  This paper is an introduction to relationships between quantum topology and
quantum computing. We take a foundational approach, showing how knots are
related not just to braiding and quantum operators, but to quantum set
theoretical foundations and algebras of fermions. We show how the operation of
negation in logic, seen as both a value and an operator, can generate the
fusion algebra for a Majorana fermion, a particle that is its own anti-particle
and interacts with itself either to annihilate itself or to produce itself. We
call negation in this mode the mark, as it operates on itself to change from
marked to unmarked states. The mark viewed recursively as a simplest discrete
dynamical system naturally generates the fermion algebra, the quaternions and
the braid group representations related to Majorana fermions. The paper begins
with these fundmentals. They provide a conceptual key to many of the models
that appear later in the paper. In particular, the Fibonacci model for
topological quantum computing is seen to be based on the fusion rules for a
Majorana fermion and these in turn are the interaction rules for the mark seen
as a logical particle. It requires a shift in viewpoint to see that the
operator of negation can also be seen as a logical value. The quaternions
emerge naturally from the reentering mark. All these models have their roots in
unitary representations of the Artin braid group to the quaternions.
