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Lenses and Waves

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LENSES & WAVES 259<br />

phenomena. The coherence I see is therefore not one of content of theories,<br />

but one of a common approach <strong>and</strong> of disciplinary-connected fields of<br />

study. He believed in the power <strong>and</strong> fertility of rigorous mathematical<br />

reasoning, as opposed to the mere empiricism of ordinary craftsmen. Our<br />

pre-Parisian Huygens was a mathematician, a seventeenth-century<br />

mathematician with an idiosyncratic approach. A new Archimedes, Mersenne<br />

concluded when he was confronted with the youthful Huygens. 8<br />

From mathematics to mechanisms<br />

What happens, we may now ask, when a mathematician of this Archemidean<br />

inclination meddles with questions of the mechanistic nature of light?<br />

Nothing special needs to happen <strong>and</strong> nothing did at first. The nature of light<br />

became of interest to Huygens when he needed a preparatory chapter for his<br />

‘Dioptrique’ that would explain the laws of optics. No problem, Pardies had<br />

shown how refraction could be explained by waves of light. Only an exotic<br />

phenomenon displayed by Icel<strong>and</strong> crystal posed a bit of a problem. A<br />

refracted perpendicular ray negated the perpendicularity of rays <strong>and</strong> waves<br />

that was crucial to Pardies’ explanation. Although the problem of strange<br />

refraction thus pertained to the wavelike nature of light, Huygens first<br />

approached the phenomenon in the meanwhile traditional, mathematician’s<br />

way. He sought a law of strange refraction in terms of the properties of rays.<br />

Not surprisingly, the law he found did not solve the problem of strange<br />

refraction.<br />

Five years later, Huygens returned to the problem. And this time<br />

something special did happen. Following on his analysis of waves refracted<br />

by curved surfaces, he considered the question what happened to waves<br />

when they traverse Icel<strong>and</strong> crystal. The special thing is that he now took the<br />

propagation of waves mathematically. He defined a wave as the result of a<br />

disturbance propagated with a specific velocity in all directions, which he<br />

could then apply by geometrical construction only. At the background was<br />

the conviction that the mechanics of wave propagation ought to follow from<br />

the laws of motion. But the mechanistic picture was explicated – <strong>and</strong> maybe<br />

also recognized – only afterwards. In the notes of 1677 we see Huygens less<br />

concerned about the broad ideas of his principle <strong>and</strong> of spheroidal waves<br />

than about their mathematical elaboration. The same line of reasoning that<br />

explained refraction should also explain the other properties of light rays,<br />

including strange refraction. The result was a law of wave propagation<br />

yielding an indissoluble tie between the mechanistic nature of light <strong>and</strong> the<br />

laws governing the behavior of rays.<br />

What Huygens did not realize, was that he had not just solved another<br />

problem in optics. It was a problem regarding the physical foundations of<br />

geometrical optics, but Huygens had phrased it in a particular way.<br />

Reconciling strange refraction with waves was a problem of reconciling<br />

8<br />

Yoder, Unrolling time, 179. OC1, 47. “Je ne croy pas s’il continue, qu’il ne surpasse quelque jour<br />

Archimede.”

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