658 IX. ON EMPIRICAL AND VERBAL STRUCTURES
We have been contrasting finite and 'infinite' velocities. Let us say frankly that 'infinite* velocity is a polite way of speaking about blunders of observation. 'Infinite' velocity is meaningless. Velocity is defined asand if t is taken
as zero or in other words, if one of the fundamental factors in our definition is lacking, our definition ceases to define the term in questionin this case, velocity. So when the term 'time' is lacking, we have no velocity, by definition; so, to speak or speculate about 'infinite* velocity is simply making noises, and not saying anything. The negative of this noise; namely, saying that velocity is not 'infinite', or in a positive sense, that velocity is 'finite', is on a different verbal footing, although it remains a polite invitation to stop talking non-sense.
It should be noticed carefully that the general theory of Einstein is a high structural generalization of the special theory; and that both of them are generalizations of the classical mechanical principle of relativity. It is founded, not on the introduction of any extraordinary structural assumptions, but on the elimination of some unjustified and false-as-to-facts structural assumptions, such as that of the 'infinite' velocity of light.
Both the theory of Einstein, and the theory presented in this work are long overdue. The Einstein theory could have been formulated as soon as we discovered the finite velocity of light, in 1676. It should be noticed that this last discovery was also overdue, as it did not require experiments to establish the finite velocity of light. It was sufficient to establish the meaningless character of 'infinite' velocity, which on symbolic grounds, could have been accomplished much earlier, and to conclude, that the velocity of light must be finite. This example shows the hampering, blocking, semantic effect which different meaningless verbal structures have on us. To express this high and satisfactory structural generalization, Einstein had to select the most general and structurally appropriate language in existence. He chose at some stage of his work the language of and four-dimensional geometries in general and that of the differential geometry and the tensor calculus in particular. In the latest field theory, Einstein and Mayer introduce a new more general and very revolutionary mathematical language where vectors and tensors in an n-dimensional spread may have m components.
At present it appears that two other very general mathematical disciplines will be used increasingly in the future. One of them is the theory of groups; the other is analysis situs. In the latter we study only these characteristics of figures that are unaffected (invariant) by continuous deformation produced without tearing. Two structural points are relevant for us in this connection: namely, that the analysis situs is fundamentally a differential and also an ordinal discipline, based on asymmetrical relations. In the next chapter, as an illustration of the actional, behaviouristic, functional, operational, differential, contact method a short account will be given of the way Einstein structurally treated 'simultaneity'. The elimination of the old structural dogma about 'simultaneity' resulting from the semantic disturbance of objectification of 'time', is one of the outstanding achievements of Einstein and is historically the beginning of his theory.