A design is a (small) subset of points in space on which simple functions ("low-degree polynomials") average to their total average. We will discuss what 'simple' means in various nice spaces (it will mean lying in the span of low-eigenvalue eigenvectors of a nice linear operator) and give new proofs to some known (and possibly some new) bounds on the cardinality of designs. In particular, the following geometric claim holds: a design is large, because a union of "spheres" around its points "covers" the whole space.