MATHEMATICS AND THE NERVOUS SYSTEMS 301
With such an enormous amount of data of experience, he can re-evaluate the data, 'see' them anew, and so produce new and more useful and structurally more correct higher order abstractions. In their turn, these will produce similar semantic effects with other individuals,. The mechanism is, after all, well known and general, obvious even in the relations between some feeble-minded parents and their eventually feeble-minded children. It is entirely obvious on racial grounds; but, at present, it is not so obvious, and often but slightly effective, on personal and individual grounds, because we have had no means of training structurally and effectively the s.r in proper evaluation. The mechanism is entirely general, but it is obvious and seen at work in the majority of creative scientists and so-called 'geniuses'. These processes have not been analysed in terms of order, and so, although we use them often, we are not conscious of their mechanism and have no means of training our s.r. The s.r are a product of training, education., and are not inborn in o given form. Even birds bred in a laboratory which have never heard their parents or other birds sing will sing, as this is an inborn reflex, but the melody produced is different from that of their parents. Under normal conditions, the form of the song is standardized and is a result of copying parents. In other words, the melody-environment has affected them. With humans, it is not only a question of the given noises, the 'melody-environment' which we relate with some experiences, but the s.r involve affective responses to meanings, and this depends on the structure of language, involving unconscious, yet vital, evaluation factors and our attitude toward language, which ultimately depends on our knowledge of the mechanism and use of language.
These problems are extremely complex and subtle, and, at this stage, we are not ready to go into further details, the more so that there is a very simple and effective physiological structural method given in Part VII, which in practice eliminates enormous theoretical difficulties. There is little doubt that this mechanism of recasting, or translation of abstractions, is present in all of us, but this mechanism requires knowledge of the proper way to handle it, and that knowledge is not inborn, but has to be acquired by education. Up to the present date, these problems have been disregarded, and the s.r treated in a haphazard way; once the physiological mechanism of these reactions is discovered, however, we shall be able to use its benefits without the inherent dangers of disturbances.
Here we must face a rather unexpected fact.
Mathematics is alone and unique in that it has no content or definite meanings ascribed to the undefined terms; and, therefore, only in mathe-