Lenses and Waves

122 CHAPTER 4
not beyond doubt, Kepler preferred his own data over Witelo’s because it
was based on “regularity and order”. In the final propositions of this section
and the remaining sections of the chapter, Kepler was now able to dealt with
proper subject of the chapter: the quantitative treatment of atmospheric
refraction.
Kepler’s search for a ‘measure’ refraction clearly reveals the idiosyncrasies
of his thinking. He laboriously reported on his persistent efforts to find a
satisfactory law, and although – so we can see with hindsight – he came
tantalizingly close he did not succeed. The successive stages of his attack
display his ever inventive mathematical reasoning, mixed with those typical
Renaissance conceptions of his that make it hard for a modern reader to
distinguish mathematics and physical ideas. In the light of ensuing
developments in seventeenth-century optics, the final stage of Kepler’s
struggle with refraction is the most interesting. Here he took his conception
of the nature of light into account in order to find a law of refraction. In a
kind of microphysical, though far from corpuscular, analysis he considered
the interaction of a surface of light and the refracting medium. At this stage
he move farthest away from traditional approaches. Although the resulting
‘rule’ was phrased in terms of rays, he had taken the true nature of light into
account while analyzing the interaction of rays and (refracting) media. As I
see it, this was possible because of his realist view of mathematical
description. With Kepler, the mathematics of light propagation necessarily
reflected the nature of light.
One may argue that mathematics took the lead in his thinking. Kepler
more or less reduced light to a mathematical entity, a two-dimensional
surface. The geometry of refraction was rather autonomous in his final
attempt to derive a law. 63 Yet, pure formalisms would have been meaningless
for him. Kepler maintained geometrical optics as a mathematical theory
explaining the behavior of light rays. He adopted many concepts of
perspectivist theories of light and refraction, but he applied them in a radical
and sometimes radically different way. On the level of methodology, all
relevant components – physics, mathematics, observation – had been
present in perspectivist optics, but Kepler sought a closer connection
between them and often used these means in a much stricter way. He
repeatedly allowed Witelo’s data to refute the outcome of his trials. Kepler’s
wanted to establish a closer tie between the nature of light and the laws of
optics and derive ‘measure’ from ‘cause’. He openly acknowledged that he
could not realize this ideal. He resorted to a freer mode of reasoning
because, as I see it, he was far too creative a thinker to stick too rigidly to his
ideals.
63 See for example: Buchdahl, “Methodological aspects”, 291.