Do binaries in clusters form in the same way as in the field?
  We examine the dynamical destruction of binary systems in star clusters of
different densities. We find that at high densities (10^4 - 10^5 Msun pc^-3)
almost all binaries with separations > 10^3 AU are destroyed after a few
crossing times. At low densities (order(10^2) Msun pc^-3) many binaries with
separations > 10^3 AU are destroyed, and no binaries with separations > 10^4 AU
survive after a few crossing times. Therefore the binary separations in
clusters can be used as a tracer of the dynamical age and past density of a
cluster.
  We argue that the central region of the Orion Nebula Cluster was around 100
times denser in the past with a half-mass radius of only 0.1 - 0.2 pc as (a) it
is expanding, (b) it has very few binaries with separations > 10^3 AU, and (c)
it is well-mixed and therefore dynamically old.
  We also examine the origin of the field binary population. Binaries with
separations < 10^2 AU are not significantly modified in any cluster, therefore
at these separations the field reflects the sum of all star formation. Binaries
with separations in the range 10^2 - 10^4 AU are progressively more and more
heavily affected by dynamical disruption in increasingly dense clusters. If
most star formation is clustered, these binaries must be over-produced relative
to the field. Finally, no binary with a separation > 10^4 AU can survive in any
cluster and so must be produced by isolated star formation, but only if all
isolated star formation produces extremely wide binaries.
