The AP is one of science’s big mysteries. We put together an isolating membrane, isolating membrane tubes connected to the membrane, voltage-controlled ion channels in their walls, and an electrolyte solution around them. We apply currents/voltage levels or pulses to the tubes, and at some point (at some appropriate combination of parameters; too small or too large currents result in stopping APs, the system starts to issue APs: the non-living matter turns into living matter. In contrast with the expectations of HH [9], the AP can be described from the first principles of physics when using the right physical approximations and abstractions.
Neurons interface the living and the non-living components of nature. To understand the details of their respective operation, an exact interpretation of notions and laws of non-living matter is also needed. Applying the laws derived for an approximation abstracted for the conditions of classic science is misleading and prevents us from understanding that, at different abstraction levels, neurons are living components and simultaneously, still, they can be described by the laws of non-living science; provided that we use the right abstractions and approximations, as their case requires. They are studied by research methods and tools of fellow sciences and are described by the universal language of nature: mathematics. However, not necessarily by the mathematical procedures developed for other goals and used in classic science.
HH attempted to find a mathematical formalism for their very precise measurements [9] and find out empirically what kind of mathematics (invented for the approximations used in classic science) can – more or less – describe their experiences, despite that ”a number of points were noted on which the calculated behaviour of our model did not agree with the experimental results to provide a correct picture of the membrane.” Their followers forgot the doubts and question marks HH described and took their unproven hypotheses as facts. ”These equations and the methods that arose from this combination of modeling and experiments have since formed the basis for every subsequent model for active cells. The HH model and a host of simplified equations derived from them have inspired the development of new and beautiful mathematics.” [45]. That mathematics is beautiful but describes some alternative nature instead of the real one, see also section 3.10.
Despite the impressive advances in neuroscience during the past decays, there are still ’white spots’. ’Why action potentials are initiated in the axon is still unclear’ [50] and ”we should not seek a special organ for ’information storage’ – it is stored, as it should be, in every circuit” [144]. This latter source points to the important point ’Communication consumes 35 times more energy than computation’. [78] One more point why computation and communication must not be handled separately [3]. It also asks the questions what is information, how it is stored, processed and transmitted.
We can model a neuron as an oscillator where the membrane changes its potential above a resting potential, receives (gated) synaptic currents through its axons and through its ion channels, furthermore external currents/voltages provided by the experimenter. Those currents are slow, so we must consider their speed to produce the membrane’s correct behavior, either as a time delay or a time course of a current intensity.