Friday, July 17, 2009
More Keplerian ruminations - math and nature
Kepler remarks in his Astronomia Nova that he had considered applying the ellipse too simple a solution for earlier astronomers to have overlooked. It is an interesting problem. Did it really never occur to anyone before Kepler to describe the orbit of planets as ellipses? If that is true, then why? None of the major theories of planetary motion devised before 1600 I've reviewed uses ellipses instead of circles to describe orbits; though that doesn't mean none exists. It seems as though the assumption from Aristotle and possibly before is that the celestial bodies must move in circular orbits (whether perfectly or also in epicycles). Why? The math of the conic sections was known since ancient times and developed throughout medieval times in the Arab-speaking world. Why not apply it to the celestial motions?
I don't know the answer to this question, but I think there are three common and wrong answers. The first is that it is the fault of tradition (Aristotle and/or religion). The second is that it contracted immediate experience, to which all ancient and medieval thought was wed. And underlying both these assumptions is a third, namely, that people weren't free to imagine outside the confines of tradition or immediate experience until Copernicus, Galileo, Kepler, et al came along to liberate them, thanks be to their courage to stand up against arbitrary authority.
The mere force of Aristotle, "the tradition", Christianity, Islam, or anything else is too ridiculous to contemplate as an answer to this question. Every single aspect of Aristotlean physics and metaphysics was attacked viciously throughout the middle ages. It's useful to note that the most thoroughgoing criticism took place in the Islamic world, which was in many respects far more tolerant than the Christian world in the era following the collapse of the Roman empire. By the time Galileo and Kepler came on the scene, Avicenna had dismantled Aristotlean physics, metaphysics, and logic, and al-Haytham had already formulated a modern mechanics. In western Europe, Philoponus and Hasdai Crescas had undone Aristotle's concept of "place", and Buridan had already created a forerunner to the concept of inertia. So it's not as though "the tradition" had such a grip on people that alternatives weren't possible.
As for contradicting experience, scientists at Maragheh had already empirically and mathematically proved the motion and axial tilt of the earth by the 13th century, perhaps the most important leap beyond "immediate" experience mankind has ever made. And even the ancient Greek philosophers understood themselves as going beyond experience. What else could be assumed when Thales says "all is water"? It evidently isn't (to the senses), and yet it is. And what else is the trial of Socrates about than the contradiction between who Socrates appears to be and who he is? The idea that the ancients held some kind of naive view of the world is shallow. Things were far more complex than that.
So then why hadn't anyone previously considered that the ellipse might describe the motion of the celestial bodies? It's not because Aristotle said they were circles. It's not because when you look up, things appear to move in circular orbits. What then?
I'm not entirely sure, but I think it has something to do with how people understood the relationship between mathematics and nature generally. Mechanics (a purely mathematical and empirical understanding of motion) only because to become a science in its own right in the 13th century. Before that it was blended imperceptibly into "physics", which was the philosophy of nature. I think in order to apply the conical sections on to observed motion, you first have to be able to "see" nature in the right way. You have to be able to see it as an abstract, geometrical object.
(But, one might object, what else is the application of the epicycles and the equants in the Ptolemaic theory than a free (a too free!) application of geometry to the observed data? I don't know. Is it because Ptolemy and those following him believed the earth to be stationary?)
I think it ultimately comes down to what a person looking out on to the world understands by the word "motion". "Motion" is an elementary concept, a concept by means of which we understand a host of other concepts but which itself is very general and poorly understood from an everyday perspective. In the ancient world, "motion" primarily meant development and growth, the way a thing changes in accordance with its essence. Mere change of place - "locomotion" - was a species of motion-as-growth, and so whatever change of place was, it had to accord with the ancient logic of motion-as-growth. It could not contradict it. This isn't a matter of conception of senses experience. It is a matter of how one lives one life and what the world in general means.
Throughout the Islamic middle ages, largely owing to the attack against Aristotle and the relatively extreme level of intellectual tolerance in the Muslim world, locomotion gets gradually liberated from motion-qua-growth. It doesn't become fully independent from metaphysics. That never happens, not even in modernity. Rather, it acquires a new metaphysical basis. It gets wrapped up in a complex way with mathematics, especially with algebra and trigonometry. (These latter disciplines were not seen as being purely independent in the medieval world. They were seen as separate from logic and language, for example, unlike in modern philosophy.) I think the event that gives the strongest impetus to the transplanting of the study of locomotion—which becomes "mechanics"—from the philosophical account of becoming or growth into an intellectual space which it can share with pure mathematics and geometry, is the discovery that the earth moves. The previous account of becoming—it was called "phusis" or "physics" in the ancient world—was firmly rooted in the experience of an earth that does not move. The discovery in the middle ages that the earth moves created enough of a disturbance that it made sense to study change-of-place separately from becoming. That's what allowed mechanics to start to come into existence.
Obviously I'm not sure of any of the details of this, but in terms of its general features, this appears to make sense. Why it then took an extra 300 years to apply the conic sections to the celestial motions? I don't know. On the historical scale, that's a relatively short amount of time. But there's still a lot to fill in.
(Another consideration: more shapes than just the circle were imputed to the heavens. A crude form of spherical geometrical using triangles was known in ancient times. It was used to predict the positions of the planets and the stars. Two factors led to the invention of a better method. The first is that so many rituals in Islam rely upon the position of the moon and other celestial bodies, it became necessary to come up with a better method. And the second factor is that the method developed in ancient times was so time-consuming and clumsy. So triangles were used in calculating the positions of the celestial bodies. But of course no triangular motions were imputed to them...)
(And another: you can't escape from the fact that the thorough-going application of geometry to nature occurs in the budding mercantilist nations in the 17th century. Classical mechanics doesn't come to fruition in Persia, India, or China. It comes to fruition in the place where people are about to start using machines to make other machines. The practical ability to force nature into geometric configurations does not cause classical mechanics to come into existence. Classical mechanics largely predates that. But the fact that the two things come into existence in such close proximity to one another (in space and time) can't be overlooked. An interesting project would be to trace this development backward. What socio-political transformations were taking place during the golden age of Islam when mechanics first came into existence as a science? In what concrete context did people discover that the earth moves?)