  Regardless of how small non-ideal effects may be, phenomena associated with
changes in magnetic field line connections are frequently observed to occur on
an Alfv\'enic time scale. Since it is mathematically impossible for magnetic
field line connections to change when non-ideal effects are identically zero,
an ideal evolution must naturally lead to states of unbounded sensitivity to
non-ideal effects. That such an evolution is natural is demonstrated using
Lagrangian coordinates based on the flow velocity of the magnetic field lines.
The Lagrangian representation of an evolving magnetic field is highly
constrained when neither the magnetic field strength nor the forces exerted by
the magnetic field increase exponentially with time. The development of a state
of fast reconnection consistent with these constraints (1) requires a
three-dimensional evolution, (2) has an exponentially increasing sensitivity to
non-ideal effects, and (3) has a parallel current density, which lies in
exponentially thinning but exponentially widening ribbons, with a magnitude
that is limited to a slow growth. The implication is that exponential growth in
sensitivity is the cause of fast magnetic reconnection when non-ideal effects
are sufficiently small. The growth of the non-ideal effect of the resistivity
multiplied by the parallel current density is far too slow to be competitive.
