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Metafísica y Persona. Filosofía, conocimiento y vida
Año 15, Núm. 30, Julio-Diciembre, 2023, ISSN: 2007-9699
A critical reection on the Antikythera Mechanism
from an idealist perspective and its implications
on technological development as a means of
understanding our Cosmos
Una reexión crítica sobre el Mecanismo de Antikythera desde una
perspectiva idealista y sus implicaciones en el desarrollo tecnológico
como medio para entender nuestro Cosmos
The Churchill School and College
carlos.carbajal@churchill.edu.mx
Technology can be an insight into how humanities’ needs have changed along the centuries
and how science has been applied in order to solve these conundrums, to make the world our
own and understand it to learn about what surrounds, what is true, and what is unchangeable.
The Antikythera Mechanism’s complexity and recent discoveries allow the academy to know
its functions and how exact it was, as a new model has been proposed that shows that it was a
device to unravel one of the biggest mysteries of antiquity: The Cosmos and the Stars. Along
with the help of the perspective of Collingwood’s sense II and sense III, this paper aims to
-
chanism, by looking into what is says about the old world and how it contrasts with the new.
Keywords: Antikythera Mechanism, Epistemology, Methodology, Idealism, Collin-
gwood, Minimum Space, Minimum Time, Parmenides Proposition, Metaphysics, Astro-
nomy, Theodore of Smyrna, Thinking and Being.
La tecnología muestra una mirada perspicaz hacia cómo las necesidades de la humani-
dad han cambiado a lo largo de los siglos, y cómo la ciencia ha sido aplicada para resolver
estos acertijos, para hacer el mundo nuestro y entenderlo para aprender lo que rodea,
lo que es cierto y lo que es inmutable. La complejidad del mecanismo de Antikythera y
1
Metafísica y persona. Filosofía, conocimiento y vida
Año 15, Núm. 30, Julio-Diciembre, 2023, ISSN: 2007-9699
22
recientes descubrimientos permiten a la academia saber sus funciones y qué tan exacto
era, ya que un nuevo modelo ha sido propuesto que muestra que era un dispositivo para
descifrar uno de los más grandes misterios de la antigüedad: El cosmos y las estrellas.
Con la ayuda de la perspectiva del sentido II y el sentido III de Collingwood, este artículo
Antikythera, al estudiar lo que dice del viejo mundo y cómo contrasta con el nuevo.
Palabras clave: Mecanismo Antikythera, Epistemología, Metodología, Idealismo, Co-
llingwood, Espacio mínimo, Tiempo mínimo, Proposition de Parménides, Metafísica, As-
tronomía, Teodoro de Esmirna, Pensamiento y Ser.
This paper will explore the historical device and the mathematical and an-
thropological research done upon it, particular the work done by the University
College London team headed by Tony Freeth; having presented a mostly nar-
-
wood’s propositions on natural science whilst touching on some related con-
cepts in philosophy of nature as found in the thought of Theodore of Smyrna.
the Greek Island of Antikythera– has proven a mystery to scientist for the
past twenty years. And not only because there is no signature, dating, or pos-
sible provenance, but because it was incomplete and what was recovered was
a mechanical marvel too formidable to unravel.
very recently that a team from University College London
2
pieced together
-
essary, as the ANTIKYTHERA MECHANISM, was broken up into 82 pieces
forming 3 distinct bodies) digital rendering of the working of the mechanism.
view this from Robin Collingwood’s idea of causation and minimum time
and space as applied to the ANTIKYTHERA MECHANISM.
-
er in the XXI century and analog computing devices. The ANTIKYTHERA
2
23
A critical reection on the Antikythera Mechanism from an idealist perspective and its
implications on thechnological development as a means of understanding our Cosmos
time, actually bridging humanity’s ability to use minimum space to describe
cosmic spatial and temporal notions.
The aforementioned UCL team describes the mathematical principle be-
hind the ANTIKYTHERA MECHANISM as that delineated by Plato in Par-
menides 154 b-155b.
This model, described by Fowler as the Parmenides’ Proposition,
3
details
the ratios between temporal coordinates which translate into spatial ones in
the ANTIKYTHERA MECHANISM. According to Plato, two temporal co-
added or subtracted to them. This ratio considers the numbers as relative
between them, the marginal error decreases as the relative amounts also are
fractioned. This is expressed as p:q < (p + r):(q+s) < r :s. As Fowler accurate-
constant relative values that can then be applied to points in space and time,
namely, orbital positions.
The orbital positions of the planets in the ANTIKYTHERA MECHANISM
are calculated as being relative one to another according to the constraints
of minimum space and time as dictated by gear ratios. These follow a very
be determined by the same homogenous ratio that follows Parmenides’
Proposition.
4
This discussion will be developed further, but for the time being, it is im-
perative that we explain the theoretical basis for a minimum space and mini-
mum time, and for that, we will refer to two works by Robin George Colling-
wood, ie, An Essay on Metaphysics and The Idea of Nature.
In An Essay on Metaphysics,
5
Collingwood ventures forth the concept of
-
pertain most closely to the study of the cosmos and the application of mathe-
matical principles to astronomical observation. To be succinct, sense II is that
of relativistic causation, that is, when an event in nature can derive its cause
from the observation carried out from the point of view of humans. Now, one
3
, D., The mathematics of Plato’s Academy (2
nd
-
versity Press, 1999, p. 41.
4
, D., The mathematics of Plato’s Academy, p. 42.
5
, R., An essay on metaphysics (2
nd
ed.), Lanham, Md: Univ. Pr. of America, 1984, p. 314.
Metafísica y persona. Filosofía, conocimiento y vida
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might argue that this is not the case for orbital paths of planets as they were
there millions of years before humans and they will inexorably continue their
paths around the Sun and Milky Way whether we are there to measure and
observe them or not. However, the measurement of orbital paths that corre-
spond to mathematical propositions does tell us one thing about mathemat-
ical science, ie: principles are as much derived from Nature as explanatory of
nature.
Which leads to Sense III as Collingwood applies it to theoretical sciences,
of which astronomy was until not too long ago one of the most prominent. It
is not so anymore as it is squarely set within the realm of applied sciences, but
we will address this topic at length further on.
Sense III for Collingwood is that contrary to the contingency of the observ-
er-observation synergy required in Sense III, these are necessary events both
6
Let us rephrase this as a positive statement: the conditions
must always be there for its existence and operation.
But which conditions are these if the necessary inference is that they can-
chronologically but also ontologically simultaneous. As applied to the orbits
of the planets in the Greek and also our modern Cosmos, the orbits and plan-
ets are both chronologically and ontologically simultaneous, necessary one
for the other in what Collingwood calls a one-to-one tight relationship.
The ANTIKYTHERA MECHANISM, as a computational device for such
orbital paths, is then a product of Sense III in which Collingwood describes
allow the smallest number of related gears within the mechanism to explain
more than one orbital path. These two interrelated concepts interestingly are
part of Collingwood’s Sense II, inasmuch as there was a volitional and condi-
tional aspect in generating the physical body of the Mechanism. How so? The
calendar count used for this was the ever-so-popular in the Ancient World Me-
tonic Calendar, developed fully in its Lunar synodical observation by Meton of
Athens, but widespread amongst the Hebrews and Babylonians, from whence
the count for the Antikythera Mechanism was devised. The volitional aspect,
association of Prime Numbers and the very idea of a compact astronomical
6
, R., An essay on metaphysics, p. 317.
25
A critical reection on the Antikythera Mechanism from an idealist perspective and its
implications on thechnological development as a means of understanding our Cosmos
device over against a large-scale observatory– show us the explanatory view of
mathematics, over against the derivational view as seen in Sense III.
This seems elegant, albeit being incomplete, as something else was re-
quired to be able to apply the Metonic Calendar, the factorisation using
Parmenides’ Proposition to the orbital paths of the known planets, and the
calculation of exacting periods for multiple celestial bodies using a lim-
itedphysical space. And it is exactly that, what Collingwood describes as
Minimum Space and Minimum Time.
7
For Collingwood, the advent of contemporary physics, as he draws a dis-
tinct line from Newton to Whitehead, has brought back a most important idea
that he seems to draw from Pythagoreanism, mainly, that the quantitative
and qualitative notions of physical reality are tied in together at the most
or time and space. As he states, the mathematics behind modern physics is a
as he is, with the metaphysics behind it. We cannot help but see here Aristo-
telian principles at work. In Physics II (154b-d), Aristotle already established
-
However, it is our suspicion that Collingwood, whilst not mentioning this
notion by name, is closer to Theodore of Smyrna’s supposition of a dynamic
a Byzantine commentator of Aristotle’s and one of his original insights is that
Theodore to separate place and motion, that is motion requires space, but
If we look at the combined elements that make up the Antikythera Mecha-
nism, we see that these three elements are at play: in having a Metonic Cycle
ruling the basic calculations alongside Parmenides’ Proposition, we have the
in Prime Numbers which in turn gives us the gearing required to establish the
This is most important as it is through a secondary place, devoid of vacuum
–which Collingwood says is one of the advantages of modern physics, whilst
7
, R., The idea of nature (1
st
Metafísica y persona. Filosofía, conocimiento y vida
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26
making it clear that only in our modern Copenhagen Interpretation and thank
to the General Theory of Relativity can we understand this vacuum proper-
ly– that the dynamic cosmos can come into play. Place and Location are thus
necessary, and we come full circle with our third Sense of Causation in the
dynamics of astronomical observation.
Collingwood, of course, was for the most part laying out a historical argu-
ment from the metaphysics of science. We merely complement it with some
elements from Theodore, but it is the application of such principles to the
study of the Antikythera Mechanism that are our focus.
The Antikythera Mechanism was built, as we have shown, with the pre-
suppositions of the physical science available at the time, which includes the
aforementioned metaphysical implications of time, space, motion, and place.
Perhaps we should explain this point further. Not only did Aristotle and his
commentators explain these topics at length for they were ultimately trying
to understand what Collingwood sees as one of the pivotal points in astrono-
my, that is: the relation between force and motion. This cannot be understated,
as it is a central aspect of both Newton’s and Kepler’s models for planetary
motion but one that, given the context from Theodore, we can see was also
paramount for Greek Cosmology.
energy and activity. It is always forceful. So, for Theodore’s and Colling-
wood’s dynamic cosmos, movement and so space- time will be dynamic, that
is, there is a positive activity, a drive that is intrinsic, a priori, and necessary
to the cosmos. So, inasmuch as the cosmos exists and we can perform
derivative mathematics from it, it is so because of this dynamism which, as
Collingwood explains, is not only a physical quality but a metaphysical real-
ity that underlies the material properties of space and that ultimately allows
for an understanding of the cosmos. So, we can establish with certainty that
this ontological realm grants epistemic quality to the cosmos which allows for
mathematical principles to be derived and explained. The Antikythera Mech-
that calculates and measures dynamic relations of orbital planes and cycles.
We must clarify once more, lest the reader think that Collingwood was
Greek Cosmology, that this is a personal insight from this author and one that
should be taken with a moderate view as Byzantine sources are scarce and
Greek and modern understanding of cosmology that is valuable and unique
as it allows for a more thorough understanding of the metaphysical under-
pinnings of this venture.
27
A critical reection on the Antikythera Mechanism from an idealist perspective and its
implications on thechnological development as a means of understanding our Cosmos
Having established a theoretical foundation for this discussion, let us cen-
The Mechanism is comprised of a central dome representing the Earth.
The discussion on Heliocentrism vs Geocentrism is an interesting one, but it
will not concern us so long as the metaphysical principles established from
Collingwood and Theodore remain true for either and all systems.
Adjacent and tied into the Geodome is a sphere to mark out the lunar
phases and its Zodiac position. The gears that are interlinked with the Me-
tonic Cycle according to the mathematical principles described above are, in
order: Mercury, Venus true Sun, Mars, Jupiter, and Saturn. Uranus and Nep-
tune would not be a part of the cosmic array until 1781 by Herschel and 1846
-
lations for a reason. As discussed above, one of the main concerns with the
theory behind orbital location was that of gravity as a force. We now know
8
9
as the Suns, so, as long as Jupiter accounts as a bridge in its ratio between Mars
and Saturn, all of the planetary locations and secondary locations can be more
or less accurately pinpointed as the prime factorisation will make Jupiter’s
calculation of its synodic and Metonic cycle the most accurate. The outer-
most disc marks the date, as well as the oppositions that will mark Lunar
and Solar Eclipses. The mechanisation process that was required to build the
mechanism is truly remarkable, as the authors of the article mention, as it al-
the philosophical value of analysing this mechanism.
What can we learn about the epistemic need to understand Nature, how are
we able to do so; what are our metaphysical presuppositions when approach-
ing the study of nature, and where does this lead in our contemporary society?
The metaphysical presuppositions have been discussed at length; howev-
er we can say more about the epistemic requirements and motivations.
And we point to both Collingwood and Harvard Professor Irad Kimhi
to give us a satisfying explanation of this. In Thinking and Being, Profes-
Parmenidean conundrum of the thought and the thinker being intrinsically
8
9
.
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linked as the category of thought can only be a category for the thinker.
10
And we would do well to recall Sense II that Collingwood proposes. The
actual computation and usage of a machine to determine relative positions
that this anthropocentrism might have to do with some utilitarian means to
brings up a radical question or rather, series of questions. They’re radical inas-
much as it can only be answered by speculation, one that must bridge almost
of the Antikythera Mechanism? Well, to study the cosmos. Yes, to what pur-
pose? What was in store for the designer of the Antikythera Mechanism?
Why go to such lengths to put together such a complex machine that involved
studying all the ancient cosmological theories and charts and piecing togeth-
er mathematical principles from logical views of the natural world?
Perhaps Collingwood wasn’t wrong in ascribing not only an anthropocen-
tric view in the study of nature –ultimately, man can only ever view nature
from his perspective and mental state– but also in its utilitarian sense. To be
able to understand the movement of the cosmos would grant the wielder a
power that was quite terrible. Indeed, that of being able to establish not only
astrological data that was important for the religious and social life of a soci-
reaping and sowing of harvests.
festivals tied into the seasonal changes are the bloodline of civilisation. The
cosmos thus becomes an icon or iconographic representation of our own vo-
litions. And not because as humans we are able to control planetary motion
in any way, shape or form. Rather, that in understanding the structure of the
cosmos that surrounds us, we can make use of that cosmos to our advan-
tage, to pursue the ultimate Aristotelian goal in life: happiness. Now, it
is not our intention to leap into an ethical conclusion, nor do we think it is
the scope of this piece. Rather, we wish to show how an understanding of the
physical and metaphysical principles of the cosmos is both an epistemic and
moral activity for man. Ultimately, knowing when to reap and sow will pro-
vide sustenance for the anthropocentric gods and for ourselves, so there is
always a utilitarian bend on things. Seeing the cosmos as an icon, or as The-
10
, I., Thinking and being (1
st
2018, p. 14.
29
A critical reection on the Antikythera Mechanism from an idealist perspective and its
implications on thechnological development as a means of understanding our Cosmos
as a wheel within a wheel, takes us to the ultimate question on the nature of
-
mos? Saint Maximos tells us that the universe has a multiplicity of parts and
places that share in a single substance. In trying to understand this is that we
see causality as a priori to the cosmos, allowing for us to intervene and derive
principles from it.
And this leads us to analysing the implications on technological devel-
wonder, especially in the art of observing the cosmos. We no longer need
the Antikythera Mechanism to help us estimate planetary positions: we have
Hubble, Cassini, Huygens, Voyagers 1 and 2, New Horizons; we have SETI
and the International Space Station; and now we even have eyes and ears on
Mars with Perseverance and Zhurong.
Firstly, we must poise the question about the Third Sense of causation in
nature. Is the Greek Cosmos, our Solar System –now augmented with Ura-
nus, Neptune, Pluto, and most recently the recognition of Ceres as a dwarf
planet
11
– still operating dynamically under no conditions without which it
wouldn’t? To put it more bluntly, does our Solar System function without
us? As philosophers trying to unravel not only the substance of the natural
world but also the minds that wish to comprehend it, we must not be coy in
seeing a transition of Astronomy from being a purely theoretical science to an
applied one in Collingwood’s sense. Ever more we are not only seeking to
understand the planetary bodies that surround us but are claiming them by
human will for human gain under a human lens. Perseverance and Zhurong
-
pability of Martian soil and atmosphere; the Israeli Beresheet lander was there
to test Lunar minerals that might work towards cleaner energy on Earth;
the Parker Solar Probe was designed to study radio-magnetic interference
-
communications. We have here a most interesting transition from seeing
the cosmos as an icon of an ontological reality to an icon of our own needs.
In that sense, we have become the primary looker towards the secondary
place that Theodore was so concerned was a purely metaphysical exercise.
In doing so, we are learning to manipulate the cosmos as we manipulate
lens, we see a most noble avocation in seeking to understand the immensity
11
.
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but rather, a historical reality that shifts according to human needs. And hu-
mans need to comprehend the cosmos in such a way that it may become an
asset, and no longer a vast expanse of mathematical wonder.
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