  We examine computer experiments that can be performed to understand the
dynamics of knots under self-repulsion. In the course of specific computer
exploration we use the knot theory of rational knots and rational tangles to
produce classes of unknots with complex initial configurations that we call
hard unknots, and corresponding complex configurations that are topologically
equivalent to simpler knots. We shall see that these hard unknots and
complexified knots give examples that do not reduce in the experimental space
of the computer program. That is, we find unknotted configurations that will
not reduce to simple circular forms under self-repulsion, and we find complex
versions of knots that will not reduce to simpler forms under the
self-repulsion. It is clear to us that the phenomena that we have discovered
depend very little on the details of the computer program as long as it
conforms to a general description of self-repulsion. Thus, we suggest on the
basis of our experiments that sufficiently complex examples of hard unknots and
sufficiently complex examples of complexified knots will not reduce to global
minimal energy states in self-repulsion environments. In the course of the
paper we make the character of these examples precise. It is a challenge to
other program environments to verify or disprove these assertions.
