Re: Ptolemy's realism
Brian D Harper (bharper@postbox.acs.ohio-state.edu)
Wed, 21 Oct 1998 18:33:24 -0400
At 04:23 PM 10/21/98 -0400, Ted wrote:
>Howard Van Till writes, in response to Al McCarrick:
>
>Some years ago I participated in a summer seminar at Yale on "The
>Mathematical Sciences in Antiquity," with Prof. Asger Aaboe. If my memory
>serves me correctly, he spoke about Ptolemy's late writing moving in the
>direction of treating his geocentric picture as a representation of reality,
>complete with specific values for the various circle radii and including the
>requirement that no two planetary domains would overlap,
>thereby excluding the possiibiility of collisions, etc.
>
>Sorry, but I have no references handy at the moment.
>
>YES, this is accurate. The relevant reference here is probably an article
>by Bernie Goldstein, "The Arabic Version of Ptolemy's Planetary Syntaxis,"
>Trans. Amer. Phil. Soc. 57 (4), 1967, pp. 1-12. Ptolemy assumed
>(apparently) the reality of spheres corresponding to the mathematical
>devices he employed to explain the details of planetary appearances. He
>assumed, eg., that the minimum distance of Jupiter equalled the maximum
>distance of Mars, from the earth of course, as required by his
>epicycle/deferent theory. No interplanetary voids were allowed. He ends up
>getting about 20,000 earth radii to the stellar sphere. In modern numbers
>(the exact value for the radius of the earth in the ancient world was never
>certain) this would be 80M miles, giving the size of the universe ("world")
>as 160M miles in diameter. Not large by modern standards, but enormous by
>human standards, as he realized. One appreciate even more his statement
>(elsewhere) that the earth is an insigificant speck, which fact (among
>others) gives the lie to the modern myth that Copernicus "degraded" us by
>moving us out of the world's center, a claim I cannot support from
>historical sources.
This is very interesting, I hope you won't mind if I
ask a few questions. I was generally under the
impression that at this time mathematics (in general)
was not thought to have any reflection on reality and
further that the statement from Al would apply, in
the views of most people, equally well to Copernicus
as it did to Ptolemy. IOW, many Copernicans also
viewed their system as a calculator and not necessarily
a suggestion that the Earth really moved. To muddy the
waters further, the general notion that the Copernican
system was simpler is not really so easy to justify. To
"save the appearances", Copernicus also needed epicycles.
It also does not seem to be the case, as Al suggested, that
the Church was blessing the Ptolemaic system as a "picture
of the real world." Consider this extract from a letter
written by Cardinal Bellarmine:
=======begin================================
It seems to me that your Reverence and Signor Galileo act
prudently when you content yourselves with speaking
hypothetically and not absolutely... To say that on the
supposition of the Earth's movement and the Sun's quiescence
all the celestial appearances are explained better than by
the theory of eccentrics and epicycles is to speak with
excellent good sense and to run no risk whatsoever. Such
a manner of speaking is enough for a mathematician. ...
========end==================================
And finally, I was under the impression that the fixity of the
Earth was not based upon Ptolemaic astronomy but rather
on Aristotlean physics.
Brian Harper
Associate Professor
Applied Mechanics
The Ohio State University
"It appears to me that this author is asking
much less than what you are refusing to answer"
-- Galileo (as Simplicio in _The Dialogue_)