  This is a revised version of a talk given at the Chiral Dynamics Workshop at
M.I.T., July 25, 1994. It reports results in three areas: (1) The
isospin-violating interactions between one non-relativistic nucleon and any
number of soft pions can be summarized in a single term in the effective chiral
Lagrangian, with no unknown parameters. (2) With D'Hoker, it has been shown
that the terms in the Lagrangian for an effective field theory with symmetry
$G$ spontaneously broken to $H$, that are not the integrals of $G$-invariant
Lagrangian densities, are in one-to-one correspondence with the generators of
$H_5(G/H,R)$. (3) If we assume that the nucleon is connected by successive
one-pion transitions only to a tower of narrow baryon states with
$T=J=1/2,3/2,\dots,N_c/2$, then the Adler-Weisberger and superconvergence
relations tell us (for any $N_c$) that (a) the tower states are degenerate, and
(b) the one-pion transition amplitudes between these states generate the {\em
uncontracted} algebra of $SU(4)\times O(3)$.
