The conclusion at once evokes the suggestion that the Lorentzian formulae are the true formulae for transformation from the space and time relations of a consentient set to those of a consentient set , both sets belonging to the Newtonian group. We may suppose that, owing to bluntness of perception, mankind has remained satisfied with the Newtonian formulae which are a simplified version of the true Lorentzian relations. This is the conclusion that Einstein has urged. Fig. 2. 10.6 These Lorentzian formulae for transformation involve two consequences which are paradoxical if we covertly assume absolute space and absolute time. Let and be two consentient sets of the Newtonian group. Let an event-particle happen at the point in the -space and at the point in the -space, and let another event-particle happen at points and in the two spaces respectively. Then according to the traditional scientific outlook, and are not discriminated from each other; and similarly for and . Thus evidently the distance is (on this theory) equal to , because in fact they are symbols for the same distance. But if the true distinction between the -space and the -space is kept in mind, including the fact that the points in the two spaces are radically distinct, the equality of the distances and is not so obvious. According to the Lorentzian formulae such corresponding distances in the two spaces will not in general be equal. The second consequence of the Lorentzian formulae involves a more deeply rooted paradox which concerns our notions of time. If the two event-particles and happen simultaneously when referred to the points and in the -space, they will in general not happen simultaneously when referred to the points and in the -space. This result of the Lorentzian formulae contradicts the assumption of one absolute time, and makes the time-system depend on the consentient set which is adopted as the standard of reference. Thus there is an -time as well as an -space, and a -time as well as -space.