Feb. 2, 1984 The Editor Dear Sir: In his review of The Neglected Facts of Science (Kronos IX2), Henry A. Hoff suggests that the two unobservable scalar dimensions are introduced ad hoc. Actually, they are necessary consequences of the existence of scalar motion, which, as I have shown, is established by observation. In a threedimensional universe there are obviously three dimensions of that motion. That is what the concept of threedimensionality means. Hoff’s problem in this case is the same as that of many others. They take it for granted that they know what the word “dimension” means, but they are thinking of geometric dimensions. The dimensions of scalar motion are purely mathematical, not geometric. The whole point of my discussion in Chapter 2 of The Neglected Facts of Science is that only one of the three scalar (mathematical dimensions can be represented in the three spatial (geometric) dimensions of the conventional reference system. The other two scalar dimensions of motion are unobservable.
