History gives another reason for the physicist's attitude toward the qualitative. The controversy between the followers of the physics of Descartes and of Newton was at its height at the end of the seventeenth century. Descartes, with his vortices, his hooked atoms, and the like, explained everything and calculated nothing; Newton, with the inverse square law of gravitation, calculated everything and explained nothing. History has endorsed Newton and relegated the Cartesian constructions to the domain of curious speculation. The Newtonian point of view has certainly fully justified itself from the point of view of its efficiency and its ability to predict, and therefore to act upon phenomena. In the same spirit, it is interesting to reread the introduction to Dirac's Principles of Quantum Mechanics, wherein the author rejects as unimportant the impossibility of giving an intuitive content for the basic concepts of quantum methods. (note) But I am certain that the human mind would not be fully satisfied with a universe in which all phenomena were governed by a mathematical process that was coherent but totally abstract. Are we not then in wonderland? In the situation where man is deprived of all possibility of intellectualization, that is, of interpreting geometrically a given process, either he will seek to create, despite everything, through suitable interpretations, an intuitive justification of the process, or he will sink into resigned incomprehension which habit will change to indifference. In the case of gravitation there is no doubt that the second attitude has prevailed, for we have not in 1975, less reason to be astonished at the fall of the apple than had Newton. The dilemma posed to all scientific explanation is this: magic or geometry.(note) From this point of view,~ men striving for understanding will never show toward the qualitative and descriptive theories of the philosophers from the pre-Socratics to Descartes the intolerant view of a dogmatically quantitative science.
However, it is not the impossibility of giving a quantitative result that condemns the old qualitative theories to modern eyes, for what matters most for everyday use is almost always a qualitative result and not the precise value of some real number. When we drive our car from town A to town B a hundred miles away, we rarely calculate our route with precision. What matters is the qualitative result: that we will arrive at B after a finite and reasonable time without having hit any obstacles Iying in our path. Such a result follows a large number of elementary steps, some of which must be computed within narrow limits, but can be arrived at after no more quantitative consideration than the amount of fuel required at the start. What condemns these speculative theories in our eyes is not their qualitative character but the relentlessly naive form of, and the lack of precision in, the ideas that they use. With the exception of the grandiose, profound, but rather vague ideas of Anaximander and Heraclitus, the first pre-Socratic philosophers, all these theories rely on the experience of solid bodies in three-dimensional Euclidean space. This intuition, however natural and innate in our development and use of our original tools, is insufficient for a satisfactory account of most phenomena, even on a macroscopic scale.