10

THE ILLUSION OF STATISTICS

 
     Returning now to the consideration of the more specifically ‘scientific’ point of view as the modern world understands it, its chief characteristic is obviously that it seeks to bring everything down to quantity, anything that cannot be so treated being left out of account and is regarded as more or less non-existent. Nowadays people commonly think and say that anything that cannot be ‘put into figures’, or in other words, cannot be expressed in purely quantitative terms, for that reason lacks any ‘scientific’ value; and this assumption holds sway not only in ‘physics’ in the ordinary sense of the word, but in all the sciences ‘officially’ recognized as such in these days, and as we have seen, even the psychological domain is not beyond its reach. It has been made sufficiently clear in earlier chapters that this outlook involves losing touch with everything that is truly essential, in the strictest interpretation of the word; also that the ‘residue’ that alone comes within the grasp of such a science is in reality quite incapable of explaining anything whatever; but there is one highly characteristic feature of modern science that deserves further emphasis, for it indicates with particular distinctness how far science deludes itself about what can be deduced from mere numerical evaluations; this feature is moreover directly connected with the subject of the previous chapter.
 
     The tendency to uniformity, which extends into the ‘natural’ domain and is not confined to the human domain alone, leads to the idea, which even becomes established as a sort of principle (only it ought to be called a ‘pseudo-principle’), that there exist repetitions of identical phenomena; but this, by virtue of the ‘principle of indiscernibles’, is no more than a sheer impossibility. A good example of this idea is afforded by the current assertion that ‘the same causes always produce the same effects’, and this, enunciated in that form, is inherently absurd, for there cannot in fact ever be the same causes or the same effects in a successional order of manifestation; is it not quite commonplace for people to go so far as to say that ‘history repeats itself ’, whereas the truth is only that there are analogical correspondences between certain periods and certain events? It would be correct to say that causes that are comparable one to another in certain connections produce effects similarly comparable in the same connections; but, alongside the resemblances, which can if desired be held to represent a kind of partial identity, there are always and inevitably differences, because of the simple fact that there are by hypothesis two distinct things in question and not only one single thing. It is true that these differences, for the very reason that they represent qualitative distinctions, become less as the degree of manifestation of the things considered becomes lower, and that consequently there is then a corresponding increase of resemblance, so that in some cases a superficial and incomplete observation might give the impression of a sort of identity; but actually differences are never wholly eliminated, and this must be so in the case of anything that is not beneath the level of manifestation altogether. Even if there were no differences left other than those arising from the ever-changing influence of time and place, they could still never be entirely negligible; it is true however that this cannot be understood unless account is taken of the fact that real space and time are not, as modern conceptions would have them, merely homogenous containers and modes of pure quantity, but that on the contrary temporal and spatial determinations have also a qualitative aspect. However that may be, it is legitimate to ask how people who neglect differences, and as it were refuse to see them, can possibly claim that an ‘exact’ science has been built up; strictly and in fact there can be no ‘exact’ science but pure mathematics, which happens to be concerned with the domain of quantity alone. That being the case, all the rest of modern science is, and can only be, a tissue of more or less crude approximations, and that not only in its applications, in which everyone is compelled to acknowledge the inevitable imperfection of the means of observation and measurement, but even from a purely theoretical point of view as well: the unrealizable suppositions that provide almost the entire foundation of ‘classical’ mechanics, while these in turn provide the basis for the whole of modern physics, could be used to furnish a multitude of characteristic examples.¹
 
     The founding of a science more or less on the notion of repetition brings in its train yet another delusion of a quantitative kind, the delusion that consists in thinking that the accumulation of a large number of facts can be of use by itself as ‘proof ’ of a theory; nevertheless, even a little reflection will make it evident that facts of the same kind are always indefinite in multitude, so that they can never all be taken into account, quite apart from the consideration that the same facts usually fit several different theories equally well. It will be said that the establishment of a greater number of facts does at least give more ‘probability’ to a theory; but to say so is to admit that no certitude can be arrived at in that way, and that therefore the conclusions promulgated have nothing ‘exact’ about them; it is also an admission of the wholly ‘empirical’ character of modern science, although, by a strange irony, its partisans are pleased to accuse of ‘empiricism’ the knowledge of the ancients, whereas exactly the opposite is the truth: for this ancient knowledge, of the true nature of which they have no idea whatever, started from principles and not from experimental observations, so that it can truly be said that profane science is built up exactly the opposite way round to traditional science. Furthermore, insufficient as ‘empiricism’ is in itself, that of modern science is very far from being integral, since it neglects or sets aside a considerable part of the evidence of experience, the very part that has a specifically qualitative character; for perceptual experience cannot, any more than any other kind of experience, have a bearing on pure quantity as its object, and the nearer is the approach to pure quantity the greater is the distance from the reality which nevertheless is supposed to be grasped and to be explained; in fact it is not at all difficult to see that the most recent theories are also those that have the least relation to reality, and most readily replace it by ‘conventions’. These conventions cannot be said to be wholly arbitrary, for it is not really possible that they should be so, since the making of any convention necessarily involves there being some reason for making it, but at least they are as arbitrary as possible; that is to say, they have as it were only a minimum of foundation in the true nature of things.
 
     It has just been said that modern science, simply because it tries to be entirely quantitative, fails to take account of differences between particular facts even in cases where those differences are most accentuated, and such cases are naturally those in which qualitative elements have the greatest predominance over quantitative elements; and it can be said that this is why the greater part of reality eludes it, and why the partial and inferior aspect of truth that it can grasp in spite of all its failings (because total error could have no meaning other than that of pure negation) is reduced to almost nothing. This is more particularly the case when facts within the human order come under consideration, for these are the most qualitative of all those that modern science regards as included in its domain; science is determined nonetheless to treat them exactly like other facts, such as are concerned not only with ‘organized matter’ but even with ‘matter in the raw’, for it has in the end only one method, which it applies uniformly to the most diverse objects, precisely because, by reason of its special point of view, it is incapable of perceiving what are the essential differences between facts. And it is above all in the human order, whether in the field of history or ‘sociology’ or ‘psychology’ or any other kind of study that could be named, that the fallacious character of the ‘statistics’ to which the moderns attach so much importance becomes most apparent; here as elsewhere, statistics really consist only in the counting up of a greater or lesser number of facts that are all supposed to be exactly alike, for if they were not so their addition would be meaningless; and it is evident that the picture thus obtained represents a deformation of the truth, and the less the facts taken into account are alike or really comparable, or the greater is the relative importance and complexity of the qualitative elements involved, the worse is the deformation. Nonetheless, the setting out of figures and calculations gives to the statistician, as it is intended to give to other people, a kind of illusion of ‘exactitude’ that might be called ‘pseudo-mathematical’; but in fact, without its being noticed and because of the strength of preconceived ideas, almost any desired conclusion is drawn indifferently from such figures, so completely without significance are they in themselves. The proof of this is that the same statistics in the hands of several experts, even though they may all be ‘specialists’ in the same line, often give rise, according to the respective theories of the experts, to quite different conclusions, which may even sometimes be diametrically opposed. That being the case, the self-styled ‘exact’ sciences of the moderns, to the extent that they make use of statistics and go so far as to extract from them predictions for the future (relying always on the supposed identicality of the facts taken into account, whether past or future), are really no more than mere ‘conjectural’ sciences, to use an expression freely employed by the promoters of a kind of modern astrology dubbed ‘scientific’; and in employing this term they admit more freely than many other people what their astrology really consists in, for it certainly has only the vaguest and most remote connection, perhaps no more than that of a common terminology, with the true traditional astrology of the ancients, which is today as completely lost as all other knowledge of the same order. This ‘neo-astrology’ does actually make great use of statistics in its efforts to establish itself ‘empirically’ and without attaching itself to any principle, statistics indeed playing a preponderant part in it; and that is the very reason why it is thought right to adorn it with the epithet ‘scientific’, whereby the scientific character of the true astrology is implicitly denied, and this denial is again very significant and very characteristic of the modern mentality.
 
     To assume that facts are identical when they are really only of the same kind, or comparable only in certain respects, while it contributes toward the illusion of an ‘exact’ science, as has already been explained, satisfies at the same time the desire for an excessive simplification, which is also strikingly characteristic of the modern mentality, so much so that this mentality could, without admitting any ironical intention, be qualified as ‘simplistic’ as much in its ‘scientific’ conceptions as in all its other manifestations. These ideas all hang together: the desire for simplification necessarily accompanies the tendency to reduce everything to the quantitative, and it reinforces that tendency, for obviously nothing can be simpler than quantity; if a being or a thing could successfully be shorn of all its distinctive qualities, the ‘residue’ thus obtained would indeed be endowed with a maximum of simplicity: at the limit this extreme simplicity would be such as can only belong to pure quantity, being then the simplicity of the exactly similar ‘units’ that constitute numerical multiplicity – a point important enough to warrant more detailed consideration.


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[1] Where, for example, has anyone ever seen a ‘heavy material point’, or a ‘perfectly elastic solid’, an ‘unstretchable and weightless thread’, or any other of the no less imaginary ‘entities’ with which this science is replete, though it is regarded as being above all else ‘rational’.