The evolution of scientific thought from Newton to Einstein

by A. D'Abro

Finally, we are led to enquire into the nature of this synthesis or co-ordination of facts which seems to be a prerequisite condition for knowledge to be possible. It is here that an analysis of the more sophisticated syntheses of science will be helpful in enabling us to understand how the mind proceeds. The reason for this is because scientific knowledge can be traced back to crude commonplace knowledge by a series of insensible gradations, the same incentives appearing to be active in all cases.

Now, when we consider the procedure of the scientist, we find that it consists in co-ordinating and linking together in a rational manner a number of experimental facts, with the maximum of simplicity. By “a rational way” we mean primarily “according to the rules of logic.” Irrespective of whether these rules are assumed to have been derived from experience or to reduce to a priori judgments, all normal men appeal to them, and all scientific theories, even the most revolutionary ones, are based on their acceptance. As for the criterion of simplicity, which enables us to select one co-ordination rather than another, it appears to be linked with our valuing of the expenditure of effort. Thus, even a dog finds it simpler to enter a house by the front door rather than clamber in through the back window. At any rate, inasmuch as, with small variations, all human beings agree unanimously on those co-ordinations which are to be regarded as the simplest, we may assume the urge towards simplicity to be fundamental. There are, of course, a number of other factors which enter into the construction of scientific syntheses, but for our present purpose the ones mentioned will suffice.

It will be noticed that in our list of fundamental facts, though our awareness of the passage of time was considered to be unanalysable, no mention was made of our awareness of space and of objects, including our own human bodies, situated in space. The concept of space was assumed to have been generated in an indirect way when we sought to co-ordinate our sensory impressions with maximum simplicity. It would thus be in the nature of a mental construct arrived at a posteriori. By this we do not wish to imply that the concept of continuity and of extension may not have pre-existed in the mind in a latent form; all we wish to assert is that the necessity for appealing to the concept of space seems to have arisen from the totality of our sensory experience.

A co-ordination of our sensations will yield us at the same time empty space and what we will interpret as filled space representing material objects, including our own human bodies, which are then recognised as being situated in space. We cannot attempt to justify these views here, but those who are interested in the subject will find the ideas expounded in Poincaré’s masterly discussion of the problem in his book, “The Value of Science,” and more especially in “Last Thoughts.”

When it comes to differentiating and locating the portions of filled space occupied by bodies as against the empty portions, we again proceed in the same way, by co-ordinating sense impressions. Our belief in the existence of a table, for instance, is attributed to the fact that a simple co-ordination of the complex of our tactual, visual and muscular sensory impressions is possible only when we concede the existence of the table as a concrete reality, situated in the space before us. It is true that in common practice we may see a table and recognise it as such without touching it. But it is to be presumed that at earlier stages of our life we have exercised all our sensory faculties and have already recognised by a synthetic process the existence of space and of material objects. The table is then immediately recognised as existing, by a mere association of past impressions, without our having to explore it tactually.

Up to this point we have restricted our attention to space as mere extension. But space, as understood in common practice, implies considerably more: it represents a three-dimensional Euclidean continuum. When thus particularised, Kant’s arguments as to its a priori character are no longer tenable in the light of modern discovery; and we must assume that this special form we credit to space arises entirely from our co-ordination of sense impressions conducted in the simplest way possible. On no account may we consider three-dimensional Euclidean space to be imposed a priori either by sensibility or by the understanding.

These discussions on the empirical origin of space are not mere philosophic fancies having no bearing on science. They are in many respects vital; and it is generally conceded by scientists that the a priori doctrine of three-dimensional Euclidean space is one of the most pernicious teachings that philosophy has ever attempted to impose upon science. Similar arguments hold for “time,” when by “time” we are referring, not to our awareness of the time-stream in our consciousness, not to the “I” time, but to physical time or duration throughout the universe, which our consciousness has exteriorised and projected into space. As Einstein remarks in a passage previously quoted:

“I am convinced that the philosophers have had a harmful effect upon the progress of scientific thinking in removing certain fundamental concepts from the domain of empiricism, where they are under our control, to the intangible heights of the a priori. This is particularly true of our concepts of time and space, which physicists have been obliged by the facts to bring down from the Olympus of the a priori in order to adjust them and put them in a serviceable condition.”

We may mention that these views on space as professed by the greatest scientists are in large measure to be attributed to the discoveries of non-Euclidean geometry supplemented by the investigations of the psycho-physicists. Still, in view of the difficulty of imagining hyperspaces and non-Euclidean spaces, the views presented might appear difficult to accept, and it might be held that three-dimensional Euclidean space imposes itself a priori regardless of experiment. But it should be noted that by the time men are of an age to philosophise, they have been subjected for so many years to beliefs based on inferences from experience, that the beliefs have remained, whereas the inferences, owing to the monotony of their repetition, have become second nature and appear intuitive.

And yet a moment of reflection should suffice to convince us that were three-dimensional Euclidean space an a priori condition of the understanding, it would have been quite impossible for mathematicians to wend their way through the non-Euclidean hyperspaces of relativity. Neither can three-dimensional space be considered to be imposed by sensibility, since, as Poincaré tells us, after a certain amount of perseverance, he was aided to a considerable degree by sensibility when investigating the problems of Analysis Situs of four dimensions.