 Spin is the canonical quantum observable that has no classical counterpart, reputedly impossible to grasp in a nonquantum way. The difficulty is not quite that spin is quantized in the sense that its allowable values form a discrete set (for a spin-1/2 particle, \(\pm \hslash/2\)). Energy too may be quantized in this sense. Nor is it precisely that the components of spin in the different directions fail to commute—and so cannot be simultaneously discussed, measured, imagined, or whatever it is that we are advised not to do with noncommuting observables. Rather the problem is that there is no ordinary (nonquantum) quantity which, like the spin observable, is a 3-vector and which also is such that its components in all possible directions belong to the same discrete set. The problem, in other words, is that the usual vector relationships among the various components of the spin vector are incompatible with the quantization conditions on the values of these components.