  The question of whether all words in two real positive definite letters have
only positive eigenvalues is addressed and settled (negatively). This question
was raised some time ago in connection with a long-standing problem in
theoretical physics. A large class of words that do guarantee positive
eigenvalues is identified, and considerable evidence is given for the
conjecture that no other words do. In the process, a fundamental question about
solvability of symmetric word equations is encountered.
