Imagining the Universe 1
Dirk L. Couprie and Heleen J. Pott
Anyone
who has visited Greece will remember how the ancient temples were flooded with
sunlight. Many will also have admired the play of light and shadow
caused by the rows of columns, or have noticed the subtle movements of
the sunlight on the flutes of a single column. These phenomena have inspired
the German author Hans Kauffmann to argue that the fluted columns of Greek
temples function as a kind of sundial. His photographs of columns, in different
seasons and at different hours of the day, are fascinating. It reminds him of Anaximander, who is said to have introduced the gnomon and
to have erected one in Sparta. We can readily imagine Anaximander
and the architects discussing columns and gnomons, or Anaximander
teaching them how to construct their columns as useful sundials. As Kauffmann
puts it, speaking about Anaximander and Pythagoras: 'Könnten sie Baukünstlern
zur Seite gestanden haben, womöglich Wegbereiter gewesen sein, gerade
auch dafür, Zeitliches in Maj3 und Zahl am Bau einzufangen?' 2 In
a sense, Kauffmann is Robert Hahn's predecessor in connecting Anaximander and the architects of the tempIes.
However, as we will see, Hahn looks elsewhere for relations between Anaximander and the architects.
As Hahn himself remarks in the first sentence, Anaximander
and the Architects is unquestionably a most unusual book. Pretending to be
a philosophical monograph, roughly half of the text is concemed
with ancient architecture and the problems of temple building, such as erecting
columns by piling up column-drums. The book contains almost nothing about what
most literature on Anaximander usually recognizes as
the two principal items, viz. the apeiron and
the one existing fragment. Were it not
for his enthusiastic way of writing, Hahn would be at great pains to
keep the philosophical reader on a path that seems to lead so far from his
usual concern7s. However, the reader' s efforts will not be in vain, for Hahn's
original approach to the dawn of presocratic
philosophy offers much to think about and to argue with.
The emergence of philosophy, Hahn maintains, has been inspired by applied
geometry as used by the architects who built the temples in the neighborhood of Miletus. By
'applied geometry' Hahn means such things as drawing circles in order to
determine the center of a columndrum,
the use of simple ratios for the dimensions of a temple, and making scale
models. Consequently, Hahn focuses on Anaximander's
achievements in astronomy and geography, being the fields where he .allegedly
applied geometrical techniques. As an example of Anaximander's
'applied geometry', Hahn treats his use of the seasonal sundial which should
have allowed him to construct terrestrial cartography. Hahn reproduces a
sundial, discovered by Hunt, which is databIe to the
second century BC. It is a device with a horizontal gnomon, on a wall bearing
indications of the tropics and the equinox. Apart from the fact that Anaximander's gnomon presumably has been a vertical rod,
this exemplar is rather instructive. Anaximander,
Hahn argues, must have used his sundial in order to mark out the frame of his
earthly map. That is, his sundial allowed Anaximander
to mark out the limits of the earth (p.206).
What can be.meant by these words 'frame' and
'limits'? The earth, according to Anaximander, is
circular, its limits being fixed by the encircling Ocean (see Hahn's
reconstruction of it on top of a columndrum on p.
210). Obviously, a sundial is of little help in defining this shape and these
limits. In a footnote (p.285), however, Hahn assures that Anaximander
is credited,not with a map ofthe
earth (ge), but with a map of the inhabited part of the earth (oikoumene). Hahn's quotation of Aristotle' s
construction in Meteorologica 363b1-1l
points to a possible understanding of what can be meant. If we imagine an observer
in Delphi, the center of the circular earth, we can
draw an equinoctial east-west line (i.e., a line from equinoctial sunrise to
equinoctial sunset) through Delphi to the limits of the earth in the Ocean.
This line, which divides the circular surface of the earth into two equal
halves; approximately crosses
Pivotal in Hahn' s book is the notion that Anaximander
not only made the first geographical map of the earth, but also a map or model
of the cosmos. Hahn takes this to mean a plan or aerial view of the cosmos,
such as drawn by Diels. As regards a
three-dimensional model, Hahn is more reticent. He avoids to say that Anaximander made or drew such a model, but
states only that he imagined it (p.211). A short commentary on the
available doxographical evidence would not have been
out of place here. No testimony exists that Anaximander
made a map or plan view of the universe. The only evidence is Diogenes Laërtius, who credits Anaximander
with the construction of a sphaira. This
word is usually translated by 'celestial globe'. Diogenes Laërtius,
being confused about the shape of Anaximander's
earth, savs that it is sphairoeides.
Therefore, onr might wonder if by sphaira he did not simply mean a terrestrial
globe. Terrestrial globes (spherical maps of the earth), however, are of a
much later date. The earliest globes of the earth date from the time of Columbus' discovery of America.3 So Diogenes
must have meant a celestial globe. But
now the question rises whether he did mean a globe on which the celestial
constellations were depicted, or a model in the sense of a so-called armillary
sphere. A globe depicting the celestial constellations would not fulfill Hahn' s requirements. On the other hand, the
attribution of a spherical model to Anaximander is an
anachronism, as Hahn rightly remarks (p.216).
Notwithstanding these meager results of the doxographical evidence, sufficient circumstantial evidence
allows us to suppose that Anaximander drew a map or
aerial view of his universe. One obvious way of reading the numbers he
attributed to the celestial bodies is to consider them as instructions for
drawing such a map. The instruction, then, reads somehow like this: “take a
compass and draw a little circle; this is the earth. Call its diameter 1 unit.
Now leave one of the legs of the compass
in the center, put the other leg at a distance of
nine units and draw a circle; this is the inner rim of the star wheel. Now put
the same leg of the compass at 10 units and draw a circle; this is the outer
rim of the star wheel, etc., etc.” This is also the way Hahn seems to look at
it, for he says, speaking about Anaximander' s
numbers:' Anaximander wrote the cosmie
syngraphe and then by means of a compass made an informal
drawing' (p.187). The resulting plan view is also, as Hahn rightly notes
(p.200), the visualization of Anaximander's argument
for the earth's stability: the earth stays in the center
of the universe because of its “equal distance from everything”, as Hippolytus reports, or because it is “equally related to the extremes”, as
Aristotle puts it.
On the other hand, no such circumstantial evidence exists whieh would indicate that Anaximander
made a three-dimensional model of the cosmos as weIl.
Hahn rightly argues that Anaximander' s universe is
not spherical, but cylindrical, and he agrees that this can be best visualized
by a kind of oblique aerial perspective, that is, seen slightly from above, as
in the picture on pp. 217 and 218. It has to be in oblique aerial perspective
('”an axonometric projection, a kind of oblique drawing'”, 216) in order to be
clear, because an elevation view of those cylinders would only show a set of
rectangles. If one imagines oneself looking from above into this set of virtual
cylinders, the plan view of Anaximander's universe
results. One glance thrown at this picture demonstrates that it is very
doubtful whether Anaximander either made a drawing in
perspective or construed a model with rings that exhibit two different movements,
one turning around an axis and another sliding up and down that axis.
Nevertheless, the picture is a correct representation of the movements of the
celestial bodies as seen by someone who thinks, like Al1aximander, that the
earth is flat and that the celestial bodies are like chariot wheels. We might
say that this is the way Anaximander must have
imagined the cosmos, without implying that he actually made such a model or
drawing. Perhaps it is permitted to point out two misprints in the drawings: 1)
where it says 'virtual earth', one has to read 'earth', and 2) the arrowed line
with the figure 57° next to it has to be somewhat longer so as to match the
height of the virtual cylinder of the up and down movements of the moon wheel.
(Here is the picture from Hahn’ s book)
Evidently, the starting-point of Hahn's considerations has been the doxographical report that Anaximander
imagined the shape of the earth to be cylindrical, like a column-drum. Here,
too, the doxographical evidence might have deserved
more attention than the footnotes on pp. 278-279. Diogenes Laërtius'
report that the shape of Anaximander's earth is
spherical is commonly regarded as mistaken. In fact, the image of a column-drum
is the interpretative result, subscribed by most authors, of a combination of
three, rather corrupted, texts. In two of them, the shape of the earth is said
to be like a column of stone, and in the third it is said to be cylindrical,
its depth being one third of its width (or, according to some: its width being
one third of its depth).4 Some scholars have wondered why Anaximander chose this strange shape. The strangeness
disappears, however, when we realize that Anaximander
thought that the earth was flat and circular, as suggested by the horizon. For
one who thinks, as Anaximander did, that the earth
floats unsupported in the center of the universe, the
cylinder-shape lies at hand. Hahn has to be credited for being the first who
takes this image of the column-drum worthy of a special study. He had to cope,
however, with two handicaps. The first is that in the literature on Greek
temples very little can be found on the height of column-drums, in
contradistinction to the length and diameter of the columns. The second
handicap is that so little is left of the temples of Anaximander's
time that many things, such as the length of the columns, have to be guessed or
reconstructed. Hahn' s question is whether the image of a column-drum has a
more than casual meaning. He argues that the use of this image is not
incidental. Anaximander, just like his
fellow-citizens, must have been impressed by the accomplishments of the
architects who built the first big Greek temples in his backyard. Hahn shows
that both philosophers like Thales and Anaximander, and architects like Theodorus,
Rhoikos, Chersiphron, and Metagenes are credited with the same kind of achievements
in applied geometry and with writing a book in prose. Architects and
philosophers were, we could say, fellow intellectuaIs.
Hahn also shows convincingly that the upper side of a column-drum, which has
been elaborated with the techniques of anathyrosis
and empolion (both meant to ensure
that one drum is exactly on top of the other), reveals a striking resemblance
with the plan view of Anaximander' s universe. The
portion of the drum inside the smoothly carved circumference ring (the result
of anathyrosis) is chiseled
out, making the interior surface concave. This observation entails an elegant
confirmation of DieIs' reading guron
('curved', i.e., concave) instead of hugron
('moist') in Hippolytus' testimony on the form of
the earth(p.196-7).5 However, the difficulty remains how to combine
the concepts of a concave earth and an encircling Ocean.
As the doxography has handed down the measures
that Anaximander assigned to the column-drum-like
earth, its diameter being three times its height, Hahn wonders what the meaning
of these dimensions could be. It is no coincidence, he argues, that Anaximander chose the 3 : 1 column-drum, for “the
column-drums at the archaic Heraion, Artemision, and Didymaion were
roughly 3: l'” (p.188). According to Hahn, “drums less than 3: 1 (...) seemed
to pose a problem, as their rarity shows' (p.147). Something seems to be wrong
here. Most of the columns of still existing temples show ratios ranging,
roughly, from1 : 1 to 3 : I, with an average of approximately 2 : 1.6
Still upright standing columns of the Didymaion (±300
BC), the height of which is 9 to 10 times the diiameter
of the lower drums, count 18 column-drums, which results in an average ratio
between diameter and height of the drums of 2 : 1. Reuther
gives the exact measures of the eleven column-drums of the one remaining
upright column of the Heraion IV (4th century BC).7
They result in ratios from 1.6 : 1 (the
lowermost drum) to 2.5 : 1 (the second drum from top). As the upper half of the
column is missing, one may suppose that the ratio went up to 3.5 : 1. It is
hard to believe that in the archaic temples these dimensions were very
different.8 Hahn himself shows how much painstaking work, such as
the chiseling of the anathyrosis,
has to be done in order to make a column-drum fit precisely. The smaller
the height of the drums, the more drums were needed for a column, so that
assembling higher drums must have meant a timesaving procedure. It is also
understandable that the upper drums were the smaller ones, because they had to
be lifted to a height of 15 meters and more. The drums with ratios 3.4 : 1 and
3.9 : I, which Hahn shows (pp.156 and 158), must have been from the upper part
of a column. Our conclusion is that no connection exists between the
dimensions of Anaximan:ier' s earth and those of the
average column-drum.
Hahn joins the authors who champion the view that Anaximander
chose the number 3 as a starting-point for the series 9, 18, 27, which denote
the distances of the celestial bodies, measured in multiples of earth-diameters.
Just like the architects, who modeled their temples
according to a definite unit, Anaximander made the
diameter of the column-drum-shaped earth
the central module of his universe (see, e.g., pp. 148 and 187). The celestial
wheels are each 1 module wide and at 9 (lx3x3), 18 (2x3x3) and 27 (3x3x3)
modules distance from the earth. Hahn suggests that 9, the first number of this
series, has also an architectural basis, and was related to the dimensions of
the archaic Ionian column. As there is no complete column left, he has to
appeal to reconstructions. These, however, are far from unanimous. As quoted by
Hahn himself (p.145-6), the estimations of the relation of the archaic columnheight to the lower diameter range from 6.4 : 1 (Hogarth), via 8 : 1
(Wesenberg), 8.2 : 1 (Gruben),9
: 1 (Vtruvius), and 10 : 1 (Reuther), to 12.7 : 1 (Gruben and Kirschen), and even
13.3 : 1 (Gruben). Some authors admit that no
conclusions can be drawn as to the length of the columns of archaic temples.9
To appeal, then, to a proportion of roughly 9 : 1 looks like pressing the data
within the frame of a preconceived idea.
Column-drums, Hahn' s argument continues, make up a column, and the
columns of a temple had a cosmic significance, as they divide the earth from
the heaven. 'Anaximander imagined the cosmos to be a
kind of temple, the cosmic house, along the analogy of the cosmic meaning of
the column' (p.188). Just like the architects, Anaximander
took a simple kind of ratio (1 : 2 : 3) in order to measure the distances of
the celestial bodies. In this way, Hahn pretends to have found a solution for
the problem of Anaximander' s numbers, which is not
only elegant, but also allows for a new interpretation of his cosmology as the syngraphe of the cosmic temple. Anaximander applied, says Hahn, the architect's rule of
proportion to cosmic architecture. He was a kind of architectural historian of
the built cosmos (p.9). However, both the mistake regarding the ratios of the
column-drums and the inaccuracy about the proportion of the column height are
like thorns in the flesh of this interpretation.
Anaximander makes use,
Hahn says, of “the same kind of simple ratios that characterize the overall
structure of the archaic temple'” (p.187-8). The ratios used by Anaximander may be simple (3 : 1 for the diameter and the
height of the earth, and 1 : 2 : 3 for the distances of the celestial bodies),
but they are different from the simple ratio 1 : 2 : 4 used by the architects
(for the height, the width, and the length of a temple, see pictures on p. 78).
Presumably, Hahn would defend himself by saying that Anaximander
did not copy the architects slavishly, but let himself be inspired by their
work (cf. pp. 10, 148). This does, however, not look like a convincing way to
justify a theory. But there is more. Hahn suggests that Anaximander
chose the column-drum as the shape of the earth, because the column of a temple
symbolically separates, or connects, heaven and earth, just like the cosmic
axis (p.87-8, 188). Against this suggestion speaks the fact that the cosmic
axis is inclined to the surface of the column-drum-shaped earth, as can be seen
on the pictures on pp. 217-18. This inclination, which is a topic of discussion
in presocratic philosophy, amounts to 380 (according to the latitude of
Let us also look somewhat closer at the image itself of the cosmos as a
temple. The temples of the architects were rectangular, with a triangular roof.
The would-be cosmic temple, on the contrary, is cylindrical and made up of
wheels. The contrast could. not be bigger. Moreover, there is a metaphysical
argument against this interpretation. The temple is certainly meant as a kind
of house for the god or gods. It is true that we are filled with awe by its
bigness. But the very intention of a temple is also to transfer or guarantee a
feeling of safety. Just as the human house offers a haven of safety within a
hostile world, so the house of the god yields a safe place to mankind.
Transposed to the image of the universe in a metaphysical sense, the world of
Homer, with the celestial dome covering the flat earth (see p. 171) can be seen
as a cosmic refuge, in which people can feel safe against the surrounding
Chaos. But it has been precisely Anaximander who
broke with this idea of the universe as a safe and dosed space. He blew up the
celestial dome and imagined the celestial bodies as being behind each other,
and he assumed that the earth was hanging free in space, which immediatelv must have evoked the fear of falling in the
minds of his audience, as his attempt to prove that there was no need for such
a fear demonstrates.
Hahn certainly has a point in emphasizing the influence of the
architects on Anaximander's astronomy. However, he
seems to have been taken away by his enthusiasm when he asks us to look upon Anaximander's cosmos as a kind of temple, and at his
astronomy as a kind of celestial architecture. He reads too much into the image
of the column-drum. In a similar way, one who is impressed by Anaximander's image of the celestial bodies as
chariot-wheels could be tempted to imagine his universe as a celestial chariot
(like that by which Apollo transports the sun), or perhaps as a celestial
machinery. Or someone who thinks that the expression presteros
aulos should be translated by 'the nozzle of a
bellows', could be eager to look upon Anaximander's
universe as a celestial blacksmith's shop, like Hephaistus'
forge in the Hades, or as a blowing and breathing organism. Anaximander,
who wrote a rather poetical prose, as Simplicius
tells us, seems to have been fond of all kinds of images and from different
fields: architecture (column-drum), war-equipment (chariot wheels), flora (the
bark of a tree), weather phenomena (the light of the celestial bodies compared
with lightning fire), and jurisdiction (in fragment B1). We may wonder whether
a better understanding of Anaximander is fostered by absolutizing one of these images.
If, then, Anaximander did not have the
intention to look upon the cosmos as a kind of temple, the question remains
what the meaning of the numbers he assigned lo the distances of the celestial
bodies could be. By maintaining that Anaximander' s way of thinking was a kind of applied geometry Hahn
follows, generally speaking, authors like Charles Kahn, who have likewise
emphasized that Anaximander provided a vision of the
universe whose organization is revealed by geometry. The
device of this vision is: '”he universe has an order, mortals can come to know
it'” (p.163). Anaximander's achievement is thought to
have been the “geometrization of the cosmos” (p.32).
The difficulty of this kind of interpretation is that Anaximander
obviously did not get his numbers by any kind of observation or measurement.
That the celestial bodies are behind each other is not something we can see,
let alone that these distances could have been measured in Anaximander's
time. The question is not, as Kahn, quoted by Hahn, thinks, that 'the celestial
dimensions given by Anaximander cannot have been
based upon any kind of accurate observation' (p.273, our emphasis). Anaximander's numbers are not based on observation at all.
They are of a completely different order.
If we want to understand the real meaning of Anaximander' s numbers, we
have to look elsewhere. As Hahn kindly quotes (p.173-4, 181 and note 73 to that
chapter), another, and simple, explanation of the numbers is possible. In the
Greek counting system, 9 (= 3 x 3) connoted great age, time, or multitude. So Anaximander's numbers, denoting the distances to the wheels
of the celestial bodies, are readily interpreted as meaning that the stars are
far away (at a distance of 9 = 1 x 3 x 3 earth diameters), that the moon is
even farther away (18 = 2 x 3 x 3), and that the sun is farthest away (27 = 3 x
3 x 3). This interpretation of Anaximander's numbers
has the advantage that it reveals the heart of his astronomical insights.
Whereas the observational astronomy of the Babylonians was enacted, so to
speak, on the two-dimensional screen of the firmament, where the movements of
sun, moon, and planets among the celestial constellations were observed, Anaximander put forward the conception of a three-dimensional
universe, a universe with depth, in which the celestial bodies lie behind each
other. The numbers 9, 18, 27, meaning 'far, farther, farthest', were his way of
expressing his 'discovery of space' in a way which his fellow citizens were
able to understand. Anaximander's new conception of
the cosmos is not an observational achievement, let alone an achievement of
applied geometry. Anaximander made use of
mathematical notions (numbers) and equipment (compass) in order to explain and
visualize this new conception. But this does not mean that the numbers are
meant as a kind of pseudo-mathematical expression of measured distances.
One main intention of Hahn's book is to serve as a reminder that
philosophical activity does not originate ex nihilo,
but is embedded in a social and political framework. He sharpens this
thesis by characterizing Anaximander asa transitional thinker: “Our grasp of originality,
not ex nihilo, required that we see innovation
in the context of transition (p.19). By this he seems to mean that Anaximander was not yet able of making adequate
observations and experiments, nor capable of using
adequate (astronomical) instruments and theories. As Hahn
puts itt: “Anaximander was
reaching out toward a structural explanation of the cosmos in an age that had
only the vaguest conception of it” (p.2). Anaximander' s cosmology is
said to mark “a transitional stage to succeeding centuries, in which
observation and experiment come to play a more pivotal role in astronomical
theories'”(p.2). This kind of interpretation is in danger of missing completely
the point of Anaximander's achievement. Long before Anaximander, observation formed the very heart of astronomy
The Babylonians, and to a lesser extent, the Egyptians, were excellent
observers.10 Ptolemy, in the second century AD, used systematic
Babylonian records of the movements of sun, moon, and planets, going back to
the time of Nabonassar (747 BC), just because of
their accuracy. The striking fact about Anaximander's
astronomy, on the contrary, is that it is not observational astronomy,
although it does not contradict the observed facts. To call Anaximander
a transitional figure amounts to measuripg his
achievements by our own standards, as if he did the same kind of things as we
do, but in a more primitive or rudimentary way (see, e.g., p. 164). Of course
we must realize that Anaximander's innovations did not
develop ex nihilo, and Hahn certainly adds a
new component to the picture of his cultural setting, but by characterizing a
thinker who stands at the very beginning of Western science and philosophy as a
transitional figure, is giving him too few credits. We can express Anaximander's originality more adequately by saying that he
conceived a new paradigm of thinking. Conceiving a new paradigm is not
a matter of observing, or measuring, or using primitive applied geometry, but
a matter of using the imagination.11 Sometimes, Hahn
seems to hint at such an interpretation, e.g., when he says that Anaximander's '”magination drew
upon architectural techniques” (p.10, our emphasis), or that “Anaximander imagined
the cosmos from more than one viewpoint” (p.215, our emphasis). We may gain
more insight in the real meaning of Anaximander's
achievements by acknowledging that we would not be able to conceive the
universe the way we do, if he had not introduced this new paradigm. Anaximander no longer considered the heaven as a celestial
dome like in a planetarium. He introduced the conception of a universe with
depth, in which the celestial bodies make full cirdes,
the earth floats unsupported in space, and the celestial bodies are behind each
other. This completely new set of ideas is unique and unlike any
vision of the cosmos in any other culture. With it, Anaximander
introduced a new paradigm, the paradigm of the western world-picture. Anaximander's achievement is much more important than one
has realized up to now. He has been one of those mental giants who made it
possible to look further, because he allows us to stand upon his shoulders.
As regards the appreciation of the reader, three types of books may be
discerned. Some books repeat, in a more or less inventive way, already known
theories; these are useful but boring books. Other books put forward theories
the reader readily agrees with; these are agreeable but basically also boring.
And there are books that open new perspectives and advocate new theories; these
are the intriguing books that are worth disagreeing with. Hahn'
s Anaximander and the Architects is
such a book.
One final correction: Hahn quotes several times Before Plato: Studies
in Ancient Greek Philosophy VI. Albany: State University of New York Press,
1998. This has to be: A. Preus (ed.), Essays in
Ancient Greek Philosophy VI: Before Plato,
NOTES
1 Review of Robert Hahn, Anaximander
and the Architects: The Contribution of Egyptian and Greek Architectural
Technologies to the Origins of Greek Philosophy. Albany, NY: State University
of New York Press 2001. US$81.50 (cloth: ISBN 0-7914-4793-6); US$27.95 (paper:
ISBN 0-7914-4794-4).
2 H. Kauffmann,
Probleme griechischer
Säulen, Opladen 1976, 28. According
to Kauffmann, this is especially the case with columns that count 24 flutes.
This is a weak point in his hypothesis, as 24-fluted columns are rare.
Moreover, as the play of shadows on the flutes differs from season to season,
this does not seem to be an adequate way to tell the time.
3 The German geographer Martin Behaim constructed
one of the fust terrestrial
globes in 1492
4 See DK
12All (Hippolytus), 12A25 (Aëtius), and 12A10 (Pseudo-Plutarch).
Roller, another predecessor of Hahn's, tends to hold that Anaximander
meant the entire column, and not a single drum (D.W. Roller, 'Columns in Stone:
Ànaximander's Conception of the World’, L’Antiquité Classique
58 [1989] 185-9).
5 Sometimes, Hahn's elucidation of architectural
features is not sufficiently clear. He explains the additional concentric rings
which sometimes appear on drum faces by saying that they were meant as
guidelines in order to be certain of the exact center
of the drum (pp.153-4,
196, 198). How this construction is supposed to work, he does not clarify.
Geometrically speaking, it is the other way round: when we define the center. we are able to draw
concentric circles.
6 According to the construction plan of the
naval arsenal in Peireus by Philon of Eleusis (340
BC), the lower width of the columns has to be 2 feet and 3 spans, and each
column has to contain one 5 feet high drum and six 4 feet high drums, which
results in a ratio of, roughly, 1 : 2 (!) (See R. Martin & H. Stierlin, Griechenland
[Reihe: Architektur der
Welt], Berlin, no date, 42). Hahn quotes part of this prescription on p.
110, but not the part on the columns and column-drums. In the archaic temple at
Assos, the height of the drum is also greater than
its diameter.
7
O. Reuther, Der Heratempel
von Samos (Berlin 1957), 2.13
8 The one remaining drum of the temple in Pherai measures, roughly, 2 : 1.
See E. 0stby, Der dorische
Temple von Pherai (no date, no place), Abb. 16. And two pieces of drums from the archaic Didymaion have ratios of 3.4 : 1
and 2 : 1. See P. Schneider, 'Neue Funde vom archaischen
Apollontempel in Didyma',
in Säule und GebalK:
Diskussionen zur archäologischen Bauforschung,
Band 6 (Mainz am Rhein 1996) 76-83.
9 E.g., W. Schaber, Die
archaischen Tempel der Artemis von Ephesos (Waldsassen-Bayern 1982), 76, and G. Gruben,
'Das archaische Didymaion', Jahrbuch
des Deutschen archäologischen
Instituts 78 (1963), 78-177, at p. 153. One of
the conclusions of a recent study is that looking for 'round' relations between
diameter and length of a column does not correspond to the practice of the
architectural design. These relations have never been the starting-point of the
design. (J.J. de Jong, De
wiskundige grondslagen van de Griekse en Romeinse tempelarchitectuur in theorie
en practijk tussen de 4e en 1e eeeuw
vChr (The Mathematical
Foundations of Greek and Roman Temple Architecture between the 4th and lst Century
BC), dissertation [Leiden 1994], thesis 6). We
have to thank Jan de Jong for his kind information on
some issues regarding the measures of columns and column-drums. which confirmed our own conclusions.
10 Whereas there is an abundancy
of Mesopotarnian astronomical observations preserved
in cuneiform texts, the doxography on Anaximander mentions only one observational accomplishment,
viz. the date the Pleiades set in the morning (DK 12A20). This testimony, by
the way, shows that he was a better observer than Thales
and Hesiodus. Nevertheless, the real meaning of his
astronomical insights lies elsewhere.
11 This imagination is something completely
different from the “wilder flights offancy” of which
Dicks accuses the Ionians (see D.R. Dicks, 'Solstices, Equinoxes, & the Presocratics’, The Journal of Hellenic Studies 80
(1066) 26-40, at p.39.