The Indeterminacies of the Brain

THE INDETERMINACIES OF THE BRAIN* DONALD O. WALTERf Heisenberg's principle ofindeterminacy in physics is paralleled by other indeterminacies, recently treated in a unified way by Barnes [i]. Various versions ofsuch principles have fascinated biologists, especially brain theorists ; some, for example, Eccles [2], have taken Heisenberg's version ofthe principle, in combination with an extrapolation ofspinal-cord physiology to the brain, to allow the Christian version offree will into brain research; others [3] have disputed this. Piatt [4] has recently raised the question in a different way. Piatt's Swiftean image ofthe difficulties ofhaving one brain apprehend another is amusing, but the difficulties he suggests (having enough recording humans to observe each nerve cell, and having enough states in the apprehending brain to correspond to states in the subject's brain) are not the primary ones. A more fundamental problem is that the subject's brain hasn't enough surface area through which enough probes can enter. Suppose we ignore the possible contribution ofthe neuroglial cells (ofwhose number an estimate is 10") and assume that with a single probe in the vicinity of each neuronal soma (about io10 ofthem) we can get an adequate measure of that neuron's state (an assumption rather analogous to ignoring internal degrees offreedom in the kinetic theory ofgases, which is sometimes accurate enough, sometimes not). Suppose that our probes have a square cross-section, of side io_î cm.; then (1er3)2 cm.2 per probe X ioTO probes = io4 cm.2. Not averynormal brain surface, with so much hardware sticking through it! This is a more fundamental reason against speaking about "the state ofall neurons in this brain" than the one Piatt offers, and one less likely to be overcome by the rush oftechnology. Because probes must be made ofmatter having atomic structure and lim- * Preparation ofthis paper was partially supported under a training grant from the U.S. Public Health Service (5 TI-MH-6415). t Departments of Physiology and of Anatomy, and the Brain Research Institute, University of California, Los Angeles. 203 ited strength, they cannot in principle be made small enough to make these measurements. Some might claim that enough electrodes could be placed at the surface ofthe brain to record electric waves from which the state of all neurons in the depths could be inferred; however, I think that the rapid attenuation ofaction potentials with distance (with a space constant ofioo microns or less) and the enormous number ofcells involved combine to make it impossible in principle to define all their states by surface recording . I claim that this barrier to our knowledge ofthe states ofall neurons in the brain is as fundamental as the photon barrier in atomic mechanics; hence, our ignorance should be treated as equally fundamental in either field. But there is a second important issue: whether the indeterminacy in our knowledge ofthe precise present state ofa particular brain can be declared significant. It requires only a couple ofmicroliters ofa gas to contain a million times more molecules than the brain's neurons: 1016 molecules at standard temperature and pressure. Measurements ofeach molecule's position and velocity (again ignoring internal states) would require a measurement operationjust as disruptive as was required for the approximate state description ofthe brain. Yet the gas "has a state," at least to a good (and known) degree ofapproximation. Now, I believe that the brain is essentially less determinate than the gas. But how can this be? The answer depends on the idea of the accuracy of predictions about the two systems. For most states ofa gas, slight errors in measurement oftemperature, slight departures from equilibrium, as well as fluctuations in state due to the randomness of the molecules' motion, and the like, produce only slight errors in prediction ofthe gas's future states, for the state function is smooth on this scale, and the fluctuations regress toward more probable states. There are only a few critical points where a distinct prediction error can result from a small measurement error. In order to make clear the way in which I propose that the brain differs from the gas, I will take the simpler example ofa real (hence unreliable) computing machine. Some machine errors...