2.1. Introduction

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This is Olga’s earring. Only one. Don’t know, where the second one. Maybe it was stolen by Mogilov A.S., Marochkin V.V., Belyaeva O.Y. and Fotteler E.V., criminals like to take some souvenir with them. Or maybe the second one is still lying somewhere at the crime scene.

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This chapter is an introduction. This is a consistent reasoning about movement, behavior, and etc. from mechanics and a material point, taken as a starting point for reasoning, to psychology and a mathematical point.

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Movement is a change in the position of the body relative to some selected point for a certain quantity of time. In motion, the body forms a straight line segment with the ends of the segment in the form of the current and previous positions relative to some selected point for a certain quantity of time. The length of such a straight line segment has a value in a given metric, and is called velocity. Movement is always relative, without some kind of starting point, relative to which the position of the body changes, there is no movement itself. As such a starting point, we will consider the position of the point in the past.

A living being moves relative to itself in the past. The segment AA' is the path, traversed by a living being, in a unit of time the length of this segment is the velocity. A straight line, that is drawn through two points A and A', is called the trajectory of the point movement. The origin of coordinates is taken each time anew in the position of a living being in the previous second. Each next coordinate (r) is the distance relative to itself in the previous second, and each next coordinate (f) is the angle of deviation from its trajectory in the previous second.

In motion, a point forms not only a straight line segment with the ends in the form of the previous and current position, the length of which reflects the velocity of movement, but also the straight line itself, which is drawn through the previous and current position of the point. Such a straight line is called the trajectory of movement or the direction of movement. The trajectory is also relative, without some kind of reference point, relative to which the direction of movement changes, there is no change in the direction of movement. As such a starting point, we will consider the past direction of the point.

A material point has two variables (velocity and direction), that define its position relative to itself in the past. Both variables are set as a result of mechanical interaction through collision with another material point. The new values, set as a result of the impact, will be derived from the existing ones, the point cannot acquire a random velocity or direction, only a natural, the value of which is defined by the function (laws of mechanics).

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A material point in motion contains an impulse (the quantity of motion). Its magnitude is the product of mass and velocity. During the interaction, the quantity of motion is distributed in accordance with any other energy process from a more charged to a less charged one — from a body with a large quantity of motion (the product of mass and velocity) to a body with a smaller quantity of motion. The role of the potential difference is performed by the mass difference and the velocity difference. Bodies cannot distribute their masses, so they distribute their velocities.

This is the collision of point A with another point. If the masses of the points are equal, then only the velocity difference v1 and v2 will act as a potential difference. The higher the difference, the greater will be the magnitude of the deflection angle (f), and the greater will be the new velocity value v1'.

Through the application of force, the body is given not only a new velocity value, but also a new direction. The new direction is derived from the direction of force application (the trajectory of the movement of points) and the ratio of charges (the difference in mass and velocity). Interaction is a collision of two points, each of which has a direction of movement and seeks to impose its direction of movement on the point it affects. Bodies cannot distribute their masses, so they distribute their directions.

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Every living being is a physical body (a material point). As a material point, it has the ability to move — to change its position relative to the origin of coordinates for a certain quantity of time. To do this, according to the rules of mechanics, need to apply force to a living being as a measure of impact, so we will set a living being the quantity of motion (velocity) and the direction of movement (trajectory). The quantity of movement, that we will set a living being, will depend on the difference in mass and velocity.

A living being is capable of changing its position in three-dimensional space without collision, such a movement we call behavior. To distinguish mechanical movement from behavior, we will choose a mathematical point model. The position of a mathematical point in three-dimensional space is also defined as the position of a geometric point relative to the origin. A mathematical point is an abstract subject with consciousness and sensitivity, a mathematical point differs from a material point by neglecting even the mass of the body.

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Newton's first law sets the rule — every body continues to be held in a state of rest or uniform and rectilinear motion, until and since it is not forced by the applied forces to change this state. This is really for the material point. To force it to change its position (to move), need to apply force (to hit another material point). This is also true for a living being, if we consider it as a material point. The magnitude of the changes will be proportional to the difference in masses and velocities (quantities of motion).

To change the velocity and direction of movement of a material point, need to hit it. The new velocity and direction will be proportional to the difference in mass and velocity. Who and what hit the living being in the picture now, changing its velocity and direction? We just showed a living being something terrible, and it changed its velocity and direction by itself, as if we hit a living being from a distance with an invisible force. Even the trajectories coincide, as a billiard ball usually bounces after a collision (in practice, living beings can bypass the irritant along an even more intricate trajectory). This is mysticism and telekinesis, there is a change in direction and velocity (so there is a transfer of impulse), but there is no impact (the interaction, through which the impulse is communicated).

A living being is able to come out of a state of rest even without applied force (impact). Moreover, the applied force can be fatal to a living being or end in injury. It comes out of a state of rest, if it is affected by some external irritant, that the living body has seen, heard, felt, etc. Therefore, if for a material point the impulse is given through mechanical interaction (collision), then for a mathematical point the impulse is given through psychological interaction (sensory organs) at a distance.

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Force is a measure of the impact on a material point, which has a magnitude. The greater the difference in mass and velocity, the greater the quantity of motion contained in the interaction. This generates a pattern called the equation of motion (mechanics), where the change in the velocity of motion is proportional to the applied force. Thanks to this regularity, we can calculate the position (coordinates) of the body, if we know the values of the initial variables. A living being can be psychologically influenced at a distance, that will set it in motion, so an analogy can be drawn.

A force acts on a material point, a given velocity is proportional to the acting force. If the force acts constantly, then with each iteration the velocity will increase (acceleration). This can be observed by the second-order increment of the coordinate (r). The mathematical point is affected by irritation, the set velocity is proportional to the irritation. If the irritation acts constantly, then the living being will run away from us faster and faster (acceleration). Which can also be observed by the second-order increment of the coordinate (r). And it is not the magnitude of our mass and velocity, that will be the reason for this.

Irritation is a measure of the impact on a mathematical point, that has a magnitude. If the psychological impact occurs at a distance without collision, then the difference in mass and velocity does not play any role. A living being starts moving if scare it, the more scared a living being is, the faster it runs. Therefore, we can assume some difference in values between zero and the magnitude of the irritant, which is similar to the difference in mass and velocity in mechanics, and performs the function of the impulse of motion. The higher the quantity of irritation (the magnitude of the irritant), the greater the quantity of motion (velocity of movement).

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If conduct an experiment, by putting in front of a living being an irritant, that causes fear, and a neutral irritant, then it will run away from the irritant, that causes fear. The more terrifying it is to a living being, the greater the quantity of irritation, the higher the velocity of movement as a law, which is equivalent to an energetic physical interaction. In mechanics, one point gives part of its velocity to another, something similar should be here, the irritant should give part of its value, as it happens with energy interaction (charge distribution). But the irritant, causing fear, does not convey part of its meaning, after interaction it will not become less scary for another a living being. The law of conservation of impulse (difference of masses and velocities) does not work here. The scary remains equally scary, and the irritant sets the velocity of movement of a living being, which it does not possess itself.

There are two irritant, one of which scares a living being. They are motionless and cannot transmit part of their velocity (there is none), but one of the irritant sets the velocity of movement (segment AA') without impacting a living being. So the impulse (the quantity of motion) is not set by the difference in mass and velocity. Then it is logical to assume, that the impulse (the quantity of motion) sets the difference between the value of the irritant and zero. The more terrible, the higher the velocity. This is not velocity and not mass, then what value does the irritant have?

We will also encounter another pattern, the quantity of irritation is inversely proportional to the distance. The farther away the irritant causing fear is, the lower the observed velocity of movement of a living being. At some distance, the irritant ceases to cause fear in a living being, because it is too far away. Consequently, a living being as a mathematical point obeys the formula of behavior, where irritation is proportional to the difference in values (analogous to the difference in masses and velocities), but inversely proportional to the distance to the irritant.

There are two irritant, both cause the same fear, they are motionless, they differ only in the distance to a living being. A living being runs away from the one, that is closest. Consequently, the difference in values is the same for both irritant, but they transmit a different quantity of irritation due to the different distance between.

Impact and velocity changes are possible only, if psychological contact is made through the senses (to see, hear, feel, etc.). The dependence of the quantity of irritation on the distance, that can be measured, tells us, that the quantity of irritation can also be measured, it has a magnitude. Similarly, for the magnitude of the irritant, if something causes a certain quantity of horror, then this something must have a magnitude of how terrible it is. Only the question of the origin of coordinates will remain open, relative to which the irritant is so terrible. We could call such a psychological impact an impact at a distance through the senses (sight, hearing, etc.). Why is it impossible to influence a stone in this way, for example, by scaring it? Because it has no sense organs, so need to hit it to set it in motion.

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In addition to velocity, material points have a direction of movement. The applied force has not only the quantity, but also the direction in space, which is distributed during the collision. The change in direction also depends on the difference in mass and velocity, in order to change the trajectory of a massive body with a high velocity by at least one degree, a high quantity of applied force (large mass or velocity) is needed. This is true for a living being, if we consider it as a material point. But a living being is capable of movement without applied force through irritation, and movement has a direction.

Force is the direction of impact on a material point, which has a certain angle in space relative to zero or is assumed to be zero. If the material point is stationary, then the direction is set by the applied force. If a material point already has a direction of motion, then it changes in accordance with the direction of the applied force. The greater the quantity of force, the greater the angle of deviation of the trajectory. A psychological influence can be exerted on a living being, which sets the direction. Therefore, an analogy can be drawn.

A force acts on a material point, the angle of deviation (f) from the trajectory is proportional to the acting force (the difference of masses and velocities). If the force acts constantly, then with each iteration the point will deviate from its trajectory. The mathematical point is affected by irritation, the angle of deviation (f) from the trajectory is proportional to the magnitude of the irritation. If the irritation acts constantly, then the living being will deviate from its past trajectory (turn somewhere). The difference in the masses and velocities of a living being and an irritant does not play a role here either.

Irritation is the direction of influence on a mathematical point, that has a certain angle in space relative to zero or is assumed to be zero. Any living being runs away, if it is frightened, and the movement of a living being has a direction from the source of fear. And any living being changes the direction of movement away from the source of fear by a certain angle. The more frightened a living being is, the greater the angle of deviation, and if a living being is very scared, then the trajectory of movement will coincide with the direction of the applied force (irritation) from the source of fear.

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Let's turn to experiments again. Let a living being move somewhere at a constant velocity, and we scared him. The greater the fright, the greater the angle of deviation from the original trajectory. It is proportional to the magnitude of the impact, the higher the impact, the greater the deviation. Also for a living being there is something more terrible, there is something less terrible, there is something absolutely not terrible, because the magnitude of this something is zero. We called this difference the difference of values, and the higher it is, the greater the irritation, which means the greater the angle of deviation.

A living being is going somewhere, there is something terrible on the way. There are two options, where can turn, but there is also something scary on the left. Then the balance of forces will begin, each will push the direction of the point away from itself. If the quantity of irritation to the left turns out to be safe enough, then a living being can try to run between two fires. If not, it will turn to the right, where it is safer. If the scarier turns out to be too scary, then the living being will turn around and go in the opposite direction.

But the further away the terrible irritant is, the smaller the observed angle of deviation from the original trajectory of movement of a living being will be. At some distance, a living being will cease to be afraid of a terrible irritant at all, because it is too far away. This is another pattern, the source of fear sets a different angle of deviation of the direction of movement, if it is at a different distance from a living being. And he does not set a change in the direction of movement at all, if the living being does not feel irritation (does not see, does not hear, does not feel, etc.).

If the quantity of fear is proportional to the quantity of scary and inversely proportional to the distance, then less scary near will scare as well, as scarier far away. This time it is impossible to pass between two fires, a living being will have to go around.

Again, we are dealing with a pattern, the magnitude of the impact is directly proportional to the magnitude of the irritant (the greater the magnitude of the irritant, the greater the magnitude of the impact), but inversely proportional to the distance (the farther the irritant, the smaller the magnitude of the impact). But the effect is different. If in the first case the impact set the quantity of motion (velocity), and the direction was set by the irritant by default, because a living being has to move somewhere, then in the second case the irritant additionally changes the direction of movement.

Another difference is the different orientation. We constantly frighten a living being, it runs away from us. The movement is directed from the source of fear in a straight line between the living being and the source of fear. Similarly, the behavior of a material point, that moves from the source of the applied force and in the direction of the applied force. But a living being can move towards an irritant. For example, food is a source of irritation, it does not repel a living being from itself, but attracts to itself. The direction of irritation is divided into two categories — which attracts to itself and which repels from itself.

There is something repulsive, from which a living being runs away (negative irritation), there is something attractive, to which a living being runs up (positive irritation). To sum it up, it moves from a negative irritant to a positive one, but this is not an energy process, but its imitation.

For a living being, the change of direction is set through his senses. A living being must see, hear or feel an irritant in order to change the direction of movement. The change in direction does not depend on the difference in mass and velocity, as is typical for a material point. This can also be called the impact on the distance. Why can't change the direction of movement of some stone by showing him something delicious, and thereby luring him to yourself? Because he has no sense organs, so need to hit him to change the direction of movement.

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We see signs of the dependence of the magnitude of the motion of a mathematical point on the magnitude of the irritant, but we cannot call such a dependence an objective law of nature, as an analogue of the law of mechanics. We have already noticed earlier, that the irritant sets the impulse (the quantity of motion), but this is not the distribution of the quantity of motion, as in mechanics, where velocity and directions are distributed after a collision. The law of conservation of impulse (energy) does not work with psychological interaction, it only simulates energy interaction.

The higher the difference in mass and velocity, the greater the velocity we can set to a material point. With a very high difference in the quantity of motion, we can accelerate a fixed point to high velocity. We should see something similar in a living being, if a quantity of irritation close to infinity acts on it, then the set velocity should also be close to infinity. But a living being has a velocity limit, it can move at the velocity of sound as a material point, but it cannot run at the velocity of sound as a mathematical point.

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Any living being, that moves from one point to another, does physical work. What is wrong from the point of view of mechanics, since physical work is done by force, there is no movement without impact. It may seem, that the acting force is an irritation, that moves the body, as in a mechanical collision, just a psychological force acting at a distance, and she's invisible. But actually the driving force is muscle contractions. They are only attached to external irritation, dependent on it and are regulated by it through nervous activity.

This phenomenon is usually called a machine. The closest analogue of a living being will be a car. Which also has its own source of motion in the form of an internal combustion engine. A living being, like any machine, requires a source of energy for its movement. For a car it is gasoline, for a living being it is food. It's just that the type of engine is completely different (muscle mass as an engine), it is arranged differently and works differently, which misleads us. Why, then, does the car not show us the behavior, that we see in any living being? Why does the car not go to the gas station itself to satisfy hunger (pour gasoline into the tank)? We already know the answer, because she has no sense organs, but it's not just that.

Any machine consists, among other things, of controls and regulation. This includes peripheral devices (control and measuring devices), which are analogs of sensory organs, and actuators. In the case of a living being, we are dealing with an extremely automated machine. Any automation implies control through commands (instructions), the type and quantity of irritation is such a command (instruction). Command regulates not only the performance of the action itself (true or false, turn on or off), but also sets the intensity and duration of the action. Such an action (the work being done) in psychology is called a reaction to irritation.

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We can consider external irritation as a command, for example, a living being should assign a value (magnitude) to itself the velocity, that corresponds to the quantity of irritation. If the command is one-time, then the psychological interaction will set the velocity of a living being, which can be changed only through a new interaction. A regular change in velocity tells us, that a living being interacts with an irritant regularly, and in each act of interaction, the magnitude of the irritation is defined anew, and hence the magnitude of the velocity of movement. This is perhaps the simplest view.

If scare a living being very much, it will run away from us as fast as possible. This is also true for the direction, in case of severe fright, a living being will turn its head towards us with the maximum possible velocity, turn the body away from us, etc. But if the fright is not very strong, then the living being will leave, and not run away. Similarly, for the direction where it is most obvious, turning the head, body or changing the trajectory will be smooth. In other words, it will be acceleration or deceleration of movement. Both cases require at least two values — the magnitude of the change (the quantity of excitation, by what value the velocity or angle will increase or decrease) and the magnitude of the stop (the quantity of irritation, to what limit the velocity or angle should increase or decrease).

A single interaction with the irritant is called consciousness (multiple is the frequency of interaction). If there is no consciousness, there is no interaction. In the picture, a living being has a past and future position (direction). Without the influence of the irritant, the future position will be symmetrical to the past. The influence of the irritant will set the asymmetry (f), the living being will turn it head to look at the irritant, and the body to escape from the irritant.

In the case of a change in direction, the angular coordinate changes with each iteration of the interaction, the stronger the irritation, the greater the angle (f) the living being should turn towards or away from the irritant. If the irritant sets only the angular velocity, then the living being will turn around its axis, the higher the irritation, the stronger it will spin. And if only the magnitude of the angle, then a living being should unfold instantly, which is not observed in practice (and physically impossible).

A living being runs away from an irritant. There is some velocity AB, with which it should run away, and there is a real velocity AA'. It is below the velocity, prescribed by the irritant.

Now we can get back to velocity. The quantity of irritation sets the quantity of velocity and the quantity, by which the quantity of velocity should increase or decrease (the quantity of acceleration or deceleration). A living being always has a velocity of movement, even if it is zero (the living being is at rest). If we draw an analogy with a car, then the quantity of irritation sets the quantity of car velocity, that need to dial, and sets the quantity, by which need to add or decrease the velocity until it becomes equal to the specified one. What is observed in practice, a living being (if not terrified) picks up and resets velocity smoothly, as any machine does.

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There is a certain contradiction between movements in one-dimensional and three-dimensional spaces. A living being can have any trajectory of movement, but to the irritant or from the irritant it can move only in a straight line, which is drawn through the position of the living being and the position of the irritant (closer to the irritant or further from the irritant). Even if a living being moves at a different angle (or the head, body, gaze, etc. are turned at a different angle.), it turns around, until the direction coincides with such a straight line. Because in objective reality there are no such concepts closer or further, they are created artificially. In other words, it is not only a movement, that is directed somewhere (any movement is directed somewhere), but also a movement, that is directed specifically to the irritant or from the irritant.

A contradiction in one picture. In order for a living being to be closer or further away from the irritant, it needs to be rotated around its axis in the right direction (to the irritant or from the irritant) and change its velocity (faster or slower). This is an algorithm for controlling the machine through external irritation, which is used as an incoming signal.

In objective reality, there are no concepts closer or further away, but there are concepts faster or slower, to the right or to the left — these are variables, the regulation (switching) of which leads to the side effect, that a living being is closer or further away. If the side effect is achieved intentionally (this is an engineering and technological task, since in the case of a living being we are dealing with a machine, that needs to eat something and not die), then the regulation of velocity and direction should be considered a solution to the engineering and technological problem.

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Velocity and direction are variables of a body, that have some magnitude relative to the origin. Velocity and direction control is a change in the magnitude of a variable. A body can have many such variables. Engineering and technological tasks, that are solved through the regulation of variables, can be even more. So, we can move on to an even broader generalization, that any value can be regulated with the help of external irritation.

For example, to regulate the release of adrenaline into the blood (and its concentration). The quantity of adrenaline in the blood is variable, it is not related to the movement in space, from which we started our reasoning. But the regulation of the value of this variable is also associated with external irritation, the higher it is (in case of fright, for example), the higher the concentration.

External irritation is also some kind of variable. Even if it is complex (it does not come down to one correspondence), for example, the correspondence of the quantity of irritation to the magnitude of the irritant and the distance to the irritant. If so, then we can go to the extreme generalization, that any variable is regulated by any other variable through correspondence. For example, the volume value is adjusted using the lighting value. We don't have to set the distance to the light source, if our siren is stationary, and we don't aim to teach her to keep her distance from the light source (to approach or move away), only the volume level, the lighter, the louder need to scream.

This is noise regulation with the help of external irritation (lighting), or adjustment of the pupil diameter, or velocity, direction, or instead of lighting, the quantity of irritation is set by something else, the options may be different.

We can have fun, as we like, and with many variables, but there are some rules of the game. We must, at a minimum, set a condition, under which the value will begin to change (for example, in the presence of an irritant). At a minimum, set a finite value, the compliance of which will become a condition for stopping the change in magnitude (this is a state of rest, from which can only get out through a new irritation). And, at a minimum, set a small value, by which a large value will increase or decrease.

This is an example of a change in magnitude. A living being changes the angular coordinate, until its value becomes zero. This is the whole psychology, and any other value changes in the same way. If we draw an analogy, then at the end of the change, the value should also become zero. But no, the distance (difference of values) will be equal to zero. This is not so much the second law of thermodynamics, as its imitation in psychology.

As a result of reasoning, we did not get objective laws of behavior, our dreams crashed into reality. It turned out something else — behavior algorithms, that have some rules. The fact, that they are set, tells us about someone's authorship, this is a set of methods and technologies of the authors of all living beings. We understand the difference between thermodynamics and the refrigerator (theory and practice). There is approximately the same difference between a living being, and the rules for creating algorithms for changing quantities.

Regulation is more or less, than the already existing value. Changing the velocity is to increase or decrease the velocity. Changing the direction is to add or subtract an angle. Changing the distance to the irritant also has only two values — closer or further. All together implies a one-dimensional space, where only one value changes in the direction of more or less, which means, that the position of the coordinate changes to the left or right. One-dimensional spaces permeate every living being, and hence the whole psychology. Therefore, it is worth starting with this.

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