  In math.GT/0106017 it was shown that thin position on Heegaard spines can be
a useful tool for analyzing the topology of knots in 3-space. The proof there
(specifically, of the Goda-Teragaito conjecture) requires masses of technical
detail; it is easy to lose track of the underlying ideas. The present paper
gives an overview of the argument, stripped of technical detail and emphasizing
the mathematical background that seems naturally to motivate the proof.
