Saving the appearances of the appearances: The foundations of classical geometrical optics

Abstract

1 Simplicius, at third hand from Eudemus through Sosigenes, reports that Plato proposed the by now dog-eared problem of finding "by the supposition of what uniform, circular, and ordered motions the appearances of planetary movements could be saved" (Tivojv vnoredevrœv of' ofxaXcbv xai eyxvxMojv xai rerayfievojv xivtjoeojv ovvrjeorai oiaoojOfjvai rei neql rovc Tikavwjbievovc (paivo/ueva, In Aristotelis De caelo commentarla II, 12, 221a30-32, ed. I. L. Heiberg, Commentaria in Aristotelem Graeca, vol. 7 [Berlin, 1894], p. 493). Moreover, Simplicius continues, it was Eudoxus, Plato's student, who first responded to the challenge by devising his theory of homocentric spheres. So if Simplicius is to be credited, Plato, by inspiring Eudoxus, was responsible for the birth of classical mathematical astronomy. Now whether it was Plato himself, or Eudoxus, who actually set out the problem has been a somewhat vexed issue, but on the whole it is accepted that the idea of regularizing the apparent planetary vagaries by means of uniform circular motion is at least consonant with Platonic doctrine (c/., however, J. Mittelstrass, Die Rettung der Phanomene [Berlin, 1962]). More vexed is the issue of what the challenge itself really intendedan issue raised to prominence by Pierre Duhem in his ZQZEIN TA A "to save" appearances meant to fit them into a preconceived mathematical model without regard for the physical reality or truth of the model itself. In short, saving the appearances was a positivist endeavor. The second alternative/school was fundamentally "realist"; it was not enough to frame an adequate mathematical hypothesis. The hypothesis itself had to reflect the real, physical nature of things. Duhem clearly had methodological fish to fry; he wanted to show that the seeds of modern science were not only sown by Plato and his astronomical followers but were nurtured (with some notable exceptions) throughout the middle ages and renaissance