What is Antikythera Mechanism !?

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A Model of the Cosmos 

in the ancient Greek Antikythera 

Mechanism

Tony Freeth1*, David Higgon1

, Aris Dacanalis1

, Lindsay MacDonald2

, 

MyrtoGeorgakopoulou3,4 & Adam Wojcik1*

The Antikythera Mechanism, an ancient Greek astronomical calculator, has challenged researchers 

since its discovery in 1901. Now split into 82 fragments, only a third of the original survives, including 

30 corroded bronze gearwheels. Microfocus X-ray Computed Tomography (X-ray CT) in 2005 

decoded the structure of the rear of the machine but the front remained largely unresolved. X-ray 

CT also revealed inscriptions describing the motions of the Sun, Moon and all fve planets known 

in antiquity and how they were displayed at the front as an ancient Greek Cosmos. Inscriptions 

specifying complex planetary periods forced new thinking on the mechanization of this Cosmos, but 

no previous reconstruction has come close to matching the data. Our discoveries lead to a new model, 

satisfying and explaining the evidence. Solving this complex 3D puzzle reveals a creation of genius—

combining cycles from Babylonian astronomy, mathematics from Plato’s Academy and ancient Greek 

astronomical theories.

Te Antikythera Mechanism is a cultural treasure that has engrossed scholars across many disciplines. It was 

a mechanical computer of bronze gears that used ground-breaking technology to make astronomical predic-

tions, by mechanizing astronomical cycles and theories1–9

. Te major surviving fragments of the Antikythera 

Mechanism are labelled A–G and the minor fragments 1–757

. Tey are partial, damaged, corroded and covered 

in accretions (Supplementary Fig. S1). Nevertheless, they are rich in evidence at the millimetre level—with fne 

details of mechanical components and thousands of tiny text characters, buried inside the fragments and unread 

for more than 2,000 years7

. Fragment A contains 27 of the surviving 30 gears, with a single gear in each of Frag-

ments B, C and D2,5,7,10. Te fragments are a 3D puzzle of great complexity.

In 2005 Microfocus X-ray Computed Tomography (X-ray CT) and Polynomial Texture Mapping (PTM) of the 

Mechanism’s 82 fragments7

 added substantial data. Tis led to a solution to the back of the machine4,7–9

, with 

the discovery of eclipse prediction and the mechanization of the lunar anomaly7

 (Supplementary Fig. S20). Te 

front remained deeply controversial due to loss of physical evidence.

Many unsuccessful attempts have been made to reconcile the evidence with a display of the ancient Greek 

Cosmos of Sun, Moon and all fve planets known in antiquity. In 1905–06, remarkable research notes by Rehm1

described Mein Planetarium, with a ring display for the planets that anticipates the model we present here—but 

mechanically completely wrong due to his lack of data (Supplementary Fig. S17). In the classic, Gears from the 

Greeks2

, Price suggested lost gearing that calculated planetary motions, but made no attempt at a reconstruc-

tion. Ten Wright built the frst workable system at the front that calculated planetary motions and periods, 

with a coaxial pointer display of the Cosmos, proving its mechanical feasibility3

 (Supplementary Fig. S18). Later 

attempts by Freeth and Jones9

 (Supplementary Fig. S19), and independently by Carman, Torndike, and Evans11, 

simplifed the gearing but were limited to basic periods for the planets. Most previous reconstructions used 

pointers for the planetary displays, giving serious parallax problems3,9

 and poorly refecting the description in 

the inscriptions—see section on Inscriptional Evidence. None of these models (Supplementary Discussion S6) 

are at all compatible with all the currently known data.

Our challenge was to create a new model to match all the surviving evidence. Features on the Main Drive 

Wheel indicate that it calculated planetary motions with a complex epicyclic system (gears mounted on other 

gears), but its design remained a mystery. Te tomography revealed a wealth of unexpected clues in the inscrip-

tions, describing an ancient Greek Cosmos9

 at the front, but attempts to solve the gearing system failed to match 

OPEN

1

Department of Mechanical Engineering, University College London (UCL), London, UK. 2

Department of Civil, 

Environmental and Geomatic Engineering, University College London (UCL), London, UK. 3

UCL Qatar, University 

College London (UCL), Doha, Qatar. 4

Science and Technology in Archaeology and Culture Research Center 

(STARC), The Cyprus Institute (CyI), Nicosia, Cyprus. *email: tony@images-frst.com; a.wojcik@ucl.ac.uk

Figure 1. Inscriptions on the Antikythera mechanism. (a) FRONT COVER: Planet cycles9,12, framed by 

moulding from Fragment 3 (Supplementary Fig. S5). FRONT PLATE: Parapegma1,2,25, above and below 

the Cosmos Display, indexed to the Zodiac Dial. BACK PLATE: Month names on the Metonic Calendar4,8

. 

Eclipse characteristics, round Metonic Calendar and Saros Eclipse Prediction Dials7,8

—indexed to the latter. 

Eclipse glyphs indexed to the Saros Dial8

. BACK COVER: User Manual, including Cosmos description9,13

(Supplementary Discussion S2), Calendar Structure8

 and Moon-Sun Cycles1,2

. (b) Front Cover Inscription 

(FCI): composite X-ray CT from Fragments G, 26 and 29 and other small fragments9,12. Te FCI describes 

synodic cycles of the planets and is divided into regions for each planet in the CCO (Supplementary Discussion 

S2). Te numbers ϒΞΒ (462) in the Venus section and ϒMΒ (442) in the Saturn section are highlighted12

(Supplementary Fig. S4). (c) Back Cover Inscription (BCI)13 (Supplementary Discussion S2): composite X-ray 

CT from Fragments A and B. A User Manual: the upper part is a description of the front Cosmos Display9

 with 

planets in the CCO; in red are the planet names as well as the word KOΣMOY—“of the Cosmos”.

Discovering cycles in theAntikythera Mechanism

Te newly-discovered periods for Venus and Saturn are unknown from studies of Babylonian astronomy. Figure 2

explores how these periods might have been derived. Clues came from the Babylonian use of linear combina-

tions of periods designed to cancel out observed errors14. Figure 2a shows how this might generate the periods

for Venus and Saturn, but choosing the correct linear combinations essentially uses knowledge about errors in

known period relations relative to the true value. Te lack of fne error-estimates from antiquity excludes these

methods for our model: errors like <1° in 100 years for (720, 1151) were beyond the naked-eye astronomy of

the Hellenistic age.

We have developed a new theory about how the Venus and Saturn periods were discovered and apply this

to restore the missing planetary periods. A dialogue of Plato19 (ffh-fourth century BC) was named afer the

philosopher Parmenides of Elea (sixth-ffh century BC). Tis describes Parmenides Proposition17,18:

In approximating θ, suppose rationals, p/q and r/s, satisfy p/q<θ<r/s.

Ten (p+r)/(q+s) is a new estimate between p/q and r/s:

If it is an underestimate, it is a better underestimate than p/q.

If it is an overestimate, it is a better overestimate than r/s.

 Assuming it is a better underestimate, the next stage combines this with the original overestimate to create

(p + 2r)/(q + 2s). Tis would be tested against q and the process repeated. Tus, from two seed ratios we can

generate increasingly accurate linear combinations that converge to θ. Te Parmenides process is facilitated and

constrained by knowledge of θ to determine whether each new estimate is an under- or over-estimate. Figure 2b

shows how a conventional Parmenides Process can generate our target periods, but again this relies on unavailable

knowledge about errors. Te key step for discovering the missing cycles is to modify the Parmenides Process, so

it is not constrained by knowledge of errors—an Unconstrained Parmenides Process (UPP). Figure 2c, d show the

exhaustive linear combinations that are systematically generated by this process. How should we choose which

period relations are suitable for our model? Two criteria were surely used for choosing period relations: accuracy

and factorizability. Te necessity of ftting the gearing systems into very tight spaces and the ingenious sharing of

gears in the surviving gear trains (Supplementary Fig. S20) inspires a third criterion: economy—period relations

that generate economical gear trains, using shared gears, calculating synodic cycles with shared prime factors7

(Supplementary Discussions S3, S6).

Here we clarify how we believe the process was used. Te designer would have generated linear combinations

using the UPP. At each stage, these possible period relations would have been examined to see if they met the

designer’s criteria of accuracy, factorizability and economy. Factorizability would have been an easy criterion to

assess. Accuracy is more problematic, since we do not believe that ancient astronomers had the ability to make

very accurate astronomical observations, as is witnessed by the Babylonian records (Supplementary Tables S3,

S4). Economy must be examined in relationship with the period relations generated for the other inferior or

superior planets to identify shared prime factors.

Venus is a good example. Te ancient Babylonians knew that the (5, 8) period for Venus was very inaccurate

and they had derived the unfactorizable (720, 1151) from observation of an error in the 8-year cycle (Supple-

mentary Discussion S3). Such periods were ofen described in the ancient world as “exact periods”, though of

course in modern terms this is not the case. When the factorizable period (289, 462) was discovered from the

UPP, it would have been easy to calculate that it is in fact very close to the “exact period” (720, 1151). Tus, the

designer would have been confdent that it was an accurate period. (289, 462) would then have been compared

with (1513, 480) for Mercury to discover that they shared the common factor 17 in the number of synodic

cycles—meaning that they were suitable for use in a shared-gear design to satisfy the criterion of economy. When

the designer had discovered period relations that matched all the criteria, the process would have been stopped,

since further iterations would likely have lead to solutions of greater complexity.

Te UPP, combined with our three criteria, leads to remarkably simple derivations of the Venus and Saturn

period relations. For Venus, Fig. 2d shows that the frst factorizable period relation is (1445, 2310)=5×(289, 462)

≡ (289, 462)=(172

, 2×3×7×11), as found in the FCI. For Saturn, it is (427, 442)=(7×61, 2×13×17), again

from the FCI. Tis discovery enables derivations of the missing planetary periods. To ensure our third criterion

of economy, some of the prime factors of the synodic cycles must be incorporated into the frst fxed gear of a

planetary train (Supplementary Discussion S4). For Mercury, we are looking for a factor of 17 in the number of

synodic cycles to share with Venus. Te frst factorizable iteration is (1513, 480)=(17×89, 25×3×5)—sharing

the prime factor 17 with (289, 462) for Venus—so, a very good choice. Multiplying by integers to obtain viable

gears leads to economical designs with a single fxed 51-tooth gear shared between Mercury and Venus (Fig. 3c,

e)16. For the superior planets, Mars and Jupiter, we are looking for synodic periods that share the factor 7 with

Saturn (Fig. 3d, f). Just a few iterations yield suitable synodic periods—leading to very economical designs with

a single 56-tooth fxed gear for all three superior planets and the true Sun.

From Supplementary Table S5,S6, in Supplementary Discussion S3 we establish that the missing periods for

Mercury and Mars are uniquely determined by our process. Tere are two additional options for Jupiter that

share the prime 7 in the number of synodic cycles (Supplementary Table S6). In Supplementary Discussion S3

we show how one of these is not possible and the other is very unlikely. Te UPP, combined with criteria of

accuracy, factorizability and economy, explains the Venus and Saturn periods and (almost) uniquely generates

the missing period relations.

Theoretical mechanisms for our model

Te calculation of the Moon’s position in the Zodiac and its phase are defned by surviving physical evidence7,10.

Since the evidence is missing for the Sun and planets, we need to develop theoretical mechanisms, based on

our identifed period relations. Figure 3 shows theoretical gear trains for the mean Sun, Nodes and the Planets.

Geometrical parameters for the planetary mechanisms in Fig. 3c, d are shown in Supplementary Table S9.

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