The unit sphere of Hilbert space, 2, is shown to contain a remarkable sequence of nearly orthogonal sets. Precisely, there exist a sequence of sets of norm one elements of 2, (Ci)i=1, and reals i0 so that a) each set Ci has nonempty intersection with every infinite dimensional closed subspace of 2 and b) for ij, xC, and yCj, |x, y|
