- a continuous area or expanse which is free, available, or unoccupied. (implicitly refers to objects ie “space as stage for things”) - the dimensions (degrees of freedom) of height, depth, and width (refers implicitly to measurement) within which all things exist and move (“space as a stage for motion”) - a blank between printed words, characters, numbers, etc. (ie a stage is a stage because it is empty. to communicate information, a prerequisite is a low entropy (ie highly ordered) channel. we would say “space as a channel for information flow” sets of mathematical abstractions capture the role of space as a stage for things, and a stage for motion. euclidean space R^n is what we are most familiar with. more specific/exotic conceptions of space could be said to be obtained by simply abstracting part of the structure possessed by euclidean space eg: - vector spaces: abstract the operations on R^n of addition and scalar multiplication (to model motion, displacement and so on) - metric spaces: abstract the function d:R^nxR^n -> R which computes the distance between two points (ie measurement) - topological spaces: abstract set of open balls (locality, proximity) - normed vector spaces: abstract addition, scalar multiplication and the norm ||v||=(∑^ni=1Vi^2)^1/2 (motion and measurement) - inner product spaces: abstract addition and scalar multiplication and the dot product. (motion and angles) hilbert spaces: abstract addition, scalar multiplication