At the upper part of the right plate we can distinguish the spiral cycle of Meton that consisted of synodic lunar months —based on the Corinthian calendar— of a total duration of 19 years. Within the metonic spiral, in its left part we can distinguish Callippus cycle that corresponded to a time duration equal to four metonic cycles, that means 76 years. It was used for the absolute correspondence of the lunar to the solar year.
At the right part of the spiral we distinguish the cycle of the Olympic Games. It was used to determine when to celebrate the most important athletic games of antiquity Olympia, Pythia, Isthmia, Nemea and Naia.
At the lower part of the right plate we distinguish the spiral cycle of the periodic time Saros cycle that was consisted of synodic months of total duration of 18 years. In the internal part of the cycle we distinguish the Exeligmos cycle that corresponded in time duration equal to three Saros cycles, that means 54 years.
In —06, remarkable research notes by Rehm 1 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. In the classic, Gears from the Greeks 2 , Price suggested lost gearing that calculated planetary motions, but made no attempt at a reconstruction.
Then Wright built the first workable system at the front that calculated planetary motions and periods, with a coaxial pointer display of the Cosmos, proving its mechanical feasibility 3 Supplementary Fig.
Later attempts by Freeth and Jones 9 Supplementary Fig. S19 , and independently by Carman, Thorndike, and Evans 11 , simplified the gearing but were limited to basic periods for the planets. Most previous reconstructions used pointers for the planetary displays, giving serious parallax problems 3 , 9 and poorly reflecting 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. The tomography revealed a wealth of unexpected clues in the inscriptions, describing an ancient Greek Cosmos 9 at the front, but attempts to solve the gearing system failed to match all the data 1 , 2 , 3 , 6 , 9.
The evidence defines a framework for an epicyclic system at the front 9 , but the spaces available for the gears are extremely limited. There were also unexplained components in Fragment D, revealed by the X-ray CT, and technical difficulties calculating the phase of the Moon 9.
Then came the discovery in the tomography of surprisingly complex periods for the planets Venus and Saturn, making the task very much harder We wanted to determine the cycles for all the planets in this Cosmos not just the cycles discovered for Venus and Saturn ; to incorporate these cycles into highly compact mechanisms, conforming to the physical evidence; and to interleave them so their outputs correspond to the customary cosmological order CCO , described below.
Here we show how we have created gearing and a display that respects the inscriptional evidence: a ring system with nine outputs— Moon , Nodes , Mercury , Venus , Sun , Mars , Jupiter , Saturn and Date —carried by nested tubes with arms supporting the rings.
The result is a radical new model that matches all the data and culminates in an elegant display of the ancient Greek Cosmos. With so much missing, we ensure the integrity of our model with a strict set of Reconstruction Principles Supplementary Discussion S1 and we assess the strength of data that validates each element—discussed in Supplementary Discussion S1.
The loss of evidence might suggest many options for a model. What has struck us forcefully in making the present model is just how few these options are: the constraints created by the surviving evidence are stringent and very difficult to meet.
Reconstructing the Cosmos at the front of the Antikythera Mechanism begins with analysing some remarkable inscriptions. S2, S3. The FCI lists the synodic cycles of the planets cycles relative to the Sun This is a systematic list, itemizing the synodic events and the intervals in days between them.
The planets are written in the same geocentric order as the BCI. S4 , whose origins are discussed in Supplementary Discussion S2. Inscriptions on the Antikythera mechanism. Eclipse glyphs indexed to the Saros Dial 8. Ancient astronomers were fascinated by the motions of the planets. As seen from Earth, they exhibit periodic reversals of motion against the stars In Babylonian astronomy these synodic cycles were the basis of planetary prediction 15 , utilizing period relations , such as 5 synodic cycles in 8 years for Venus, which we denote by 5 , 8.
The FCI describes synodic events , such as stationary points , and intervals between these events Fig. S4 , Supplementary Discussion S2. Apollonios of Perga third-second century BC created elegant albeit inaccurate epicyclic theories to explain these anomalous movements as the sum of two uniform circular motions, their periods defined by period relations—the deferent and epicycle models 15 Supplementary Discussion S3 , Supplementary Figs.
S6, S7, S8. Such theories were certainly employed in the Antikythera Mechanism, given that the Moon was mechanized using a similar epicyclic theory 7. The true Sun —the Sun with its variable motion—was also explained in ancient Greece by eccentric and equivalent epicyclic models 14 Supplementary Discussion S3.
To understand what period relations were built into the Antikythera Mechanism, the tough problem was to discover their derivation. For Venus the original designer faced a dilemma: the known period relation 5 , 8 was very inaccurate, whereas the accurate , was not mechanizable because is a prime number, requiring a gear with teeth.
Crucially, these are factorizable , meaning they can be mechanized with moderate-sized gears, with tooth counts incorporating the prime factors of the period relations. There are few such accurate period relations for the planets Supplementary Tables S5, S6.
The fact that the new period relations for Venus and Saturn from the FCI are factorizable strongly reinforces the idea that they were incorporated into planetary mechanisms in the Antikythera Mechanism The periods for the other planets are unreadable in missing or damaged areas of the FCI. To build our model, it was essential to discover the period relations embodied in all the planetary mechanisms. Previous publications 12 , 16 derived the Venus period relation , as an iterative approximation to the known Babylonian , period relation, using a number of equivalent processes: continued fractions , anthyphairesis or the Euclidean algorithm 17 , No similar method for deriving the , period relation for Saturn could be found, so this type of iterative approximation was almost certainly not the route to the original discoveries of these periods by the ancient Greeks.
The 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 combinations of periods designed to cancel out observed errors Figure 2 a 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.
Finding period relations. Blue numbers refer to synodic cycles; red numbers refer to years. All the seed periods for these processes are known from Babylonian astronomy Supplementary Tables S5, S6. The grey-shaded periods are those that are known from the FCI. The same table with errors is shown in Supplementary Table S5. Except for the periods for Venus and Saturn, all the final periods were already known in Babylonian astronomy.
The error parameters are defined in Supplementary Discussion S3. We have developed a new theory about how the Venus and Saturn periods were discovered and apply this to restore the missing planetary periods. This describes Parmenides Proposition 17 , 18 :. This would be tested against q and the process repeated. Figure 2 b shows how a conventional Parmenides Process can generate our target periods, but again this relies on unavailable knowledge about errors.
The 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 2 c, 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. The necessity of fitting 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 factors 7 Supplementary Discussions S3, S6.
Here we clarify how we believe the process was used. The designer would have generated linear combinations using the UPP.
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. The ancient Babylonians knew that the 5 , 8 period for Venus was very inaccurate and they had derived the unfactorizable , from observation of an error in the 8-year cycle Supplementary Discussion S3.
Thus, the designer would have been confident that it was an accurate period. 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.
The UPP, combined with our three criteria, leads to remarkably simple derivations of the Venus and Saturn period relations. For Venus, Fig. This 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 first fixed 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.
Multiplying by integers to obtain viable gears leads to economical designs with a single fixed 51 -tooth gear shared between Mercury and Venus Fig. For the superior planets, Mars and Jupiter, we are looking for synodic periods that share the factor 7 with Saturn Fig.
Just a few iterations yield suitable synodic periods—leading to very economical designs with a single 56 -tooth fixed gear for all three superior planets and the true Sun. Epicyclic Mechanisms for the Cosmos. Fixed gears are underlined; blue gears calculate synodic cycles; red gears calculate years; black gears are idler gears: all designated by their tooth counts.
Followers are slotted rods that follow a pin on the epicyclic gear and turn on the central axis. For each mechanism, there is a fixed gear at the centre, meshing with the first epicyclic gear, which is forced to rotate by the rotation of b1 or the CP.
There 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. The UPP, combined with criteria of accuracy , factorizability and economy , explains the Venus and Saturn periods and almost uniquely generates the missing period relations.
Since the evidence is missing for the Sun and planets, we need to develop theoretical mechanisms, based on our identified period relations. Figure 3 shows theoretical gear trains for the mean Sun, Nodes and the Planets.
Geometrical parameters for the planetary mechanisms in Fig. The way that the Saros Dial on the Back Plate predicts eclipses essentially involves the lunar nodes , but they are not described in the extant inscriptions. With their integral role in eclipses, a display of the nodes is a logical inclusion, unifying Front and Back Dials. To maximise the displayed information, we created a mechanism for a hypothetical Dragon Hand to indicate the Line of Nodes of the Moon, as included in many later astronomical clocks 20 Supplementary Fig.
We should emphasize that there is no direct physical evidence for an indication of the Line of Nodes of the Moon.
We have added this feature as a hypothetical element for the thematic reasons already explained and because it is easily mechanized to good accuracy with a simple 4-gear epicyclic system on Spoke B of b1. We follow the original proposal 10 for the Moon phase device as a simple differential, which subtracts the motion of the Sun from that of the Moon to calculate the phase, displayed on a small black and white sphere.
S21, S This turns a hypothetical double-ended Dragon Hand 20 , whose Head shows the ascending node of the Moon and Tail the descending node. Using our identified period relations for all the planets, we have devised new theoretical planetary mechanisms expressing the epicyclic theories, which fit the physical evidence.
For the inferior planets, previous 2-gear mechanisms 3 , 9 , 21 are inadequate for more complex period relations because the gears would be too large. Two-stage compound trains with idler gears are necessary, leading to new 5-gear mechanisms with pin-and-slotted followers for the variable motions 7 , 9 , 21 Fig.
For the superior planets, earlier models 3 , 16 used direct mechanisms , directly reflecting epicyclic theories with pin-and-slotted followers. Here we propose novel 7-gear indirect mechanisms with pin-and-slot devices 7 , 9 for variable motions Fig. Compared to direct mechanisms , these are more economical; a better match for the evidence; and incorporate period relations exactly for higher accuracy. The crucial advantages of indirect mechanisms are expanded in Supplementary Discussion S4.
Without these compact systems that can all be mounted on the same plate, it would have been impossible to fit the gearing into the available spaces. Proofs that the mechanisms in Fig. The key question: could we match our theoretical mechanisms to the physical data? S13, S S15, S Reconstructed plates and gear. All pillars have shoulders and pierced ends.
The Main Drive Wheel , b1 , has four spokes with prominent holes, flattened areas and damaged pillars on its periphery Fig. S11, S12 —definitive evidence of a complex epicyclic system 1 , 2 , 3 , 9. In the original Mechanism, there were four short and four long pillars with shoulders and holes for retaining pins, as shown in Fig.
These imply that the pillars carried plates: a rectangular plate on the short pillars, the Strap , and a circular plate on the long pillars, the Circular Plate CP Fig. This is the essential framework for any faithful reconstruction, with the four spokes advocating four different functions Fig.
First, we reconstruct the mechanisms between b1 and the Strap. Figure 4 i-l, Supplementary Fig. S13 show evidence of the crucial components in Fragment D.
Earlier studies 2 , 4 , 5 suggested that there are two gears in Fragment D, but this is an illusion created because the arbor has split 7 , 9 , as established in Supplementary Discussion S5 and Supplementary Fig. The original tooth count can be reliably determined as 63 teeth, given all but three of the teeth survive 5 , 7 , 9. On the machine's back, an upper dial shows a year calendar matching the solunar cycle and the timing of upcoming Olympic games. A lower dial shows a year cycle when the Olympic and solunar cycles coincide and indicates the months in which lunar and solar eclipses can be expected.
According to New Scientist , this is the first working model of the Antikythera computer to include all of the device's known features. And, like the original machine, it has been built of recycled metal plates. That's right: The Antikythera mechanism is not only the world's oldest computer, it's also the world's first green computer. View Iframe URL. Antikythera: A 2,year-old Greek computer comes back to life [Guardian.
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