Field Computing Hardware

Field computation can, of course, be performed on conventional digital computers or by special-purpose, but conventional digital hardware. However, as noted previously, neural computation and field computation are based on very different tradeoffs from traditional computation, which creates the opportunity for new computing technologies better suited for neural computation and field computation (which is broad but shallow). The ability to use slow, low precision analog devices, imprecisely connected, compensates for the need for very large numbers of computing elements. These characteristics suggest optical information transmission and processing, in which fields are represented by optical wavefronts. They also suggest molecular processes, in which fields are represented by spatial distributions of molecules of different kinds or in different states (e.g. bacteriorhodopsin). Practical field computers of this kind will probably combine optical, molecular and electrical processes for various computing purposes.

Mills (1995) has designed and implemented Kirkhoff machines, which operate by diffusion of charge carriers in bulk silicon. This is a special purpose field computer which finds the steady state defined by the diffusion equation with given boundary conditions. Mills has applied it to a number of problems, but its full range of application remains to be discovered.

To date, much of the work on quantum computing has focused on quantum mechanical implementation of binary digital computing. However, field computation seems to be a more natural model for quantum computation, since it makes better use of the full representational potential of the wave function. Indeed, field computation is expressed in terms of Hilbert spaces, which also provides the basic vocabulary of quantum mechanics. Therefore, since many field computations are described by the same mathematics as quantum phenomena, we expect that quantum computers may provide direct, efficient implementations of these computations. Conversely, the mathematics of some quantum-mechanical processes (such as computation in linear superposition) can be transferred to classical systems, where they can be implemented without resorting to quantum phenomena. This can be called quantum-style computing, and it may be quite important in the brain (Pribram 1991).