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An Introduction To Non-aristotelian Systems And General Semantics.

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he would see - and any instrument carried by him would register it - the sides of our square (AB=BC = CD =DA) in the direction of his flight, namely AB and CD, as 'contracted' to half their length. If he turned at right angles, the sides AB and CD would 'expand' and the other sides, which are at right angles, BC and DA, would 'contract'. For us the sides AB and BC axe equal, for him one appears twice the other. To him our square appears oblong.
Under such natural structural conditions it is a fundamental fallacy to ascribe to 'lengths' or 'shapes' or 'times' any 'absolute' significance. If we grasp the structural fact that 'length' and 'duration' are not things inherent in the external world, nor are 'matter', 'space', and 'time', but that they appear as relations between events and some specified observer, and forms of representations, then all paradoxes would disappear.
A suggestion which concerns visualization may be helpful. If we realize the structural fact that words are not the objects they represent, we shall always discriminate automatically between what we see, feel. , on the level of lower order abstractions, and what we say on the level of higher order abstractions. When we have conquered that single difficulty we could never then identify the two different orders of abstractions. We would evaluate the terms 'matter', 'space', and 'time' as forms of representation, and non-objects, and we would describe events in a functional, operational, behaviouristic language of order. If we realize and feel the finite velocity of propagation of all processes, we may visualize all that has been explained here. Diagrammatizing and even following with one's hand, the visualized order of occurrences, helps enormously. Try to visualize how the aviator in the last example is flying away and how much more slowly the light impressions from the earth are reaching him or his instruments, and the difficulties will soon vanish.
We shall also be greatly helped in our power of visualization when we become acquainted with the structure of the Minkowski four-dimensional world. An explanation of this appears in the next chapter.