  We show how self-referential discs in 4-manifolds lead to the construction of
pairs of discs with a common geometrically dual sphere which are homotopic rel
$\partial$, concordant and coincide near their boundaries, yet are not properly
isotopic. This occurs in manifolds without 2-torsion in their fundamental
group, e.g. the boundary connect sum of $S^2\times D^2$ and $S^1\times B^3$,
thereby exhibiting phenomena not seen with spheres. On the other hand we show
that two such discs are isotopic rel $\partial$ if the manifold is simply
connected. We construct in $S^2\times D^2\natural S^1\times B^3$ a properly
embedded 3-ball properly homotopic to a $z_0\times B^3$ but not properly
isotopic to $z_0\times B^3$.
