An example comes to mind, of some graduates of the Polytechnic School of Paris attending an advanced program at Orsay to learn solid-state physics. They would often show up convinced they knew everything on the basis of calculations. On their final exam, I would give them a problem of the following type: ``Imagine a thin, evaporated metal film, like lead, 1 micron in thickness. A cosmic ray with an energy of 10 MeV traverses the film, which is held at a temperature of 4 kelvins. A voltmeter is connected between the edges of the film. What are the amplitude and duration of the resistance pulse that can be measured across that film? Is it possible to use this design to build a simple cosmic ray detector?''
The student would go off and think about the problem for an hour in front of a blackboard. The solution was rather elementary at this level of studies. One starts by considering collisions between charged particles to evaluate how much energy a fast proton of the cosmic ray gives up to the electrons of the lead film; this determines the energy input. To specify how the energy involved diffuses, I would add: ``This lead film contains 1 percent impurities,'' which, the student should know, implies that an electron travels about 100 times the distance between lead atoms before it gives up the energy it acquired when it was hit by the cosmic ray. Two or three general concepts of this kind are all that are needed to predict the amplitude and the duration of the thermal pulse. But the typical Polytechnic graduate I inherited at the time would remain stumped in front of his bare blackboard. One of them finally blurted out (I will never forget his comment!): ``But, sir, what Hamiltonian should I diagonalize?'' He was trying to hang on to theoretical ideas which had no connection whatsoever with this practical problem. This kind of answer explains, in large part, the weakness of French industrial research.