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An Introduction To Non-aristotelian Systems And General Semantics.

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or a two-dimensional figure as one-dimensional. The co-ordinates y and z, as we have seen, do not enter into consideration as they are equal in both systems moving relatively in the X direction, and the 'time' co-ordinates are independent of them.
If a body at rest appears to the observer in the unprimed system as a sphere, it will appear as an oblate spheroid to an observer in the primed system.
We see that structurally not only 'simultaneity' and 'time' are not absolute but also that length, and therefore shape, is relative.
We have seen that the 'shortest' and 'longest' values are important characteristics of the motion. This suggests why in the general theory of Einstein we are interested in, and introduce, geodetics.
It should be mentioned here that the Lorentz transformation has been reached by difficult considerations involving Maxwell's electromagnetic field equations, unrelated to the Einstein theory. Einstein found the Lorentz transformation by the simplest consideration connected with his theory. The finding of such important equations by two methods, entirely different structurally, must be considered as a convincing proof of the fundamental importance of such formulae, the more so since they follow from very simple and fundamental structural principles which in themselves cannot be denied because they are negative in character. Negative statements are on a different footing in the new systems; they follow structurally from a orientation, just as the older positive dogmas were the structural results of aristotelianism and the delusional results of identification.
The facts mentioned concerning the measures of length and the behaviour of clocks do not present any paradoxes. They simply say that these discrepancies are mutual and inevitable, as any measurement is only a measurement when it can be registered by an instrument, or seen, or recorded in some way. If the measuring rods and clocks are moving relatively to us, what we see or what our instruments record is not what is happening on the moving system, which no one can see or record from outside the system. What reaches us is simply what the light-waves or other signals moving with finite velocity (and therefore retarded by a motion away from us) bring to us. As all existing methods of communication and all known signals have finite velocities, these structural differences which are conditioned by the inherent characteristics of the world should be taken into consideration in modern science.
If we draw a square ABCD (Fig. 5) and an aviator E were to pass this square sign with a velocity of 161,000 miles a second* in the direction AB,