“Suppose that we are in the presence of some machine. The primary and terminal gears are alone observable, while the intermediary systems of transmission are concealed. We have no means of knowing whether the motion is transmitted by means of gears or straps, by means of pistons or by other means. Does this signify that we can never understand anything about the engine unless we take it to pieces? We know that such is not the case, for the principle of the conservation of energy enables us to determine the most important point. We observe, for example, that the last wheel turns ten times more slowly than the first, both these wheels being visible. We may infer therefrom that if a couple is applied to the first wheel it will balance a ten times greater couple applied to the last one. This information is obtained without our having to consider the mechanism whereby this state of equilibrium is realised and without our having to know how the various forces will balance one another inside the machine. When we consider the universe, similar arguments will apply. Most of its workings are beyond the sphere of observation; but by observing those motions which we can perceive, we can, thanks to the principle of the conservation of energy, derive conclusions which will remain true regardless of the structural details of those parts which are invisible.”
The tendency of science was therefore to lose interest in the microscopic mechanisms and to concentrate on the general principles. It was not long, however, before a return to the atomistic attitude was again forthcoming; but this time our knowledge was more advanced, and greater success was the result. We witness this return to the atomistic procedure in Lorentz’s theory of the electronic structure of matter and electricity. Marvellous anticipations resulted from this epochal theory, and it seemed as though a great advance had been made. But, once more, difficulties arose; and here we are referring to those mysterious phenomena which were the original starting point of the theory of relativity.
Einstein again reverts to general principles. Instead of endeavouring to account for the mysterious negative experiments by ascribing all kinds of curious properties to the electrons and to matter, he accepts these negative experiments as significant of some general principle, namely, the relativity of Galilean motion through the ether, entailing the invariance of the velocity of light.
Recent theories on the nature of the atom furnish instances of a similar sort. Thus, Bohr’s theory of the atom has atomistic tendencies in that it ascribes definite paths and motions to the electrons moving round the nucleus. In this way it was able to attribute to helium certain spectral lines which before then had been ascribed to hydrogen. Accurate experiments have since confirmed the correctness of Bohr’s anticipations. But insuperable difficulties were soon forthcoming when attempts were made to extend the theory to the heavier atoms. Half-quantum numbers and spinning electrons were introduced with the result of complicating the theory considerably.
So Born and Heisenberg abandoned the atomistic outlook, stressing the necessity of following a strictly phenomenological procedure. The motions and orbits of the electrons were disregarded entirely, since these had never been observed, and nothing but the repartition, polarisation and intensities of the spectral lines was taken into account. This new departure, known as the matrix method, led to remarkable results, removing many of the difficulties which had beset Bohr’s atom.
Still more recently we have witnessed a return to the hidden-mechanism viewpoint with Schrödinger’s wave mechanics. We can scarcely refer to it as an atomistic method, since waves take the place of discrete particles. Nevertheless, from the standpoint of methodology, the general idea involved is the same—that of basing our deductions on things that cannot be observed.
This dual tendency in science, that of atomism versus the general principles, that of the microscopic versus the macroscopic, must not be thought to arise from any peculiarities in the philosophies of the various scientists. It is due to the circumstances under which they happen to find themselves. Thus, we see a theoretical scientist such as Einstein adopting a phenomenological attitude when investigating the difficulties attendant upon the negative experiments; and we see the same scientist, Einstein, adopting an atomistic attitude when studying the problems of Brownian movements, the problems of radiation, or the quantum theory of specific heats. In the same way, when we climb a ladder we raise our left leg, then our right one. It is not because we conclude we were wrong in raising our left leg; it is because we cannot progress unless we allow the right leg to catch up with the left one. So it is in science; and we may be quite assured that in the years to come, as in the past, we shall continue to witness these periodic swings from the macroscopic to the microscopic view, from the general principles to atomism. We must realise, however, that as each swing takes place we are advancing higher and higher towards that unattainable ideal, perfect knowledge.
And now let us revert to the common objective world of classical science, to the world of separate space and time in which molecules, atoms and electrons move and vibrate, and in which other types of realities, such as electromagnetic fields, are present. Let us recall once again that this real objective universe is the world as the scientist must assume it to be if he wishes to co-ordinate the complex of his experiences (reducing in the final analysis to sense impressions) in a simple and consistent manner. Whether or not this objective universe can be identified with the real world of the metaphysician is a subject we need not discuss further, since it is of no interest to science. The point we wish to investigate is somewhat different. It is to be noticed that the so-called secondary qualities, such as colour, sound and smell, have been banished as self-supporting entities. They are now ascribed to the reactions of our brain to the neural disturbances which occur when our sense organs are submitted to the action of the realities of the common objective world.
The criticism is often directed against the scientific attitude that by reducing quality to quantity we are eliminating values, substituting, for example, electromagnetic vibrations for the colour red. Of course, it is scarcely necessary to state that, aside from all philosophical considerations, the reduction of quality to quantity is a prerequisite condition if science is to exist. To illustrate: In Newton’s day the vibratory nature of light was unknown. Red light differed from green light, but this qualitative difference manifested itself as an irreducible fact for which it was impossible to account. Under the circumstances, if the observer were to rush towards a red light or to move away from it, it was quite impossible for science to anticipate what effects would arise. As soon, however, as Fresnel discovered the vibratory nature of light, red light was found to differ from green light owing to its slower rate of vibration: prevision then became attainable. It was possible to anticipate that were we to approach a red lamp with sufficient speed it would appear green, that with greater speed it would appear violet, and that with still greater speed it would become invisible. Likewise, were we to recede from the light with sufficient speed it would also cease to appear visible. This was the celebrated Doppler-Fizeau effect, which astronomical observations soon succeeded in detecting; it is thanks to this effect that we are able to determine the radial speed of approach or of recession of the stars.
We may presume, therefore, that the practical utility of the scientist’s constant endeavour to reduce differences of quality to differences of quantity is not called into question by the critic, and that his objections are directed solely against the supposedly unjustified philosophical outlook which this reduction of quality to quantity has exercised on the scientific mind. But, in order to investigate the problem, we must proceed to a more detailed discussion of the reasons that compelled scientists to differentiate between the so-called primary and secondary qualities.