300 V. MATHEMATICS A .7 I.ANGUAGE
the data given by the lower nerve centres, which are closer to experience, or rather which constitute experience. The older arguments about the connection or lack of connection between the lower order abstractions ('sense' data.,), and mathematics are due solely to a confusion of orders of abstractions and are a useless gambling in el terms. Only in severe 'mental' ills is the speech of the patients entirely unconnected with first order external 'realities', and so the study of relations of many kinds and orders, called 'mathematics', cannot, as long as it is sane, be entirely detached from 'reality'. In fact, it is useless for mathematicians to try to produce disciplines which have no practical applications. As long as it is professionally accepted as mathematics, and, therefore, a science and sane, whatever mathematicians produce will always be connected with lower order abstractions, and must have an application sooner or later. When these higher order abstractions, produced very often by many individuals, are absorbed and returned in a modified form to the lower centres as 'visualization', 'intuition', 'feelings'., the given individual is closer to the external world than he was before, because he has absorbed, digested, and appropriated the nervous results of many more experiences than he himself could have gathered alone. He is able to compare, evaluate, and relate, revise and adjust his private experiences and observations with the translated experiences from higher abstractions of many more individuals. The translation is indispensable, because the reactions of both levels are entirely different, and comparable only when they are on one level. Creative work has begun.
Experiences given by the lower centres and lower abstractions are full of meanings, colouring, affective and semantic components, and these are not directly comparable with the higher abstractions produced by the higher nerve centres. They must be first transformed, 'digested', and translated into terms of the lower centres, which are the only ones which are effective on the lower levels. We call them 'visualization', 'intuition', 'feeling', 'culture',. The exact mechanism is not well known, but we have a number of data which show that the lower nerve centres are somehow engaged in these processes.
When this is accomplished, the mathematician has at his disposal an enormous amount of data; first, his personal experiences and observation of actual life (lower centres and lower order abstractions), and also all the personal experiences and observations of past generations. Although the latter were stored in the form of higher order abstractions only as an account of past experiences in neural or extra-neural forms, his nervous cycle was affected by them, and they were translated back into experiences of the lower levels.