Fifty years later, thanks to solid state micro-electronics, the von Neumann matrix is going strong. The problem has shifted from how to achieve reliable results using sloppy hardware, to how to achieve reliable results using sloppy code. The von Neumann architecture is here to stay. But new forms of architecture, built upon the underlying layers of Turing-von Neumann machines, are starting to grow. What's next? Where was von Neumann heading when his program came to a halt?
As organisms, we possess two outstanding repositories of information: the information conveyed by our genes, and the information stored in our brains. Both of these are based upon non-von-Neumann architectures, and it is no surprise that Von Neumann became fascinated with these examples as he left his chairmanship of the AEC (where he had succeeded Lewis Strauss) and began to lay out the research agenda that cancer prevented him from following up. He considered the second example in his posthumously-published The Computer and the Brain.
"The message-system used in the nervous system... is of an essentially statistical character," he explained. "In other words, what matters are not the precise positions of definite markers, digits, but the statistical characteristics of their occurrence... a radically different system of notation from the ones we are familiar with in ordinary arithmetics and mathematics... Clearly, other traits of the (statistical) message could also be used: indeed, the frequency referred to is a property of a single train of pulses whereas every one of the relevant nerves consists of a large number of fibers, each of which transmits numerous trains of pulses. It is, therefore, perfectly plausible that certain (statistical) relationships between such trains of pulses should also transmit information.... Whatever language the central nervous system is using, it is characterized by less logical and arithmetical depth than what we are normally used to [and] must structurally be essentially different from those languages to which our common experience refers."