ABSTRACT
Thus instead of regarding ourselves as, so to speak, swimming along in an ocean of space (as we usually do), we are to think of ourselves rather as somehow pursuing a course in an ocean of time; ............. Alfred A. ROBB [417, p. 19]
Au fond, ne butons-nous pas sur la trop forte prégnance d’une représentation traditionnelle du temps qui, en définitive, l’assimile à l’espace ? Cet ”axe du temps”, c’est, après tout, une droite spatiale, dont nous ne questionnons même plus la pertinence, et que nous traçons sur ces désormais coutumiers diagrammes, horaires ferroviaires ou lignes d’univers einsteiniennes. Or ces schémas, conceptuellement spatio-temporels, sont matériellement spatio-spatiaux, dessinés qu’ils sont sur le plan du tableau ou de la feuille. Jean-Marc LEVY-LEBLOND [291, pp. 280, 281]
A geometrical representation of the time set T, or of T(.), by the corresponding time axis (denoted by T , or by T(.)) requires that the nature of time is well expressed and preserved as much as possible. The time set T, or T(.), is totally ordered and everywhere dense set in view of Axiom 47 (Section 4.2 ”Characterization of Time”). The temporal orientation (the temporal direction) and the temporal flow are its crucial and characteristic features. We say ”as much as possible” because it is not possible without a simula-
tion to show exactly geometrically and graphically the temporal flow, i.e. the permanent strict continuous monotonous increase of the time value. Hence, the
time, of the time axis T can be arbitrary under the condition that it expresses the independent nature of time and the temporal flow of time values. The first requirement can be achieved by accepting the time axis T to be orthogonal to space Rn, hence to be orthogonal to the spatial axis R(n), and to be the abscissa axis of an accepted coordinate system. The second requirement can be achieved descriptively by presenting the condition dt > 0, which has been accepted to hold without any exception in this book. Any axis that is a straight line abscissa and orthogonal to space Rn (or equivalently, to the spatial axis R(n)) may be taken for the time axis T (or T(.)). All time axes T(.) with 1◦ the same zero instant t(.)zero = 0, 2◦ the same time unit 1(.), 3◦ with the same time scale, 4◦ which are orthogonal to space Rn, hence to the spatial axis R(n), i.e.
