It is, therefore, by the firm resolution never to juggle with words or ideas, or to try and persuade ourselves or others that we understand what we do not understand, that any scientific advance can be made. CHAPTER I. All students of any subject are at first apt to be perplexed with the number and complication of the new ideas presented to them. The need of comprehending these ideas is felt, and yet they are difficult to grasp and to define. Thus, for instance, we are all apt to think we know what is meant when force, weight, length, capacity, motion, rest, size, are spoken of. And yet when we come to examine these ideas more closely, we find that we know very little about them. Indeed, the more elementary they are, the less we are able to understand them. The most primordial of our ideas seem to be those of number and quantity; we can count things, and we can measure them, or compare them with one another. Arithmetic is the science which deals with the numbers of things and enables us to multiply and divide them. The estimation of quantities is made by the application of our faculty of comparison to different subjects. The ideas of number and quantity appear to pervade all our conceptions. The study of natural phenomena of the world around us is called the study of physics from the Greek word φυσίς or “inanimate nature,” the term physics is usually confined to such part of nature as is not alive. The study of living things is usually termed biology (from βια, life). In the study of natural phenomena there are, however, three ideas which occupy a peculiar and important position, because they may be used as the means of measuring or estimating all the rest. In this sense they seem to be the most primitive and fundamental that we possess. We are not entitled to say that all other ideas are formed from and compounded of these ideas, but we are entitled to say that our correct understanding of physics, that is of the study of nature, depends in no slight degree upon our clear understanding of them. The three fundamental ideas are those of space, time and mass. Space appears to be the universal accompaniment of all our impressions of the world around us. Try as we may, we cannot think of material bodies except in space, and occupying space. Though we can imagine space as empty we cannot conceive it as destroyed. And this space has three dimensions, length, breadth measured across or at right angles to length, and thickness measured at right angles to length and breadth. More dimensions than this we cannot have. For some inscrutable reason it has been arranged that space shall present these three dimensions and no more. A fourth dimension is to us unimaginable—I will not say inconceivable—we can conceive that a world might be with space in four dimensions, but we cannot imagine it to ourselves or think what things would be like in it.