Subject: Re: [HM] Aristarchus
From: Chris Linton (C.M.Linton@lboro.ac.uk)
Date: Thu Feb 10 2000 - 12:26:36 EST
Subject: Heliocentrism
Kim Plofker wrote
<<
I think, the complex geocentric system of Ptolemy is a much more
remarkable accomplishment than the heliocentric speculations of
Aristarchus.
>>
and Al Barron wrote
<<
Now that's curious opinion. Is this a prevailing view among historians
of mathematics ?
>>
I don't know what the prevailing view is, but I definitely agree with Kim
Plofker.
Aristarchus is credited by Archimedes as having postulated that the earth
is not at the centre of the universe, but that it orbits around the sun.
However, the attribution of a fully-fledged heliocentric theory to
Aristarchus is actually based on extremely scant evidence. Much is made
nowadays of the following passage from Archimedes [Psammites (Sand
Reckoner), translation from Heath, _Greek Astronomy_, Dent & Sons, 1932]:
"But Aristarchus of Samos brought out a book consisting of certain
hypotheses, in which the premises lead to the conclusion that the universe
is many times greater than that now so called. His hypotheses are that the
fixed stars and the sun remain motionless, that the earth revolves about
the sun in the circumference of a circle, the sun lying in the middle of
the orbit, and that the sphere of the fixed stars, situated about the same
centre as the sun, is so great that the circle in which he supposes the
earth to revolve bears such a proportion to the distance of the fixed stars
as the centre of the sphere bears to its surface."
Aristarchus' heliocentric theory is discussed at length in Heath,
_Aristarchus of Samos_, Clarendon Press (1913), but, for example, Wall,
_Studies in History and Philosophy of Science_, vol 6, pp201-228 (1975) is
of the opinion that Heath has made rather too many assumptions and that
there is no evidence that Aristarchus ever wrote a treatise on his
heliocentric hypothesis. Indeed it is very likely that all known references
to Aristarchus' theory are derived from this one remark of Archimedes.
Furthermore, Aristarchus was not the only Greek astronomer to postulate a
moving earth. An alternative cosmology in which the sun, earth and the
other celestial bodies revolved around a central fire had earlier been
suggested by the Pythagorean, Philolaus.
Neither of these speculations is particularly impressive, except that (with
hindsight) we know that Aristarchus (if he did seriously suggest
heliocentrism) made a lucky guess. As Kim Plofker says "there was simply no
good physical reason to assume the counterintuitive proposition that the
earth might be
flying through space".
On the other hand, Ptolemy produced a geometrical system capable of
predicting with tolerable accuracy the future positions of all the heavenly
bodies. The magnitude of this task (as anyone who has tried to read the
_Almagest_ will know) was enormous and his solution ingenious. The fact
that his physical conception of the universe (as he later depicted it in
his _Planetary Hypotheses_) is wrong does not diminish in any way his
achievement.
Copernicus' great achievement was to take the heliocentric idea and
incorporate it into a system of Ptolemaic geometry so that it accurately
predicted the phenomena. This was another significant achievement in that
Copernicus recognized the underlying simplification that this made to the
Ptolemaic structure (though in also removing Ptolemy's equant mechanism,
Copernicus actually produced a scheme with more epicycles rather than
less).
It was not Copernicus' intention to completely revolutionize astronomy,
though his method for increasing accuracy eventually led to just such a
revolution, but he did realize that a major technical change to Ptolemaic
theory was necessary since all the minor changes and alterations that had
been proposed over the preceding thousand or so years had still not
produced a system accurate enough
to conform with good naked eye observations. That Copernicus was not trying to
start a great debate about Man's place in the universe is clear from the fact
that De Revolutionibus is not aimed at the general public or indeed at
educated lay people, but is written only for those few who were fully
conversant with the technical details of Ptolemaic astronomy. That said,
the idea of placing the sun at the centre of the universe rather than the
earth had profound consequences for the future of astronomy, but the
geometrical models that Copernicus devised so as to transport Ptolemy's
mathematical astronomy into a heliocentric context did not.
The end of tha geocentric view of the universe did not come with
Copernicus' work though. Astronomers were quite happy to use the _Prussian
Tables_ based on Copernicus geometrical schemes whilst still adhering to a
geocentric physical world view. The real "revolution" came with Kepler's
_Astronomia Nova_ and the discovery of the phases of Venus through the
invention of the telescope. The latter proved the untenability of the
Ptolemaic system and the former produced such an increase in accuracy
(through the _Rudolphine Tables_) that it could not be ignored. By using
elliptical orbits rather than combinations of circles, Kepler broke free
from all previous mathematical astronomy and produced a system that had no
sensible geocentric counterpart. Tycho Brahe's geoheliocentric system could
not last long when viewed against the accuracy of Kepler's laws of
planetary motion.
It is true that the first real "proof" of the earth's motion came in 1837
with the observation of stellar parallax, but heliocentrism was an
established scientific "fact" long before then.
Chris Linton
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* Department of Mathematical Sciences * Fax: 01509-223969 *
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