1. A unified parallel processing architecture for connecting together an extendible number of clusters of multiple numbers of processors to create a parallel processing computer system, the unified parallel processing architecture comprising: four or more clusters of multiprocessors, each cluster comprising: a cluster shared memory means for storing and retrieving data and instructions for one or more parallel tasks of one or more computer programs; two or more processor means for executing the instructions and operating directly on the data for the parallel tasks that are stored in the cluster shared memory means; one or more input/output port means for transferring the data and instructions for the parallel tasks between the cluster shared memory means and one or more external data sources via one or more block-by-block communication paths; and connection node means for connecting the cluster shared memory means with all of the processor means in the cluster such that access to the clustered shared memory means by all of the processor means in the cluster is symmetrical; means for providing a plurality of floating shared memories by adjacently connecting some, but not all of the clusters, via one or more word-by-word communication paths to create a floating shared memory that is defined by the cluster shared memory means of the cluster and the cluster shared memory means of any adjacently interconnected clusters and that can be programmed using a shared memory model; and means for providing an extended distributed memory among any non-adjacently interconnected clusters that defines an extendible address space encompassing the cluster shared memory means of all clusters that can be programmed using a distributed memory model.