1.3.1 Concepts of the play

In this section – in the spirit of Johnston and Wu [2] – we review how the relevant significant components, actors and actions of a single neuron follow the ’basic principles’. Textbooks usually skip how the neuron, a piece of living material, is modeled. Instead, they put behind their formulas (unfortunately, referring to HH), without validating them for biology, the picture taken from classical physics, which was validated for different circumstances (non-living matter) in a classical disciplinary concept. HH seem to be one of the rare exceptions, also in the context that they admit that the ’interpretation given is unlikely to provide a correct picture of the membrane’, furthermore that ’physical theory of this kind does not lead to satisfactory functions … without further ad hoc assumptions’ [9]. Their followers introduced further ad-hoc assumptions, needed to provide satisfactory agreement with the experimental evidence, into their admittedly wrong physical picture. Those models assume that the circuits comprise point-like ideal discrete elements such as condensers and resistors, and some mystic power changes their parameters; furthermore, ideal batteries with a voltage that, again, may change their voltage. All of them are connected by conducting (metallic) ideal wires, and their interaction speed is infinitely high (the Newtonian ’instant interaction’). That approach leads to the ’electrotonic model’ [55], which is half-century old. It was question marked whether they can be realistic [48] at all. That abstract model enables them to use the well-known classic equations named after Ohm, Kirchoff, Coulomb, Maxwell, and others. However, those abstractions have severe limitations when applied to living material; moreover, they mislead research in some aspects. It could be useful in its time of discovery, at a very elementary level, but it surely cannot describe the details discovered during the past half century.

We provide a ”birds’ eye view” of our model’s operation. We must refer back to the need of the zigzag discussion. We introduce our fundamental terms and notions in a way that we assume the audience has at least a fundamental knowledge of the subject. We refer to the corresponding sections, discussing the physics that establishes them, and the sections which, in terms of ”abstract physiology” (without biological details), provide more details.

When describing neuronal operation, we start with the point: ”neurons are sites where information is handled in analog rather than digital form. There may be hundreds of excitatory nerve endings on the surface of one postsynaptic cell. Each terminal is capable of secreting the excitatory (or inhibitory) chemical. The rate of secretion is governed by the rate of arrival of presynaptic impulses. True, each impulse in one terminal liberates a definite amount of transmitter, but there may be many impulses in many such terminals. The postsynaptic depolarization that ensues is essentially a continuously gradeable process. The membrane potential of a neuron waxes and wanes with the ceaseless variations of excitatory and inhibitory input, and with it varies the stream of impulses issued in its axon. The digital pulse code of presynaptic fibers is thus converted into an analog process at the junction, only to be reconverted into a digital pulse code again in the axon of the postsynaptic cell. The logical operations are all performed in the analog mode at the synapses.” [56] We emphasize that all processes are slow (in the sense that they have well-observable time course as opposed with sudden changes and ’non-ordinary’ laws of science describe them), furthermore, that neurons exist only in their dynamic way; their static discussion is misleading. Note that those ”ceaseless variations” can be correctly handled by our dynamic methods.

Following the path to understanding neural functionality (mainly: the brain and life in general) involves creating the necessary microbiological components, their elementary functions (physical function, stimulus processing, cooperation, and reproduction), and their higher-level cooperation (networks). The overview of the entire operation requires not only a multitude of scientific disciplines but also their cooperation and periodic coordination (reconciliation) of their approaches. A fundamental aspect is the precise description of the temporal behavior [26] of the participating processes (very slow compared to the interaction speeds usual in physics), for which the laws derived from generally used physical approaches are not suitable (their use produces misleading results) - almost the same holds also for technical computing. Computing science is still based on the principles laid down by von Neumann [3]. However, the technology in the meantime has reversed the ratio of transfer and processing times, so the theory is used far outside its range of validity. Since approximately 2000, the theoretical description has become increasingly inadequate for actual computing technology [11], particularly for computing accelerators and networked solutions, as it overlooks Feynman’s warning [19] that computers belong to the engineering field rather than mathematics. The finite speed of interaction (data transmission) becomes increasingly important as the operating speed increases. It enforces technical limitations [25, 11] on the performance of supercomputers [57] and neural networks [58] (whether biology-imitating or technical ones); their performance strongly decays as the system’s size increases. The technical solutions inherited from the single-processor age, combined with the non-time-aware viewpoint of their theories in both computing and biology [11], prevent the correct discussion, and even more, combining them, whether attempting to imitate one with the other (biomorphic architectures, brain simulation, or artificial intelligence) or combining them (brain-computer interfaces). We aim to continue researching ways to improve cooperation between these disciplines by analyzing their features theoretically and simulating them.