Chapter I: The Intensity of Psychic States (2)

If such be the case, we shall not compare a pain of increasing intensity to a note which grows louder and louder, but rather to a symphony, in which an increasing number of instruments make themselves heard. Within the characteristic sensation, which gives the tone to all the others, consciousness distinguishes a larger or smaller number of sensations arising at different points of the periphery, muscular contractions, organic movements of every kind: the choir of these elementary psychic states voices the new demands of the organism, when confronted by a new situation. In other words, we estimate the intensity of a pain by the larger or smaller part of the organism which takes interest in it. Richet[12] has observed that the slighter the pain, the more precisely is it referred to a particular spot; if it becomes more intense, it is referred to the whole of the member affected. And he concludes by saying that "the pain spreads in proportion as it is more intense."[13] We should rather reverse the sentence, and define the intensity of the pain by the very number and extent of the parts of the body which sympathize with it and react, and whose reactions are perceived by consciousness. To convince ourselves of this, it will be enough to read the remarkable description of disgust given by the same author: "If the stimulus is slight there may be neither nausea nor vomiting.... If the stimulus is stronger, instead of being confined to the pneumo-gastric nerve, it spreads and affects almost the whole organic system. The face turns pale, the smooth muscles of the skin contract, the skin is covered with a cold perspiration, the heart stops beating: in a word there is a general organic disturbance following the stimulation of the medulla oblongata, and this disturbance is the supreme expression of disgust."[14] But is it nothing more than its expression? In what will the general sensation of disgust consist, if not in the sum of these elementary sensations? And what can we understand here by increasing intensity, if it is not the constantly increasing number of sensations which join in with the sensations already experienced? Darwin has drawn a striking picture of the reactions following a pain which becomes more and more acute. "Great pain urges all animals ... to make the most violent and diversified efforts to escape from the cause of suffering.... With men the mouth may be closely compressed, or more commonly the lips are retracted with the teeth clenched or ground together.... The eyes stare wildly ... or the brows are heavily contracted. Perspiration bathes the body.... The circulation and respiration are much affected."[15] Now, is it not by this very contraction of the muscles affected that we measure the intensity of a pain? Analyse your idea of any suffering which you call extreme: do you not mean that it is unbearable, that is to say, that it urges the organism to a thousand different actions in order to escape from it? I can picture to myself a nerve transmitting a pain which is independent of all automatic reaction; and I can equally understand that stronger or weaker stimulations influence this nerve differently. But I do not see how these differences of sensation would be interpreted by our consciousness as differences of quantity unless we connected them with the reactions which usually accompany them, and which are more or less extended and more or less important. Without these subsequent reactions, the intensity of the pain would be a quality, and not a magnitude.

[Sidenote: Pleasures compared by bodily inclination.]

We have hardly any other means of comparing several pleasures with one another. What do we mean by a greater pleasure except a pleasure that is preferred? And what can our preference be, except a certain disposition of our organs, the effect of which is that, when two pleasures are offered simultaneously to our mind, our body inclines towards one of them? Analyse this inclination itself and you will find a great many little movements which begin and become perceptible in the organs concerned, and even in the rest of the body, as if the organism were coming forth to meet the pleasure as soon as it is pictured. When we define inclination as a movement, we are not using a metaphor. When confronted by several pleasures pictured by our mind, our body turns towards one of them spontaneously, as though by a reflex action. It rests with us to check it, but the attraction of the pleasure is nothing but this movement that is begun, and the very keenness of the pleasure, while we enjoy it, is merely the inertia of the organism, which is immersed in it and rejects every other sensation. Without this _vis inertiae_ of which we become conscious by the very resistance which we offer to anything that might distract us, pleasure would be a state, but no longer a magnitude. In the moral as in the physical world, attraction serves to define movement rather than to produce it.

[Sidenote: The intensity of representative sensations. Many also affective and intensity is measured by reaction called forth. In others a new element enters.]

We have studied the affective sensations separately, but we must now notice that many representative sensations possess an affective character, and thus call forth a reaction on our part which we take into account in estimating their intensity. A considerable increase of light is represented for us by a characteristic sensation which is not yet pain, but which is analogous to dazzling. In proportion as the amplitude of sound-vibrations increases, our head and then our body seem to us to vibrate or to receive a shock. Certain representative sensations, those of taste, smell and temperature, have a fixed character of pleasantness or unpleasantness. Between flavours which are more or less bitter you will hardly distinguish anything but differences of quality; they are like different shades of one and the same colour. But these differences of quality are at once interpreted as differences of quantity, because of their affective character and the more or less pronounced movements of reaction, pleasure or repugnance, which they suggest to us. Besides, even when the sensation remains purely representative, its external cause cannot exceed a certain degree of strength or weakness without inciting us to movements which enable us to measure it. Sometimes indeed we have to make an effort to perceive this sensation, as if it were trying to escape notice; sometimes on the other hand it obsesses us, forces itself upon us and engrosses us to such an extent that we make every effort to escape from it and to remain ourselves. In the former case the sensation is said to be of slight intensity, and in the latter case very intense. Thus, in order to perceive a distant sound, to distinguish what we call a faint smell or a dim light, we strain all our faculties, we "pay attention." And it is just because the smell and the light thus require to be reinforced by our efforts that they seem to us feeble. And, inversely, we recognize a sensation of extreme intensity by the irresistible reflex movements to which it incites us, or by the powerlessness with which it affects us. When a cannon is fired off close to our ears or a dazzling light suddenly flares up, we lose for an instant the consciousness of our personality; this state may even last some time in the case of a very nervous subject. It must be added that, even within the range of the so-called medium intensities, when we are dealing on even terms with a representative sensation, we often estimate its importance by comparing it with another which it drives away, or by taking account of the persistence with which it returns. Thus the ticking of a watch seems louder at night because it easily monopolizes a consciousness almost empty of sensations and ideas. Foreigners talking to one another in a language which we do not understand seem to us to speak very loudly, because their words no longer call up any ideas in our mind, and thus break in upon a kind of intellectual silence and monopolize our attention like the ticking of a watch at night. With these so-called medium sensations, however, we approach a series of psychic states, the intensity of which is likely to possess a new meaning. For, in most cases, the organism hardly reacts at all, at least in a way that can be perceived; and yet we still make a magnitude out of the pitch of a sound, the intensity of a light, the saturation of a colour. Doubtless, a closer observation of what takes place in the whole of the organism when we hear such and such a note or perceive such and such a colour has more than one surprise in store for us. Has not C. Féré shown that every sensation is accompanied by an increase in muscular force which can be measured by the dynamometer?[16] But of an increase of this kind there is hardly any consciousness at all, and if we reflect on the precision with which we distinguish sounds and colours, nay, even weights and temperatures, we shall easily guess that some new element must come into play in our estimate of them.

[Sidenote: The purely representative sensations are measured by external causes.]

Now, the nature of this element is easy to determine. For, in proportion as a sensation loses its affective character and becomes representative, the reactions which it called forth on our part tend to disappear, but at the same time we perceive the external object which is its cause, or if we do not now perceive it, we have perceived it, and we think of it. Now, this cause is extensive and therefore measurable: a constant experience, which began with the first glimmerings of consciousness and which continues throughout the whole of our life, shows us a definite shade of sensation corresponding to a definite amount of stimulation. We thus associate the idea of a certain quantity of cause with a certain quality of effect; and finally, as happens in the case of every acquired perception, we transfer the idea into the sensation, the quantity of the cause into the quality of the effect. At this very moment the intensity, which was nothing but a certain shade or quality of the sensation, becomes a magnitude. We shall easily understand this process if, for example, we hold a pin in our right hand and prick our left hand more and more deeply. At first we shall feel as it were a tickling, then a touch which is succeeded by a prick, then a pain localized at a point, and finally the spreading of this pain over the surrounding zone. And the more we reflect on it, the more clearly shall we see that we are here dealing with so many qualitatively distinct sensations, so many varieties of a single species. But yet we spoke at first of one and the same sensation which spread further and further, of one prick which increased in intensity. The reason is that, without noticing it, we localized in the sensation of the left hand, which is pricked, the progressive effort of the right hand, which pricks. We thus introduced the cause into the effect, and unconsciously interpreted quality as quantity, intensity as magnitude. Now, it is easy to see that the intensity of every representative sensation ought to be understood in the same way.

[Sidenote: The sensations of sound. Intensity measured by effort necessary to produce a similar sound.]

The sensations of sound display well marked degrees of intensity. We have already spoken of the necessity of taking into account the affective character of these sensations, the shock received by the whole of the organism. We have shown that a very intense sound is one which engrosses our attention, which supplants all the others. But take away the shock, the well-marked vibration, which you sometimes feel in your head or even throughout your body: take away the clash which takes place between sounds heard simultaneously: what will be left except an indefinable quality of the sound which is heard? But this quality is immediately interpreted as quantity because you have obtained it yourself a thousand times, e.g. by striking some object and thus expending a definite quantity of effort. You know, too, how far you would have to raise your voice to produce a similar sound, and the idea of this effort immediately comes into your mind when you transform the intensity of the sound into a magnitude. Wundt[17] has drawn attention to the quite special connexions of vocal and auditory nervous filaments which are met with in the human brain. And has it not been said that to hear is to speak to oneself? Some neuropaths cannot be present at a conversation without moving their lips; this is only an exaggeration of what takes place in the case of every one of us. How will the expressive or rather suggestive power of music be explained, if not by admitting that we repeat to ourselves the sounds heard, so as to carry ourselves back into the psychic state out of which they emerged, an original state, which nothing will express, but which something may suggest, viz., the very motion and attitude which the sound imparts to our body?

[Sidenote: Intensity and pitch. The part played by muscular effort.]

Thus, when we speak of the intensity of a sound of medium force as a magnitude, we allude principally to the greater or less effort which we should have ourselves to expend in order to summon, by our own effort, the same auditory sensation.

Now, besides the intensity, we distinguish another characteristic property of the sound, its pitch. Are the differences in pitch, such as our ear perceives, quantitative differences? I grant that a sharper sound calls up the picture of a higher position in space. But does it follow from this that the notes of the scale, as auditory sensations, differ otherwise than in quality? Forget what you have learnt from physics, examine carefully your idea of a higher or lower note, and see whether you do not think simply of the greater or less effort which the tensor muscle of your vocal chords has to make in order to produce the note? As the effort by which your voice passes from one note to another is discontinuous, you picture to yourself these successive notes as points in space, to be reached by a series of sudden jumps, in each of which you cross an empty separating interval: this is why you establish intervals between the notes of the scale. Now, why is the line along which we dispose them vertical rather than horizontal, and why do we say that the sound ascends in some cases and descends in others? It must be remembered that the high notes seem to us to produce some sort of resonance in the head and the deep notes in the thorax: this perception, whether real or illusory, has undoubtedly had some effect in making us reckon the intervals vertically. But we must also notice that the greater the tension of the vocal chords in the chest voice, the greater is the surface of the body affected, if the singer is inexperienced; this is just the reason why the effort is felt by him as more intense. And as he breathes out the air upwards, he will attribute the same direction to the sound produced by the current of air; hence the sympathy of a larger part of the body with the vocal muscles will be represented by a movement upwards. We shall thus say that the note is higher because the body makes an effort as though to reach an object which is more elevated in space. In this way it became customary to assign a certain height to each note of the scale, and as soon as the physicist was able to define it by the number of vibrations in a given time to which it corresponds, we no longer hesitated to declare that our ear perceived differences of quantity directly. But the sound would remain a pure quality if we did not bring in the muscular effort which produces it or the vibrations which explain it.

[Sidenote: The sensations of heat and cold. These soon become affective and are measured by reactions called forth.]

The experiments of Blix, Goldscheider and Donaldson[18] have shown that the points on the surface of the body which feel cold are not the same as those which feel heat. Physiology is thus disposed to set up a distinction of nature, and not merely of degree, between the sensations of heat and cold. But psychological observation goes further, for close attention can easily discover specific differences between the different sensations of heat, as also between the sensations of cold. A more intense heat is really another kind of heat. We call it more intense because we have experienced this same change a thousand times when we approached nearer and nearer a source of heat, or when a growing surface of our body was affected by it. Besides, the sensations of heat and cold very quickly become affective and incite us to more or less marked reactions by which we measure their external cause: hence, we are inclined to set up similar quantitative differences among the sensations which correspond to lower intensities of the cause. But I shall not insist any further; every one must question himself carefully on this point, after making a clean sweep of everything which his past experience has taught him about the cause of his sensations and coming face to face with the sensations themselves. The result of this examination is likely to be as follows: it will be perceived that the magnitude of a representative sensation depends on the cause having been put into the effect, while the intensity of the affective element depends on the more or less important reactions which prolong the external stimulations and find their way into the sensation itself.

[Sidenote: The sensation of pressure and weight measured by extent of organism affected.]

The same thing will be experienced in the case of pressure and even weight. When you say that a pressure on your hand becomes stronger, see whether you do not mean that there first was a contact, then a pressure, afterwards a pain, and that this pain itself, after having gone through a series of qualitative changes, has spread further and further over the surrounding region. Look again and see whether you do not bring in the more and more intense, i.e. more and more extended, effort of resistance which you oppose to the external pressure. When the psychophysicist lifts a heavier weight, he experiences, he says, an increase of sensation. Examine whether this increase of sensation ought not rather to be called a sensation of increase. The whole question is centred in this, for in the first case the sensation would be a quantity like its external cause, whilst in the second it would be a quality which had become representative of the magnitude of its cause. The distinction between the heavy and the light may seem to be as old-fashioned and as childish as that between the hot and the cold. But the very childishness of this distinction makes it a psychological reality. And not only do the heavy and the light impress our consciousness as generically different, but the various degrees of lightness and heaviness are so many species of these two genera. It must be added that the difference of quality is here translated spontaneously into a difference of quantity, because of the more or less extended effort which our body makes in order to lift a given weight. Of this you will soon become aware if you are asked to lift a basket which, you are told, is full of scrap-iron, whilst in fact there is nothing in it. You will think you are losing your balance when you catch hold of it, as though distant muscles had interested themselves beforehand in the operation and experienced a sudden disappointment. It is chiefly by the number and nature of these sympathetic efforts, which take place at different points of the organism, that you measure the sensation of weight at a given point; and this sensation would be nothing more than a quality if you did not thus introduce into it the idea of a magnitude. What strengthens the illusion on this point is that we have become accustomed to believe in the immediate perception of a homogeneous movement in a homogeneous space. When I lift a light weight with my arm, all the rest of my body remaining motionless, I experience a series of muscular sensations each of which has its "local sign," its peculiar shade: it is this series which my consciousness interprets as a continuous movement in space. If I afterwards lift a heavier weight to the same height with the same speed, I pass through a new series of muscular sensations, each of which differs from the corresponding term of the preceding series. Of this I could easily convince myself by examining them closely. But as I interpret this new series also as a continuous movement, and as this movement has the same direction, the same duration and the same velocity as the preceding, my consciousness feels itself bound to localize the difference between the second series of sensations and the first elsewhere than in the movement itself. It thus materializes this difference at the extremity of the arm which moves; it persuades itself that the sensation of movement has been identical in both cases, while the sensation of weight differed in magnitude. But movement and weight are but distinctions of the reflective consciousness: what is present to consciousness immediately is the sensation of, so to speak, a heavy movement, and this sensation itself can be resolved by analysis into a series of muscular sensations, each of which represents by its shade its place of origin and by its colour the magnitude of the weight lifted.

[Sidenote: The sensation of light. Qualitative changes of colour interpreted as quantitative changes in intensity of luminous source.]

Shall we call the intensity of light a quantity, or shall we treat it as a quality? It has not perhaps been sufficiently noticed what a large number of different factors co-operate in daily life in giving us information about the nature of the luminous source. We know from long experience that, when we have a difficulty in distinguishing the outlines and details of objects, the light is at a distance or on the point of going out. Experience has taught us that the affective sensation or nascent dazzling that we experience in certain cases must be attributed to a higher intensity of the cause. Any increase or diminution in the number of luminous sources alters the way in which the sharp lines of bodies stand out and also the shadows which they project. Still more important are the changes of hue which coloured surfaces, and even the pure colours of the spectrum, undergo under the influence of a brighter or dimmer light. As the luminous source is brought nearer, violet takes a bluish tinge, green tends to become a whitish yellow, and red a brilliant yellow. Inversely, when the light is moved away, ultramarine passes into violet and yellow into green; finally, red, green and violet tend to become a whitish yellow. Physicists have remarked these changes of hue for some time;[19] but what is still more remarkable is that the majority of men do not perceive them, unless they pay attention to them or are warned of them. Having made up our mind, once for all, to interpret changes of quality as changes of quantity, we begin by asserting that every object has its own peculiar colour, definite and invariable. And when the hue of objects tends to become yellow or blue, instead of saying that we see their colour change under the influence of an increase or diminution of light, we assert that the colour remains the same but that our sensation of luminous intensity increases or diminishes. We thus substitute once more, for the qualitative impression received by our consciousness, the quantitative interpretation given by our understanding. Helmholtz has described a case of interpretation of the same kind, but still more complicated: "If we form white with two colours of the spectrum, and if we increase or diminish the intensities of the two coloured lights in the same ratio, so that the proportions of the combination remain the same, the resultant colour remains the same although the relative intensity of the sensations undergoes a marked change.... This depends on the fact that the light of the sun, which we consider as the normal white light during the day, itself undergoes similar modifications of shade when the luminous intensity varies."[20]

[Sidenote: Does experiment prove that we can measure directly our sensations of light?]

But yet, if we often judge of variations in the luminous source by the relative changes of hue of the objects which surround us, this is no longer the case in simple instances where a single object, e.g. a white surface, passes successively through different degrees of luminosity. We are bound to insist particularly on this last point. For the physicist speaks of degrees of luminous intensity as of real quantities: and, in fact, he measures them by the photometer. The psychophysicist goes still further: he maintains that our eye itself estimates the intensities of light. Experiments have been attempted, at first by Delbœuf,[21] and afterwards by Lehmann and Neiglick,[22] with the view of constructing a psychophysical formula from the direct measurement of our luminous sensations. Of these experiments we shall not dispute the result, nor shall we deny the value of photometric processes; but we must see how we have to interpret them.

[Sidenote: Photometric experiments. We perceive different shades and afterwards interpret them as decreasing intensities of white light.]

Look closely at a sheet of paper lighted e.g. by four candles, and put out in succession one, two, Photometric three of them. You say that the surface remains white and that its brightness diminishes. But you are aware that one candle has just been put out; or, if you do not know it, you have often observed a similar change in the appearance of a white surface when the illumination was diminished. Put aside what you remember of your past experiences and what you are accustomed to say of the present ones; you will find that what you really perceive is not a diminished illumination of the white surface, it is a _layer of shadow_ passing over this surface at the moment the candle is extinguished. This shadow is a reality to your consciousness, like the light itself. If you call the first surface in all its brilliancy white, you will have to give another name to what you now see, for it is a different thing: it is, if we may say so, a new shade of white. We have grown accustomed, through the combined influence of our past experience and of physical theories, to regard black as the absence, or at least as the minimum, of luminous sensation, and the successive shades of grey as decreasing intensities of white light. But, in point of fact, black has just as much reality for our consciousness as white, and the decreasing intensities of white light illuminating a given surface would appear to an unprejudiced consciousness as so many different shades, not unlike the various colours of the spectrum. This is the reason why the change in the sensation is not continuous, as it is in the external cause, and why the light can increase or decrease for a certain period without producing any apparent change in the illumination of our white surface: the illumination will not appear to change until the increase or decrease of the external light is sufficient to produce a new quality. The variations in brightness of a given colour--the affective sensations of which we have spoken above being left aside--would thus be nothing but qualitative changes, were it not our custom to transfer the cause to the effect and to replace our immediate impressions by what we learn from experience and science. The same thing might be said of degrees of saturation. Indeed, if the different intensities of a colour correspond to so many different shades existing between this colour and black, the degrees of saturation are like shades intermediate between this same colour and pure white. Every colour, we might say, can be regarded under two aspects, from the point of view of black and from the point of view of white. And black is then to intensity what white is to saturation.

[Sidenote: In photometric experiments the physicist compares, not sensations, but physical effects.]

The meaning of the photometric experiments will now be understood. A candle placed at a certain distance from a sheet of paper illuminates it in a certain way: you double the distance and find that four candles are required to produce the same effects, sensation. From this you conclude that if you had doubled the distance without increasing the intensity of the luminous source, the resultant illumination would have been only one-fourth as bright. But it is quite obvious that you are here dealing with the physical and not the psychological effect. For it cannot be said that you have compared two sensations with one another: you have made use of a single sensation in order to compare two different luminous sources with each other, the second four times as strong as the first but twice as far off. In a word, the physicist never brings in sensations which are twice or three times as great as others, but only identical sensations, destined to serve as intermediaries between two physical quantities which can then be equated with one another. The sensation of light here plays the part of the auxiliary unknown quantity which the mathematician introduces into his calculations, and which is not intended to appear in the final result.

[Sidenote: The psychophysicist claims to compare and measure sensations. Delbœuf's experiments.]

But the object of the psychophysicist is entirely different: it is the sensation of light itself which he studies, and claims to measure. Sometimes he will proceed to integrate infinitely small differences, after the method of Fechner; sometimes he will compare one sensation directly with another. The latter method, due to Plateau and Delbœuf, differs far less than has hitherto been believed from Fechner's: but, as it bears more especially on the luminous sensations, we shall deal with it first. Delbœuf places an observer in front of three concentric rings which vary in brightness. By an ingenious arrangement he can cause each of these rings to pass through all the shades intermediate between white and black. Let us suppose that two hues of grey are simultaneously produced on two of the rings and kept unchanged; let us call them A and B. Delbœuf alters the brightness, C, of the third ring, and asks the observer to tell him whether, at a certain moment, the grey, B, appears to him equally distant from the other two. A moment comes, in fact, when the observer states that the contrast A B is equal to the contrast B C, so that, according to Delbœuf, a scale of luminous intensities could be constructed on which we might pass from each sensation to the following one by equal sensible contrasts: our sensations would thus be measured by one another. I shall not follow Delbœuf into the conclusions which he has drawn from these remarkable experiments: the essential question, the only question, as it seems to me, is whether a contrast A B, formed of the elements A and B, is really equal to a contrast B C, which is differently composed. As soon as it is proved that two sensations can be equal without being identical, psychophysics will be established. But it is this equality which seems to me open to question: it is easy to explain, in fact, how a sensation of luminous intensity can be said to be at an equal distance from two others.

[Sidenote: In what cases differences of colour might be interpreted as differences of magnitude.]

Let us assume for a moment that from our birth onwards the growing intensity of a luminous source had always called up in our consciousness, one after the other, the different colours of the spectrum. There is no doubt that these colours would then appear to us as so many notes of a gamut, as higher or lower degrees in a scale, in a word, as magnitudes. Moreover it would be easy for us to assign each of them its place in the series. For although the extensive cause varies continuously, the changes in the sensation of colour are discontinuous, passing from one shade to another shade. However numerous, then, may be the shades intermediate between the two colours, A and B, it will always be possible to count them in thought, at least roughly, and ascertain whether this number is almost equal to that of the shades which separate B from another colour C. In the latter case it will be said that B is equally distant from A and C, that the contrast is the same on one side as on the other. But this will always be merely a convenient interpretation: for although the number of intermediate shades may be equal on both sides, although we may pass from one to the other by sudden leaps, we do not know whether these leaps are magnitudes, still less whether they are _equal_ magnitudes: above all it would be necessary to show that the intermediaries which have helped us throughout our measurement could be found again inside the object which we have measured. If not, it is only by a metaphor that a sensation can be said to be an equal distance from two others.

[Sidenote: This is just the case with differences of intensity in sensations of light. Delbœuf's underlying postulate.]

Now, if the views which we have before enumerated with regard to luminous intensities are accepted, it will be recognized that the different hues of grey which Delbœuf displays to us are strictly analogous, for our consciousness, to colours, and that if we declare that a grey tint is equidistant from two other grey tints, it is in the same sense in which it might be said that orange, for example, is at an equal distance from green and red. But there is this difference, that in all our past experience the succession of grey tints has been produced in connexion with a progressive increase or decrease in illumination. Hence we do for the differences of brightness what we do not think of doing for the differences of colour: we promote the changes of quality into variations of magnitude. Indeed, there is no difficulty here about the measuring, because the successive shades of grey produced by a continuous decrease of illumination are discontinuous, as being qualities, and because we can count approximately the principal intermediate shades which separate any two kinds of grey. The contrast A B will thus be declared equal to the contrast B C when our imagination, aided by our memory, inserts between A and B the same number of intermediate shades as between B and C. It is needless to say that this will necessarily be a very rough estimate. We may anticipate that it will vary considerably with different persons. Above all it is to be expected that the person will show more hesitation and that the estimates of different persons will differ more widely in proportion as the difference in brightness between the rings A and B is increased, for a more and more laborious effort will be required to estimate the number of intermediate hues. This is exactly what happens, as we shall easily perceive by glancing at the two tables drawn up by Delbœuf.[23] In proportion as he increases the difference in brightness between the exterior ring and the middle ring, the difference between the numbers on which one and the same observer or different observers successively fix increases almost continuously from 3 degrees to 94, from 5 to 73, from 10 to 25, from 7 to 40. But let us leave these divergences on one side: let us assume that the observers are always consistent and always agree with one another; will it then be established that the contrasts A B and B C are equal? It would first be necessary to prove that two successive elementary contrasts are equal quantities, whilst, in fact, we only know that they are successive. It would then be necessary to prove that inside a given tint of grey we perceive the less intense shades which our imagination has run through in order to estimate the objective intensity of the source of light. In a word, Delbœuf's psychophysics assumes a theoretical postulate of the greatest importance, which is disguised under the cloak of an experimental result, and which we should formulate as follows: "When the objective quantity of light is continuously increased, the differences between the hues of grey successively obtained, each of which represents the smallest perceptible increase of physical stimulation, are quantities equal to one another. And besides, any one of the sensations obtained can be equated with the sum of the differences which separate from one another all previous sensations, going from zero upwards." Now, this is just the postulate of Fechner's psychophysics, which we are going to examine.

[Sidenote: Fechner's psychophysics. Weber's Law.]

Fechner took as his starting-point a law discovered by Weber, according to which, given a certain stimulus which calls forth a certain sensation, the amount by which the stimulus must be increased for consciousness to become aware of any change bears a fixed relation to the original stimulus. Thus, if we denote by Ε the stimulus which corresponds to the sensation S, and by ΔΕ the amount by which the original stimulus must be increased in order that a sensation of difference may be produced, we shall have ΔΕ/E = const. This formula has been much modified by the disciples of Fechner, and we prefer to take no part in the discussion; it is for experiment to decide between the relation established by Weber and its substitutes. Nor shall we raise any difficulty about granting the probable existence of a law of this nature. It is here really a question not of measuring a sensation but only of determining the exact moment at which an increase of stimulus produces a change in it. Now, if a definite amount of stimulus produces a definite shade of sensation, it is obvious that the minimum amount of stimulus required to produce a change in this shade is also definite; and since it is not constant, it must be a function of the original stimulus. But how are we to pass from a relation between the stimulus and its minimum increase to an equation which connects the **"amount of sensation" with the corresponding stimulus? The whole of psychophysics is involved in this transition, which is therefore worthy of our closest consideration.

[Sidenote: The underlying assumptions and the process by which Fechner's Law is reached.]

We shall distinguish several different artifices in the process of transition from Weber's experiments, or from any other series of similar observations, to a psychophysical law like Fechner's. It is first of all agreed to consider our consciousness of an increase of stimulus as an increase of the sensation S: this is therefore called S. It is then asserted that all the sensations ΔS, which correspond to the smallest perceptible increase of stimulus, are equal to one another. They are therefore treated as quantities, and while, on the one hand, these quantities are supposed to be always equal, and, on the other, experiment has given a certain relation ΔΕ = ∫(E) between the stimulus Ε and its minimum increase, the constancy of ΔS is expressed by writing ΔS = C ΔE/∫(E), C being a constant quantity. Finally it is agreed to replace the very small differences ΔS and ΔΕ by the infinitely small differences _d_S and _d_E, whence an equation which is, this time, a differential one: _d_S = C _d_E/∫(E). We shall now simply have to integrate on both sides to obtain the desired relation[24]: S=C ∬_d_E/∫(E). And the transition will thus be made from a proved law, which only concerned the _occurrence_ of a sensation, to an unprovable law which gives its _measure._

Without entering upon any thorough discussion of this ingenious operation, let us show in a few words how Fechner has grasped the real difficulty of the problem, how he has tried to overcome it, and where, as it seems to us, the flaw in his reasoning lies.

[Sidenote: Can two sensations be equal without being identical?]

Fechner realized that measurement could not be introduced into psychology without first defining what is meant by the equality and addition of two simple states, e.g. two sensations. But, unless they are identical, we do not at first see how two sensations can be equal. Undoubtedly in the physical world equality is not synonymous with identity. But the reason is that every phenomenon, every object, is there presented under two aspects, the one qualitative and the other extensive: nothing prevents us from putting the first one aside, and then there remains nothing but terms which can be directly or indirectly superposed on one another and consequently seen to be identical. Now, this qualitative element, which we begin by eliminating from external objects in order to measure them, is the very thing which psychophysics retains and claims to measure. And it is no use trying to measure this quality Q by some physical quantity Q' which lies beneath it: for it would be necessary to have previously shown that Q is a function of Q', and this would not be possible unless the quality Q had first been measured with some fraction of itself. Thus nothing prevents us from measuring the sensation of heat by the degree of temperature; but this is only a convention, and the whole point of psychophysics lies in rejecting this convention and seeking how the sensation of heat varies when you change the temperature. In a word, it seems, on the one hand, that two different sensations cannot be said to be equal unless some identical residuum remains after the elimination of their qualitative difference; but, on the other hand, this qualitative difference being all that we perceive, it does not appear what could remain once it was eliminated.

[Sidenote: Fechner's method of _minimum_ differences.]

The novel feature in Fechner's treatment is that he did not consider this difficulty insurmountable. Taking advantage of the fact that sensation varies by sudden jumps while the stimulus increases continuously, he did not hesitate to call these differences of sensation by the same name: they are all, he says, _minimum_ differences, since each corresponds to the smallest perceptible increase in the external stimulus. Therefore you can set aside the specific shade or quality of these successive differences; a common residuum will remain in virtue of which they will be seen to be in a manner identical: they all have the common character of being _minima._ Such will be the definition of equality which we were seeking. Now, the definition of addition will follow naturally. For if we treat as a quantity the difference perceived by consciousness between two sensations which succeed one another in the course of a continuous increase of stimulus, if we call the first sensation S, and the second S + ΔS, we shall have to consider every sensation S as a sum, obtained by the addition of the minimum differences through which we pass before reaching it. The only remaining step will then be to utilize this twofold definition in order to establish, first of all, a relation between the differences ΔS and ΔΕ, and then, through the substitution of the differentials, between the two variables. True, the mathematicians may here lodge a protest against the substitution of differential for difference; the psychologists may ask, too, whether the quantity ΔS, instead of being constant, does not vary as the sensation S itself;[25] finally, taking the psychophysical law for granted, we may all debate about its real meaning. But, by the mere fact that ΔS is regarded as a quantity and S as a sum, the fundamental postulate of the whole process is accepted.

[Sidenote: Break-down of the assumption that the sensation is a sum, and the minimum differences quantities.]

Now it is just this postulate which seems to us open to question, even if it can be understood. Assume that I experience a sensation S, and that, increasing the stimulus continuously, I perceive this increase after a certain time. I am now notified of the increase of the cause: but why should I call this notification an arithmetical difference? No doubt the notification consists in the fact that the original state S has changed: it has become S'; but the transition from S to S' could only be called an arithmetical difference if I were conscious, so to speak, of an interval between S and S', and if my sensation were felt to rise from S to S' by the addition of something. By giving this transition a name, by calling it ΔS,** you make it first a reality and then a quantity. Now, not only are you unable to explain in what sense this transition is a quantity, but reflection will show you that it is not even a reality; the only realities are the states S and S' through which I pass. No doubt, if S and S' were numbers, I could assert the reality of the difference S'--S even though S and S' alone were given; the reason is that the number S'--S, which is a certain sum of units, will then represent just the successive moments of the addition by which we pass from S to S'. But if S and S' are simple states, in what will the _interval_ which separates them consist? And what, then, can the transition from the first state to the second be, if not a mere act of your thought, which, arbitrarily and for the sake of the argument, assimilates a succession of two states to a differentiation of two magnitudes?

[Sidenote: We can speak of "arithmetical difference" only in a conventional sense.]

Either you keep to what consciousness presents to you or you have recourse to a conventional mode of representation. In the first case you will find a difference between S and S' like that between the shades sense. Of rainbow, and not at all an interval of magnitude. In the second case you may introduce the symbol ΔS if you like, but it is only in a conventional sense that you will speak here of an arithmetical difference, and in a conventional sense, also, that you will assimilate a sensation to a sum. The most acute of Fechner's critics, Jules Tannery, has made the latter point perfectly clear. "It will be said, for example, that a sensation of 50 degrees is expressed by the number of differential sensations which would succeed one another from the point where sensation is absent up to the sensation of 50 degrees.... I do not see that this is anything but a definition, which is as legitimate as it is arbitrary."[26]

[Sidenote: Delbœuf's results seem more plausible but, in the end, all psychophysics revolves in a vicious circle.]

We do not believe, in spite of all that has been said, that the method of mean gradations has set psychophysics on a new path. The novel feature in Delbœuf's investigation was that he chose a particular case, in which consciousness seemed to decide in Fechner's favour, and in which common sense itself played the part of the psychophysicist. He inquired whether certain sensations did not appear to us immediately as equal although different, and whether it would not be possible to draw up, by their help, a table of sensations which were double, triple or quadruple those which preceded them. The mistake which Fechner made, as we have just seen, was that he believed in an interval between two successive sensations S and S', when there is simply a _passing_ from one to the other and not a _difference_ in the arithmetical sense of the word. But if the two terms between which the passing takes place could be given simultaneously, there would then be a contrast besides the transition; and although the contrast is not yet an arithmetical difference, it resembles it in a certain respect; for the two terms which are compared stand here side by side as in a case of subtraction of two numbers. Suppose now that these sensations belong to the same _genus_ and that in our past experience we have constantly been present at their march past, so to speak, while the physical stimulus increased continuously: it is extremely probable that we shall thrust the cause into the effect, and that the idea of contrast will thus melt into that of arithmetical difference. As we shall have noticed, moreover, that the sensation changed abruptly while the stimulus rose continuously, we shall no doubt estimate the distance between two given sensations by a rough guess at the number of these sudden jumps, or at least of the intermediate sensations which usually serve us as landmarks. To sum up, the contrast will appear to us as a difference, the stimulus as a quantity, the sudden jump as an element of equality: combining these three factors, we shall reach the idea of equal quantitative differences. Now, these conditions are nowhere so well realized as when surfaces of the same colour, more or less illuminated, are simultaneously presented to us. Not only is there here a contrast between similar sensations, but these sensations correspond to a cause whose influence has always been felt by us to be closely connected with its distance; and, as this distance can vary continuously, we cannot have escaped noticing in our past experience a vast number of shades of sensation which succeeded one another along with the continuous increase in the cause. We are therefore able to say that the contrast between one shade of grey and another, for example, seems to us almost equal to the contrast between the latter and a third one; and if we define two equal sensations by saying that they are sensations which a more or less confused process of reasoning interprets as such, we shall in fact reach a law like that proposed by Delbœuf. But it must not be forgotten that consciousness has here passed through the same intermediate steps as the psychophysicist, and that its judgment is worth here just what psychophysics is worth; it is a symbolical interpretation of quality as quantity, a more or less rough estimate of the number of sensations which can come in between two given sensations. The difference is thus not as great as is believed between the method of least noticeable differences and that of mean gradations, between the psychophysics of Fechner and that of Delbœuf. The first led to a conventional measurement of sensation; the second appeals to common sense in the particular cases where common sense adopts a similar convention. In a word, all psychophysics is condemned by its origin to revolve in a vicious circle, for the theoretical postulate on which it rests condemns it to experimental verification, and it cannot be experimentally verified unless its postulate is first granted. The fact is that there is no point of contact between the unextended and the extended, between quality and quantity. We can interpret the one by the other, set up the one as the equivalent of the other; but sooner or later, at the beginning or at the end, we shall have to recognize the conventional character of this assimilation.

[Sidenote: Psychophysics merely pushes to its extreme consequences the fundamental but natural mistake of regarding sensations as magnitudes.]