  The goal of this short note is to point out three observations around the
Grothendieck norm and semidefinite programming. The first is that the
Grothendieck norm captures the difficulty of relating the off-diagonal entries
of a real, symmetric matrix to a probabilistic correlation, the second is that
there is an interesting ``Fourier''-type duality between the Schur and
Grothendieck norms of a real matrix, and the third and last centers around the
difficulty of finding an efficiently computable noncommutative analog to the
Grothendieck norm.
