Impelled by this desire for permanence the mind has formed the concept of permanent space, which may be defined as the sum of the enduring spatial relations in a given Experience or finite section thereof (understanding by a finite section of Experience the whole intervening Experience between two “distant” moments). Permanent space thus appears as the space of an imaginary moment which the mind has allowed to become, as it were, petrified in thought, by preserving from given successive moments only those relations which remain unchanged in these moments. This space, or the imaginary moment which it represents, the mind carries over from moment to moment, compares it with momentary spaces, and in the spatial ordering of these moments notes its deviations with respect to permanent space.
When, therefore, we speak of two non-contemporaneous objects or events in space, it is simply an assertion of the fact, that we compare the position of these two events in their respective moments by means of corresponding positions in this petrified enduring moment, which we have unwittingly identified with each of the two moments.
38. In order that we may be able to distinguish between elements of real moments of experience and elements of this imaginary “enduring” moment, we call the latter elements timeless points. These will be imaginary elements of experience which will retain eternally the same spatial relations towards one another; in every momentary space which “underlies” them, one element of experience will correspond to (or coincide with) each point of permanent space, so that each timeless point will be a route of “instantaneous points”.
38.1. A one-dimensional aggregate of timeless points of a given permanent space (a timeless line) will intersect each one of the moments belonging to it in an instantaneous line, a two-dimensional aggregate (a timeless surface) in an instantaneous surface, and a three-dimensional aggregate (a timeless body) in an instantaneous body. In the Experience belonging to this space a point will form a progressive figure of the first order, a timeless line a progressive figure of the second order, a timeless surface a progressive figure of the third order, and a timeless body a figure of the fourth order.
Movement.—39. It is only through the idea of permanent space that the ideas of “rest and motion in space” and the idea of “matter” acquire any meaning. In a moment everything is at rest; to speak of change of position in a moment is meaningless, since the position of a given event
