  We study aspects of obtaining field theories with noncommuting time-space
coordinates as limits of open-string theories in constant electric-field
backgrounds. We find that, within the standard closed-string backgrounds, there
is an obstruction to decoupling the time-space noncommutativity scale from that
of the string fuzziness scale. We speculate that this censorship may be
string-theory's way of protecting the causality and unitarity structure. We
study the moduli space of the obstruction in terms of the open- and
closed-string backgrounds. Cases of both zero and infinite brane tensions as
well as zero string couplings are obtained. A decoupling can be achieved
formally by considering complex values of the dilaton and inverting the role of
space and time in the light cone. This is reminiscent of a black-hole horizon.
We study the corresponding supergravity solution in the large-N limit and find
that the geometry has a naked singularity at the physical scale of
noncommutativity.
