Fig. 1.
Suppose that we draw a curve AB freehand with a single undivided sweep of the pencil. By making a certain assumption—that the curve which we drew was one that might be regarded as cyclical, that is, might be repeated over and over again—we can subject it to harmonic analysis. We can decompose it into a number of other curves (CD, EF, etc.), each of which is a separate “wave” rising above and falling below the axis OX in a symmetrical manner. If we draw any vertical line MN cutting these curves, we shall find that the distance between the axis OX and the main curve AB is always equal to the algebraic sum of the distances between the axis and the other curves. These latter we call the harmonic constituents of the curve AB, supposing them to “add up” so as to form it. But AB was something quite simple and elemental and its constituents cannot be said to have existed in it when we drew it freehand; it was only by an artifice of practical utility in mathematical computations that we constructed them. It may be, of course, that the harmonic constituents of a curve had actual existence apart from the curve itself, but, in the case that we take, they certainly had not. Now we must think of our stream of consciousness in much the same way. It is something immediately experienced and elementary; it is the concomitant, if we choose so to regard it, of the external processes that go on outside our bodies. We can investigate it by thinking about it, and attending to one aspect of it after another, thus arbitrarily detaching one “part” of it from all the rest, but immediately we do this we rise above the flux of experience into the region of intellectual concepts. We have converted a multiplicity of states of consciousness, all of which co-exist along with each other, and in each other, and which have no spatial existence, into a multiplicity of states, visual, auditory, olfactory, etc., which have become separated from each other and have therefore acquired extension. This dissociation of the flux of experience is the process of conceptual analysis carried out by thought.
If we dissociate the stream of consciousness in this way, breaking it up into states which we choose to regard as separate from each other, we shall see that of the elements which we thus isolate many are like each other and can be associated. Obviously there is a greater resemblance between different smells than between smells and sounds. Different musical sounds are more like each other than are sounds, and feelings of heat and cold. There is a greater likeness between the states of consciousness which arise from the stimulation of the same receptor organ, than between those that arise from the stimulation of different receptors. Those differences of sensation accompanying the stimulation of different sense organs we regard as different in kind; there is absolutely no resemblance between a colour and a sound, we say, however much the modern annotator of concert programmes may suggest the analogy. But we say that there may be different degrees of stimulation of the same sense organ, and that the sensations that we thus receive are of the same kind though they differ in intensity. The whistle of a railway engine becomes louder as the train approaches, that is to say, more intense, and if we study the physical conditions that are concomitant with the stimulation of our tympanic membranes we shall see that waves of alternate rarefaction and compression are set up in the atmosphere outside our ears. All the time that the train approaches the frequency of these waves remains the same, that is, just as many occur in a second when the train is distant as when it is near. But the amplitude of the waves has been increasing, and the velocity with which the molecules of air strike against the tympanic membranes becomes greater the nearer is the source of sound.
Fig. 2. We can represent this by means of a diagram which shows that the amplitude of the waves—which represents the loudness of the sound—increases while the frequency—which represents the pitch—remains the same. The amplitude is represented by the straight vertical lines, 11, 22, 33, etc., which are of increasing magnitude. Thus we represent the physical cause of the increasing loudness of the sound by space-magnitudes, and then we transfer these magnitudes to the states of consciousness concomitant with the vibrating molecules of air. Suppose that we knew nothing at all about the cause of the differences of pitch of musical sounds and that we listen to the notes of the octave, C, D, E,——C, sounded by an organ; all that we should experience would be that the sounds were different. If we were to sing the notes we might attain the intuition that the notes G, A, B were “higher” than the notes C, D, E, because a greater effort was required in order to produce these sounds, but obviously this is a different thing from saying that the notes themselves were “higher” or “lower.” But let us match the notes by striking tuning-forks, and then having selected forks which give the notes of the octave let us fix them so that they will make a tracing, while still vibrating, on a revolving strip of paper. We shall then find that the fork emitting the note C makes (say) 256 vibrations per second, the fork D 9/8 256 vibrations, the fork E 5/4 256 vibrations, and so on. Thus we associate the notes of the octave together and we say that their quality was the same but that their pitch differed, and since the pitch depends on the frequency of vibration of the fork, or of the air in its vicinity, we say that pitch differences are quantitative ones, and that the states of consciousness which accompany these physical events are also quantitatively different.
So also with colour. If we had no such apparatus as prisms or diffraction gratings, which enable us to find what is the wave length of light, should we have any idea of the spectral hues, red, yellow, orange, green, etc., as differing from each other quantitatively? It is certain that we should not. But observation and experiment have shown that the nerve-endings of the optic nerve in the retina are stimulated by vibrations of something which we agree to call the ether of space, and that the frequency of vibration of light which we call red is less than that which we call orange, while the frequency of vibration of orange light is less again than that of blue light, and so on. To our consciousness red, orange, yellow, and blue light are absolutely different, but we disregard this intuition and we say that our perceptions of light are similar in kind but differ, in some of them are more intense than are some others. Again, have we any intuitive knowledge of increasing temperature? If we dip our hands into ice-cold water the sensation is one of pain, if the water has a temperature of 5° C. it feels cold, if it is at 15° C. we have no particular appreciation of temperature, if at 25° C. it feels very warm, if it is at 60° it is very hot, and if it is at 90° we are probably scalded and the feeling is again one of pain. If we place a thermometer in the water we notice that each sensation in turn is associated with a progressive lengthening of the mercury thread, and if we investigate the physical condition of the water we find that at each stage the velocity of movement of the molecules was greater than that at the preceding stage. We say, then, that our different perceptions were those of heat of different degrees of intensity, so transferring to the perceptions themselves the notions of space-magnitudes acquired by a study of the expansion of the mercury in the thermometer, or by the adoption of the physical theory of the kinetic structure of the water. Yet it is quite certain that what we experienced were quite different things or conditions, cold, warmth, heat, and pain, and indeed, in this series of perceptions different receptor organs are involved.
Suppose we listen to the note emitted by a syren which is sounding with slowly increasing loudness but with a pitch which remains constant. We do not notice at first that the sound is becoming louder, but after a little time we do notice a difference. Let us call the amplitude of vibration of the air when the syren first sounds E, and then, when we notice a difference, let us call the amplitude ΔE + E, ΔE being the increment of amplitude. Let us call our sensation when the syren first sounds S, and our sensations when the sound has become louder S + ΔS, ΔS being the “increment of sensation.” Then the relation holds:—
ΔE | = constant. |
E |
