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Summary: The
ubiquitous concept of the universe, in which mankind could feel safe, is that of a flat earth with the cupola of the
celestial vault above it. The Presocratics replaced this world-picture
by that of a free floating earth, surrounded by celestial bodies at different
distances. No other culture has ever conceived this world-picture,
to which we are so accustomed. The different outcomes of the same
experiment by Eratosthenes (who believed in a spherical earth) and Chinese
astronomers, (who believed that the earth was flat) illustrate these two
world-pictures. The price which the ancient Greeks had to pay for their
paradigm shift was that they had to cope with the fear of falling: why does the
unsupported earth not fall, why do we not fall off the
earth, why do the celestial bodies not fall upon the earth? They even envisaged
the possibility of an infinite universe. The existential question behind this
discussion was: how can mankind feel safe again within
this new conception of the universe. Aristotle settled the battle among the
Presocratics with metaphysical rather than empirical arguments. His theory of
natural motion, which takes falling not as the problem
but as the solution, furnishes the answer to three main questions: why does the
earth not fall, what is the earth’s place in the universe, and what is the
shape of the earth. The theory also explains why we do not
fall off the earth, and why the celestial bodies do not fall upon the earth.
Moreover, Aristotle closed the universe again by arguing that it is finite. In
this way he could for many ages to come suppress the fear of falling. In a
recent study, O’Grady shows little understanding for this discussion, as she
holds that already Thales should have taught the sphericity of the earth. In
order to achieve this, he should have used arguments which are known only since
Aristotle. O’Grady’s theory is a typical example of the anachronistic fallacy
in interpreting the Presocratics. In the sixteenth and seventeenth centuries
A.D., by the work of Copernicus, Kepler and Digges, three pillars of
Aristotle’s building were pulled down: the earth is no longer the center of the
universe, the planets move in ellipses and not in
circles, and the universe is considered as infinite. The new conception of the
world which resulted from these mortal blows renewed the fear of falling.
Newton’s gravitational laws tried to remove this fear
of falling again. However, as is shown by questions asked by Bentley, Newton
was not able to remove this fear completely. Pascal
has uniquely expressed the existential fear of falling of modern man within
this newly conceived universe. The history of our civilization in the light of
this fear of falling still has to be written.
This picture, called "Ubermensch" (sic) is of a sculpture by Jake and Dinos Chapman. It shows Stephan Hawking, who plays a certain role in the article, sitting in his electric chair on the top of a rock. The image is representative for the title of our article.
·
"’Hatte die Welt ein
Ziel, […] so wäre es […] mit allem Werden längst zu Ende’. Ein Beitrag zur
Geschichte einer Argumentation”, in: Nietzsche-Studien 27.1998(1999),
pp.107-118.
For the full text of the article (in German) click here
· “How Thales Was Able
to "Predict" a Solar Eclipse without the Help of Alleged Babylonian
Wisdom”, in: Early Science and Medicine 2004, vol. 9/4, p.321-337.
Summary: The first part of this article examines Patricia O’Grady’s
recent attempt to identify the method by which Thales might have successfully
predicted a solar eclipse. According to O’Grady, some 60% of the potentially
visible lunar eclipses were followed 23½ months later by potentially visible
solar eclipses. It is shown that this ratio is no more than 23%, and that the
method fails to predict after which specific lunar eclipse a solar eclipse will
appear. In the second half of the article it is argued that
on the basis of his own observations of major solar eclipses, Thales could have
concluded that solar eclipses come in clusters of three, the second appearing
17 or 18 months, and the third 35 months, after the first one. In the
years after the “predicted” eclipse of 28 May 585 BC, this apparent pattern disappeared
again, which would explain why Thales managed to “predict” no further eclipse.
This is, approximately, what Thales saw on May
25, 585 B.C.
Summary: Plutarch, Hippolytus, and Diogenes Laërtius
report that Anaxagoras compared the size of the sun
with the Peloponnesus. It is the aim of this article to show that Anaxagoras
was not mad when he said this, but that it was a fair
estimate, from his point of view, which is that of a flat earth. More precisely, it is shown that, with the instruments (gnomon,
clepsydra, sighting tube) and with the geometrical knowledge (the properties of
similar triangles, simple equations, Pythagoras’ theorem) available, Anaxagoras
must have been able to use the procedures and perform the calculations needed
to obtain approximately his result.
This is one
of the pictures from the article: Sunset at San Diego.
Summary: Both
the doxography on the tilting of the celestial axis in Presocratic cosmology
and its reception in recent times are full of misunderstandings. This is due to
the fact that ancient authors and modern scholars alike did not
distinguish clear enough between the phenomena as seen by someone who thinks
that the earth is flat and someone who knows that the earth is spherical. The
article tries to disentangle the ways in which the phenomenon of the tilted
axis of the heavens has been misrepresented and misinterpreted. It is argued
that the Presocratics, including Leucippus and Democritus, taught a tilting of
(the axis of) the heavens, and that the accounts on a dip of the earth
are mistaken. The direction of this tilt of the celestial axis must be thought
to the north, not to the south, and downwards, not
upwards. This tilting of the celestial axis was not
meant as an explanation for the obliquity of the ecliptic.