Footprints in the Snow?

I want to dwell for a moment on the significance of this transition from the­ory to fact. It is a phase-change that has often taken place in the history of science. Assertions to the effect that, say, the blood circulates in the human body, or that water is made of hydrogen and oxygen, may once have been speculations but today can be taken as matters of fact. It would be a question­able use of language to keep calling them theories. How is this change of sta­tus, from theory to fact, best described? One attractive answer was provided in the form of a striking metaphor used by the Cambridge mathematician William Kingdon Clifford.34 Clifford, who had been a second wrangler in 1867, a fellow of Trinity, and a friend of Rayleigh, had wide-ranging interests in mathematical physics. In a lecture he gave in Manchester (some fifty years before the experiments that concern us), Clifford took as his example not hydrodynamics but the wave theory of light. This conception of light, he said, must now be accepted as fact. The difference between a theory and a demon­strated fact, he went on, “is something like this”:

If you suppose a man to have walked from Chorlton Town Hall down here say in ten minutes, the natural conclusion would be that he had walked along the Stretford Road. Now that theory would entirely account for all the facts, but at the same time the facts would not be proved by it. But suppose it happened to be winter time, with snow on the road, and that you could trace the man’s footsteps all along the road, then you would know that he had walked along that way. The sort of evidence we have to show that light does consist of waves transmitted through a medium is the sort of evidence that footsteps upon the snow make; it is not a theory which merely accounts for the facts, but it is a theory which can be reasoned back to from the facts without any other theory being possible. (117)

The thought is that if you can track a process in great detail, and see it de­velop step by step, then you can reach a stable understanding that is unique, unchallengeable, and enduring. Such an understanding, said Clifford, deals with facts, not theories.

Clifford’s metaphor may be a tempting one, but it cannot be wholly right, and it led Clifford himself astray. The development of physics showed that what he thought of as a demonstrated fact was actually a theory. The alleged impossibility of any alternative to the wave theory was refuted by the emer­gence of an alternative. In Clifford’s time the wave theory had superseded an older particle theory, but in 1905 Einstein once again postulated light par­ticles. These new-style particles or “photons” were invoked to explain the photoelectric effect, something that was proving difficult to understand in terms of waves. The photoelectric effect takes place when light is incident on a metal surface and releases electrons from the surface. How could the energy spread across a wave front be concentrated in the way necessary to release a charged particle? This was the problem Einstein’s theory was designed to answer. The light energy, he argued, was concentrated because light consists not of waves, but of particles, albeit particles with unusual properties.35 These developments took place after Clifford’s death. He cannot be blamed for not anticipating them, but they amount to a counterexample to Clifford’s argu­ment and show the need to introduce qualifications into his overconfident picture.

What was Clifford’s error? It was that of assimilating fundamental scien­tific inquiry to commonsense knowledge. While there are many similarities and connections, Clifford ignored a crucial difference. Everyone has seen, or could see, a man creating footprints in snow. The cause and the effect can be conjoined in experience, and both are open to inspection. This is the basis of subsequent inferences from footprints to their human causes and the basis of the conclusions that can be drawn about, say, the route someone had taken from Chorlton Town Hall to the location of Clifford’s lecture. The physicist, on the other hand, did not come to the wave theory of light by seeing light waves creating diffraction patterns or rainbows. The two things were not con­joined in experience in the way people and footprints have been conjoined. The inference to light waves did not have the same inductive basis as the com – monsense inference with which Clifford was comparing it.36

Clifford’s metaphor may have broken down for light waves, but it might still be applicable to Fage and Simmons’ achievement. It could be argued that Fage and Simmons were confronting the vortices and observing them bringing about their effects. Was not this conjunction precisely what the ex­periment was designed to expose? Even if the experimenters could not actu­ally see the flow of air, they could have made it visible, and others had done exactly that. In any case, the diagrams showing the streamlines of the vortices and the contour lines of equal vorticity allowed them to follow the path and development of the postulated vortices. The experimenters could set these diagrams side by side with the measured lift forces on the wing. Causal con­nections and correlations of phenomena that were originally speculative had, in a sense, been exposed to view, and the step-by-step progress of the cir­culation had been traced. Perhaps tracking the vortices through the pattern of measurements registered in Fage and Simmons’ diagrams was, after all, similar to tracking footprints in the snow.

If Clifford’s metaphor is applicable to the aerodynamic work, does this mean that the question “How does a wing produce lift?” can now be answered with the same level of certitude as the question about the man walking down the Stretford Road? In a sense, yes, it does. The phenomena of circulation, vortices, and lift had been made, or were on the way to being made, part of the routine and reality of daily life. At least, this was true for the laboratory life of some of the experimentalists working in this area. They were becoming increasingly familiar with the patterns in the data and the range of effects to be accounted for. Expectations were crystallizing, and experimenters were learning what they could take for granted. Techniques of calculation and pre­diction were becoming more confident and refined. What was once strange was becoming familiar and part of predictable, daily experience—like getting to know a new town. Learning to live with the theory of circulation was like learning to live in a new environment with new architectural styles and a new street plan. You want to get to Prof. Clifford’s lecture starting out from Chor – lton Town Hall? Then go down the Stretford Road! You want to calculate the induced drag? Then use Prandtl’s formula!37

Significantly, this was not yet how some of the most influential British experts saw the issue. They acknowledged that Fage and Simmons’ results represented a triumph of sorts for Lanchester, Prandtl, and Glauert, but they did not accept that the answer was now known to the question How is lift produced? On the contrary, they maintained that, despite the experimental advances and the increase in empirical knowledge, the answer to this ques­tion remained wholly unknown. Many questions, they acknowledged, had now been answered, but not this one. These experts were not simply being stubborn or blind in the face of mounting evidence, and their reaction un­derlines just how careful one must be in applying Clifford’s metaphor. It must be accepted that what looks like demonstrated fact from one point of view may appear less compelling or revealing from another point of view. This skeptical response to the mounting experimental evidence was articu­lated with great clarity by Richard Vynne Southwell (fig. 9.10). Southwell has already been mentioned in connection with the postwar contact with Prandtl and Gottingen, but it is appropriate to look more closely both at the man and at his response to the growing experimental literature.