Physical science stands apart. It is basically nineteenth century physics, chemistry, thermodynamics, and the differential equations in which they are expressed. Twentieth century relativity is a carefully reasoned extension into high-speed phenomena. Discrete quantum-mechanical phenomena must be summated before using in deterministic analysis.
In 1952 physical science invaded neurophysiology. Hodgkin and Huxley published a series of four papers in the "Journal of Physiology" that presented a quantitative theory for the action potential, together with careful experiments to support it. The experimental animal was the Atlantic squid. Specimens of approximately the same size and freshness were tested repeatedly, and the results agreed to about two significant figures. Hodgkin and Huxley suspected, and later experiments confirmed, that the theory could be applied to neurons of many other species by a mere change of parameters.
Implied in this result is the possibility that, with the additional support of quantitative understanding of synapses, physical science might also conquer neural networks.
Donald O. Hebb's 1949 book, "The Organization of Behavior", preceded Hodgkin and Huxley's papers, and so missed their implication. But reading Hebb's Introduction, it is apparent that he understood at least most of the issues. He was still young enough (45) to freely consider the possibility that physical science could ultimately explain psychology, and his guess was that it would follow the pattern of his theory of cell assemblies.
So how come Hebb the old man rejected cell assemblies? In the 2006 edition of "Psychology: The Science of Mind and Behavior", edited by D. C. Donderi, Hebb considers the applicability of cell assemblies to various processes. One is perception. On page 160 he says "A conflict with the theory of learning is due to the apparent fact that the perception does not, or need not, depend on the excitation of any particular input lines, and hence the apparent necessity of concluding that a perceptual process is not localized." I don't believe that conclusion is justified. A cell assembly consisting of many interacting neurons might have enough redundancy to get going without one or two of its neurons. But this mathemaical behavior has not been demonstrated. Could it be?
Mathematical demonstration takes the enquiry to a different stage, necessarily involving modern computers with large capacity hard disks and RAM memories. With such capacity, computers can be used in a way that really simulates neurophysiological systems, but atill on a small scale. An easily accessible programming system for doing this is now available. It is named NEURON. Unfortunately NEURON does not yet include modeling of learning. There is an older programming system named GENESiS that does include a Hebbian synapse for learning, but it requires the linux operating system.
It must be emphasized that theories of the social science type (such as psychological), and tests of them, cannot constrain physicomathematical science. Its own tests determine whether its theories are mathematically possible. If the theoretical mechanism is biological, evolution will have determined whether it is also reality.
I wrote the above review based on the 1949 edition, before I had received the 2002 edition. Richard E. Brown and Peter M. Milner are to be congratulated for establishing this new link to Hebb's original ideas. If physical science eventually vindicates the theory of cell assemblies, it will be due in part to such links.
The short biography of Hebb by Brown and Milner makes clear that Hebb's model for sensory input was vision. If cell assemblies participate in vision, they could easily be obscured by the complexity of the many other mechanisms present there. Wouldn't cell assemblies be more prominent in the sense of touch?
Discussions of the theory of cell assemblies at the nonmathematical level have often been critical, but I think that if everything is considered the theory will be supported. Most important is the fact that perfectly modulated response occurs within less than a second. This could not be accomplished if response had to be constructed sequentially from one brain region to the next. Instead, all of the required brain regions must be working on the response simultaneously, and this can only be done with cell assemblies. An assembly can go through enough reverberation to define itself in 100 ms or so.
Another bit of evidence is the combined holistic and analytic phenomenon sometimes experienced by mathematicians and composers of music, when a basically complete theory or composition emerges from their subconscious. It was all fitted together by cell assemblies.
Freudian psychoanalysis is a way of gaining access to the subconscious, short of physicomathematical analysis. There are obviously associations short of the giant id and superego. Elements of conscious thought from the preceding day often appear in dreams, perhaps in bizarre associations. Physically, these must be cell assemblies.
The trouble with understanding multidisciplinary phenomena like neural network behavior is that academic departments usually do not really talk to each other. They claim to get together for discussions, but they only talk to each other in English. They don't teach the other department to think in the specialized language of their department. How different would Hebb's evaluation of his theory have been if he were familiar with Poincaré's mathematical treatment of celestial mechanics, and therefore gained insight into nonlinear dynamics? Incidentally, Poincaré and the astronomers are an exception. He was willing to study their problem in calculating planetary orbits because it gave him a chance to create a new mathematical theory. And they were willing to go through the tedious mathematical computations because they were accustomed to doing the math in computing positions of planets.