No offense but your conclusion doesn't follow from the logic. Given your
statement:
"[Which can] generate action potentials..." Can you not conclude that
moving from one potential to another is a change in state? I believe you
are following the same logic as the sandpile problem. Given a sandpile and
removing a grain of sand at a time - when is the sandpile no longer a
sandpile? The exact point in time of "change in state" from sandpile to
'not sandpile' is difficult to determine, however you must agree that there
is definitely a change in state involved, i.e., sandpile, 'not sandpile'.
The nervous system is not stateless. Hit yourself in the finger with a
hammer and then decide if there is a difference in your current and previous
state. Same with biological neurons, firing, not firing; firing, firing
stronger..., etc. When modeled in the continuous mathematics of the
calculus you can derive instantaneous state in continuous systems....
FWIW, no disrespect intended....
/dave waterman, PhD
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