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Updated: May 10, 2025
Accordingly Euclidean metrical geometry in space is completely established and lengths in the spaces of different time-systems are comparable as the result of definite properties of nature which indicate just that particular method of comparison. The comparison of time-measurements in diverse time-systems requires two other axioms.
The stream of events which form the continuous series of situations of the electron is entirely self-determined, both as regards having the intrinsic character of being the series of situations of that electron and as regards the time-systems with which its various members are cogredient, and the flux of their positions in their corresponding durations.
The recognition of the fact of an indefinite number of families of parallel durations is what differentiates the concept of nature here put forward from the older orthodox concept of the essentially unique time-systems. Its divergence from Einstein's concept of nature will be briefly indicated later.
In the instantaneous space of M the level λ is perpendicular to the direction of β in M, and in the instantaneous space of N the level λ is perpendicular to the direction of α in N. This is the fundamental property which forms the definition of perpendicularity. The symmetry of perpendicularity is a particular instance of the symmetry of the mutual relations between two time-systems.
The first of these axioms, forming the fifth axiom of congruence, will be called the axiom of 'kinetic symmetry. It expresses the symmetry of the quantitative relations between two time-systems when the times and lengths in the two systems are measured in congruent units. The axiom can be explained as follows: Let α and β be the names of two time-systems.
Namely, amid the alternative time-systems which nature offers there will be one with a duration giving the best average of cogredience for all the subordinate parts of the percipient event. This duration will be the whole of nature which is the terminus posited by sense-awareness. Thus the character of the percipient event determines the time-system immediately evident in nature.
You will have noticed that by the aid of the assumption of alternative time-systems, we are arriving at an explanation of the character of space. In natural science 'to explain' means merely to discover 'interconnexions. For example, in one sense there is no explanation of the red which you see. It is red, and there is nothing else to be said about it.
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