ABSTRACT
Numbers, in the dimension of space, can be used in two ways. The first is to name, and implicitly to order, recognised points, the second is to measure the distance between them. The first use is of ordinal, the second, of cardinal numbers. These alternative uses suggest an analogy with time, where points, jiten, are separated by periods, jidai. The analogy is, however, imperfect. It implies that the properties of space, or sora, are comparable to those of time, or toki. Noting the on reading, k*, corresponding to the kun reading, sora, one would expect some conceptualisation of space in terms of k*ten and k*dai, but in fact these words do not exist. Nor are there any other Japanese words which convey the meaning sought after. True there is chiten, literally a ‘land-point’, but this depends upon space reduced to two dimensions. This is the nub of the whole problem. Space, as such, is too inchoate to support any sort of order, whether or not it is numerical.1 The ordered movement of the celestial bodies, which is critical for the measurement and definition of time, is a meagre basis for organising space at terrestial level.
