Of all the ideas that human reason can form, Hooke considered the simplest and the most fundamental to be the geometrical concepts of point and straight line. Undoubtedly we are able to think these, but the naïve consciousness takes for granted that it also perceives them as objective realities outside itself, so that thoughts and facts correspond to each other. We must now ask, however, if this belief is not due to an optical deception. Let us turn to the microscope and see what point and line in the external world look like through it.

In the following way Professor Schrödinger, another leading thinker among modern theoretical physicists, explains the philosophical basis for the principle of Indeterminacy, which scientists have established in the meantime:¹

For his investigation Hooke chose the point of a needle and a knife-edge, as providing the best representatives among physical objects of point and straight line. In the sketches here reproduced we may see how Hooke made clear to his readers how little these two things, when observed through the microscope, resemble what is seen by the unaided eye. This fact convinced Hooke that the apparent agreement between the world of perception and the world of ideas rests on nothing more solid than an optical limitation (Plate I).

'Every quantitative observation, every observation making use of measurement, is by nature discontinuous. ... However far we go in the pursuit of accuracy we shall never get anything other than a finite series of discrete results. ... The raw material of our quantitative cognition of nature will always have this primitive and discontinuous character. ... It is possible that a physical system might be so simple that this meagre information would suffice to settle its fate; in that case nature would not be more complicated than a game of chess. To determine a position of a game of chess thirty-three facts suffice. ... If nature is more complicated than a game of chess, a belief to which one tends to incline, then a physical system cannot be determined by a finite number of observations. But in practice a finite number of observations is all that we could make.'

Compared with the more refined methods of present-day thought, Hooke's procedure may strike us as somewhat primitive. Actually he did nothing more than has since been done times without number; for the scientist has become more and more willing to allow artificially evoked sense-perceptions to dictate the thoughts he uses in forming a scientific picture of the world.

Classical physics, the author goes on to show, held that it was possible to gain a real insight into the laws of the universe, because in principle an infinite number of such discrete observations would enable us to fill in the gaps sufficiently to allow us to determine the system of the physical world. Against this assumption modern physics must hold the view that an infinite number of observations cannot in any case be carried out in practice, and that nothing compels us to assume that even this would suffice to furnish us with the means for a complete determination, which alone would allow us to speak of 'law' in nature. 'This is the direction in which modern physics has led us without really intending it.'

In the present context we are concerned with the historical import of Hooke's procedure. This lies in the fact that, immediately after Descartes had satisfied himself that in thinking man had the one sure guarantee of his own existence, Hooke proved in a seemingly indubitable manner that thinking was entirely divorced from reality. It required only another century for philosophy to draw from this the unavoidable consequence. It appeared in the form of Hume's philosophic system, the outcome of which was universal scepticism.

What we have previously said will make it clear enough that in these words of a modern physicist we meet once more the two fundamentals of Hume's philosophy. It is just as obvious, however, that the very principle thus re-affirmed at the latest stage of modern physical science was already firmly established by Hooke, when he sought to prove to his contemporaries the unreality of human ideas.

As we shall see in due course, Hume's mode of reasoning continues to rule scientific thought even to-day, quite irrespective of the fact that science itself claims to have its philosophical parent in Kant, the very thinker who devoted his life's work to the refutation of Hume.

Let us recall Hooke's motives and results. The human reason discovers that certain law-abiding forms of thought dwell within itself; these are the rules of mathematical thinking. The eye informs the reason that the same kind of law and order is present also in the outer world. The mind can think point and line; the eye reports that the same forms exist in nature outside. (Hooke could just as well have taken as his examples the apex and edge of a crystal.) The reason mistrusts the eye, however, and with the help of the microscope 'improves' on it. What hitherto had been taken for a compact, regulated whole now collapses into a heap of unordered parts; behind the illusion of law a finer observation detects the reality of chaos!