Fast magnetic reconnection refers to annihilation or topological rearr
angement of magnetic fields on a timescale that is independent (or nea
rly independent) of the plasma resistivity. The resistivity of astroph
ysical plasmas is so low that reconnection is of little practical inte
rest unless it is fast. Yet, the theory of fast magnetic reconnection
is on uncertain ground, as models must avoid the tendency of magnetic
fields to pile up at the reconnection layer, slowing down the flow. In
this paper it is shown that these problems can be avoided to some ext
ent if the flow is three dimensional. On the other hand, it is shown t
hat in the limited but important case of incompressible stagnation poi
nt flows, every flow will amplify most magnetic fields. Although examp
les of fast magnetic reconnection abound, a weak, disordered magnetic
field embedded in stagnation point flow will in general be amplified,
and should eventually modify the flow. These results support recent ar
guments against the operation of turbulent resistivity in highly condu
cting fluids. (C) 1998 American Institute of Physics.