itself to us in this respect is the fact that the elements of one n-dimensional continuum can be brought into a unique one-to-one correspondence with the elements of any other n-dimensional continuum; in particular, a one-dimensional continuum can be so correlated with the series of real numbers, an n-dimensional continuum with an n-dimensional series of numbers. Such correlation, the assignment to each element of the given continuum of an element of a corresponding number-series (containing n real numbers in an n-dimensional series) we call the introduction of co-ordinates, and the numbers thus assigned the co-ordinates of the respective elements. It follows from the properties of the number-continuum that there is an infinite number of possible correlations of a given continuum to its number-series: it is the task of the theory of measurement to indicate a method by which, once a certain finite number of elements is assigned its co-ordinates, the co-ordinates of any other element can be determined uniquely. But even before this method is known, co-ordinates serve a certain purpose, namely as mere names of the elements to which they are assigned: they are purely descriptive.
With this preliminary equipment we can embark upon our main task of analysing our perceptions and extracting from them that something which we so unconcernedly call space and time.
Analysis of Perception.
20. The thirst of the mind for knowledge of something outside itself must be regarded as a disposition inherent in the nature of mind. The way in which mind comes into contact with the object of its knowledge is a mystery which neither physics nor philosophy will probably ever solve. If we accept the postulate of the existence of the external world as something which is common to all minds, but independent of each individual one, then perceptions are the result of contact between the mind and this external world, and the bodily senses, themselves parts of the external world, enlarged both in the scope and the precision of their powers by physical instruments, are the media through which the contact is effected.
In perception the external world is presented to the mind as a phenomenon, a something of which the first quality distinguishable by the mind is variety, manifoldness, or, in other words, divisibility into parts. Consciousness of this manifoldness results from the recognition that in perception, as it is found in the mind, there is more than the mind is
