CHAPTER XII |
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ON ORDERThe fundamental importance of the subject of order may be inferred from the fact that all the concepts required in geometry can be expressed in terms of the concept of order alone. (237) e. v. hwntingtonDimensions, in geometry, are a development of order. The conception of a limit, which underlies all higher mathematics, is a serial conception. There are parts of mathematics which do not depend Upon the notion of order, but they are very few in comparison with the parts in which this notion is involved. (455) bertrand russellThe notion of continuity depends upon that of order, since continuity is merely a particular type of order. (454) bertrand russellLogistic may be denned as the science which deals with types of order asSUch. (300) C. I. LEWISThe branch of physics which is called Elementary Geometry was long ago delivered into the hands of mathematicians for the purposes of instruction. But, while mathematicians are often quite competent in their knowledge of the abstract structure of the subject, they are rarely so in their grasp of its physical meaning. (529) Oswald veblenWe often think that when we have completed our study of one we know all about two, because "two" is "one and one". We forget that we have still to make a study of "and". Secondary physics is the study of "and" - that is to say, of organisation, (149> a. s. eddington. . . the geometry of paths can be regarded as a generalization both of the earliest part of elementary geometry and of some of the most refined of physical theories. The study of the projective, the affine and the metric geometry of paths ought to result in a comprehensive idea of what types of physical theory it is possible to construct along the lines which have been successful in the past. (529) _ _ _ Oswald veblenWhat I wish to emphasize now is the need of logistic studies which will make it possible to say more definitely than is yet possible in this field what is assumed, what is proved, and how the group of theorems and definitions hang together. (529) Oswald veblenMemory, in fact, is nothing but the reinforcement and facilitation of the passage of the nervous impulse along certain paths. (411) henri pieronBut before dealing with the brain, it is well to distinguish a second characteristic of nervous organization which renders it an organization inlevels. (411) HENRI pieronThis affective repercussion seems to take place at the penultimate stage of the nervous system and governs complicated reflexes or instinctive reactions. (411) HENRI PIERON Furthermore, there are even symbols of symbols, evocative of images only in the second degree, by means of primary stations of the co-ordination centres. (4ii) henri pieronIn this way it is seen that the order in which a given group of stimuli taking part in a stimulatory compound are arranged, and the pauses between them are the factors which determine the final result of the stimu-151 |
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