What is Vector Space?
David M. Berry "The abstraction ruling over thought is not thought's own doing but is the effect of the society in which it takes place." Alfred Sohn-Rethel Figure 1: The vector space Technical accounts of artificial intelligence sometimes describe vector space as though it were a mathematical a priori, already existent, like a ready-made object. It is often described as a high-dimensional space, complete, continuous, equipped with an inner structure that defines angles and distances between any two points. This description is borrowed from linear algebra, where vector spaces are abstract structures. In this register, vector space is a space of real numbers, which is to say, a space of infinite precision. Any point can be specified exactly. Any distance can be measured without error. The space is mathematically smooth, continuous, and homogeneous, the same everywhere, with no grain, no texture, no material substrate. This matters because the gap between the mathematics an...
