  A technique is presented for multiplexing two ergodic measure preserving
transformations together to derive a third limiting transformation. This
technique is used to settle a question regarding rigidity of weak mixing
transformations. Namely, given any rigidity sequence for an ergodic measure
preserving transformation, there exists a weak mixing transformation which is
rigid along the same sequence. This establishes a wide range of rigidity
sequences for weakly mixing dynamical systems.
