Greetings.
I have recently been doing some reading in early 17th century mathematics,
which included what we would now classify as mathematical physics. Some
questions I'd like to know the answers to have to do with the status of
such fields. When did mathematical astronomy become thought of as an
instrumental theory (useful for prediction, but not a theory of what really
happens)? Does this go back to Ptolemy? Earlier? Later? And what about
the other mixed mathematical sciences (optics, mechanics, etc): were they
also viewed in instrumental terms, or was it only astronomy?
Answers or references would be greatly appreciated.
Calvin Jongsma
Dordt College
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Few main references:
(1) Babylonian astronomy was probably oriented toward predictions without
models of the sky. With the words of Neugebauer (A history of ancient
mathematical astronomy):
"Not much before 300 or 400 BC there originated in Mesopotamia arithmetical
methods for very accurate predictions of lunar and planetary phenomena...(2)
...it will reveal us the working of a theoretical astronomy which operates
without any model of a spherical universe, without circular motions and all
the other concepts which seemed a priori necessary for the investigation of
celestial phenomena (348)"
Not very different sentences can be found in J.Needham's "Science and
Civilization in China".
(2) A 'model-driven' approach can instead be found in Greece, since its
beginning. The general framework is the Pythagorean "quadrivium" which sets
out the double connection astronomy-geometry and music-arithmetic.
An extreme "theoretical" approach in Plato despises any attempts of comparing
the theoretical models with the actual data. But this does not seem to be the
general view in greek astronomy (see again in Neugebauer).
More relevant it will be the Aristotelean thesis of the inapplicability of
mathematics to physics because the former concerns with "being" and the
latter with "becoming". Beyond astronomy and music, Greek mathematical
applications included (Euclides, Archimedes) even optics and static.
Model driven approaches were maybe present already in the first Greek
philosophers. But Aristarchus, Eudoxus, Ptolomeus are the main authors who
first employed geometrical models even for predictions (see Neugebauer)
Agronomy, surveying, accounting and architecture will be instead applicative
fields from the first eastern civilzations to the ellenistic and roman ones.
It is relevant that the roman empire, indifferent toward theoretical
disciplines, was very fond of these applications which included however very
little Euclid and rough arithmetic. Vitruvius' "De architectura" shows a
deeper competence both in geometry and astronomy, but probably it was not
very common among Roman intellectuals.
(3) This approach will last even in the Middle Ages: Saint Thomas considered
mathematics useful only in few physical disciplines (the socalled "scientiae
mediae"), and in general did not show great interests toward mathematics.
The situation did not change till the beginning of the debates about the
"intensio et remissio formarum", which began to 'embed' the changes of the
"forms" (which are in Aristotle only qualitative) in an 'extensional' view
(see Clagett's "History of mechanics in the Middle Ages").
I do not know many references about Middle Ages' astronomy. I think it was
largely under the influence of astrological interests, who were framed in
Ptolomeus' theory.
Yours sincerely,
Luigi Borzacchini