that slotted teeth, rotates at the centre. The resulting variable motion is carried by a tube to the output pointer. it is hopelessly inaccurate, because it fails to properly track the irregular retrograde arcs that the foll actual planets 5. 5.1 developed developed by Apollonios of Perga and his contemporaries in the late 3 BC. Attached to its circumference is an epicycle, with a pin on planet. its It turns at circumefernce the right representing rate so that the the planet satisfies its period relation. Here I will simple period relation from that Babylonian astronomy Venus goes through 5 synodic phases in if the planets: the of motions retrograde and the nicely prograde models very theory The 8 years. planets had circular , it would be an exact geocent Building the Cosmos in the Mechanism Antikythera simple epicyclic models, combining two constant circular rotations. PoS(Antikythera & SKA)018

, What What In In this

Tony FreethTony ray CT slice - I I want to make

n X These are relatively easy

1 crown geara1.

On the right a

at they demand an explanation. .

1

. A suitable mechanism for Mercury will

) 12

10

At the bottom Atis the thebottom

that that the bearings match those on the spokes. It is Fig. Fig. so we must be careful not to make too many

(

— ray ray CT slices through the pillars reveal shoulders and -

of the Mean Sun Wheel, b1 one long pillar and two short pillars and they are fixed to the y were y toplatesdesigned carry that to were fixed the pillars with — PTM

up

-

surviving onpillars b1.

mos

shares shares its fixed gear with Venus and needs an equal epicyclic gear, separated by he mechanisms for the inferior planets and the Sun. For Venus, we use 5 synodic cycles in 8 years from Babylonian astronomy. two theof three the Sun | | On the left, a close Antikythera Mechanism Research Project Antikythera Mechanism Research

tooth tooth counts that exactly reflect the period relation for the planet. Here I have chosen 104 First t We can now reconstruct the Mean Sun Wheel, with its bearings and eight pillars. The The pillars are such a prominent feature of the wheel th

9 Inferior Planets & Sun Planets Inferior

Building Cos the

2005 an idler gear. At every stage my aim is to match the gears to apparent bearings and fittings on because because these bodies all “go with the Sun” have synodic cycles in 33 years because it means Babylonian from known not is it because it with not happy am but I relation, period aquite good astronomy. model, a reconstruction of the lost gearing on this wheel. Because of the evidence, missing this must of necessity be a conjectural reconstruction it. about claims dogmatic 6.1 6. functions did these features have? at The mechanism the back, so the likely candidates be must the Sun and the planets. Moon is already spoken for by the lunar anomaly showing Round the periphery of the wheel, there is evidence that shows that there must originally have been four short and four long pillars. X pierced isends. It theclear that model. in our role an essential play will plates These pins. © Fig. circumference of b1. of circumference Building the Cosmos in the Mechanism Antikythera located, there are three pillars PoS(Antikythera & SKA)018

to in

6 were were tooth tooth - —

. ) Tony FreethTony 11 orporated and retrograde scheme. scheme. These

Fig. Fig. ( this this problem. The

e inc

on

How How to include them in axial distance of the two I I had failed to find any - the the long pillars, to which I

pointers. fill fill the space between their Mercury Mercury and Venus Just four gears that work in

— use , which attached be must rigidly Date another another attempt

For For these, we 13

1 to make

mean mean that the gears

The inferior planets ean Sun is the I I had (SPP). (SPP).

they they simply —

Date pointer for the on the front of the Mechanism. the of front on the calendar Egyptian the for pointer Date are carried by circular plates, following Michael Wright’s

th th parameters for suitable the pin distance and the inter Originally, Originally, I had serious doubts that all five planets could b Superior Superior Planet Plate her parameter her that parameter follows the m | | The Mean Sun Wheel b1, with the Venus mechanism at 1 o’clock, the Mercury mechanism attached to the to attached

Tony Freeth, Images First Ltd First Tony Freeth, Images

For Mars for (and similarly the the other superior tooth planets) of counts the 69 two So now we need to add the superior planets. The ot this this the 10 o’clock and the solar at 7 mechanism o’clock. Superior Planets Superior

2012 epicyclic epicyclic gears, this exactly models the epicyclic theory of Mars. exactly the same way as the lunar anomaly mechanism to works. model scheme that this me stunned completely It planets. thethe of motions prograde solution solution then came fairly quickly. It was astonishing to discover that the same gearing structure planets superior the for work also would anomaly Moon’s the for worked that gears have no special meaning two centres. Wi call fairly easy; it was the superior planets that I always found problematic. a simple way? the Mechanism in harmony with the gearing that simple we solution after already several years knew. of attempts. When Alexander Jones told me about his work on the Back Cover planetary inscription, to the Mean Wheel. Sun For this we use the short to pillars, which we add a plate, which carries a tube 6.2 am going to attach a conjectural annular plate to carry the superior planet mechanisms. I shall © Fig. at 4 engage with slotted followers, which carry their outputs via tubes to tubes via their outputs carry which followers, with slotted engage Building the Cosmos in the Mechanism Antikythera the spokes. The pins PoS(Antikythera & SKA)018

. at 8

fixed gear

striking Jupiter Tony FreethTony

mechanisms th are too

and - s 37 on a different axis;

but

mechanisms in the space at around the same time

and carried epicyclically on at 5 o’clock

s s face Saturn epicyclic on b1

on axis b, which carries the output to the discovered discovered that

also

and solar anomaly a pin on it ,

14 Saturn, Moon. All the planetary

ith at 2 o’clock,

, w

slot gear output gear Mercury tooth pin gear - Bottom row: tooth

- th 69

oo t -

other between the lunar anomaly and the Saturn mechanism a 79

17 Mars, Jupiter.

The planet module with the planetary

Superior planet plate with

Top row: Carlos Carlos Carman from Jim Evans’ group in Puget Sound, came up with the same idea

Left: Right: | | Diagrams of the new superior planet mechanism with the lunar anomaly mechanism for |

Tony Freeth, Images First Ltd First Tony Freeth, Images Tony Freeth, Images First Ltd First Tony Freeth, Images

After After we had written our draft publication, we 11 12 2012 2012 o/clock. © Fig. Zodiac dial. similaritiesThe Christián planets. superior the for comparison. work on the same Babylonian astronomy. For Mars, with 37 synodic periods in 79 years: there is a principle, with tooth on axis b; counts this meshes with exactly reflecting b1; the the pin engages with a slot period on a 69 relations the from slot gear engages with an © Fig. Building the Cosmos in the Mechanism Antikythera PoS(Antikythera & SKA)018

°

led led by

rtly rtly based Tony FreethTony Antikythera is is pa

superior superior planetary Tek Systems - X explains explains much of the article any any thanks also to the new Antikythera Antikythera Mechanism M . complete the assembly. model model of the This

support device

. This model Cosmos g g and short pillars. It all fits exactly the the remarkable conference in Kerastari,

new

of

. All the superior planets fit neatly at 90 ) 15

12 . The similarity of the

) is persuasive of the inter and phase phase inter and

led by T. Malzbender.

13 With similar spacing as the surviving gearwork, the the gearwork, as the surviving With spacing similar , N. Kaltsas (director), the Fig. Fig.

exactly exactly how this was accomplished because of lost ( 1

heir heir much appreciated Fig. Fig. he organizers (

Packard certain - ere ere is enough evidence to suggest that our Cosmos model is a reconstruction and for t

to thank t Hewlett compelling compelling evidence that this is essentially how the ancient Greeks the bearings as well as the lon

The evidence that all five planets were included in the Mechanism is — mputer mputer

on b1 very very much , M. Edmunds (academic lead), T. Freeth, J. Seiradakis, X. Moussas, Y. for for inviting me

reconstruction reconstruction of the Mechanism. It is the first model since the Mechanism was

.

Exploded co Project

| with the levels of gearing and outputs designed not to interfere with each other. each with interfere not to designed outputs and of gearing levels the with

believe that there is

, Tony Freeth, Images First Ltd First Tony Freeth, Images

in the ancient Greek Cosmos. MoonThe po I I would like I My My aim is to include mechanisms for all the planets inside the space defined by the long 13

Acknowledgments

2012 R. R. Hadland; the team from on data processed, with permission, from the archive of experimental investigations by the 6.3 Greece in 2012 National Archaeological Museum in Athens Research Bitsakis, A. Jones, J.M.Tselikas, M. A. Anastasiou, from the team Steele; and appears to be right. now overwhelming. We cannot be data. However, I believe that th convincing evidence. surviving the all matches that in 1901 found Fig. Mechanism designed the Antikythera Mechanism mechanisms to the lunar anomaly mechanism puzzling evidence © pillars on b1 at the front of the Mechanism. of the front on b1 atpillars inferior planets take up just under half this space, so it is natural to include the superior planets attached behind the Superior Planet Plate angles Building the Cosmos in the Mechanism Antikythera defined by the long pillars. The pointers include place marker beads at different distances to indicate PoS(Antikythera & SKA)018

-

. 617. 617. 67. 13 - - - Papers, Papers,

. diography diography Tony FreethTony , pp. 8 SIGGRAPH SIGGRAPH

. 2002 s1.pdf s1.pdf - - display display Olympiad tory of tory the Moon No. 87 No.

June 1959, 60 June 1959, .

,

. er er Back Dial of the ational ational Archaeological ) The development of a ) The development 2005

03

Bayerische Bayerische Staatsbibliothek, Bayerische Bayerische Staatsbibliothek, .

. 591. Supplementary Notes: .

. – omputer omputer graphics and interactive Calendars with Calendars for for the Antikythera Mechanism.

September

tomography tomography and digital ra

329. Polynomial Polynomial texture maps Scientific American Scientific 63,

-

-

Transactions Transactions of the American Philosophical 16

. llaboration llaboration with the N pp. 51 pp. 29, 319

Antikythera Mechanism: still a mystery of Greek of Greek a mystery still Mechanism: Antikythera Bitsakis (2008) (2008) Bitsakis

New York, NY, USA NY, York, New in co , Y. Y.

3 The

ray ray computed of the Scientific Instrument Society Instrument the Scientific of -

173 and 193. . - ACM Steele, Steele, Bull (2000) A A Planetarium Display .

Epicyclic Epicyclic gearing and the Antikythera Mechanism, Part II. Counting Counting Months and Years: The Upp applications. applications. International Symposium on CT and Image Vol. 29, No. 1, 29, No. Vol.

The Exact in Antiquity. 2nd ed. Providence. Antiquity. in ExactThe Sciences 528 ,

M

. - ,

The The Antikythera Mechanism: 2. Is it ’ Orrery?, The Antikythera Mechanism and the The Mechanism His Early Antikythera 144, 169 J. the the 28th annual conference on c

, Notizbuch Notizbuch (unpublished notebook) 519

Athener Vortrag (unpublished paper) Morgan (2003) (2003) Gears Gears from the Greeks

Antiquarian Horology Horology Antiquarian

P. (2006) (2006) y Notes (amended June 2, 2011): (amended Notes y aatsbibliothek, Rehmiana III/7. Rehmiana aatsbibliothek,

Jones (2012) The Cosmos in the Antikythera Mechanism, ISAW ISAW Mechanism, in theThe Antikythera Cosmos Jones (2012)

r Mechanism. Mechanism. Pages

(1906) , A. Jones A. A. A. (1905) Meteorologische Instrumente der Alten (unpublished manuscript). et et al. (2006) Decoding the ancient Greek astronomical calculator known as

(1974) (1959) An Ancient Greek Computer. Greek Ancient An (1959) .

Wright Wright Wright (2005b)

precision precision microfocus X

m m for industrial - T. T. Wright (2005a) T. Freeth Freeth (2002b) T. Wright Edmunds, C. C. Carman, A. Thorndike, J. Evans (2012) A new kinematic proposal for the , Proceedings of

Freeth, Freeth, Freeth, Freeth,

Athens

astronomy?, Astronomy & Geophysics, Vol 41, Issue 6, Dec. 2000 6, Dec. 41, Issue Vol & Geophysics, Astronomy astronomy?, T. 2, December No. 2 Vol. Archaeometry, & Mediterranean M. Journal Horological M. Horology Antiquarian C. planetary display in xliii, 2012 Astronomy the Antikythera Mechanism. Journal for the History of Phase Display. T. Malzbender, D. Gelb, H. Wolters (2001) '01 techniques A. T.G. S. R. Hadland Dermody, Ramsey, G. & (20Haig I. high syste 2003 June Berlin, Radiology, for Industrial Processing Price D. M. Rehmiana Rehmiana III/7. III/9. Rehmiana D. Price 64.7. N.S. Society M. Antikythera T. and eclipse prediction Supplementa on the Antikythera http://www.nature.com/nature/journal/v454/n7204/extref/nature07130 Mechanism. Nature 454, 614 M. T. 2012. (1957) Neugebauer O. T. Freeth the Antikythera http://www.nature.com/nature/journal/v444/n7119/extref/nature05357 Mechanism. Nature 444, A. Rehm 587 St Bayerische A. Rehm

] ] ] ] ] ] ] ]

hera Mechanism Research Project ] ] ] ] ] ] ] ] ] 17 15 16 12 13 14 11 9 10 7 8 5 6 2 3 4 1 [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ References

Museum in Museum 6.4 Building the Cosmos in the Mechanism Antikythera Antikyt