Reading: “Antikythera Mechanism” by Edmunds

Contemporary PhysicsISSN: 0010-7514 (Print) 1366-5812 (Online) Journal homepage: http://www.tandfonline.com/loi/tcph20
The Antikythera mechanism and the mechanical
universe
M.G. Edmunds
To cite this article: M.G. Edmunds (2014) The Antikythera mechanism and the mechanical
universe, Contemporary Physics, 55:4, 263-285, DOI: 10.1080/00107514.2014.927280
To link to this article: https://doi.org/10.1080/00107514.2014.927280
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Contemporary Physics, 2014
Vol. 55, No. 4, 263–285, http://dx.doi.org/10.1080/00107514.2014.927280
The Antikythera mechanism and the mechanical universe
M.G. Edmunds*
School of Physics and Astronomy, Cardiff University, Cardiff, UK
(Received 7 April 2014; accepted 20 May 2014)
How did our view of the Universe develop? By the mid-eighteenth century, a world view had developed of a system
constrained by physical laws. These laws, if not entirely understood, showed regularity and could be handled mathematically to provide both explanation and prediction of celestial phenomena. Most of us have at least some hazy idea of the
fundamental shift that came through the work of Copernicus, Kepler, Galileo and Newton. The idea of a ‘Mechanical
Universe’ running rather like a clock tends to be associated with these sixteenth- and seventeenth-century pioneers. It
remains a useful – and perhaps comforting – analogy. Yet, recent investigations based around the Antikythera Mechanism, an artefact from ancient Greece, reinforce a view that the ‘Mechanical’ conception has been around for a much
longer time – indeed certainly as far back as the third century BC. The extent of mechanical design expertise existing
around 100 BC as witnessed by the Antikythera Mechanism comes as a great surprise to most people. It is certainly a
very ingenious device, often referred to as ‘The World’s First Computer’ although it is really a sophisticated mechanical
astronomical calculator with its functions pre-determined rather than programmable. In this review, the structure and
functions of the Antikythera Mechanism are described. The astronomy, cosmology and technology inherent in the
machine ﬁt surprisingly well into the context of its contemporary Classical world. A strong claim will be made for the
inﬂuence of such mechanisms on the development of astronomical and philosophical views, based on literary reference.
There is evidence that the technology persisted until its spectacular and rather sudden re-appearance in Western Europe
around 1300 AD. From then on it is not hard to chart a path through the astronomical clocks of the sixteenth century to
Kepler’s aim (expressed in a 1605 letter) to ‘show that the heavenly machine is not a kind of divine, live being, but a
kind of clockwork …’, and on to the widespread development of popular visualisation of the heliocentric Solar System
in the orreries of the eighteenth century.
Keywords: History of Science; history of technology; history of astronomy; history of cosmology; mechanistic philosophy
a tiny device pregnant with the world, a portable sky, a
compendium of the universe, a mirror of nature which
reﬂects the heavens.
–Cassiodorus, sixth century AD, trans. Barnish [1]
1. Discovery and recognition
The Antikythera Mechanism was found in the ﬁrst ever
major under-water archaeological expedition, mounted
from November 1900 until September 1901 by the Greek
Navy, Ministry of Education and Archaeological Society.
The exploration of the wreck of a Roman-Era trading ship
very close to the Mediterranean island of Antikythera had
been organised after sponge divers discovered the wreck
and its rich cargo of statues and other artefacts in spring
1900. Material from the wreck was transferred to the
National Archaeological Museum in Athens, and the
Mechanism itself was only recognised a few months later
when gear wheels were noticed in a lump of corroded
bronze. The reading of Greek text on its surface made it
known as an astronomical device. The story of the wreck
and recovery of the Mechanism is well covered in de Solla
*Email: mge@astro.cf.ac.uk
© 2014 Taylor & Francis
Price [2], Marchant [3], Tsipopoulou et al. [4] and Jones
[5], although some minor details vary between the
accounts. The wreck is fairly reliably dated to the decade
following 60 BC, particularly from recovered coins [6],
with earlier conﬂicting radiocarbon dates for the ship’s
timbers now resolved by recalibration [7] to 211–40 BC at
84.8% probability. The epigraphy (letter forms) of
inscriptions on the Mechanism are consistent with its
having been made in the last half of the second century
BC [8, supplementary material], with an uncertainty of a
few decades either way. The present best estimate of its
construction date is around the middle of the range
150–60 BC – although a date as early as 220 BC is not
completely ruled out.
The Mechanism ﬁrst became widely known through a
popular article by de Solla Price [9], but it was as a result
of radiography of the surviving fragments by Price and
Ch. Karakalos in the early 1970s that the true complication of the Mechanism became apparent. It was evident
that 30 gear wheels remained, and that originally it
contained more. There is no known surviving geared
mechanism as complicated as this until the era of the
cathedral and town clocks in the fourteenth century AD,
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M.G. Edmunds
over a millennium later. The work of de Solla Price [2],
Wright [10] and the international Antikythera Mechanism
Research Projects (AMRP) [8,11,12] has led to a broad
agreement about reconstruction of the structure and function of Mechanism’s main calendrical, solar and lunar displays, as described in Section 2 below. There is good
evidence from the inscriptions on the device that it would
also have displayed planetary positions, a function which
we will see is also supported by contemporary literature
descriptions of similar devices. The way in which planets
were actually displayed on the Mechanism remains controversial (Section 2.4). Except where relevant we will
concentrate on the mechanics of the Mechanism, rather
than the inscriptions. These have yet to be published in
full, although many preliminary details may be found in
Freeth et al. [8,12], Jones and Freeth [24] and
Zapheiropoulou [13]. The recent X-ray tomographic
examinations have yielded a great increase (by a factor of
about three) in the number of deciphered characters over
de Solla Price’s [2] work.
Before describing the functions of the Mechanism, it
must be admitted that there is no real consensus as to its
purpose. The limitations in the accuracy of some of its
positional displays (see Section 3) suggests that it would
not be particularly useful for an astronomer or astrologer
as calculator – except in so far as it could give reasonable
calendrical data and rapid approximate celestial positions,
which might impress a client! There is no evidence to suggest its use in a temple, although lunar calendrical information was certainly important in arranging religious
ceremony. Despite having been found in a shipwreck,
none of the functions of the device would have been useful for navigation. Its most likely application was as a display or teaching device [14], and certainly more than just
an ‘executive toy’ – as we shall see, it is too sophisticated
for that, although it would be unwise to underestimate the
importance of entertainment activities in the classical
world. Perhaps the best notion of the device is as a statement of what is known about the Universe – or ‘Cosmos’
– a sort of hardware publication that would be accessible
to non-astronomers, and whose purchase would at least
show commendable aspirations. The astronomy in the
device certainly represents very well the astronomical
knowledge current around 100 BC, and indeed the word
‘Cosmos’ is found in its inscriptions.
The Antikythera Mechanism could certainly not have
been unique, because its complexity and design requires
a considerable tradition of development from simpler
mechanical devices (explored by Tassios [15] and Keyser
[16]). In Section 5, we shall show that literary references
to geared mechanical astronomical display, both simple
and complex, occur over at least 700 years of the classical era and into the sixth century AD. Although the references do not really help with the identiﬁcation of the
purpose of such devices they do show that the market
must have continued, since most individual devices
would surely have broken or worn out on something less
than a 100-year timescale if the technology was that of
the thin (2 mm) bronze gears of the Antikythera Mechanism. The lack of surviving artefacts from before 1000
AD – we only have two certain ones, the Antikythera
Mechanism and a much simpler geared sundial from c
520 AD – is not surprising. When broken such devices
would have had little value – they are not art objects,
decorated with gold or jewels. Metal was valuable and a
thriving recycling industry existed through the classical
era into the mediaeval, so preservation would be
expected only in special circumstances.
2. Basic structure of the mechanism
The modern discovery of the basic structure of the
Antikythera Mechanism owes a great deal to the investigations of the historian and sociologist of science, de Solla
Price [2,9] and to the ‘mechanician and historian of mechanism’ Wright [10]. Reasonable agreement on what
original structure can reliably be deduced from the surviving fragments came with the application of detailed, highresolution X-ray tomography and optical surface imaging
by the AMRP ([8,12; also discussion by Wright [10]). The
AMRP is a collaboration between academics in Greece,
the UK and the USA, staff at the National Archaeological
Museum of Athens, and two industrial corporations who
freely loaned staff effort and equipment – X-Tek (now part
of Nikon Metrology, www.nikonmetrology.com) and
Hewlett Packard Laboratories (www.hpl.hp.com/research/
ptm). A short overall account of the imaging and computing methods used is given in Edmunds and Freeth [17].
There was considerable damage and loss to the device during its shipwreck, and some inevitable separation of parts
during a century of cleaning and conservation. There are
82 known surviving fragments, now ﬁnely displayed in
the National Archaeological Museum in Athens. Most of
the information is in the largest fragments (designated
A–G, with smaller fragments numbered 1–75). The gears
are in fragment A (remains of 28 gears), fragment B (one
gear) and fragment D (one gear).
A conservative reconstruction of the exterior appearance of the Antikythera Mechanism is shown in Figure 1.
Constructed mainly out of bronze sheet, it was housed in
a wood or wood-framed box roughly 320–330 mm tall,
170–180 mm wide and at least 80 mm from front to
back. It was worked by turning a handle or knob on the
side of the box, which was connected to a crown gear
(designated a1) of 48 teeth. The AMRP reconstruction of
the gear trains is shown in Figure 2. The reconstruction
uses 29 of the 30 surviving gears plus 3 conjectural ones
– now missing but with assumed tooth counts that would
be consistent with their necessary sizes. Gear designations are given by a lower-case letter for the shaft or axis
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265
Figure 1. An impression of the front (left) and back (right) faces of the Antikythera Mechanism. The casing may have been wood
framed, rather than solid wood, and was about the size of a shoe-box. Both front and back also had protective doors or plates made
of sheet bronze, which carried inscriptions. The front dials certainly showed the position of the Sun and Moon in the Zodiac, and the
phase of the moon, but the nature of the planetary pointers is speculative. The spiral dials at the rear showed the Metonic lunar-solar
cycle (top) and Saros eclipse cycle (bottom). Details are given in Section 2. The right-hand sub-dial inside the Metonic spiral is a
pan-Hellenic games indicator, and a left-hand sub-dial is conjectured to show the lunar-solar Callipic cycle – although no physical
evidence for this survives. An Exeligmos dial to cover three Saros eclipse cycles is present inside the Saros spiral.
Copyright: Hublot, Genève, with fonts from the Aristotle University of Thessaloniki.
Figure 2a. The established gear trains of the Antikythera Mechanism. The gears and shafts are shown in their correct geometric relationship, except that the front-to back spacing has been arbitrarily expanded. The surviving gears are shown in red, and the three conjectured missing (but almost certainly present in the original) gears in green. The manual input drive is indicated by the white arrows.
Graphic: M.G. Edmunds, Copyright Antikythera Mechanism Research Project.
on which they are mounted, together with a number. The
designations and data used here are as given in Freeth
et al. [8], except for the addition of the conjectural gear
n3 [12] in a slight re-arrangement of the sub-dial on the
upper back dial. The crown gear a1 drove the large main
four-spoked gear b1, clearly visible in Figures 3 and 4.
One turn of this main wheel represents one year in
driving the subsequent gear trains and displays. It is unlikely that the device was used as a daily calendar,
advancing the main wheel by one day – 1/365th of a
revolution – at a time. Although this might have been
possible by careful turning and inspection of the sun’s
266
M.G. Edmunds
l1
m1
b1
n1
n3
o1
m2
l2
a1
b2
Figure 2b. From a different viewpoint, showing highlighted in yellow the drive train to the 19-year Metonic Cycle dial on the top
back, with its subsidiary four-year-games dial. In the following gear train nomenclature a − sign indicates meshing of two gears, a +
sign indicates the connection of the two gears on the same shaft or axis, and italic indicates a conjectural gear. The measured or conjectured tooth count is given in brackets after the gear designation. All trains are driven by the 48-tooth crown wheel (a1) turning the
223-tooth ‘Sun wheel’ (b1). For N turns (years) of b1 which is directly coupled to b2 the corresponding rotations are:
Metonic Dial: b2(64) − l1(38) + l2(53) − m1(96) + m2(15) – n1(53) → N × 64/38 × 53/96 × 15 /53 = N × 5/19
Games Dial: b2(64) − l1(38) + l2(53) − m1(96) + m2(15) − n1(53) + n3(57) − O1(60) → N × 64/38 × 53/96 × 15 /53 × 57/60 = N × 1/4
So 19 turns of b1 gives the ﬁve turns of the spiral on the Metonic dial, four turns of b1 gives one turn of the four-year games dial.
Graphic: M.G. Edmunds, Copyright Antikythera Mechanism Research Project.
l1
m3
m1
e4
e3
b1
l2
g2
i1
f2
f1
b2
g1
h2
h1
Figure 2c. The Saros and Exeligmos drive, highlighted in yellow, viewed from the other side compared to Figure 2a.
Saros Dial: b2(64) − l1(38) + l2(53) − m1(96) + m3(27) − e3(223) + e4(188) − f1(53) + f2(30) − g1(54) → N × 64/38 × 53/96 × 27/
223 × 188/53 × 30/54 = N × (4/19) × (235/223) = N × (4/18.029..)
This gives the four turns of the spiral in just over 18 turns of b1 for the 18 years 1113 days of the Saros eclipse Cycle.
The gearing from the Saros dial shaft for the Exeligmos dial is: g2(20) − h1(60) + h2(15) − i1(60) → 20/60 × 15/60 = (1/3) × (1/4)
so that it needs 3 cycles of 4 turns on the Saros dial and just over 54 turns (years) of b1 to give one Exeligmos cycle.
Graphic: M.G. Edmunds, Copyright Antikythera Mechanism Research Project.
position pointer on the front dial, there is no evidence of
gearing and a dial for easier day-to-day adjustment. It is
more likely that the device was moved forward or backwards at a much faster rate to allow prediction or retrodiction of astronomical and calendrical events.
2.1. Front dials
On the front of the device (see Figure 1), behind a protective plate or door carrying inscriptions, there was a circular dial, part of which survives (see Figure 5). The inner
annulus represents the ecliptic with its division into zodiac
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267
q1
e5
b3
a1
e2
b2 c2
e6
e1
c1
b1
d1
d2
k2
k1
Figure 2d. The Lunar drive, highlighted in yellow.
b2(64) − c1(39) + c2(48) − d1(24) + d2(127) − e2 (32) + e5(50) − k1(50) [+] k2(50) − e6(50) + e1(32) − b3(32)
The symbol [+] is coupling via a pin-and-slot variable-speed device (see Section 3.3 and Figures 7–9) which replicates the ﬁrst
anomaly of the lunar motion. The last gear b3 is attached to the shaft of the lunar pointer, involving a double concentric shaft, and a
second double shaft connects e2 with e5 and e6 with e1 . The epicyclic mounting of gears k1 and k2 on the ‘turntable’ gear allows
replication of the ﬁrst anomaly of the lunar motion at its correct period.
Since the last three pairs of meshing gears in the train have unit ratio, then the rotation relative to b1 can be represented by:
(64/36) × (48/24) × (127/32) = (2/19) × 127 = 13.368 …
which is a good representation of the ratio of the lunar sidereal month to the solar year, i.e. giving how many times the moon would
go around the zodiac in a year, compare to the single journey of the Sun.
The Sun pointer on the front dial may have been directly driven from b1 as shown in pink in the ﬁgure, but the drive is missing
and might have incorporated another variable-speed device (analogous to the lunar one) to simulate the slight inequality of the lengths
of the seasons between solstices and equinoxes. The details of the drive of the lunar phase ball is also uncertain (Section 10),
although one 20-tooth crown gear (q1) survives in it and an addition of a meshing gear of 20 teeth ﬁxed to the sun pointer shaft
would fulﬁl the function.
Graphic: M.G. Edmunds, Copyright Antikythera Mechanism Research Project.
signs through which the Sun passes during the year, and
the outer annulus gives the corresponding Egyptian calendar months. The relatively stable Egyptian calendar was
preferred for astronomical purposes over the much more
variable local civil calendars. The outer dial could be
rotated manually and has 365 small holes around it to
allow registration and occasional manual adjustment for
the effect of the quarter of a day by which the year
exceeds 365 days. On the surviving part of the front dial,
there is a radial mark just outside the Egyptian calendar
scale. Although this is probably a damage crack, it has
been interpreted by some researchers ([2], Evans and
Carman [46]) as a ﬁducial reference mark for setting the
calendar ring. Price suggested a reference date of 87 BC,
although he was unsure, since he felt that there were conﬂicts in the dating evidence using the mark. Evans and
Carman suggest that a very early reference date around
222–198 BC would be implied, but they allow that the
mark – if real – might simply have been copied from an
earlier version of the Mechanism.
To show the motion of the Sun and Moon there
would have been pointers – that for the Sun being identiﬁed according to the inscriptions by ‘a little golden
sphere’, and that for the Moon incorporating a half-silvered ball driven by simple gearing to indicate its phase
[18]. It is very probable, based on the inscriptions that
the changing positions of the planets around the ecliptic
were also shown by pointers on the dial.
Around the zodiac annulus there are index letters which
refer to a ‘Parapegma’ inscription which was displayed near
the front dial and partially survives. A parapegma is a calendar of ‘heliacal risings’ during the year, when stars or
constellations ﬁrst become visible in the night sky just
before dawn. The index letters link the risings to the solar
calendar of the zodiac. Parapegma were widespread around
the Mediterranean, and this one on the Mechanism is quite
similar to one given by Geminos in the ﬁrst century BC
[19,20]. An analysis by Anastasiou et al. [21] suggests that
it was designed for use close to a geographical latitude of
33–37° North, consistent with Rhodes or Syracuse but not
particularly favouring the more northerly Greek provinces
which might be implied (see next section) by the month
names on the upper back dial.
2.2. Back dials
Three numbers – 76, 19 and 223 – are clearly visible in
the inscriptions of fragment 19, part of the plate or door
protecting the back of the Mechanism. These numbers are
fundamental to the luni-solar cycles displayed on the two
large dials on the rear of the Mechanism. Both were spiral
in form, with the upper dial having ﬁve turns and 235
divisions and the lower having four turns and 223 divisions. The division into 235 is mentioned in the inscription ‘the spiral divided into 235 sectors’ on fragment E,
again from the back door. The spirals are deﬁned by a slot
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M.G. Edmunds
Figure 3. Fragment A, which contains 28 of the Mechanism’s gears. The large four-spoke ‘chariot’ or ‘Sun’ wheel (nomenclature:
b1) has 223 or 224 teeth around its rim, and is 130 mm is diameter. In use, one turn of this wheel represented one year of time.
National Archaeological Museum, Athens, Greece. –– Ο Μηχανισμός των Αντικυθήρων. Εθνικό Αρχαιολογικό Μουσείο. Αθήνα.
© User: Marcus Cyron/Wikimedia Commons/CC-BY-SA-2.0.
cut through the bronze sheet of the dial, as can be seen in
Figure 6. The pointers – pieces survive – were designed
with one end carrying a pin which ﬁtted into the slot while
the other end could pull at right angles out of the rotating
shaft at the centre of the dial. This allowed the pin end of
the pointer to indicate the relevant turn and division on
the spiral. Once the pointer had traversed the whole dial,
rather like a needle on a vinyl gramophone disc, it could
be manually reset to the beginning.
The upper dial showed the Metonic calendar, 235
lunar synodic months (i.e. full moon to full moon, 29.53
days) which is equivalent to almost exactly 19 years. This
luni-solar cycle was known to the Babylonians from
recording of observational data over several centuries.
Many clay cuneiform tablets of systematic observation
and interpretation survive from around 750 to 50 BC, and
knowledge of the cycle is believed to have passed to the
Greeks in the late ﬁfth century BC, possibly through
the astronomers Euktemon and the eponymous Meton.
The cycle’s virtue is in keeping track of lunar months and
the phase of the moon relative to the solar year, and is
necessary because of course there are not an integer number of lunar months in a year. The cycle is still used
today as the basis of setting the date of the Christian
Easter festival as the ﬁrst Sunday after the new moon
following the spring equinox.
The names of the months varied greatly around the
classical world [22], but those on the Metonic dial are
characteristic of the Corinthian colonies of north-east
Greece or Syracuse ([12], although [23] pp. 60–62 has
doubts), prompting Freeth et al.’s [12] suggestion of a
Corinthian manufacture and possible association with
Archimedes. It may be safer to suggest that an identiﬁcation of month names would imply manufacture for use
in a particular region or to suit a particular client’s taste
– indeed the device was in transit when shipwrecked on
a trade route past Antikythera. The dial divisions are laid
out on the ﬁve-turn spiral in a way that takes account of
the pattern of ‘full’ 30-day and ‘hollow’ 29-day months
characteristic of a calendar described in the astronomy
textbook by Geminus written sometime between 90 and
35 BC [19, 20]. The gear train driving the Metonic dial
is highlighted in Figure 2(b).
The Callipic cycle of 76 years (slightly more accurate
that four metonic cycles, involving subtraction of one
day) is implied by the number 76 in the fragment 19
Contemporary Physics
Figure 4. X-ray image (150 kV) of Fragment A. The teeth of
the main wheel (b1), and its double central shaft are visible.
The double row of teeth of the surviving half of the ‘turntable’
gear (e3/e4) can be seen behind b1.
Copyright: Antikythera Mechanism Research Project.
inscriptions. The cycle might have been displayed by a
subsidiary dial, but no evidence remains of such a dial or
its gearing. However there is a subsidiary dial on the face
of the Metonic dial which is divided into quarters and
shows the four-year cycle of the pan-Hellenic athletic
games [12]. It includes the biennial Isthmian and Nemean
games, and the four-yearly Olympic Games. This might
imply a social function in an otherwise astronomical display, but it may have acted as a ‘reality check’ in anchoring the year by the games cycle (of which people would
be aware) in a world where many different calendars
existed. There are remnants of a 60-tooth gear (o1) on the
axle of its pointer, the stump of which survives [24], and
the drive could easily have been made by engagement
with a (lost) gear of 57 teeth (n3) on the axis n of the
Metonic dial pointer, as included in Figure 2(b).
The lower dial on the back shows a Saros cycle of
eclipses [8,12]. A ‘glyph’ of some six characters occurs in
one of the 223-lunar month divisions whenever there is
the possibility of a solar (character H for Helios) or lunar
(character Σ for Selene) eclipse during that month. The
eclipse must, of course, occur at the new or full moon,
respectively. The cycle was again known to the
Babylonians, but known by other names until the term
Saros was coined by Edmund Halley. Simply stated, if an
eclipse occurs then a very similar eclipse is likely 223
synodic lunar months later, but shifted later by about eight
hours in time. Such behaviour can persist over hundreds
269
of years. Equipped with a list of historic eclipses it is thus
possible to predict into the future the months in which
eclipses are likely to occur. At a given location a particular
solar eclipse may not be seen, or be only partial, since the
total solar eclipse path on the surface of the Earth is quite
narrow (nearly always less than 270 km), but lunar
eclipses are more generally observable. The glyphs on the
Saros dial give some additional information about the
expected time of the eclipse, although the basis for these
extra predictions (or indeed the extent of their reliability)
is not yet fully understood. The one-third of a day shift
from cycle to cycle is indicated by a subsidiary dial
divided into three equal segments. The ﬁrst segment is
blank, the second has the number 8, and the third the
number 16, showing the number of hours to be added to
predicted eclipse time in each successive Saros to make
up an Exeligmos (in Greek – ‘turn of the wheel’) cycle
after which the predicted times would return to the glyph
values. The gear chains for the Saros and Exeligmos dials
are highlighted in Figure 2(c). At ﬁrst sight double gear
e3/e4 is un-necessarily large and the chain could have
been designed more economically in a way similar to the
Metonic train. In fact the design is ingenious, as we shall
see in Section 2.3.
Although remnants of pointers for the Metonic and
Saros dials survive, only the Metonic pointer points to a
month on the dial, but is not of help in providing an
overall dating. The eclipses speciﬁed by the ‘glyphs’ at
various month positions on the Saros dial repeat over
many cycles. The glyph positions are consistent with
modern calculations of eclipses during the three centuries
from 300 BC, and with methods of prediction that would
have been available at the time. It has not proved possible to establish a unique ‘in use’ date (or indeed a tighter
constraint on an interval) within the 300–60 BC period
that it is bracketed by a fairly deﬁnite earliest possible
manufacturing date and the latest date for the shipwreck.
2.3. The lunar motion
The motion of the moon in the sky is remarkably complicated, and indeed made even Newton claim that ‘his head
never ached but with his study on the moon’ [25, p. 544].
In a mean ‘sidereal’ month of 27.32 days the Moon would
return to the same point in the sky relative to the background stars as viewed from Earth. The ‘moon phase’ synodic month mentioned in the last section is longer due the
Earth and Moon’s joint motion around the Sun. But the
lunar orbit around the Earth is elliptical, not circular, and
the moon moves more slowly and is further away at apogee – both effects leading to slower apparent motion. At
perigee, the apparent motion is faster. The resulting variation has an amplitude of about 6° compared to the mean
position on the sky expected if the orbital motion were
circular. The Babylonians knew of the anomaly – later
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M.G. Edmunds
Figure 5. Fragment C, which shows the remnant of the front dials of the Mechanism. The inner annulus showed the twelve signs of
the Zodiac at 30° intervals, while the outer annulus showed Egyptian month names, a calendar convenient for astronomy. The division
between the two annuli is 144 ± 3 mm in diameter. National Archaeological Museum, Athens, Greece. © User: Marsyas/Wikimedia
Commons/CC-BY-SA-3.0.
known as ‘ﬁrst anomaly of the lunar motion’ – and
Hipparchos (active around 160–128 BC) developed a geometric theory to explain it. Nowadays, we know that it is
the gravitational effect of the Sun that causes the Moon’s
elliptical orbit to precess, so that the period of the variation is the anomalistic month of 27.55 days – slightly different from the sidereal month. Viewed from above, and
exaggerated in ellipticity, the lunar orbit would trace out a
‘ﬂower petal’ pattern in just less than nine years. Many
smaller anomalies were later identiﬁed which also arise
from the gravitational inﬂuence of the Sun. The largest
are the second anomaly or evection of about 1.3° amplitude, the existence of which Ptolemy (c.90–168 AD) was
aware, and a 0.66° ‘variation’ noted by the Tycho Brahe
at the end of the sixteenth century AD, which vanishes at
full or new moon.
The mechanical representation of the ﬁrst anomaly of
the lunar motion in the Antikythera Mechanism was ﬁrst
identiﬁed by Freeth et al. [8] following recognition by
Wright of the components of a pin-and-slot variable-speed
device. As shown in Figure 7, four gears in the lunar drive
train provide the modulation. Gear e5 is turned by the
outer part of a double shaft which passes (unattached)
through the centre of the large ‘turntable gear’ e3/e4. Gear
e5 drives gear k1. This gear has a pin perpendicular to its
surface which pushes on the side of a radial slot in gear
k2. The gear k2 is mounted above and almost co-axially
with gear k1. Because the axes of the two gears are not
exactly aligned, the pin is pushing sometimes closer,
sometimes further away, from the axis of gear k2 and
rotating it faster for half its cycle, and slower for the other
half. Gear e6 picks up the modulated drive from k2
and passes it back through the centre of the turntable gear
e3/e4 via the inner part of the double coaxial shaft to the
lunar display on the front dial. A simple mathematical
demonstration can be given by following Evans and Carman
[45]. Using the notation shown in Figure 8, sine rule on
¼ sinðhþbÞ.
triangle C1C2D gives Csin1 Cb2 ¼ sin½180ðhþbÞ
C1 D
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃC1 D
Setting e ¼ C1 C2 =C1 D, using cos b ¼ 1 sin2 b and
re-arranging
to
solve
for
sin
β
gives
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
sin b ¼ e sin h= 1 2e cos h þ e2 . With gear k1 rotating
uniformly θ will increase linearly with time. In the Antikythera Mechanism, the measured C1C2 = 1.1 mm and C1D =
9.6 mm give e = 0.11 and an angular variation amplitude of
6.5°, corresponding reasonably well (within the CT measurement errors) to modern values and to what historically
was estimated by Hipparchos from eclipse data. Figure 9
Contemporary Physics
271
Figure 6. Fragment B showing part of the ﬁve-turn spiral slot of the Metonic Cycle dial from the upper back face of the Mechanism. Each turn is formed from two semi-circles of different radii. The outer radius of the slot would have been about 150 mm.
National Archaeological Museum, Athens, Greece. –– Ο Μηχανισμός των Αντικυθήρων. Εθνικό Αρχαιολογικό Μουσείο. Αθήνα.
© User: Marcus Cyron/Wikimedia Commons/CC-BY-SA-2.0.
k2
e6
k1
e5
Figure 7. The Pin-and-Slot Variable-Speed Device: All four of
these gears have 50 teeth. The lunar drive (here initially shown
in yellow) enters by the outer tube of the co-axial shaft on the
right, which passes through (but is not connected to) the centre
of the large ‘turntable’ gear (e3/e4) of the Saros dial drive. The
shaft turns gear e5 which engages with and turns gear k1. The
pin in gear k1 pushes on the slot in gear k2, but as this gear is
mounted ‘off centre’ its rotation rate varies slightly faster and
slower over one rotation. The modulated drive (now shown in
red) is transmitted to gear e6, back through the centre of the double shaft and on to the lunar position indicator on the front dial.
Figure 8. The geometry of the pin-and-slot variable-speed
device of Figure 7. Gear k1 turns on centre C1, with pin at radius
D pushing on slot in gear k2, centre C2. For details see text.
gives a plot of β through a 360-degree rotation of both k1
and k2 for e = 0.11, demonstrating clearly the quasi-sinusoidal behaviour as the rotation of k2 ﬁrst leads and then falls
behind k1.
272
M.G. Edmunds
6
4
2
50
100
150
200
250
300
350
-2
-4
-6
Figure 9. The operation of the pin-and-slot variable-speed
device. The plot shows angle β of Figure 8 as a function of θ,
where 360o represents a complete rotation of gear k1. The rotation of k2 ﬁrst leads and then falls behind k1 in a quasi-sinusoidal fashion. The equation for β is given in the text.
To ﬁnd a variable-speed device may seem surprising
in itself, but the true sophistication of the Antikythera
Mechanism’s design is realised in the mounting of these
gears (i.e. the shafts of k1 and k2) on the turntable
gear e3/e4, which itself is driven in the Saros train of
gears (Figure 2(c)) to rotate the equivalent of once
every 8.88 years – a reasonable representation of the
8.85 year period of rotation of the Moon’s perigee
about the Earth (known as the period of the precession
of the line of apsides). The remarkable result is that the
modulation in the lunar rate not only has about the correct amplitude but also the correct period, the anomalistic month. The lunar and solar gear trains are illustrated
in Figure 2(d).
2.4. Planetary display in the Antikythera mechanism
de Solla Price [9] mentions that he had seen inscriptions on the back of the Mechanism ‘which refer to stations and retrogradations of the planets’, although he
does not give further details in his later magnum opus
[2]. The AMRP X-ray tomography [8, supplementary
material] conﬁrmed the reference to Venus and stationary points. Jones and Freeth [24] give good evidence
that all the known ‘planets’ of the time were listed in
the inscriptions the order of the contemporary visible
‘cosmos’ above the Earth – i.e. Moon, Mercury, Venus,
Sun, Mars, Jupiter and Saturn. So it seems very likely,
supported by literature descriptions of similar devices
(Section 5), that planetary positions were displayed.
That ‘stationary points’ are mentioned in the
inscriptions does imply that the Mechanism’s geocentric
representation was more realistic than simply uniform
mean-speed circular motion of the planets around the
zodiac. Unfortunately, almost all the planetary part of
the Mechanism has been lost – presumably detached
during the shipwreck. All that remains is that (i) on the
main fragment (A) and its large main wheel b1 there
are tantalising small details of structure which might be
associated with the bearings of additional gearing; and
(ii) there is one extant gear (r1) of 63 teeth on its own
in fragment D which is not required for the accepted
reconstruction of the solar, lunar and calendrical functions, and might therefore be part of a planetary drive.
There have been several possible theoretical reconstructions of planetary displays, involving sub-mechanisms of epicyclic gears (i.e. gears mounted on gears),
compound gear trains, sliding arms, pins-in-slots, etc.
to reproduce the retrogrades [24,26–33]. Suggested
displays involve pointers on the main front dial, or
individual dials for each planet. The proposed arrangements tend to echo either the pin-in-slot-in-gearwheel
technology of the Mechanism’s lunar motion, or pivoted slotted arms driven by rotating pins – as used in
much later astronomical clocks. It is not currently possible to make any ﬁrm statement about which reconstruction is closest to the original, and none accounts
completely for all known aspects of the surviving
fragments. Nevertheless, what is signiﬁcant is that viable reconstructions can be made, and it is clear that
the makers of the Mechanism would have been able
to build planetary displays using the level of technology and techniques that they had already achieved, as
witnessed by the clever design and construction of the
rest of the Mechanism.
3. The performance of the mechanism
How well would the Mechanism have worked? The gear
teeth are triangular, with perhaps a slight tip rounding by
wear or ﬁling, and it is believed that the gears were cut
by hand. The triangles appear roughly equilateral, but
the tip angles are probably closer to 75o [34] than 60o.
Five of the 30 extant gears have complete teeth.
Although the other gears are damaged and incomplete,
seven of them have contiguous runs of half or more
teeth. For the incomplete gears, it has proved possible to
estimate tooth counts and uncertainties by ﬁtting model
gears to the X-ray tomographic images using meansquare error minimisation [8, Supplementary Notes 3]. A
total of 14 gears have deﬁnite counts and 14 have counts
estimated to be within two teeth of the original. Noteworthy deﬁnite values are the 127 teeth for gear d2 and
53 teeth for gear l2, both primes of importance in the
functioning of the Mechanism. Unlike more subtle teeth
proﬁles (see Appendix 1), triangular teeth will not give
smooth transmission of motion, but when physical replicas of the Mechanism have been made (e.g. by John
Gleave and by Michael Wright) they do in fact turn reasonably well. Imperfect spacing of the gear teeth would,
however, have had an effect on the accuracy of the functions of the original, and a ﬁrst analysis [35] has been
Contemporary Physics
based on the statistical characteristics of the measured
tooth spacings. Using these characteristics in computer
simulations of the gear trains suggests that the Metonic
month indicator would be on average two days away,
and the Saros indicator on average ﬁve days away, from
what the designer would have intended. This is probably
a satisfactory performance – since, for example, an
eclipse must occur at either the full or new moon and all
that need be known is whether such an eclipse is likely
in that particular month. These are average values, and
larger deviations would occur during the complete cycles
and it is possible that an eclipse might be predicted in
the wrong month. The lunar pointer is geared up from
the main drive, rather than down as for the other dials,
and hence the angular errors are larger. The result could
easily be as far as 20° away from its intended position at
some time during the year, an error greater than the ﬁrst
lunar anomaly that it was designed to incorporate. If prediction of the date of new or full moon were done by
aligning moon and sun pointers – then typically about
half the predictions would be one day out, and once a
year two days out. These are effects due to unintended
random and systematic errors in manufacture. Backlash
in the gear trains must have been considerable, resulting
in some inconvenience in use. But there is another
source of inaccuracy, which is particularly signiﬁcant in
considering possible planetary mechanisms, which is representational error. By this, we mean a situation in
which the particular design of the gear trains (including
sliding arms, pins-in-slots, etc.) does not allow particularly good representation of the celestial motion because
the underlying theory is not sufﬁciently accurate or is
difﬁcult to put into mechanical form. Simple sub-mechanisms can be designed that follow the major mean periodicities of the planets reasonably well, but which may
often have a positional error of 30o in the short term.
The overall implication may be that the Antikythera
Mechanism would have been used for display purposes,
rather than for ‘accurate’ calculation. But the attitude of
the classical era astronomers and their audiences to the
notion of accuracy was probably very different from
modern ideas, and deserves closer study.
4. Design elements
Very little has been recognised by way of ‘decoration’ on
the surviving fragments of the Antikythera Mechanism.
There may, however, be a few ‘design elements’ that hint
at a tradition. The most striking visual element is the large
gear wheel b1 of 223 or 224 teeth on the main fragment.
In the functioning of the mechanism, one turn of this
wheel represents one year, and it has sometimes been
referred to as the ‘Sun’ wheel. It is the only wheel in
the Mechanism that has spokes, and its four-spoke
273
construction is reminiscent of a chariot wheel. As it was
inside the case, the wheel might not have been immediately visible, but it may be no coincidence that the idea of
a sun-chariot with four-spoke wheels was widespread in
the ancient world – for example in the Bronze-Age Trundholm sun-chariot sculpture and Scandinavian rock
carvings that may have been inﬂuenced by Mycenaean
Greece ([36,37]. Image at http://natmus.dk/en/historicalknowledge/denmark/prehistoric-period-until-1050-ad/thebronze-age/the-sun-chariot/). The symbol ⊕ of the Sun and
the cycle of the seasons appears in prehistoric art
worldwide [38], and in Greek pendants and votive
offerings. If the correct number of teeth on the gear is 223,
the symbolic link with the Saros eclipse cycle could be
coincidence rather than intentional, but a more easily laidout gear of 240 teeth would easily ﬁt in the box. No reason
for the 223 teeth on this gear has been suggested – other
than that the 223-tooth e3 turntable gear might have been a
convenient pattern for its angular tooth spacing. The b1
gear meshes with the 48-tooth crown gear (a1) which
would have been attached to the driving handle or knob on
the side of the box. This implies 4.6458 … (for 223 teeth)
or 4.666 … (for 224 teeth) turns of the handle to represent
one year. An integer number of turns might seem more
logical – for example, a 240/48 combination would give
exactly ﬁve turns – surely preferable unless the 223 is
signiﬁcant for representational reasons. We hasten emphasise that we are not suggesting some kind of ‘ritual’ signiﬁcance, merely that there might have been a design tradition.
Seiradakis [39] has reported that the ⊕ design is found on
the top of the remains of the sliding pointer of the Metonic
solar/lunar cycle dial. The ‘double spiral’ of the back dials
is certainly distinctive. It is probably pushing the analogy
too far, but images of double spirals have been associated
with calendars and are present on the Trundholm sunchariot [40], and on some megalithic monuments. Persistence over long periods of design elements can easily
be shown by dentils – the architectural detailing consisting
of lines square or rectangular blocks in relief around a
roof line. This was particularly popular in architecture of
the eighteenth and nineteenth centuries AD, and is
still occasionally used today. It is a two-thousand year
survival of the appearance of roof-beam ends on Greek
temples.
The cross-section of the shaft carrying gear e5 shows
up in the X-ray tomography as an exquisite pentagon
with sides of length 2.5 mm [8], but the temptation to
interpret in terms of Pythagorean shapes should be
quickly tempered with realisation that a pentagonal shaft/
gear-centre combination is an excellent engineering solution to prevent slipping.
Further engineering details that are seen such as
retaining pins, horseshoe-shaped spacers on gear shafts
and shaft/arbour design all await detailed consideration.
274
M.G. Edmunds
5. Evidence of geared astronomical displays from
classical literature
When people today hear about the Antikythera Mechanism for the ﬁrst time, its complexity and ingenious
design seem to come as considerable surprise. Indeed,
there have been claims that it is so anachronistic that it
must be a fake from a much later era, or even part of
an alien navigation system for interplanetary travel. Its
uniqueness as an artefact inevitably provokes suspicion.
Fortunately, there is ample evidence in classical
literature, discussed below, to provide contemporary
collateral evidence for the existence of geared mechanisms, and in particular of mechanisms representing the
cosmos. Compared to present-day amazement, it is
interesting that the compiler of an encyclopaedia in
1819 AD had no difﬁculty is assuming – guided by literary sources – that Archimedes could have constructed
such a device [41], although this was some 80 years
before the Antikythera Mechanism was found. Perhaps
it reﬂects beneﬁts of rather more classical education
than would be usual today, allowing appreciation of
the capabilities of the ancient Greeks. Even the briefest
look at the jewellery of the era shows their superb
metal-working skills. What does surprise is the sophistication of the engineering design, with its spiral displays, interleaved gear trains and variable-speed device.
Table 1 is a list, no doubt incomplete, of references in
classical literature to mechanisms which represented
motions of or in the heavens. It traces a long-lived
tradition c250 BC–600 AD.
A particular link is the use of the word sphairai
(Greek) or sphearae (Latin). The word can be interpreted
in at least three ways: (i) as a primer on elementary
astronomy by classical authors, sometimes in verse, two
of the best-known being Phenomena by Aratus [43] from
c.276 BC and the previously mentioned Geminos [20],
(ii) as an armillary sphere, a spherical structure with
rings to represent the main circles on the sky associated
with astronomical phenomena (e.g. the equator, the ecliptic – the path on the sky of the Sun as the Earth moves
around its yearly orbit, the tropics) or (iii) as a mechanical representation of the motion of heavenly bodies, particularly of the Sun, Moon and planets. Such devices
could be three- or two-dimensional, but there is little
doubt that 2-d devices were referred to as ‘sphaerea’. It
is this third meaning of the word that concerns us.
Some commentators ([44, p. 14], quoting Brumbaugh;
[45, p. 398]) have suggested that the record of mechanical
models of the Universe might date back as far as Plato c 360
BC (reference 21 in Table 1), but the model implied might
not be a geared one. We will restrict our consideration of
‘mechanical universe models’ to those that did use gearing.
Our selection is chosen because there are other devices
which may have helped the visualisation of astronomical
phenomena, and even heavenly motions, and which may
have provided metaphors to prompt physical explanations of
such motion, but do not have the transmitted causal element
which geared technology suggests. Use of pulleys and belts
would also imply causality, but there does not seem to be
any reference to belt-driven astronomical mechanisms. An
example of an excluded device without ‘causal transmission’
would be the armillary sphere. Because of its simplicity we
also exclude references to the anaphoric clock, a water- or
weight-driven disc, typically engraved with zodiac constellations, arranged so as to replicate the apparent daily rotation
of the sky. But we note in passing that the anaphoric clock
could be regarded as an excellent conceptual mechanical
model of a geocentric Universe.
6. The signiﬁcance of geared sphaerea
A geared sphaera has certain characteristics which will
illustrate general properties of the ‘Cosmos’. Even in its
simplest form – just showing the mean passage of the
Sun and Moon through the sky – it displays regular
motion and is ‘deterministic’ in the sense that future
and past behaviour can be predicted. The gearing itself
shows that a physical ‘mechanism’ (a word of obvious
derivation!) can exists to account for, or at least approximately represent, the behaviour of the heavens.
Recently, Evans and Carman [46] have proposed that
the conceptual development may have been two-way,
and that the development of the epicyclic theory of the
planets by Apollonius and others within a few decades
of 200 BC might itself have been stimulated by, and
have stimulated, mechanical modelling. With all models
– mechanical, mathematical or heuristic – there is
always (to quote Samburski [47])
the question … [as to] whether these models are only
convenient means of illustration, devices adapted to our
needs for an ordered description, or whether they represent to a greater or lesser degree some faithful image of
a physical reality corresponding to them.
Whether there was ever actually a belief that a geared
mechanism has any connection with how the motions of
heavenly bodies are ‘actually’ achieved is interesting, but
ultimately not important. What is signiﬁcant is the possibility that there could be a physical or ‘mechanistic’
explanation, whatever its nature and even if it might
need substantial future reﬁnement. A rather poor analogy
might be drawn from the existence theorems for the
solutions to equations – where it is known that there is a
solution, even if ﬁnding it may be rather difﬁcult.
A recent book by Berryman [48] has looked in detail
at mechanical ideas in ancient Greek philosophy, but in a
much wider context than just the mechanical models of
the heavens considered here. She does not push our view
Cicero
Cicero
Cicero
Vitruvius
Theon of
Smyrna
Ptolemy
Ptolemy
Galen
Sextus
Empiricus
Pappus
Agrestius
Chromatius
Lactantius
Claudian
Proclus
Martianus
Capella
Nonnus
John
Philoponus
3A
3B
4
5
6
8
9
10
11
12
13
14
15
16
17
18
7
Cicero
2
Dionysiaca
De Anima 106, 25
De nuptiis 6.583-5
Institutiones divinae II,
5, 18
Carmina minora Li
(LXVIII)
On Providence
Adversus mathematicos,
IX, 115
Works VIII, 2
quoted by St Sebastian
and St Polycarp
Planetary Hypotheses
1.70.11–23
De Usu Partium 14.5
Almagest XIII, 2
Tusculan disputations 1,
36
De Architectura 10.1.4
Expositio rerum
De natura deorum II, 97
ca. 400
AD
? 432 (age
20) – ?
485 AD
Early 5th
C AD
5th C AD
6th C AD
4th C AD
3rd C AD
3rd C AD
3rd C AD
ca 20 BC
ca. 70 -ca.
135 AD
120–150
AD
Mid 2nd
C AD
169–176
AD
ca. 45 BC
45 BC
45 BC
ca 260?
−212 BC
54–51 BC
‘De Sphaerae
Constructione’
De Re Publica 1,14
Archimedes
1
De natura deorum II, 88
Date
Work
References to sphaerae in classical literature.
Ref Author
Table 1.
Sphaera with planets, kept in a box
‘… in the case of the bronze sphere the axis moves … but the parts
driven by it move … partly in the same sense as the axis, partly in the
opposite one’
Archimedes sphaera
Universe as mechanical device with wheels interlocking in proportion
Archimedes sphaera
Archimedes sphaera
Spheres..motions..Archimedes..
Cubiculum holovitrium with moon phase and planets ‘in which the
whole learning and science of the stars is constructed mechanically’
Archimedean sphere …
Models of planetary motion
‘models constructed on earth … difﬁcult to achieve in such a way that
the motions do not hinder each other’
‘motions … sphaera-making …’
Machines as inspired by heavens
Spheremaking, gearwheels
‘Posidonius’ sphaera
See: Note (i) to Table, below.
Sphaera, horae and many other things in motion ‘cum machinatione
quandam’
Archimedes sphaerae
(Continued)
‘Sicily was amazed by this copy of the
cosmos..’
Used for astrology
Discussing Aristotle and soul and body
moving in same direction
Implications of impiety – ‘monstrous
demons displayed an art hostile to the
deity’
Used as analogy for the biological body to
function as succession of transmitted
actions
.. amazed by … the devices and causes of
the movements.
Implies sphaerae
Gears allowing opposite rotations
Referred to by Pappus Coll. 8.3. citing
Karpos of Antioch as source
Motions of Sun, Moon and ﬁve planets.
Eclipses
Mechanism must have been made by a
rational being
Lost book on ‘spheremaking’
Archimedes Sphaerae
Comment
Content
Contemporary Physics
275
Variae I. 45.
19
c.506 AD
Date
Ovid
Manilius
Manilius
Mesomedes
of Crete
22
23
24
25
Astronomica Book 4,
lines 262 and 267/8
Astronomica Book 2,
line 127
On Generation and
Corruption Book II,
Chapter 11, 338a18-b6
Fasti VI
Early 2nd
C AD
1st C AD
1st C AD
8 AD
350 BC
‘… to transform the ﬂow of water so as to spray the very stars …
water will even set in motion the face of the heaven and the starry
habitations, and will cause the skies to move in a novel rotation.’
‘a circle the course of the stars – a brass likeness of the cosmos …
symbols of the golden constellations wheeling round …’
Suggestive of gear train, but not certain.
Does imply an early mechanical
interpretation of Eudoxus’ model.
Direct reference to Archimedes, but might
not be moving model
Might not refer to sphaerae, but
demonstrates opposition to mechanical
models
In passage about water driven devices.
May refer to anaphoric clock rather than
water-driven sphaerae
Probably anaphoric clock
Models not necessarily geared
Letter to philosopher Boëthius, implying
he knows about sphaerae
‘shown how the moon recovers from waning, and set turning by an
invisible mechanism a tiny device … a portable sky, a compendium of
the universe, a mirror of nature which reﬂects the heavens’ (Trans.:
Barnish)
‘To describe … the counter-revolution of their circles relatively to one
another … to tell which … come into line with one another at their
conjunction, and which in opposition … to describe all this without
visible models of these same would be labour spent in vain.’
‘For if that which moves in a circle is always moving something else,
the motion of the latter too must be circular – for example, since the
upper movement is circular, the sun moves in this way’
‘There’s a globe suspended, enclosed by Syracusan art, That’s a small
replica of the vast heavens’
‘Who could deny the sacrilege of grasping an unwilling heaven,
enslaving it, as it were, in his own domain, and fetching it to earth’
Comment
Content
Notes: We quote here more fully the well-known reference (3A) by Cicero, since it is probably represents a device existing within a few years of the Antikythera wreck. ‘Our friend Posidonius
[c. 135–51 BC, Stoic philosopher and astronomer] has recently fashioned an orrery [“sphaera(m)”]; each time it revolves it makes the sun, the moon and (ﬁve) planets reproduce the movements which
they make over a day and a night in the heavens’ (trans. Walsh, [42]). Cicero had seen the device on a visit to Rhodes sometime during 78–44 BC.
Many of the references refer to the ‘Sphere of Archimedes’. This does not imply that Archimedes was himself involved in the design or manufacture, for the term had simply become generic for
the type of device, much the same as in the modern usage of ‘hoover’ or ‘biro’ for vacuum cleaner or ball-point pen.
It is evident that ‘Sphaerae’, speciﬁcally those that involved gears in representing the motions, or the changing positions, of celestial objects were known about (at least to the literati) during a
period of some 750 years from c 250 BC to 500 AD.
Aristotle
21
The following are less direct or doubtful references
20 Plato
Timaeus 40c-d
c. 360 BC
Cassiodorus
Work
(Continued).
Ref Author
Table 1.
276
M.G. Edmunds
Contemporary Physics
of the fundamental importance of ‘sphaerae’ in the development of philosophy and cosmology, perhaps because of
her uncertainty as to whether putting planetary pointers on
dials really is an attempt to represent the topography of
the heavens (op. cit. p. 152). Support for our more
extreme view does seem to come from the likelihood the
front dial of the Antikythera Mechanism was indeed a
‘cosmos’ in miniature (Jones and Freeth [24]) and from
the quotation (see below) from Cassiodorus of such mechanisms as ‘a mirror of nature which reﬂects the heavens’.
de Solla Price [44] suggests that ‘some strong innate urge
towards mechanistic explanation led to the making of
automata’. We prefer the inverse interpretation – or perhaps a synergy – that actual mechanical models encouraged the development of mechanistic philosophy.
We focus brieﬂy on a few of the references in
Table 1. Number 9 is from Galen, the foremost medic of
Antiquity. Note that he is not an astronomer but is certainly familiar with sphaerae:
For just as there are those who imitate the revolutions of
the wandering stars [planets] with models … they endow
with the principle of motion and who go away themselves
while the instruments [continue to] act as if their creator
were present and always controlling them, so in the same
way, I suppose, each of the bodily parts by a certain
consecution and succession of motion always from
the very beginning acts without needing a supervisor.
[trans. 49]
This is one of the few references that imply some
sphaerae were driven by an external force, possibly
water power. He is applying the ‘mechanical’ analogy to
animals, with the idea of eternal mechanical motion and
that a ‘prime mover’ is necessary. The sphaerae is relevant since either the user through a knob or handle (as
in the case of the Antikythera Mechanism), or the water
power, is seen to be able to drive all the different functions of the machine. The notion of the Universe as a
‘clockwork’ machine re-emerges several times in history
– although of course regulated mechanical clocks were
not invented until the thirteenth century AD. But we
should perhaps be careful to distinguish two themes
here: (i) the Universe as a machine which is causally
connected by physical mechanism – i.e. a ‘gearwork’
rather than ‘clockwork’ Cosmos and (ii) the Universe
which is causally connected by physical mechanism and
whose prime mover eventually runs down like a clock
spring, or is rewound by a deity, or simply continues for
eternity without intervention. The second theme would
be a cause of considerable debate for Newtonian physics
as the ‘Clockwork Universe’, while the ﬁrst theme at
least eliminates the need for individual gods to push
round the planets.
To the properties of regularity, causality and a prime
mover can be added to the mechanical generation of
277
‘regular irregularity’ such as retrograde motions of the
planets. The evidence is in both the pin-and-slot device
and the inscriptions of the Antikythera Mechanism. Ptolemy (Table 1 references 7 and 8) seems to have been
rather unimpressed by mechanical models, but even his
rejection is good evidence for the stimulus that such
models gave to discussion of the physical nature of
motions in the heavens. We would suggest that the widespread knowledge of such devices (as implied by Galen’s
casual reference) shows that they also formed an
important debating point in the general development of
philosophy.
A particularly noteworthy reference is number 19 of
Table 1 to Cassiodorus, Roman statesman and sometime
secretary to Theodoric, king of the Ostrogoths. Cassiodorus is writing, probably in 506 AD [1], to Boëthius –
author of ‘Consolation of Philosophy’ and a very major
ﬁgure in late classical and mediaeval philosophy. Cassiodorus implies that Boëthius already knows about complicated astronomical mechanisms – indeed the wording
is that Boëthius is ‘adorned with acquaintance with
such matters’ – and Cassiodorus is asking him to
procure one:
I shall say a little about the skill that represents the heavens without sin. This has set a second sun to revolve in
the sphere of Archimedes: by human ingenuity, this has
constructed another circle of the Zodiac; by the light of
art, this has shown how the moon recovers from waning,
and set turning by an invisible mechanism a tiny device
pregnant with the world, a portable sky, a compendium
of the universe, a mirror of nature which reﬂects the
heavens. (trans. [1])
The mention of ‘represents the heavens without sin’ may
be interesting in view of at least one other reference from
around the 3rd C AD (Number 12 in Table 1) which hints
at impiety in constructing models of the Heavens. Theological criticism might be invoked as an explanation of the
apparent disappearance of such devices in the West in
early mediaeval times. The use of Archimedes’ name is,
as mentioned in the notes to Table 1, probably generic.
Apart from the obvious implication that important intellectuals still knew about such devices in the early sixth century, the marvellous and rather poetic last line of this
extract – ‘A portable sky, a compendium of the universe, a
mirror of nature which reﬂects the universe’ – supports
the view that mechanisms like the Antikythera Mechanism
were indeed inﬂuential in the development of astronomical
thought and philosophy. The passage that follows this in
Cassiodorus also shows how a mechanical device could
be regarded as giving insight into physical phenomena
[our annotation in brackets]:
Although we know the course of the stars, our eyes
cheat us, and we cannot see them moving in this way;
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M.G. Edmunds
indeed their transit is static [i.e. things move too slowly
for us to see directly their motion]; and you cannot see
in motion what you know by true reason is passing
swiftly. What it is for man actually to create this device!
– even to understand it may be a remarkable achievement. (trans. [1])
7. A continuing mechanical tradition 500–1250 AD
Cassiodorus’ description at the end of last section was
written at about the same time as the construction of the
only other well-established surviving metal-geared artefact
from before 1000 AD, parts of a Byzantine sundial
[50,51]. The place names in its inscriptions, and the stylistic details of its dials, strongly suggest a Byzantine origin
in the late ﬁfth or early sixth century AD. Two shafts (or
‘arbours’) of the gearing survive, one with a seven-lobed
ratchet and two gears of 7 and 10 teeth, the other carrying
two gears of 19 and 59 teeth. The gears are made from a
low-grade brass, and resemble the gears of the Antikythera
Mechanism in that they have triangular teeth and a thickness of about 2 mm (although the ratchet is double this).
Field and Wright give a very plausible reconstruction of
the original device, guided by a later (996 AD) manuscript
source (see below). A total of eight gears and the ratchet
would allow a display of the age and phase of the Moon,
and the position of the Sun and Moon in the zodiac. The
likely gear ratios imply the device would be out by one
day in its new moon prediction after about 32 months, and
would need re-setting. This is a useful practical and portable device, much simpler than the Antikythera Mechanism
but showing that the technology still existed – and we
deduce from the contemporary Cassiodorus that this technology was still being used for complicated displays.
Our view of subsequent developments will not fundamentally differ from that of de Solla Price [52], in that
we show a clear trail of geared technology to be followed
up to the fourteenth century AD, when there is a sudden
explosion of complexity and development in the era of
the mediaeval cathedral and city clocks. We suggest that
a lesson from the Antikythera Mechanism – that literature
sources may underestimate the complexity or sophistication of contemporary technology – might be applied to
allow that memory, record or devices as complicated as
the Antikythera did indeed persist during the intervening
period. From the time of Cassiodorus there appears to be
a gap in the record of nearly 500 years until the Arabic
manuscript description of an eight- geared mechanism by
Al Biruni in 996 AD [53]. Hill suggests that the diffusion
from Byzantium to the Arabic world occurred in the ﬁrst
part of the ninth century BC. The structure of Al Biruni’s
described mechanism is so consistent with what is left of
the Byzantine geared sundial, and so similar to a surviving Arabic geared astrolabe by Abi Bakr from 1221/2
AD that the basic technology and tradition of this particular kind of device can be clearly seen to persist between
500 AD and 1220 AD. A continuity of technology may
also be inferred from accounts of automata in the classical, Byzantine and Arabic worlds.
The Abi Bakr astrolabe with gearing, made in
Isfahan, is illustrated in Figure 10 based on details from
Field and Wright [50], King [54], personal inspection
and the website of its custodial Oxford museum
(Museum of the History of Science [55] in the references). The Byzantine and Al Biruni devices showed the
position of the Sun and Moon in the zodiac on separate
dials, but it is noteworthy here in the Abi Bakr device,
they are shown on the same dial – and hence reminiscent
of the ‘topographical’ front dial of the Antikythera
Mechanism, and seen later in mediaeval clock sun and
moon displays. Inscriptions on the astrolabe’s casing
b1 b2
a1 a2
c1 c2
d2
d1
Figure 10. Schematic rear and side view of the Abi Bakr
geared astrolabe from Isfahan 1221/2 AD, made in brass with
triangular-toothed gears. It is about 185 mm diameter. The front
of the device is an astrolabe, but the rear (shown left) is a
geared display of the lunar phase (top aperture) by rotation of
circles on the back face of gear b1 past a circular aperture –
there are two black circles on opposite sides of the axis – and
numbers showing through a small aperture give the age of the
Moon in the lunar month. The gearing is shown side-on at
right, with the depth exaggerated. The motion of the Moon
around the zodiac is shown by a black dot (probably originally
silvered) on the annular or ring gear (d2, shown pink), and the
motion of the Sun by a gold dot on the face of the annular gear
wheel d1 (shown light blue). The mechanism would have been
operated by turning the central axis. The train to the lunar
phase display is a1(8)−b1(64), the train to the lunar position in
the zodiac is a2(13)−d2(48), and the train to the solar position
is a1(8)−b1(64) + b2(64)−c2(64) + c1(10)−d1(60). N turns of
the shaft carrying a1 and a2 a will give N/4 lunations, 13 N/48
lunar orbits and N/48 solar orbits. Thus the sun will go around
the zodiac once in 48 turns, while the moon will go around 13
times with 12 lunations. The implied year is a pretty inaccurate
354 days, but the motions are elegantly demonstrated.
A ﬁne animation is available at http://www.mhs.ox.ac.uk/
almizan/AstrolabeAnimation.htm
Image of astrolabe by permission and copyright of the
Museum of the History of Science, University of Oxford. Image
inventory No. 48213.
Contemporary Physics
mention ‘different motions [of the heavenly bodies] with
a single mover’ – although the reference here was
intended as predominantly theological rather than philosophical.
It seems that more complex designs with planetary
displays did persist in the Arab world, as can be inferred
by accounts of a gift made in 1232 AD by the Sultan of
Egypt to the Holy Roman Emperor Frederik II. It ‘was
made to resemble the celestial sphere [similitudinem
sphaeraum caelestium] in which moved likenesses of the
Sun, Moon and the other planets … set in motion by
weights and wheels’. This excerpt [56,57, p. 350 note 1]
is from a rather later account by the German abbot and
historian Trithemius (1462–1516 AD), but is corroborated (North op. cit.) by other sources. Within another
70 years of the gift to Frederick, three manuscripts from
around 1300 AD in northern Italy [56] describe the
setting of gear ratios and some constructional details for
making an ‘Opus quarundam rotarum mirabilium quibus
sciuntur vera loca omnium planetarum …’ – a ‘device of
certain remarkable wheels by which the true places of all
the planets are known’. North (summarised, discussed
and illustrated in King [54] and Lehr [58]) notes the possibility that this design, whose origin may date from
some years before the surviving manuscripts, might share
ancestry with Frederik’s present. He proposes a reconstruction as a mechanism with over 21 gears, showing
the Sun, Moon and planets displayed on discs or annuli
carried on concentric-tube axes. Motions were probably
only mean period circles, except possibly for the Moon.
Here is evidence of complexity almost to match the
Antikythera Mechanism, and in the next section we will
see the evidence of such complexity being exceeded
(with a suggestive Greek connection) only 50 years later.
No attempt is made in this narrative to incorporate
the invention and development of astronomical clocks in
China from the seventh century AD onwards. Although
pioneering, there seems little evidence that it had any
major inﬂuence in the West. Some transmission of ideas
may have come through the Islamic world after 1200
AD, and the interested reader is referred to the excellent
book of Needham et al. [59].
8. The development of mechanical astronomical
clocks 1250–1400 AD
It was around 1280 AD that the fundamental invention
of the escapement was made, although where (northern
Italy?) or by whom remains unknown. From antiquity,
‘clepsydra’ or water clocks had used ﬂuid ﬂow to regulate time. A consistent ﬂow was difﬁcult to maintain.
The escapement provided time intervals needed for the
regulation of a mechanical clock by the method of regular alternate stopping and release of a crown gear by two
small vanes on an oscillating shaft (or ‘foliot’). The
279
crown gear’s teeth are of a special shape which allows
some of its rotational energy to feed through into keeping the foliot oscillating. It was not until 1656 AD that
Huygens introduced the more accurate pendulum regulation. Although mechanical clocks may initially not have
been as accurate as carefully-maintained clepsydra,
Landes [60] points out two critical advantages that led to
their dominance – they did not freeze (important in
Northern European climates) and their technology could
be miniaturised, eventually allowing portability while
maintaining timekeeping. Mills [61] usefully outlines the
basic physics of the limitations of clepsydra. The foliot
escapement led to a century of clock building and innovation, well established by 1300 AD, and the timepieces
were sometimes enhanced by coupled astronomical displays. Richard, Abbott of Wallingford left some extensive (but incomplete) details with gear ratios and
diagrams (‘Tractatus Horologii Astronomici’ [62]) of a
clock he was still constructing at the time of his death in
1336. It would certainly have shown Sun, Moon and
eclipses, and was possibly intended to show the other
planets. Reconstructions have been attempted by North
(op. cit.) and by Lehr [58], his ﬁg 236).
This was the era of the great cathedral and city
clocks, often showing mean solar and lunar motions.
Examples of construction dates are Norwich Cathedral
Priory c 1322–1325, Strasbourg 1352–1354, Salisbury
Cathedral c 1385 and Prague 1410.
The extent of new invention becomes apparent with
the construction of a complicated ‘Planetarium’ or
‘Astrarium’ astronomical display clock by Giovanni di
Dondi in Padua, northern Italy, completed in 1364. His
father, Jacopo di Dondi, had already made an astronomical town clock for Padua in 1344. Giovanni left a
detailed and fairly comprehensive account of his own
construction which is preserved in several manuscripts
(the name Planetarium or Astrarium varies between
them), the earliest believed to date to 1389. A useful
English translation with original diagrams was prepared
by Baillie et al. [63] – rather harshly reviewed by Turner
[64], and a French translation and facsimile published by
Poulle [65]. The history of the device is covered by
Bedini and Maddison [66], and its function discussed in
King [54], chapter 3) and Lehr [58, ﬁgs. 238–264]. Several physical reconstructions have been made – e.g. see
Figure 11. The Astrarium contained 107 gear wheels,
was weight-driven and regulated by an escapement. Individual dials showed the diurnal motion of the stars and
the annual motion of the Sun, and the positions of the
Moon and each of the ﬁve planets in the Zodiac, with
arrangements of gears with slotted arms and pins to allow
retrograde motion. There was a dial showing the position
of the Moon’s ascending node, allowing prediction of
eclipse possibilities. This form of prediction is obviously
mechanically different from the pointing to pre-calculated
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M.G. Edmunds
Dondi does not make explicit reference to sphaerae in his
account, but does give credit to the Greeks for their astronomical achievements, and his clock was referred to as ‘a
sphere … for celestial movements’ in 1385 [66]. It is
known that both he and his friend, the scholar and poet
Petrarch, were familiar with the works of Archimedes
and Cicero [67]. Even more suggestive of a direct link is
a letter of 1388 to de Dondi from his friend Giovanni
Manzini of Pavia (quoted in [66], and referring to Reference 3A in our Table 1) –
I saw your … clock … Cicero tells how Posidonius has
constructed a sphere which revolved showing, through
the Sun, Moon and ﬁve planets what happens in the
heavens … I do not believe there was such competency
in art at that time, nor was there such a mastery of skill
as is shown in this.
We suggest that Manzini is not claiming that the Greeks
couldn’t do it, but simply that de Dondi is doing it better
and that de Dondi would already have been familiar with
the Cicero reference – indeed that he took his inspiration
from the Greek sphaerae tradition.
Figure 11. A modern reconstruction of the astrarium clock of
Giovanni de Dondi completed in 1364 AD. This is the ﬁrst
known device that is more complicated than the Antikythera
Mechanism. The seven faces on the upper part show the daily
motion of the stars and annual motion of the Sun, and individually the motions in the zodiac of the Moon and ﬁve planets.
At about 1 m high it was not nearly as conveniently portable as
the Antikythera device.
Image by permission and copyright of the Time and
Navigation Collection, Division of Work and Industry, National
Museum of American History, Smithsonian Institution. http://
timeandnavigation.si.edu/timeline2.
information on the Saros dial that is employed in the
Antikythera Mechanism. It comes from the fact that the
Moon’s orbit about the Earth and the Earth’s orbit about
the Sun (the ecliptic) are not coplanar, so an eclipse can
only occur when the moon and Sun are at or very near
one of the two crossing points or ‘nodes’. The positions
of the nodes precess around the ecliptic, so prediction
must be based on calculating the positions of nodes, Sun
and Moon. Richard of Wallingford’s clock was also
based on this method. The Astrarium does use the 19
years of the Metonic cycle in a mechanical perpetual calendar of Christian moveable feasts that had 19-link
chains. Although some gear wheels still show triangular
teeth, there are other gears with blunt-nosed teeth, and to
reproduce irregularities some are intentionally oval in
shape or with varying tooth spacing. The Astrarium is
chronologically the ﬁrst known device that is deﬁnitely
more complicated than the Antikythera Mechanism. De
9. The inﬂuence of mechanism 1400–1720
The mechanical inspiration continued, in that there is
good evidence that the major ﬁgures of the Copernican
Revolution would have been familiar with astronomical
clocks and mechanical devices, and their classical roots.
Johannes Muller von Königsberg, known as Regiomontanus and ‘arguably the best mathematical astronomer of
ﬁfteenth century Europe’ [68] was an inﬂuence on Copernicus and a key critic of the shortcomings of the Ptolemaic system. Regiomontanus suggested that ‘to restore
the heavens … [we must] remove the rust from the heavenly spheres’ (Swerdlow [69]). In 1463 he saw, and was
very impressed by, De Dondi’s Astrarium [70]. Bedini
and Maddison [66] and Zinner claim that clock still survived (although no longer working) in 1529, and was on
display in Pavia in north Italy (where Regiomontanus had
seen it) until at least 1495. Copernicus was in Bologna in
1496–1500 and Padua 1501–1503, and even if he did not
see de Dondi’s clock himself, he must surely have heard
reports of it. A copy of de Dondi’s account of the clock
was sent to Cracow ca. 1494 [66].
Although de Dondi’s clock is lost, there are others
with strong similarities from 150 to 200 years later which
do survive. The oldest is that in the Bibliothèque SainteGeneviève in Paris, said to have been restored by Oronce
Fine in 1553 for the Cardinal of Lorraine, but of which
parts – particularly the planetary display dials – probably
date back as far as the beginning of that century or the
last years of the ﬁfteenth century [71,72]. It has dials,
with slotted arms and wheels to allow retrograde motion
where appropriate, showing individually the position in
Contemporary Physics
the zodiac of the ﬁve planets, Sun, Moon and nodes.
The slightly later 1554–60 Tübigen clock by Philippus
Immser [54, p. 71] has a ‘topographical’ dial analogous
to the front of the Antikythera Mechanism, combining
the display of the position of the planets, Sun, Moon and
nodes by pointers on one dial. These devices are of
course geocentric.
Copernicus’ heliocentric de Revolutionibus was published in 1543, although a ‘preprint’ version of the ideas
– the Commentariolus [73] – had been written ca. 1507
and circulated around Europe. The continuing but evolving use of mechanical analogy on the way to mathematical models may be seen in Tycho Brahe’s (1546–1601)
remark (Rosen op. cit., footnote to page 12):
But really there are no solid spheres in the heavens …
those which have been devised exist only in the imagination, for the purpose of permitting the mind to conceive
the motion which the heavenly bodies trace in their course
and, by the aid of geometry to determine the motion
numerically through the use of arithmetic. [our italics]
We would interpret this as mechanical models acting as
an essential conceptual prop, irrespective of their ﬁdelity
to the ‘actual’ physical structure – but it might alternatively be argued that Brahe is trying to reject any interpretation other than a mathematical one. The direct
inﬂuence of mechanism on Brahe’s successor Kepler is
easier to establish. There is his well-known comment in
a letter from 1605 ‘My aim is to show that the heavenly
machine is not a kind of divine, live being, but a kind of
clockwork … in so far as all the manifold motions are
… taken care of by one single force’ [74, p. 136], and a
little earlier in 1598 [54, p. 92, 75] he had informed the
astronomer Michael Mästlin that he proposed to
construct a heliocentric planetarium-type device with the
paths of the planets traced out by arms supported on a
‘set of coaxial tubes rotated by wheelwork [i.e. gears] at
the lower ends’ and he gives calculated values for the
gear ratios. It would have incorporated some kind of representation of the elliptic nature of the orbits. He is
believed to have given up the project in 1599. The
Greek connection is clearly evident from another letter to
Mästlin in the same year (Letter 99 in Caspar [76]) in
which Kepler discusses Archimedes’ and Posidonius’
sphaerea using references 2, 3A and 14 of our Table 1.
We shall only brieﬂy sketch the further development
of mechanical models, for details see King [54]. By
1600 in Amsterdam W.J. Blaeu was producing a simple
geared ‘tellurion’ or ‘tellurian’ to show the motion of the
Earth around the Sun and the Moon around the Earth.
The ﬁrst views through a telescope of the changing positions of the satellites of Jupiter in 1609, hastily published
by Galileo [77], must have suggested a ‘solar system in
miniature’, and a geared ‘Jovilabe’ or ‘Jovilabium’ was
designed by in 1672 by Ole Rømer (who is best known
281
for the ﬁrst determination of the speed of light from
observations of Jupiter’s moons). The device reproduced
Galileo’s view by incorporation in a box with a suitable
viewing aperture. Rømer had designed a full heliocentric
planetarium by 1680, and Huyghens built an extant planetarium with offset circular orbits in 1682, whose design
he later published in 1703 in ‘Descriptio Automati
Planetarii’.
It was of course Newton’s Principia of 1687 with a
‘ﬁeld’ theory of gravity which provided a mathematically
rigorous and causal explanation for the elliptical orbits
of the planets. The Principia was not easy for non-specialists to understand – indeed, some claimed that Newton had intentionally made it abstruse to avoid being
taxed by ‘little smatterers’ in mathematics. However,
more popular accounts spread its inﬂuence rapidly, and
by the ﬁrst years of the eighteenth century it had created
a demand for exposition on which ﬂourished geared
models, both of the Sun-Earth-Moon system and of the
whole known Solar System. Prominent were the devices
by clockmakers George Graham and Thomas Tompion c
1704–1709 which led Charles Boyle, 4th Earl of Orrery
(in Ireland) to commission one from John Rowley
around 1712, with ‘Orrery’ subsequently sticking as the
name for such devices. Their power for ‘outreach’ activity was beautifully captured in the ca. 1766 painting ‘A
Philosopher Lecturing on the Orrery (1764–1766)’
(image widely available on the WEB) by Joseph Wright
of Derby. Indeed, Westman [78] suggests that ‘the orrery
… contributed importantly to the naturalisation of the
Copernican system in the eighteenth century’ – showing
the continuing value of mechanical visualisation in astronomical thought.
10. Conclusions
It is hoped that the recent resurgence of interest in the
Antikythera Mechanism will result in more artefacts of
gearing being discovered or recognised in collections,
both public and private. We have two surviving forms of
‘sphaerea’ in the Antikythera mechanism and the lunar/
solar displays of geared astrolabes and sundials. It seems
likely that there would have been both intermediate and
even more advanced forms, but speculation without more
evidence is likely to be rather fruitless.
One perhaps surprising aspect is that, apart from the
late (ﬁfth century AD) and rather garbled reference by
the poet Nonnus (Table 1 reference 17), there is no evidence of use of sphaerea for astrological, rather than
astronomical, purposes. Throughout the AMRP investigations, a watch was kept for astrological function (e.g.
a mechanisation of the ‘lot of fortune’) or inscription,
but none has so far been found. This does not mean
that the machine could not have been used for
282
M.G. Edmunds
astrology, but probably implies that it was not its prime
purpose.
For the Antikythera Mechanism itself the major
unknowns are whether it incorporated variability of the
solar motion, and the exact form of the planetary display.
The function of the 63-tooth gear (r1) remains unknown.
There is some uncertainly about the detailed scheme of
eclipse time prediction used to produce the Saros dial. It
is worrying that the small crown gear (q1) in the lunar
phase display is apparently the wrong way round in its
mounting, assuming a simple reconstruction. This might
indicate either a more complicated device, or evidence of
incompetent ancient repair.
Where was the Mechanism made? Possibilities include
Alexandria, Pergamon and Syracuse. The latter had the
advantage of any heritage left by Archimedes, but the
problem that it was sacked in at the time of his death in
212 BC, although something may have remained. The best
candidate must be Rhodes, a port at which the Antikythera
ship had called (judged by some of its cargo) not long
before its wreck. Rhodes was a highly technological naval
centre around 100 BC with a ﬁne bronze industry and an
astronomical tradition. It is also one place where we know
that a similar contemporary device was reputedly made
and seen. What form of workshop or workshops produced
sphaerea is an open question, with its eternal conundrum –
within some concepts of Greek society – of requiring close
co-operation of astronomical and mathematical knowledge
with technological expertise and craft, skills that perhaps
had to be combined in a single individual. What is certain
is that the tradition of ‘sphere making’ lasted for a very
long time, and could have ﬂourished in different places at
different times.
We will end with a summary of the philosophical
implications. Sphaerea were mechanical representations
of the Universe that were causal, deterministic and regular, driven by a single ‘prime mover’ and also in some
cases showing ‘regular irregularity’. Irrespective of the
extent to which they were regarded as a true representation of comic structure, their demonstration of the possibility of mechanical explanations for heavenly motions
must have been a major driver of philosophical and cosmological argument. Even as a spur for the conscious
rejection of mechanical explanations they were inﬂuential. The realisation of the complexity and sophistication
of the mechanical design of the Antikythera Mechanism,
and the evidence that the knowledge of such mechanisms
were reasonably widespread, forces us to acknowledge
the inﬂuence of mechanical models in stimulating ideas
of a mechanical universe not only for the Renaissance,
but as far back as Plato. Design elements within the
Mechanism may even hint at symbolic traditions carried
through from the Bronze Age.
The use of mechanical models or analogies continues to this day – a good example is the damped
harmonic oscillator, used as a conceptual model for a
wide range of applications from tides to spectral line
shapes. But physics may have grown away from physical models, and it could be that the lack of good
mechanical analogies for much of quantum mechanics
contributes to the apparent difﬁculty of comprehension
– indeed in a ‘Copenhagen’ interpretation such models
would be impossible. Maxwell made considerable use
of rather complex mechanical models in developing a
dynamic ﬁeld theory of electromagnetism c 1865 – a
recent illustration can be found in Morrison [79,
p. 31]. A quote from Freeman Dyson [80] seems
relevant:
The scientists of that time, including Maxwell himself,
tried to picture ﬁelds as mechanical structures composed
of a multitude of little wheels and vortices extending
throughout space … If you try to visualise the Maxwell
theory with such mechanical models, it looks like a
throwback to Ptolemaic astronomy with planets riding
on circles and epicycles in the sky. It does not look like
the elegant astronomy of Newton … Maxwell’s theory
becomes simple and intelligible only when you give up
thinking in terms of mechanical models. Instead of thinking of mechanical objects as primary … you must think
of the electromagnetic ﬁelds as primary …
Perhaps ‘throwback’ is the wrong word here. The
Antikythera Mechanism and other sphearae of the classical world, with their later legacy, serve as a reminder
that mechanisms and machines have not only been
important in the development of technology but also a
critical aid in the development of our comprehension and
visualisation of the Universe and its physical behaviour
over the last 2500 years.
Acknowledgements
I am very grateful for discussion and support from my
colleagues in the AMRP, in particular Lina Anastasiou,
Yanis Bitsakis, Tony Freeth, Alexander Jones, Xenophon
Moussas, John Seiradakis, Agamemnon Tselikas and Mary
Zafeiropoulou. The AMRP investigations would not have been
possible without the expertise and generosity of Roger
Hadland, Andrew Ramsey and others at X-Tek, and Tom
Malzbender formerly of Hewlett-Packard. Essential grants
came from the Leverhulme and A.G. Leventis Foundations.
For bringing to my attention literature sources included in
Table 1, and for discussions, translations, data and encouragement I thank Sylvia Berryman, Niels Bos, Paul Cartledge,
James Evans, Richard Evans, Paul Keyser, Daryn Lehoux, A.
P. D. Mourelatos, Stephanie Pambakian, Giovanni Pastore,
Jurgen Renn, Tracey Rihll, Liba Taub, Theodosios Tassios,
Frank Weiden, Andrew Wilson, Michael Wright and Rien van
de Weygaert. My debt to Price and King’s classic texts is
obvious. For access to the geared artefacts of Section 7, I
thank the Museum of the History of Science, Oxford, and the
Science Museum, London. The goodwill and cooperation of
the Directors and staff of the National Archaeological
Museum, Athens is greatly appreciated.
Contemporary Physics
Notes on contributor
Mike Edmunds is emeritus professor of
Astrophysics in, and a former head of, the
School of Physics and Astronomy, Cardiff
University, UK. He is currently a vice-president of the Royal Astronomical Society.
His research career focussed on the chemical evolution of galaxies and the origin of
interstellar dust. He has a long-standing
interest in the history and philosophy of
science. His research into the Antikythera
Mechanism was sparked by the supervision of a ﬁnal-year
MPhys student project in 1999, and led on to him becoming
the academic lead in the international Antikythera Mechanism
Research Project (www.Antikythera-Mechanism.gr).
References
[1] S.J.B. Barnish, Cassiodorus Variae, Liverpool University
Press, Liverpool, 1992.
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