Brain as a unique object (Neural Cell Behavior and Fuzzy Logic)

Brain is the most complex, puzzling and attractive object in the universe. Everybody knows that brain is responsible for control of our learning, memory, motivations, consciousness, etc. Moreover, a brain by a certain mysterious way produces the Subject (or Self, Person, Ego, Observer – whatever you like), which tries to look into brain and understand the Subject itself. The means for the objective observation of a subjective world are absent, but we can observe the consequences of objective existence. Neurobiology is the only science that considers the subtle facet between substance and mind.

Besides the fact that brain generates goals and does not need external programming, it possesses many particular properties that make it an appealing object for research. Brain works using fuzzy laws on the one hand and produces fuzzy logic on the other hand [1269]. The brain has the highest metabolic rate of all bodily organs and depends predominantly on oxidative metabolism as a source of energy [755]. The brain spends 20% of total body oxygen consumption, although its mass is less than 2% of the total body and a brain does not produces mechanical efforts, as does a muscle, does not synthesize enzymes for food digestion, as does a liver and does not pump overlarge volumes of blood, as does a heart. Energy-consuming processes include maintenance of ion equilibriums, generation of the basal electrical activity, neurotransmitter uptake, etc. There are two main consumers of cellular energy, protein synthesis (55%) and Na+, ^+-ATPase (45%), but during hypoxia Na+, ^+-ATPase becomes dominant (80%) [158]. The Na+, ^+-ATPase, or the sodium pump, is a transmembrane protein accountable for maintaining electrochemical gradients across the membrane in all cells. However, even in the resting awake state, around 80% of energy used by the brain supports events associated with cycling of glutamate and gamma-aminobutyric acid (GABA) neurotransmitters [1139, 541], the main transmitters of excitation and inhibition, connected also with cell damage and protection. Therefore, equilibrium between neuronal damage and protection plays an important role in the normal brain function.

In the brain, at any one moment, a lot of neurons, although not every one, are active. Brainy activity is perceptible even when it appears to be doing absolutely nothing. The basic diversity of chemical reactions in a body also belongs to brain. Properties of neurons are much more complex than for any other cell. This is partially concerned with the excitability of neurons. Brain has infinite memory in a finite volume (in the sense that nobody sees as memory come to an end). Physical damage of brain structure causes only subtle impairment of memory, which is usually less for remote, important and learned-by-heart memory [1252, 1255]. By some evaluations, a massive parallel processing capacity permits our visual system to successfully decode complex images in 100 ms, and our brain to store information that many times exceeds the text contained in the US Library of Congress [794]. Neuronal memory is not reversible, but brain scarcely contains any empty storage medium. The capability to recognize exceeds the capability to recollect. Sometimes, one cannot recall required information from one’s past experience, but images in the long-term memory are never destroyed: for example, one doesn’t remember only half of the face of a friend, and one doesn’t remember a vacation in black and white but in color. Brain does not contain moving parts or valves, works exclusively and consistently, and memory stays intact after a short-term shut down of all dynamic processes. Signals in the brain are spread slowly (ten million times slower than electrical signals), but time response for many tasks is exceptionally short. Brain contains billions of neurons, ten or more trillions of synaptic connections, and processes information during milliseconds. It has a highly parallel organization, but does not suffer from the dictates of a few processors.

Brain is a unique object. However, is brain a subject? Are you your brain? Is one the activity of his brain? When brain produces thinking, neurons and glial cells generate electrical fields, the distribution of ionic concentrations alters, various substances are synthesized and degraded, numerous enzymes are activated or inhibited, gases spread through nerve tissue, etc. How, when and where is physiology converted into sense and what kind of physiological activity is decisive? This is the crucial problem. Can we some day solve it? For sure, problems that are inaccessible to our brain do exist. Just as a crocodile cannot be timed and a dog can not speak, the human mind also has borders. Our brain can’t read two texts simultaneously, can’t remember its prenatal life, can’t imagine how the electron runs through two holes at once and maybe never can comprehend how the outer environment is converted into an inside, subjective word. In fact, there are environmental features that our brain can’t perceive, our memory is not ideal and imagination is not infinite. However, our capability to realize is exceptionally powerful. For instance, we can’t imagine four-dimensional space but can comprehend that in four-dimensional space, the loss of one’s keys from your safe is not worrying: one always can penetrate through the fourth dimension. If we never understand consciousness, this will be the first problem that humanity cannot manage.

The foremost mission of neurobiology is the cognition of subjective phenomena and this includes the disproving of supernatural or mystic explanations for this extremely hard problem. Thermodynamics teaches us that disorder in closed-loop systems increases, but the brain gives a kind of an object, which introduces order in the world. One may imagine Maxwell’s daemon, (that little homunculus!) controlling microscopic damper in the vessel. When a high-speed molecule in the environment draws near to the vessel, the homunculus opens slightly the damper and accumulates energy, thus violating thermodynamic laws. If we mark on the cerebral cortex the points receiving information from the body (face, knees, belly, etc.) we will observe an ugly dwarf at the surface of the cortex with its huge jaws, widely spread fingers and colossal genitals (the more sensitivity, the more cortical representation). This homunculus has only technical, ancillary meaning. However, sometimes one imagined one’s Self as the Homunculus living in the brain. Any problem is easy to explain by means of a homunculus, but this is an inadmissible explanation in science. If one says that the theory may work only with the contribution of the homunculus (that is as being run by a Homunculus inside), this means that the theory is not scientific theory.

At present, we poorly comprehend a brain. Sometimes comprehension of an object is identified with the skill to recreate and/or to improve this object. This is not our goal. Animals recreate brain naturally and improve it in evolution without any comprehension. To be more accurate, we want to understand some brain functions. Among them there are some so intricate that even vague explanations are absent.

Neurobiologists run into several hard problems:

1. After learning, the reaction to a specific signal depends upon its significance, which was acquired during learning. Reactions become specific to input, and one signal may increase its effect, whereas another signal turns out to be ineffective. Why are some signals preferred? It is not the rule that a stronger impact evokes a stronger reaction. Gentle footsteps in one’s bare apartment may exert a stronger impression than the harsh noise of one’s TV. A specific reaction to a given signal may be both innate and acquired during experience. Thus, a task is related to the nature of memory: reaction depends on past experience. Moreover, is the physical appearance of memory elements predetermined by their real appearance in the environment? If the response is "yes" and similar images or events retain similar material traces of memory in different brains, a one-to-one correspondence exists between possible events and memory elements, even if you will never meet these events in your life: for instance, the image corresponding to the face of my grandmother preexists in any brain in a passive form ("grandmother" cells, synapses or pathways). It is scarcely likely that whole world’s diversity may be squeezed into the brain. However, if the response is "no" and the memory elements are specific for each brain, who decides that an activated memory trace corresponds to a specific image or event? Therefore, the puzzle is how neurons recognize the representations they keep. Should we suppose the existence of a certain mysterious homunculus, living at the skull, which observes the environment through our senses and executes his wishes by means of our muscles? Some people think that we are our homunculi.

2. The same signal may evoke one or another reaction, depending upon circumstances. Reactions are specific for an output and brain somehow decides what action is desirable. But there is the question about how the reaction is chosen if each neuron has only one output? Let an organism choose the correct response to the signal, say, to run in or out. Its neurons can generate different reactions in response to dissimilar stimuli, but are not necessarily able to send the right signal in the right direction. For a single neuronal output, where an axon may be branched, a neuron does not have the means to send a signal to the specific branch. Even if axonal output is not symmetric, real choice is impossible, as the degree of non-symmetry is predetermined. A neuron may only send or not send a spike in the axon. Who chooses the decision? Even if we will suppose that our reactions are chosen by a homunculus, it does not have the means in order to accomplish its will: when it has chosen decision, it cannot send it to a correct target (if we try to proceed from neuron’s doctrine).

3. Brain responds to an image by the formation of electrochemical representation within neural tissue. It is easy to imagine that each image corresponds to the specific constellation of activated and inhibited neurons. How does brain know that a current neuronal constellation correctly matches a given picture? Perhaps, changes of these pictures in time produce successive frames, such as in the cinema. If so, who looks at the film? One’s homuncu-lus? Or, maybe, odd elements of brain’s picture interact and are integrated in a new entity? Each image is characterized by size, form, time, color, smell, time, etc. How are spatially and temporally different processes united in the awareness? This problem is known as the "binding problem".

4. An aware performance is always the sole act and currently active brain elements are somehow amalgamated in decision-making. An actual action is dominant. If scattered brain neurons generate various subthreshold actions, they ought not to prevent the actual action. If there is no homunculus in the skull, why do the decisions in various brain areas have a tendency to turn out similarly? Moreover, if a central processor is absent in the brain, the actions in brain areas must be synchronized within a narrow time window and this time window is shorter than necessary for a neural excitation transmission through the brain.

5. If action is predetermined by the environment and by the state of the brain, goal-directed behavior can be treated as an ordinary reflex, i.e. as a reaction to stimuli (inner or outer), based on memory and heredity. This predetermination would preclude voluntary action as the object of physiological description. The issue of predetermination of action has been the subject of philosophical and psychological analysis, as free will, but has not yet been addressed in depth by neurobiologists. The problem remaining unsolved is how behavior can be both unpredictable and goal-directed, if we do not consider there to be a homunculus in the head.

6. Living beings generate aware actions. How is neuronal activity transformed into qualia (saltiness, redness, pleasure, painfulness, etc.)? We are capable of understanding physiological processes and neuronal computations, but how does Self begin, as a tangle of desires and expectations? Is this, once again, the trace of the notorious homunculus? Does a homunculus have its own control center or must we, at this point, stop our efforts? This is the same hard problem. No one can suggest an experiment for examination of a working hypothesis, because nobody may propose any hypothesis and even vouch for the scientific validity of the problem itself. By the way, Niels Bohr, Er-win Schroedinger, Wolfgang Pauli and Werner Heisenberg, the great quantum physicists of the twenty century, all admitted that consciousness is as primary as a substance [1152]. They believed that the explanatory gap between the subjectivity and the physicochemical activity of neurons is analogous to wave-particle duality. The smallest units of matter are not substance objects in the ordinary sense; they are not hard and not soft, do not have dimension, are impossible to see, to touch, to smell and they do not reside at a given time in a given place. They display themselves only during the process of observation and have an aspect of subjectivity: one cannot determine the coordinates of the electron until carrying to completion the measurements. There are forms and ideas which can be expressed only in mathematical language. Equally, it may be that both the material universe and the human mind are equally ‘objective’. The great quantum physicists were unanimous in considering that consciousness arises before humanity.

These hard problems are rather far from being solved. We do not promise to settle them, but let us try. Our task is to appreciate some, still unexplained, brain functions, or at any rate, to outline pathways to their understanding. Some of our explanations will be preliminary. We are considering as unacceptable only two extremes: when any explanation is absent and when there are several equivalent explanations.

Which "logic" does the brain use for description of an environment and for decision-making? Numerous literature’s sources and our original experiments considered in this topic, allow us to believe that capability of perceiving could take place already on a neuron level. So, if we want to develop an adequate mathematical description of neuron information processing, we are, in a certain sense, compelled to search an apparatus, which could operate with "perceptions" as with mathematical objects. In this topic we show that the subjective attitude of the brain to an expected event can be the reason for the advent of the brain’s "logic of perception". Another reason to develop a phenomenological theory of neuron’s behavior, which is based on notation of perception, is the nature of the experimental data for the real neurons. In fact, in these experiments only a few parameters of a system are observable and controllable, while a number of the other ones are "hidden" or remain out of control. For a complex phenomenon it leads to considerable variability in experimental results from trial to trial and makes it difficult to estimate accuracy of the obtained values. For such a phenomenon fair description of a system behavior is based on our "percept" of observed tendencies rather than on precise numerical values of the experimental data.

Mathematical basis for "computing of perceptions" was proposed by L.Zadeh almost half century ago and one was named as "fuzzy logic". In the following decades fuzzy logic has been intensively developed and applied to numerous applications in several thousand articles and topics. It has been shown that fuzzy logic is amazingly effective in processing of information with high level of uncertainty. A real neuron is a complex dynamic system, so for description of it behavior we need an extension of fuzzy logic on evolutionary processes: "evolution of perceptions". Such a theory called "fuzzy dynamics" has been developed and studied during the last decade. Fuzzy dynamics can be successfully used in the situation, where both the system states and the dynamics laws have considerable uncertainty, which is typical for description of the systems on a "perceptive level". Actually, these laws are naturally formulated in terms of "neuron activity", "neuron damage", "level of compensation" and "expectation of punishment", which can be considered as phenomenolog-ical variables describing our "perception" of a neuron state. Of course, such variables are very qualitative and have considerable level of uncertainty, but they fair reflect our real knowledge about the considered system.

It is important, that fuzzy dynamics can directly operate with above mentioned variables and dynamics laws without additional arbitrary assumptions and hardly verified hypotheses. In this topic we explain how fuzzy dynamics equations can be obtained. An undoubted advantage of this approach is an ability to use well-developed apparatus of the theoretical physics for analysis and solution of the dynamics equations. It will be shown that the fuzzy dynamics approach to a neuron behavior leads to good compatibility with experimental observations and allows understanding some basic features of the neuron being. In particular, it predicts strong sudden, non-stochastic alterations in the neuron’s activity. Such alterations are typical for a real neuron’s behavior and it has an effect on macro-behavior of an animal. It is well known that even when it know a good solution to a given problem, an animal from tries time-to-time to find a new solution and if the new solution is a worse then the old one the animal returns to its previous behavior. Such "researcher’s instinct" is very beneficial, since it enables the animal to effectively optimize its behavior in continuously changing environmental conditions. It should be emphasized, that in fuzzy dynamics approach such behavior is neither the consequence of random inner influences of the neural system nor only the result of the sudden changes in environment, but rather a fundamental feature of neurons. It seems very likely, that the inner logic of the neuron’s behavior is close to fuzzy logic.

The idea of using some of the features of physiological processes in cybernetics is very old, but it is still attractive. For example, a concept of self-consciousness and emotion for robotic systems has been discussed recently in set of international conferences and congresses. Because fuzzy logic is easily computerized, it is feasible to design new kinds of artificial neurons: "motivational artificial neurons", which seem to be very promising as elements of the "brain of the feeling robot". Behavior of such robot will be initiated by a few artificial drives included energy recovering, avoidance of injury and aspiration to survive. So, in a "feeling robot" performance of the main task, trial-and-error learning, aspiration to survive and "instinct of researcher" could be naturally combined.

Reading this topic, the readers will encounter a number of molecular, electrical and morphological devices that brain uses in its performance. The reader is not committed to understanding the fine dynamics of their functioning. We have used these data for a purpose. Simplified explanations for some brain functions sometime contradict easy explanations of other functions as well as the occurrence of more complex material substratum. However, it is productive to compare in which functions (sometimes rather different) the same material device participates. This may reveal relationships between these outwardly different functions. Therefore, for us it was more essential to delineate what function performs a given molecular device, than to linger on the fine details of its performance. Obviously, this approach cannot lead us to recreation of the working brain scheme. However, we hope to advance in this direction.

We don’t assume that the readers are familiar with the fuzzy logic paradigm, so short introduction to the fuzzy sets theory and the fuzzy logic will be presented. Note that the Sections are designated by star (*) contain more specialized material and can be omitted by a reader, which is interesting, mainly, in general information.

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