Lenses and Waves

234 CHAPTER 6
Books 2 and 3 concern his later experimental investigations of the colors in
thin films and of diffraction. Although Newton’s mathematical perspective is
unmistakable in the concepts employed and the quantification effected, the
mathematical reasoning at the heart of his understanding of colors is implicit.
Opticks presented the new science of colors as an experimental theory.
The core of Newton’s optical investigations consisted of the search of
phenomenological laws and properties of light. He did speculate on the
corpuscular nature of light and color and their properties, but from the onset
he barred these from his established theories. In his view, experimental
philosophy should not be contaminated by hypotheses or other ill-founded
assumptions, as Descartes had done. This level of causation, distinguished
from the level of experimentally demonstrated properties, implied so-called
hypothetical philosophizing which Newton pursued publicly only once, in
his 1675 paper for the Royal Society ‘Hypothesis explaining the properties of
light’. Speculations on unobservable matter in motion, did play a part in
Newton’s optics however. One of the reasons he dropped the ‘Cartesian’
dispersion law seems to have been that it conflicted with his most private
thought on the corpuscular nature of colors. Yet, this remained concealed
from its readers.
To stress the lucidity of mathematics against the obscurity of natural
philosophy was rather a ‘topos’ in the seventeenth-century. Like Newton,
Huygens thought that Descartes had gone astray in presuming that the laws
of optics could be derived from a priori truths. A mechanistic hypothesis
could not by itself prove anything. Unlike Newton however, Huygens did
not banish hypotheses from his optics. On the contrary, the question how to
establish proper ‘raisons de mechanique’ and built a mathematical science of
optics from them, was his main concern. According to Huygens, the causes
of the behavior of light were ultimately hypothetical. His problem was how
to find the right hypotheses. In the first place, this meant to establish
veritably mechanistic causes of the properties of light. As contrasted to the
speculations of Hooke and Descartes, Huygens wanted his mechanistic
explanations to be comprehensible. That is, a hypothetical mechanism had to
be exact and to conform to the established laws of motion. Huygens’
principle defined ethereal waves mathematically and prescribed how a
propagated wave could be constructed geometrically. In this way it explained
the laws of optics accurately, by means of mathematical derivation.
From the perspective of seventeenth-century geometrical optics,
Huygens’ principle can be seen as a law. But it was a new kind of law: a law
of unobservable waves instead of rays. Light consisted of waves and these
could be treated in the same manner as the rays of traditional optics. He
defined the properties of these waves in the same law-like manner. By
mathematizing the mechanistic causes of the laws of optics, Huygens
extended geometrical optics into the realm of the unobservable. For
methodological reasons Newton would not allow such a thing, although he
was quite capable of mathematizing mechanistic causes. As compared to the