Providing the required interconnections between the processors of a parallel computer is a difficult problem: latency, switching control, cost, and crosstalk effects have to be taken into account. It is widely believed that the design might be simplified if optical technology is used. However, even optical interconnections cannot cater for an unlimited number of processors. For systems with up to about 1O -106 processors, it seems that the arrangement of the processors in space so that each can "see" the others is the limiting factor; A large part of the volume involved must stay empty for the information-bearing light beams. above that, diffraction effects and power requirements place a limit on the number of processors.