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An Introduction To Non-aristotelian Systems And General Semantics.

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718            X. ON THE STRUCTURE OF 'MATTER'
An 'intuitive' theory has a creative aspect, but always ought later to be revised and scrutinized by non-intuitive means. In fact, because of our nervous structure, we should always strive to produce both aspects of theories - strive consciously - for thus we facilitate progress. Historically, we can never completely avoid producing both types of theories, as they are inherent in our nervous structure and in the different orders of abstractions we produce.
It is precisely in the newer quantum mechanics that a typical example of this simple neurological fact is found. The non-intuitive handling of data was introduced by Heisenberg: the translation of the matrix calculus into operational and 'Poisson brackets' methods; and, finally, the new 'wave mechanics' of de Broglie, Schrodinger, and others, gives us a perfect translation into intuitive methods.
It should be noticed that according to the old notions such two methods, the intuitive and the non-intuitive, were not supposed to be a neurological necessity. We still assumed that they were separated 'absolutely', and even today in many quarters we argue as if they were absolutely separable. If we accept the principle of non-elementalism, we realize that this distinction is verbal only and that the invention of verbal means has little or nothing to do with the world around us, but that it depends on human structural ingenuity.
Investigation of the ordered cyclic nerve currents shows unmistakably that such sharp differentiation is unjustifiable; and we must conclude, in accordance with historical experience, that translation from one method to the other must be a necessity, and so will be accomplished some day in every field. It is true that at present the Einstein theory has not been translated with entire success into terms of lower order abstractions. This is a task which is facilitated by this present work. The newer quantum mechanics gives us an unparalleled example of such translation, and hence our main interest should be concentrated on this structural aspect.
On neurological grounds it seems certain that visualization involves in some way the lower nerve centres, which again, by evolutionary necessity, involve macroscopic forms of representation. Our macroscopic experience led us to geometrical intuitions. These were framed three-dimensionally in 'absolute emptiness', and were impossible in higher dimensions. The old structure represented a static empty 'space' in which nothing could happen and which was thus unfit to represent this world around us where something is going on everywhere.
The new structure represents 'fulness' or a plenum. We can visualize it as a network of intervals or world-lines and then, by the notions of the differential calculus, as already explained, we pass easily to the visualization of the many-dimensional space-time world of Minkowski-Einstein. Now, in such a world, the curves are represented by functions, and, vice versa, functions represent curves. Thus it is obvious that analytical 'non-intuitive' methods have 'intuitive' structural geometrical counterparts. From this point of view the method of operators represents a passing step from the non-intuitive to intuitive