  We present a new paradigm for three dimensional chaos, and specifically for
the Lorenz equations. The main difficulty in these equations and for a generic
flow in dimension three is the existence of singularities. We show how to use
knot theory as a way to remove the singularities. Specifically, we claim:
  (1) For certain parameters, the Lorenz system has an invariant one
dimensional curve, which is a trefoil knot. The knot is a union of invariant
manifolds of the singular points.
  (2) The flow is topologically equivalent to an Anosov flow on the complement
of this curve, and even to a geodesic flow.
  (3) When varying the parameters, the system exhibits topological phase
transitions, i.e. for special parameter values, it will be topologically
equivalent to an Anosov flow on a knot complement, and different knots appear
for different parameter values.
  The steps of a mathematical proof of these statements are at different
stages. Some have been proven, for some we present numerical evidence and some
are still conjectural.
