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Boris Sidis, Ph.D., M.D.

© 1914




        Taking an initial stimulus with its concomitant sensory effect as the starting point we add by degrees small unperceived stimuli until a point is reached when a barely perceptible change of the external stimulation is effected in consciousness. The sum of the differential stimuli up to the point where the perceptible change is produced is found out, and brought into relation with the quantity of the initial stimulus. Working with this method of least observable differences Weber succeeded in expressing the relation of the differential stimulus to sensation in the formula known as "Weber's law." Within certain limits, no matter what the absolute value of the stimulus be, the differential stimulus, or what is the same the barely sensible addition to the initial total stimulus, must bear the same proportion to the total stimulus. By many experiments Weber found that in the case of weight, for instance, the relation is one-third. Thus if the first weight be nine pounds the barely sensible addition will be one-third of nine, or three pounds; in twelve pounds the increment is one-third of twelve, or four pounds; in fifteen pounds the barely sensible increment is again one-third of the total stimulus that is one-third of fifteen, or five pounds, and so on.

        Further investigations have shown that, within certain limits, there is for all the senses which admit of exact measurement a constantly uniform quantitative relation between the stimulus and the just noticeable stimulus-difference. Experimentation by different investigators have confirmed "Weber's law" for the different senses by showing that, within a certain range of intensities of stimuli, there is a more or less constant ratio between the increase of the stimulus necessary to produce a just noticeable difference of sensation and the total stimulus intensity. Thus, it has been shown that noise stimuli must increase by one-third; pressure stimuli by one-fortieth; stimuli of muscular sensations, such as lifting weights, by one-fortieth; achromatic light stimuli by one-hundredth. Weber in his paper De Tactu expressed his law as follows: "In observando discrimine rerum inter se comparatarum non dillerentiam rerum, sed rlltionem differentiae ad magnitudinem rerum inter se comparatarum percipilnus."

        Gustav Theodor Fechner, the founder of psychophysics and its methods, starting with Weber's law worked out a general formula for the quantitative relation between physical stimuli and sensations. Assuming that the just noticeable differences of sensation given by ascending or descending series of different stimuli to be equal units, he finds by means of different psycho-physical methods, first elaborated by him, the threshold of sensations or that stimulus which is just near the limit of giving rise to a sensory effect, but which is still not sufficient to awaken a sensation; in short, he finds the stimulus the correlating sensation of which is zero.

        The minimum perceptible or stimulus-threshold is found by measurements of the different senses. Thus two parallel lines are for most people barely distinguishable when the distance between them subtends an angle of less than 60 seconds. In the sense of hearing the vibrations recurring between 30-35 per second are barely distinguishable. Below 16 vibrations per second no sensation of sound can be produced. Thresholds have been similarly determined for all other sensations. Thus the sense of touch, when tested by the aesthesiometer, an unsatisfactory instrument, gives the average for the tip of the forefinger about 1.65 mm., on the back of the hand about 16.0 mm. Sensibility to pain as tested by the algeometer varies from 10 to 15 degrees. Sensitivity to smell varies with different substances; thus for smell of garlic sensitivity varies in detecting 1 part in 44,000 parts of water to one part in 57,000 parts of water; for oil of lemon from 1 to 116,000 to 1 to 280,000. Taste can detect the bitterness of quinine in a solution of 1 part quinine to about 400,000 to 459,000 of water; the sweetness of sugar can be detected in a solution of 1 part sugar to 200 of water; the taste of salt can be detected in a solution of 1 part salt to about 2,000 parts of water.

        After discovering the zero point of sensation and the minimum perceptible he finds the constant ratio for the just noticeable difference. The minimum perceptible forms the unit of sensation. Each increase of the stimulus giving a just noticeable difference is counted as an additional sensation-unit to the total sum of sensations.

        Let A be the threshold giving sensation zero, and let r be the constant ratio of increase then we have the following series of stimuli and their corresponding sensations:

Sensation 0 is given by stimulus A


" (1+r)1
2 " (1+r)2
3 " (1+r)3
4 " (1+r)4
n " (1+r)n

        Thus we find that while the stimulus increases in a geometrical ratio, the sensation grows in an arithmetical ratio. The sensations stand therefore in the same relation as the logarithms to their numbers. Hence we may say that sensation increases as the logarithm of the stimulus. If S be the sensation, R the stimulus and C the magnitude of the constant ratio, then we have the following formulć:

S=C log. R.

        This formula is known as "Fechner's law."

        Fechner's expression of Weber's law is rather questionable. Fechner assumes that the just noticeable difference of different stimuli are qualitatively and quantitatively equal,―a dubious assumption. A third of an ounce added to an ounce does not feel the same as a third of eighteen pounds added to the same number of pounds, or as nine pounds added to twenty-seven pounds. These units even, if they have a quantitative expression, do not stand in a simple quantitative relation and are rather incommensurable.

        Furthermore, it may even be considered that Fechner's assumption is fundamentally wrong and unpsychological. In opposition to the first elementary principle of psychology Fechner tacitly postulates that sensations can be measured and that one sensation or a complex sensation is a multiple of another. Now the peculiar trait of the phenomena of mental life is essentially their qualitative character. Sensations are not quantities to be measured, but are essentially qualities. A strong sensation is not a weak sensation many times over, but its very strength, its intensity is its own separate individual quality constituting the essence of that particular sensation. An intense sensation of pure white is not a multiple of a weak sensation of grey just as the thought "nation" is not the thought "man" raised to the nth degree.

        In psychological investigations one must be careful not to confound the nature of the physical stimulus with that of the sensation. A physical stimulus can be measured quantitatively, but a sensation does not consist of quantitative units, and hence, is not measurable. The only relation that can be measured and expressed quantitatively is that between stimulus and physiological process, the physical concomitant of psychic states.

          Whether or no we accept Fechner's statement of Weber's law we may safely assume that the threshold rises with successive stimulations. This law holds true of all life processes, from the life of an ameba to the life activity of a highly organized moment-consciousness. In the sphere of sensation we find such a rise of threshold. We are all acquainted with the fact that an additional candle or lamp, for instance, in a well lighted room does not produce the same sensory effect as when brought into a more or less dark room. An electric light in the sun is scarcely perceptible. An additional ounce to a lifted pound does not feel as heavy as when raised by itself. A sound added to another sound or noise, sounds less loud than when appearing isolated, or when the same sound is breaking upon silence.

        The same relation holds true in the case of other senses. This same truth is still more clearly brought out in the fact that, if we take a certain stimulus as a unit, giving rise to a definite sensation, then as we progressively ascend and add more and more units of the same stimulus, the intensity of stimulation is far from rising proportionately. If we take, for instance, the weight of an ounce as our unit of stimulation, then the successive moments of unit stimulations, that is, of ounces, will not give rise to as distinct and similar sensations as the initial sensation. The second ounce will give a sensation fainter than the first one, and the third fainter than the second, and so on until a point is reached when the sensation of an additional ounce will not at all be appreciated, will dwindle away and almost reach the zero point.

        In the same way, if the pressure of a gramme is excited in the hand, successive increments of grammes will not in equal degree increase the sensory effect; the additional increments of grammes, though they are equal units of stimulation, give rise to fainter and fainter sensations, until finally all sensory appreciation of the added unit fades away and disappears. If the hand is immersed in water, say at the freezing point, an addition of ten degrees will be perceptibly appreciated, while successive increments of ten degrees each will be felt less and less, and finally will not be noticed and will be difficult to detect. In short, the threshold rises with the process stimulation.

        To bring about a sensory response of an already stimulated sense-organ the intensity of the stimulus must be relatively increased. This is what constitutes Weber's law. The continuous progressive sensory response of a sense-organ requires a constant increase of stimulations which, within certain limits, bears a constant ratio to the total stimulus. This law is sometimes summed up by psychologists in the statement that "the increase of the stimulus necessary to produce an increase of the sensation bears a constant ratio to the total stimulus." Activity raises the threshold; it is the beginning of fatigue.

        The rise of threshold after stimulation holds true in the whole domain of biological activity. If the gastrocnemius muscle of a frog, for instance, is stimulated by an electric current, the muscle, with each successive stimulation, responds less readily with a contraction, and this becomes more evident with the onset of fatigue. Pffefer, in a series of extremely interesting experiments, has shown that spermatozoids of ferns are attracted by malic acid, the progressive response of attraction of the cell requiring a constant increase of the degree of concentration of the acid, the increment of stimulations, as in the case of sensation, bearing, within certain limits, a constant ratio to the total stimulus. The threshold rises with each successive stimulation.

        The rise of thresholds increases with intensity and duration of stimulation as we approach the state of fatigue. Through the influence of exhaustion, fatigue, or the influence of toxic, autotoxic, emotional, and other stimulations, the thresholds of certain moments have been raised so that ordinary or even maximal stimuli can no longer callout any response. When such a rise of thresholds is present the moments with raised thresholds can no longer enter into association with systems of moments with which they are usually associated, and the result is dissociation, giving rise to the great multitude of phenomena of functional psychosis with a subconscious background, the extent of which depends on the number of raised thresholds, on the extent of the dissociation effected.

        When a moment or aggregate of moments begins to function, it radiates stimulation to other moments or aggregates of moments. All the aggregates which these radiated stimulations reach do not equally begin to function. It will depend largely on the state of the aggregate and its threshold. If the radiated stimuli be minimal, the many aggregates that have a high threshold will not be effected at all. Furthermore, many aggregates whose arousal could otherwise be easily effected by the given stimulus may temporarily be in a condition in which their thresholds have become raised and thus fall outside the sphere of activity of the functioning aggregate. On the other hand, aggregates that are usually inaccessible to those minimal stimuli may under certain conditions be set into activity by minimal stimuli, if there is a lowering of the threshold of the total aggregate. Thus the aggregates set into activity by the functioning aggregate are conditioned by the rise and fall of their thresholds.

        In case where the threshold of an aggregate is raised the radiated minimal stimuli coming from a particular functioning aggregate may become efficient and reach the threshold, when another aggregate begins to function simultaneously. This holds true even in the case when the minimal stimuli, coming from two different aggregates are just below the threshold-stimulus. Thus, under certain conditions, when visual stimuli are barely or not at all discernible, they can become intensified by re-enforcing them with auditory stimuli. This is commonly found in the mode of recovery of some forgotten name, or of some lapsed experience. We try to find the name and seek to come to it in one line of thought, but of no avail; new lines are attempted, and finally the combined activity of the systems reaches the lapsed aggregate whose threshold has become temporarily raised.

        We find the same law further exemplified in the case of the infant under my observation. When with the nipple in his mouth the infant ceased nursing, the sucking movements could be induced again by stimulating some other sense-organ. The tactile, pressure, temperature, and taste stimuli coming from the nipple in the infant's mouth became insufficient to stimulate to activity the functioning aggregate of sucking movements, on account of its raised threshold; only additional stimulation could bring about a further functioning of the lapsed aggregate. This, of course, could also be effected by making the tactual and pressure stimuli more intense, such, for instance, as shaking the nipple while the infant kept it in its mouth. This increase of intensity, however, mainly indicates that the stimuli were no longer effective, and an additional stimulus was requisite, a stimulus that might come either from the same aggregate or from a totally different aggregate.

        In the many cases of post-hypnotic amnesia, we find the same truth further illustrated. In the deeper stages of hypnosis, from which the subject awakens with no remembrance of what had occurred during the state the lapsed memories can be brought into the upper consciousness by plying the subject with many questions. During the trance or during the intermediate stages, with subsequent trance and suggested amnesia, the subject is made to perform a certain action,―to light and extinguish the gas four times in succession, or to open and close the door a certain number of times. The subject is then awakened from his trance; he remembers nothing of what has taken place. If he is asked point-blank whether he remembers any incidents of his hypnotic state, he answers with an emphatic negative. If now the subject is asked whether he knows how much two times two are or his attention is incidentally directed to the gas or to the door, he at once becomes reflective, the subconscious memories are on the way to surge up, and a few further indirect questions, the number depending on the depth of hypnosis, finally bring out the lost memories. The threshold that has risen at the end of the trance is stepped over by the combined effect of the many stimulations coming from different directions, and the subconsciously submerged moment or aggregate of moments surges up to the focus or nucleus of the upper consciousness.

        Once a particular moment is stimulated in its appropriate way, it may go on developing, and usually does so by stimulating and setting into activity aggregates of moments associated with it, or may form new combinations of aggregates. The solution of a problem may present great difficulties, but once started on the appropriate line, the whole series of combination goes on unfolding, stimulating other moments and aggregates and forming more and more complex combinations. Thus, Archimedes, as the story runs, while in the bath, made the discovery of the law of specific gravity. According to the popular account Newton was led to his discovery of universal gravitation by the accidental fall of an apple. Hughes was started by the idea of symmetry in his discovery of the laws of crystallography. Goethe was led to his conception of metamorphosis and evolution by a skull on the plains of Italy. Darwin by reading Malthus' economical treatise on population was inspired to work out the great principles of the struggle for existence and natural selection. Myers was led by the greater redness of blood in the blood-vessels of tropical patients to, his grand conceptions of transformation, equivalence, and conservation of energy. All these examples illustrate the fact that once a moment has been started it goes on developing by stimulating other cognate moments and aggregates to functioning activity.

        The same condition is also found in psychopathic borderland states, such as dreams. In dreams a peripheral stimulus gives rise to sensations that start the activities of moments, which in turn give rise to phantastic combinations of different aggregates. This phantastic combination of aggregates, giving rise to the functioning of otherwise unusual, or what may be termed abnormal constellations, is largely due to the fact of redistribution of thresholds in the dream state.

        The dream state is characterized by a rise of the thresholds of moments and their aggregates that have been functioning during the waking states, the thresholds of these aggregates having been raised through activity. In the sleep state moments that have their thresholds relatively or absolutely lowered through inactivity, moments or aggregates that are unusual or have not been in use during the waking state, become aroused, and begin to function. Hence the arousal of hypnotic dream states reproducing long lapsed moments of child-life, hence the phantasms of the world of dreams.


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