Beyond the puny three dimensions of human existence. The space where documents exist is very large and high-dimensional. I encourage you to suspend your intuitions from the two and three dimensions in which we puny humans live (cf. [Abbott, 1952]), because many of the intuitions that apply in a small number of dimensions do not generalize to the high-dimensional spaces that we discuss here. Some of these involve the curse of dimensionality, which makes the computational expense of many important questions grow exponentially with the number of dimensions.