Not explanation, but prediction is our most stringent test of understanding. Many are the explanations after the fact; few are the predictions that agree with later observation. This holds especially for complex phenomena, whether of astrophysics, cosmology, economics, history, or social behavior.

When statistical thermodynamics first yielded distribution functions for cosmological many-body systems, neither simulations nor observations had been analyzed for comparison. Only Hubble's galaxy counts in the limit of large cells were known, though not to us at the time. Correlation functions then dominated studies of largescale structure.

Old simulations, after their spatial distribution functions were analyzed, first showed that the theory was reasonable. As a result, many new simulations, sketched in Part V, began to explore the range of conditions to which the theory applies; this exploration continues.

It took a couple of years to persuade observers to analyze distribution functions for modern catalogs. Would the distributions created by the great analog computer in the sky agree with those of digital computers here on Earth? Is the pattern of the galaxies dominated by simple gravitational clustering? The answer is still a continuing saga. Although observed spatial distribution functions are now moderately well studied, velocity distributions are just beginning to be determined, and predictions of past evolution remain to be observed in our future.