The Cosmos in the Antikythera Mechanism

1.5. The Cosmos in the Antikythera Mechanism

Improved readings of an inscription that was on the Mechanism's back cover and that described its external features and displays leave little room for doubt that the front display incorporated revolving pointers bearing little spheres to represent all five planets known in antiquity making their apparent motions around the Earth.¹⁸⬈#p11

Each sphere is said to move through a "circle" belonging to the planet, strongly suggesting that a certain feature of the front display that the inscription calls the "cosmos" was in fact the entire front dial, portraying in cross-section the Aristotelian conception of the universe as a system of nested geocentric spherical shells.⬈#p15

1.6. Overview of the New Model

One of the key questions that arises from the “Cosmos” theory about the front face of the Mechanism is whether mechanisms for all five planets can realistically be included, using similar design and mechanical principles to those found in the surviving gear trains.⬈#p20

The first person to interpret the Mechanism's fragments as the remains of a planetarium and to propose that it displayed the five planets known in antiquity as well as the Sun and Moon was the classicist Albert Rehm, though his prescient research notes, written in 1905-1906, were never published.¹⁹ His idea was that the five turns of the dial in Fragment B, which we now call the Upper Back Dial, represe ted the five planets. This idea could only make sense prior to 2004, when Wright established that the dial does not consist of concentric rings, but is in fact a spiral. There is now ample evidence that this dial was a 19-year Metonic calendar and had nothing to do with planets.²⁰⬈#p21

In 2002, Wright showed through a working physical reconstruction of the Mechanism that it was possible to include all the planets at its front, though, in our view, at the expense of avoidable complication and insufficient correlation with the evidence from the fragments.²¹ This model—with its eight coaxial pointers at the front of the Mechanism—was a remarkable view of the possible capabilities of ancient Greek technology. It was an exercise in showing what might have been possible: essentially a demonstration of principle. We discuss this model in more detail in 3.5.⬈#p22

This present study aims to show how all five planets can be included in the Antikythera Mechanism in a way that conforms to the observed data and explains several puzzling pieces of evidence that have been previously unresolved. The solution is economical and elegant and is in complete harmony with the design virtuosity that has already been uncovered in the existing gear trains. Despite the lack of physical evidence in the form of surviving gears, we believe that the close match of our model with other physical evidence as well as its intimate conceptual association with the known gear trains create a compelling case that this was in essence the way that the Mechanism was originally constructed.⬈#p23

The inferior planets are those whose orbits are inside the Earth’s orbit—namely Mercury and Venus. The superior planets have orbits outside the Earth’s. Those known in ancient times were Mars, Jupiter and Saturn. All the planets appear from the Earth to orbit nonuniformly, with a periodic alternation of prograde and retrograde motion. Ancient Greek models of planetary motion prior to Ptolemy were based on the idea that these "anomalistic" motions could, at least in first approximation, be modelled using a combination of two circular motions—the so-called “deferent-and-epicycle” and "eccentre" models.²² This theory apparently originated in the early second century BC with Apollonios of Perga and his contemporaries, though an earlier date cannot be ruled out.²³ Using these ideas, the motions of the inferior planets can be mechanized fairly easily with just two gears—a fixed gear on the central axis and an epicyclic gear that engages with this fixed gear—combined with a pin and slotted follower.²⁴ The superior planets have proved more difficult to model in a way that fits the mechanical constraints of the Mechanism’s design. Our reconstruction proposes mechanisms for the superior planets based on the known mechanization of the lunar anomaly at the back of the Antikythera Mechanism. Surprisingly, these models look exactly the same as the lunar anomaly mechanism. They have just four gears, including an epicyclic gear with a pin on its face and a second epicyclic gear, which rotates on an eccentric epicyclic axis and has a slot in its face that engages with the pin. They provide an elegant solution to the long-standing problem of how the superior planets might have been shown in the Antikythera Mechanism. It is noteworthy that similar mechanisms can serve both to model the lunar anomaly and the synodic phases of the planets.⬈#p24

Though the physical evidence is sparse due to the great loss of material in the fragments, our new model explains the existence of bearings and fittings on the Main Drive Wheel, b1, as well as the mysterious “pillars” attached to its circumference.²⁵ The model also accounts for the dimensions of the pillars. All of our planetary mechanisms are contained in the space in front of b1 that is defined by the support pillars—a circumstance that could also help explain how all the planetary gearing could have fallen out before the Mechanism's rediscovery. It is surprising that all these mechanisms can be crammed into the relatively small space in front of b1. Price proposed this nearly forty years ago, without any details as to how it might be accomplished.²⁶⬈#p25

“Alternatively there is a possibility that this space... may have held a gearing system, now totally vanished, which served to exhibit the rotations of all of the planets other than the Sun and Moon. If such gearing was to be part of the device it would be most appropriate at this place where annual and monthly rotations were available just under the front dial plate.”

It is not clear to us why the “monthly rotation” might be relevant to the planets, but the rest of this idea is preserved in our model. Our model also retains the simplicity in the outward design of the Mechanism as a rectangular box that Price proposed. As previously mentioned, Wright has demonstrated the feasibility of including all five planets in the Antikythera Mechanism using essentially the same technology and engineering that we see in the surviving fragments. We discuss this important model later in 3.5. In Wright's model, the solar anomaly was mechanized as well. In the light of the subsequent discovery of the mechanization of the lunar anomaly in the Antikythera Mechanism, we believe that it was very likely that the solar anomaly was also included.⬈#p26

A recent careful study has demonstrated that the graduation of at least one of the two extant front dial rings, the Egyptian calendar ring and the zodiac ring, had a small apparently systematic nonuniformity, which can be explained as a deliberate nonuniform spacing of the degrees on the zodiac ring so that a uniformly revolving mean Sun pointer would simultaneously indicate both the true Sun's longitude and the Egyptian calendar date.²⁷ On this hypothesis, the motion of pointers representing the motions of the Moon and planets would incorporate a solar anomaly component (a not inconceivable notion, though contrary to known ancient theories) unless the pointers revolved around an eccentric axis. An alternative planetary display also explored in that study hypothesizes that there were no pointers for the planets revolving around the zodiac dial, but instead a system of five subsidiary dials with uniformly revolving pointers indicating the planets' synodic cycles. We believe that the inscriptional evidence examined below rules out such subsidiary dials. Moreover, the division of circles into ostensibly equal arcs elsewhere in the Mechanism is sometimes evidently nonuniform, for example in the spacing of teeth on gears,²⁸ the holes for mounting the Egyptian calendar dial,²⁹ and the divisions of the Saros eclipse dial, as we have confirmed from observations of the X-ray CT data. Hence we are not convinced that the Mechanism's designer intentionally represented solar anomaly through nonuniform graduation of the zodiac ring instead of by epicyclic gearwork and we have reconstructed all the pointers as radiating from the central axis.⬈#p27

The Back Cover Inscription indicates that the Sun, Moon and planets were almost certainly represented at the front of the Antikythera Mechanism using “little spheres” (as mentioned in the Back Cover Inscription, 2.3.2) in a geocentric picture of the heavenly bodies. There are mechanical difficulties in creating this image of the planets, since the lunar phase mechanism requires that the solar output is adjacent to the lunar output in the coaxial output system.³⁰ This is because the lunar phase mechanism acts as a differential system to calculate the Moon’s phases from the difference between the lunar and solar rotations. The lunar phase mechanism must therefore have access to the solar rotation. The lunar output is carried by a central axle from the back of the Mechanism and the Sun must therefore be the first tube in the coaxial system. This would naturally place the Sun next to the Moon in the output display, leaving no room for Mercury and Venus between Moon and Sun. However, there is a way round this problem. Our conjectural solution is to retain the pointer system and to mark the pointers with “little spheres” at different distances along the pointers to indicate their orbits. The solar pointer is marked by a “little golden sphere” (as mentioned in the Back Cover Inscription, 2.3.2) and the planetary pointers with appropriately coloured spheres for the planets. These spheres are placed at distances, which represent their geocentric orbits in the prevailing ancient Greek order of proximity to the Earth: Moon, Mercury, Venus, Sun, Mars, Jupiter, and Saturn. In this way the “Cosmos” idea is preserved, whilst the lunar phase mechanism has access to the Sun rotation. Rehm's idea to display the planets on concentric rings would not work for exactly this reason. In a coaxial system with outputs as rings, the order of the rings must follow the order of nesting of the coaxial outputs—so the Sun would have to be adjacent to the Moon, which would contradict the standard order of the bodies in the Aristotelian cosmology. The idea of small marker spheres on pointers circumvents this problem.⬈#p31

In our “Cosmos” proposal for the front of the Antikythera Mechanism the stars are represented in a more conceptual manner by the fixed graduated dial inscribed with the names of the zodiacal signs and with key letters referring to the list of dates of first and last risings and settings of constellations in the Parapegma Inscription above and below the central dials. Visual representations of the ancient geocentric cosmology in medieval and Renaissance manuscripts and art commonly use the zodiac in this way to stand for the "sphere of fixed stars."⬈#p32