Hermann Ebbinghaus

“ For, if observation of processes that resemble each other from any point of view are thrown together in sufficiently large numbers, fairly constant mean values are almost everywhere obtained which, nevertheless, possess little or no importance for the purposes which we have here. ”

“ On the other hand the number of suicides in a certain month, the average length of life in a given place, the number of teams and pedestrians per day at a certain street corner, and the like, are also noticeably constant, each being an average from large groups of observations. But both kinds of numbers, which I shall temporarily denote as constants of natural science and statistical constants, are, as everybody knows, constant from different causes and with entirely different significance for the knowledge of causal relations. ”

“ The physical scientist generally knows beforehand that he will have to deal with a single causal combination, the statistician knows that he has to deal with a mass of them, ever inextricable despite all analysis. Both know this from the elementary knowledge they already possess of the nature of the processes before they proceed with the more detailed investigations. Just as, a moment ago, the present knowledge of psychology appeared to us too vague and unreliable to be depended upon for decision about the possibility of constant experimental conditions ”

“ That the value of the separate factors must be very different is, so to say, self evident. That, nevertheless, approximately constant values appear even here by the combining of large groups—this fact we may make intelligible by saying that in equal and tolerably large intervals of time or extents of space the separate causal combinations will be realised with approximately equal frequency; we do this without doing more than to acknowledge as extant a peculiar and marvellous arrangement of nature. ”

“ He who considers the complicated processes of the higher mental life or who is occupied with the still more complicated phenomena of the state and of society will in general be inclined to deny the possibility of keeping constant the conditions for psychological experimentation. Nothing is more familiar to us than the capriciousness of mental life which brings to nought all foresight and calculation. ”

“ Such is the great complexity of our mental life that it is not possible to deny that constant mean values, when obtained, are of the nature of such statistical constants. To test that, I examine the distribution of the separate numbers represented in an average value. If it corresponds to the distribution found everywhere in natural science, where repeated observation of the same occurrence furnishes different separate values, I suppose—tentatively again—that the repeatedly examined psychical process in question occurred each time under conditions sufficiently similar for our purposes. ”

“ In the case of the special field of memory (learning, retention, reproduction) the second difficulty may be overcome to a certain extent. Among the external conditions of these processes some are directly accessible to measurement (the time, the number of repetitions) . They may be employed in getting numerical values indirectly where that would not have been possible directly. We must not wait until the series of ideas committed to memory return to consciousness of themselves, but we must meet them halfway and renew them to such an extent that they may just be reproduced without error. ”

“ The constant flux and caprice of mental events do not admit of the establishment of stable experimental conditions. ”

“ A poem is learned by heart and then not again repeated. We will suppose that after a half year it has been forgotten: no effort of recollection is able to call it back again into consciousness. ”

“ If the conditions are kept as much alike as is possible, is the average number of repetitions, which is necessary for learning similar series to the point of first possible reproduction, a constant mean value in the natural science sense? ”

“ All such unruly factors are of the greatest importance for higher mental processes which occur only by an especially favorable concurrence of circumstances. The more lowly, commonplace, and constantly occurring processes are not in the least withdrawn from their influence, but we have it for the most part in our power, when it is a matter of consequence, to make this influence only slightly disturbing. ”

“ Here there is only one alternative, a reproduction is either possible or it is not possible. It takes place or it does not take place. Of course we take for granted that it may approach, under different conditions, more or less near to actual occurrence so that in its subliminal existence the series possesses graded differences. But as long as we limit our observations to that which, either by chance or at the call of our will, comes out from this inner realm, all these differences are for us equally non-existent. ”

“ When all the observations are arranged in this way the outer contour of the figure may be so compacted that the projecting corners of the separate squares are transformed into a symmetrical curve. If now the separate measures are of such a sort that their central value may be considered as a constant as conceived by physical science, the form of the resulting curve is of the kind marked a and b in Fig. 1. If the middle value is a statistical constant, the curve may have any sort of a form. ”

“ The exact distance of two signal poles, the position of a star at a certain hour, the expansion of a metal for a certain increase of temperature, all the numerous coefficients and other constants of physics and chemistry are given us as average values which only approximate to a high degree of constancy. ”

“ Sensorial perception, for example, certainly occurs with greater or less accuracy according to the degree of interest; it is constantly given other directions by the change of external stimuli and by ideas. ”

“ Whether the first difficulty, the establishment of stable experimental conditions, may also be overcome satisfactorily cannot be decided a priori<. Experiments must be made under conditions as far as possible the same, to see whether the results, which will probably deviate from one another when taken separately, will furnish constant mean values when collected to form larger groups. ”

“ Whether we possess in them correct measures for these inner differences, and whether we can achieve through them correct conceptions as to the causal relations into which this hidden mental life enters—these questions cannot be answered a priori. Chemistry is just as little able to determine a priori whether it is the electrical phenomena, or the thermal, or some other accompaniment of the process of chemical union, which gives it its correct measure of the effective forces of chemical affinity. ”

“ However, taken by itself, this is not sufficient to enable us to utilise such numerical results for the establishment of numerical relations of dependence in the natural science sense. Statistics is concerned with a great mass of constant mean values that do not at all arise from the frequent repetition of an ideally frequent occurrence and therefore cannot favor further insight into it. ”

“ Imagine a certain observation to be repeated 1,000 times. Each observation as such is represented by a space of one square millimeter, and its numerical value, or rather its deviation from the central value of the whole 1,000 observations, by its position on the horizontal line p q of the adjoining Figure 1. ”

“ The second learning requires noticeably less time or a noticeably smaller number of repetitions than the first. It also requires less time or repetitions than would now be necessary to learn a similar poem of the same length. In this difference in time and number of repetitions we have evidently obtained a certain measure for that inner energy which a half year after the first learning still dwells in that orderly complex of ideas which make up the poem. ”

“ If now this calculation is tried out tentatively for any group of observations, a grouping of these values according to the “law of errors” is recognised by the fact that between the sub-multiples and the multiples of the empirically calculated probable error there are obtained as many separate measures symmetrically arranged about a central value as the theory requires. ”