14.2 More Realistic Neuron Models
583
A finite “automaton” is a device which accepts a finite set of input symbols,
acts on this input with a finite internal state, including programming operations, and
produces a new internal state and an output. Arbib 5 has shown that the behavior of
every finite automaton corresponds to the behavior of a McCulloch–Pitts network,
and visa versa. We also should expect that the behavior of our brain can at least be
approximated by a McCulloch–Pitts network. The seemingly continuous elements,
such as nerve impulse frequencies and axon delay-time lengths, we propose are all
discretizable.
Although the brain, like all other natural systems, is successfully described by
quantum theory, we should not expect that the effects of non-classical quantum
behavior to be important in the operation of our brain, except to the extent that
quantum uncertainty can cause uninitiated neuronal firings. Evolution would favor
mechanisms which would minimize these effects. Now, you may ask what about
free thought? If our brains act mechanistically, you argue, then our thoughts are
determined by input and memory.
We can define ‘free thought’ as neuronal activity which was not initiated by a
mechanistic reaction to input and memory. Classical noise, chaotic nerve firings, and
even quantum decoherence could be used to explain such effects. However, given
the need and advantage for determined brain function, evolution likely suppressed
such undetermined thoughts. Besides, our close interaction with our environment
through our senses is sufficient to cause many fluctuations in our thoughts associated
with external inputs. These external inputs also contain noise from various sources
and the consequences of any chaotic behavior in non-linear external systems. In
fact, external noise can be very difficult to eliminate. We do not yet know how to
eliminate the passage of cosmic neutrinos through our brain! Quantum theory allows
for the coherence of wave functions for particles at far distances with the wave
functions of our particles. (Einstein’s ‘spooky action at a distance’.) We can build
such couplings, but decoherence is rampant for particles open to the environment,
as ours are.
14.2 More Realistic Neuron Models
14.2.1 Electrical Activity of a Neuron Membrane
Cell membranes have special channels made from protein molecules embedded in
their lipid bilayer. These channels transport ions and other small biologically important molecules across the membrane. Neurons use these channels to build a resting
potential of about −70 mV, making the inside of the cell membrane negatively
charged, and the outside positively charged. This is achieved by allowing potassium
ions into the cell, while pumping sodium ions out. A single sodium-potassium pump
5 Michael A. Arbib, Brains, Machines and Mathematics [Springer-Verlag] (1964).
583
A finite “automaton” is a device which accepts a finite set of input symbols,
acts on this input with a finite internal state, including programming operations, and
produces a new internal state and an output. Arbib 5 has shown that the behavior of
every finite automaton corresponds to the behavior of a McCulloch–Pitts network,
and visa versa. We also should expect that the behavior of our brain can at least be
approximated by a McCulloch–Pitts network. The seemingly continuous elements,
such as nerve impulse frequencies and axon delay-time lengths, we propose are all
discretizable.
Although the brain, like all other natural systems, is successfully described by
quantum theory, we should not expect that the effects of non-classical quantum
behavior to be important in the operation of our brain, except to the extent that
quantum uncertainty can cause uninitiated neuronal firings. Evolution would favor
mechanisms which would minimize these effects. Now, you may ask what about
free thought? If our brains act mechanistically, you argue, then our thoughts are
determined by input and memory.
We can define ‘free thought’ as neuronal activity which was not initiated by a
mechanistic reaction to input and memory. Classical noise, chaotic nerve firings, and
even quantum decoherence could be used to explain such effects. However, given
the need and advantage for determined brain function, evolution likely suppressed
such undetermined thoughts. Besides, our close interaction with our environment
through our senses is sufficient to cause many fluctuations in our thoughts associated
with external inputs. These external inputs also contain noise from various sources
and the consequences of any chaotic behavior in non-linear external systems. In
fact, external noise can be very difficult to eliminate. We do not yet know how to
eliminate the passage of cosmic neutrinos through our brain! Quantum theory allows
for the coherence of wave functions for particles at far distances with the wave
functions of our particles. (Einstein’s ‘spooky action at a distance’.) We can build
such couplings, but decoherence is rampant for particles open to the environment,
as ours are.
14.2 More Realistic Neuron Models
14.2.1 Electrical Activity of a Neuron Membrane
Cell membranes have special channels made from protein molecules embedded in
their lipid bilayer. These channels transport ions and other small biologically important molecules across the membrane. Neurons use these channels to build a resting
potential of about −70 mV, making the inside of the cell membrane negatively
charged, and the outside positively charged. This is achieved by allowing potassium
ions into the cell, while pumping sodium ions out. A single sodium-potassium pump
5 Michael A. Arbib, Brains, Machines and Mathematics [Springer-Verlag] (1964).