  There seems to be a common prejudice that asymptotic safety is either
incompatible with, or at best unrelated to, the other topics in the title. This
is not the case. In fact, we show that 1) the existence of a fixed point with
suitable properties is a promising way of deriving emergent properties of
gravity, and 2) there is a sense in which asymptotic safety implies a minimal
length. In so doing we also discuss possible signatures of asymptotic safety in
scattering experiments.
