  Defining finite entanglement entropy for a subregion in quantum field theory
requires the introduction of two logically independent scales: an IR scale that
controls the size of the subregion, and a UV cut-off. In AdS/CFT, the IR scale
is the AdS lengthscale, the UV cut-off is the bulk radial cut-off, and the
subregion is specified by dimensionless angles. This is the data that
determines Ryu-Takayanagi surfaces and their areas in AdS/CFT. We argue that in
asymptotically flat space there exists the notion of a ``spi-subregion" that
one can associate to spatial infinity (spi). Even though geometrically quite
different from an AdS subregion, this angle data has the crucial feature that
it allows an interpretation as a bi-partitioning of spi. Therefore, the area of
the RT surface associated to the spi-subregion can be interpreted as the
entanglement entropy of the reduced density matrix of the bulk state under this
bi-partition, as in AdS/CFT. For symmetric spi-subregions, these RT surfaces
are the waists of Asymptotic Causal Diamonds. In empty flat space they reduce
to Rindler horizons, and are analogues of the AdS-Rindler horizons of Casini,
Huerta \& Myers. We connect these results to previous work on minimal surfaces
anchored to screens in empty space, but also generalize the discussion to the
case where there are black holes in the bulk. The phases of black hole RT
surfaces as the spi-subregion is varied, naturally connect with those of black
holes (small and large) in AdS. A key observation is that the radial cut-off is
associated to an IR scale in flat space -- and in fact there are no UV
divergences. We argue that this is consistent with previous suggestions that in
sub-AdS scales the holographic duality is an IR/IR correspondence and that the
degrees of freedom are {\em not} those of a local QFT, but those of long
strings. Strings are of course, famously UV finite.
