Theory of ideals
The human brain is a live control system so it is possible to apply cybernetics in order to describe its operation. The first question is a model of its architecture. Technical solutions often use a computer for this purpose, but it is different. Something like a computer may be found inside, but the brain as a whole is a complicated regulator. This principle emerged at the early stages of evolution with the primitive nervous system and was inherited from previous organisms which had no nervous system at all. Neurons use spikes - short pulses which may be transmitted over long distances and provide digital encoding, but the encoded signals remain analog. They are usually represented by spike frequency.
The principle of regulation is a very solid foundation for the theory of behavior. On one hand, the theory of automatic regulation is a perfectly elaborated branch of mathematics so we immediately have quantitative approach. On the other, this principle helps to choose between alternatives at the very basic levels. For example, regulation is basically maintenance. Human behavior is essentially dynamical, but is based on the static principle. This was confirmed by anatomy and physiology. The hypothalamus is the highest center of the vegetative nervous system. Its operation may be described in the same terms as systems of industrial automation.
The brain is a multiparametric regulator. This imposes yet another constraint. A single regulator is mathematically described by a differential equation. If we have several parameters, this will be a system. Systems of differential equations already have different properties. For example, they may have no solutions despite all separate equations have them.
Each regulator has a normal value which it maintains. For multiparametric regulation this naturally leads to the concept of ideal - normal values of all the parameters taken together. Mathematically, it will be a vector. The full definition is as follows.
Each living system consists of 3 parts: an ideal (its internal description), an organism (its material implementation), and regulatory gear which maintains the organism in accordance with the ideal.
Note that the last 2 components are material, the first is not. Just information. This definition perfectly works on all levels of living nature: a single cell, a multicellular organism, and social systems. The problem is that not all vectors are viable in principle. In the real world, different parameters are mutually dependent. Suppose one of them was deflected from its normal value. You launch some actions for compensation, but these actions force another parameter out of equilibrium. An ideal is a lucky combination which is convenient to maintain as a whole.
Rational theory of human needs
In terms of psychology and physiology, different parameters correspond to different needs. Activation of some need means that the value of some important parameter moved out of its normal range. For example, low concentration of glucose in your blood will lead to the feeling of hunger. Human needs form a hierarchy of 3 levels. At the first, it is just the existence of the organism. The corresponding parameter may be defined as a probability density f(t) that it will stop existing. For a large representative group of N similar individuals, N1 = N * f(t) * dt of them will be terminated during the period from t to t + dt. The level of living standard may be introduced as
L(t) = 1 / f(t)
To ensure that ultimate goal, the brain has a few biological or primary needs. They are inborn and genetically predetermined. Each vitally important parameter makes its own contribution to the overall probability.
According to Bayes theorem
f(Fin and Prim_i) = f(Fin | Prim_i) * f(Prim_i)
Here Fin denotes the final probability and Prim - activation of some primary need. For example
Prim_i(t) = abs(p_i(t) - p0_i(t))
p_i(t) and p0_i(t) - the ith parameter and its normal value.
All conditional probabilities form the conditional vector of cause-consequence links
c_i = f(Fin | Prim_i)
which may be considered constant over time.
f(t) = Sum(c_i * f(Prim_i(t)))
Now let's repeat the same once again. On the third level, each individual acquires a set of secondary needs which serve each other and those below them.
f(Prim_i and Second_j) = f(Prim_i | Second_j) * f(Second_j)
Here Prim and Second are activation of some primary and secondary need. Now we will use the conditional matrix of cause-consequence cross-links
c1_ij = f(Prim_i | Second_j)
Thus, if we know which secondary needs are not satisfied, we can calculate their effect on the second level
f(Prim_i(t)) = Sum(c1_ij * f(Second_j(t)))
and their cumulative effect
f(t) = Sum(c_i * Sum(c1_ij * f(Second_j(t))))
The aforementioned problem of viability means that such sets are not randomly chosen. They grow slowly like trees and each new element is thoroughly checked against those which already exist. In the end they form personality of this human being.
Copyright (c) I. Volkov, December 24, 2018