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This chapter is devoted to the rules of behavior (movement) of a living being for movement in three-dimensional physical space through a combination of conducting excitation in the coordinate space (or movement in the coordinate space) and the movement of a point in the value space (or conducting excitation in the value space).
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Each physical body contains a certain quantity of movement. Even if it seems to us, that the body is at rest in some coordinate system, then it moves along with the coordinate system itself. Therefore, even if in reality there are bodies in which the quantity of movement is zero (similar to the complete absence of the quantity of heat, for example), we will never be able to determine this, because the analytical geometry accepted in science implies an arbitrary point as the starting point. Therefore, the accepted analytical geometry shows us the difference in values between the quantity of movement of the selected coordinate system and the quantity of movement of the body in the selected coordinate system. There is nothing terrible in this, but need to know, that any mechanical action is a change in the quantity of movement, that already have (even if it is zero). Any change in the quantity of movement occurs as a result of mechanical interaction (with the exception of gravity) as an energy process. A more charged body (having a greater quantity of movement in itself) gives part of the quantity of movement to a less charged body. Just as it happens with two electrically charged bodies, or two thermal charges. The difference in the quantity of movement (charges) here is completely analogous to the potential difference or temperature difference. In addition to one detail, if it takes some time to equalize electrical or thermal potentials (so that the battery is discharged, the heated water cools down, etc.), then the equalization of potentials during mechanical interaction (collision) occurs immediately, in one act of collision. We will not touch on gravity, where the equalization of potentials does not occur immediately, as well as the mechanical collision itself, where the equalization of potentials is not always an average value, because even such things as thermal or mechanical charge are something beyond the wild physics at the current time. We are interested in psychology.
A sign of the presence of the quantity of movement is a change in its position relative to some selected point. The greater the quantity of movement, the faster the position changes in time. Therefore, when a beetle crawls on the ground, this is the presence of the quantity of movement. But there are two subtleties. First, to change the quantity of movement, need to hit a living being. We understand, that such a blow would be fatal for a living being. But if look at a living being through the eyes of physics, then it is impossible to change the quantity of movement (speed and direction of movement) in any other way. It is impossible to change the position of the billiard ball without hitting it (we will leave the tales about telekinesis to the storytellers). If a living being moves, while it regularly changes its speed and direction, it means, that someone or something regularly hits a living being. Something invisible that doesn't lead to injury, but still. Secondly, a living being does not need to set the quantity of movement through a collision, because a living being has nervous and muscular mass, i.e. it is a machine (robot, if modern). The machine needs fuel (food), but don't need to beat the machine, otherwise it will die. But if so, then the machine needs to be controlled.
So we come to psychology, where there is an irritant, the interaction with which controls a living being. The irritant gives commands (instructions) to increase or decrease the speed, turn to the side, etc. These are very high technologies, these are technologies of autonomous control of the machine without an operator. But that's not all we're interested in. Any mechanical collision sets not only the speed, but also the direction. If there is no mechanical collision, and the direction is set by an external irritant, then we can say, that psychology is a kind of physics. Can push a billiard ball with a cue in some direction, or can show the ball something, that will scare it, and it will run away from us in some direction. Telekinesis and mysticism are still possible, especially if we close our eyes, that we do not communicate the quantity of movement to a living being in this way, which is mandatory with telekinesis. A living being even without us has a source of movement (an engine), through an irritant we only regulate its work. But physically, when a material body collides, it acquires a direction, that is derived from its own direction and the direction, that the external influence sets. In other words, our living being must move "anywhere", or the irritant must give a command (instruction) exactly where the living being should move. Which also makes sense "anywhere", because the body has many degrees of freedom (there are 360 degrees on the plane — this is anywhere), i.e. the irritant should set the angle in the same way, as it happens in a mechanical collision. But in practice we will never see this. In fact, the irritant can set the angle, but this is an exception, that works for the general rule, where the irritant sets only two options for the direction of movement — towards itself or away from itself in a straight line (the shortest path). Yes, we can find an explanation for this, it is rational, consistent with the tasks. But first of all, this gives rise to the phenomenon of directional movement, which does not exist physically in nature. In other words, this type of movement is characteristic only for a living being, it is artificial, it is impossible for an inanimate body. We understand why. Because an inanimate body is not a machine, it does not understand, what it means to itself or from itself, the billiard ball moves where the blow directed it. And even if telekinesis happens, the billiard ball will move in a given direction, which can be "anywhere". And this draws a line between a real machine (a living being) and any other controlled technique. A living being begins only where there are only two directions (to the irritant or from the irritant in a straight line as the shortest path). I.e. only where there is interaction with the irritant, and where it is possible to draw a straight line through the living being and the irritant. Such a straight line is called a coordinate space, and a change in position on such a straight line is called a movement in the coordinate space
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Geometrically, the movement of a point is a change in the length of a straight line segment (the distance between points) through a change in the coordinate of one of the ends of the segment relative to the other. For an external observer, this is a movement in three-dimensional space from the irritant (move further away, increase the distance between) or to the irritant (get closer, reduce the distance between).
Getting closer or moving away implies some distance (the difference in positions), how much closer or further away. There is some distance BA between the irritant and the living being. Point A' is the new position of the living being relative to the irritant B. Accordingly, the distance has increased or decreased to the value of BA'. The value AA' is the difference of positions, the distance traveled for a certain amount of time. Usually such a path for a certain amount of time is called speed, in psychology it is some distance traveled in one or more definition calls.
Mathematically, the movement of a point is a change in its coordinate relative to the irritant. The coordinate of the irritant is defined as a certain quantity (distance), which is reflected into the coordinate space according to the rules of conversion of quantities.
Everything is relative, so the origin of coordinates can be at point B, in this case the coordinates (x) and (x') are the distance, the distance between the irritant and a living being. Accordingly, the difference in positions is a change in distance, which is considered as a difference (x – x'). Similarly, if the origin of the coordinates is at point A, the coordinate (r') is the path traveled in any direction for one or more calls of consciousness.
Physically, the movement of a point is a movement from one position to another in three-dimensional physical space relative to the irritant. As a result, the part of the physical space allocated in length (the distance) between the subject and the irritant either increases or decreases
Physically, the segment AA' is the physically traveled path over a certain period of time, which is usually called physical speed. Or the physical work that the point performed by moving itself from one position to another. This path is not the movement of a point in the coordinate space, although the point moves in physical space. And if a point changes only its angular coordinate (f), but does not change the distance (r), then such a point does not move in the coordinate space at all and does not perform psychological work. Since the segments AA and AA' are not equal, if desired, we can find acceleration or deceleration in the physical movement of the point. The segment (rr') is the path traveled in the coordinate space, the value by which the distance to the irritant has increased or decreased. This segment can also be called speed, but already psychological. Or the psychological work that the point has done by moving itself from one position to another (changing the distance between the points). Physical and psychological speed coincide in magnitude only when moving to or from the irritant in a straight line (at zero angular coordinates). In other cases, they only correspond to each other. When moving in a circle around the irritant or when moving in parallel, the psychological speed and work are equal to zero. Accordingly, the movement of a point in the coordinate space is part of the physical movement from one (movement in a straight line) to zero.
Technically, the movement of a point is the regulation of the speed and direction of movement of a technical device (machine), that has its own motion source and computing power, so that the distance between the signal source and the device (machine) increases or decreases.
The regulation of distance (between points) is the task and the regulation of speed or direction is the solving the task. There are two extreme options – it can be a change in the trajectory of its movement without changing the speed (in this case, only the angular coordinate changes) or a change in speed without changing the trajectory (in this case, only the distance between the current and previous positions of the point changes). In both cases, the distance will decrease or increase. It is not obvious from the coordinate space, what exactly happened, because the distance measurement returns only the magnitude of the change in distance (the change in position in the coordinate space). Therefore, to determine the performance of psychological work (and to perform psychological work), point A is placed at the origin, relative to which there is a past position of the point, and the length of the segment between two points (coordinate (x)) corresponds to the physical velocity, and the future position of the point, where the length of the segment between the points (coordinate (x')) corresponds to the new physical speed, and the position difference corresponds to physical acceleration or deceleration. Similarly, for angular coordinates, where angle (a) corresponds to the difference of angles and physical angular acceleration or deceleration.
The reason for this separation is not only, that we live in a physical space, where there are three coordinates instead of one. The movement of a point in the coordinate space implies some distance between the points and the distance between the past and future position of one of the points. These distances are measured in units of the extent of space, and psychology is not interested in anything else. Psychology is not interested, in what angle a living being will end up at relative to the irritant, because this angle will always be zero (infinitesimal). Wherever we stick a living being around the irritant, it will always lie on the same straight line. Psychology is not interested, in what the final speed of a living being will be relative to its speed in the past, because this speed will always be zero (an infinitesimal value). Wherever we stick a living being in a straight line, it will always be some distance between it and the irritant. But movement in the coordinate space is a change coordinate relative to the origin, which is set by the irritant. And movement in physical space is a change coordinate relative to itself, which is the origin of coordinates, i.e. recursion.
We understand, that the physical velocity A1A2 and the same segment in the coordinate space are not the same thing. The angle change is also not reflected in the coordinate space, but this is also not necessary. The coordinate space is virtual, it is a special mathematical space, where only the distance between is taken into account.
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Physical reality has three dimensions, there is no directional movement closer or further, because this type of movement is possible only in an artificial one-dimensional space. Therefore, both points must have coordinates in physical reality (some position). Then a straight line is drawn through two points, which becomes a coordinate space, three-dimensional reality is straightened into one-dimensional. The presence of a living being on such a straight line is a prerequisite for the transformation of a living being into a subject, without which it is impossible to "closer or further". Similarly, the presence of an irritant on such a straight line is mandatory, relative to which "closer or further" is defined. The irritant does not need to be taken literally, it is the same point in three-dimensional space, which has three coordinates, and which lies on a straight line with a living being.
The response point must have a sign, and it must have two meanings – "to me" or "from me". The coordinate space does not have a direction, so it must be set forcibly. The physical position of point B cannot have a sign, because if point A is always the origin (the observer's position), then point B always has only one value (in front of the observer). Therefore, both points are given additional coordinates in the value space (to have the same property, which is expressed differently). This means that the irritant must not only have geometric coordinates in order to draw a straight line through the irritant and the living being, but also some property, that is greater or less, than the value of the living being. Then the rules for converting quantities are included, the orientation of "more" or "less" is transformed into the orientation of "to me" or "from me".
The direction of space has nothing to do with the movement of the living being itself. Moreover, a living being can move away from the irritant in the positive direction of the coordinate space. This is necessary for further transfer of the difference in values, which can be reflected directly (proportionally) or mirrored (inversely proportional). Because shortening or increasing the distance implies a certain magnitude, by which the position will change, this is the difference of positions between it was and it became. If this is not done, then the living being will understand, which way to move, but will not understand, which position (how far to move). If mechanically move the coordinate (x) to the coordinate (y) so, that (y) is greater, than (x), and move it behind the irritant's back, then the living being will reduce the distance to negative values. In this world, they have not yet learned how to pass through material bodies, and even those, who invented life (the pinnacle of evolution) could not do such tricks. Therefore, an important condition is such a transfer, when the transformed difference of values never exceeds the distance between the points, when reflected to the irritant.
We remember, that a living being has a certain range of acceptable values, above which there is no sense to define the difference in values, the living being will already be dead. On the other side, there is a range of acceptable distances, beyond which there is also no sense in interaction. If combined, then the maximum allowable difference in values corresponds to the maximum allowable distance. In other words, if point B can be located within the range of acceptable values (but not beyond its limits), then point A can move back and forth within the range of acceptable distances (but not beyond it limits).
The space of values and the space of coordinates are two different spaces, that have different dimensions, so the dimension of the spaces must be set by matching which distance corresponds to one unit of difference of values. If we ignore the correspondence, then the ratio of the maximum distances in both spaces are equal to each other.
Value (max) / Difference of values (x) = Distance (max) / Reflected difference of values (y)
The maximum definitions, as well as the correspondence of dimensions, are established at the design stage of a living being, these are its basic settings with which it is born and which it inherits to descendants. The difference in values is determined through the senses. The only unknown remains only the reflected difference of values (y), which a living being must calculate through correspondence and correlation. This is not the distance between a living being and an irritant, nor is it the value by which a living being should change its coordinate. This is the distance from one of the limits to the second limit. Therefore, depending on the origin, the position (y) may be different. Since the distance limits are a straight line segment inside which point A is located, there are two variants of the origin relative to which the conversion is performed — at point O(max +), which corresponds to the position of the irritant, and point O(max -), which corresponds to the maximum allowable difference in values.
The value of the distance traveled is the distance, that must be traveled to the irritant or from the irritant, in order to establish a new distance between themselves and the irritant, which is the total distance traveled (s). For an external observer, this is not relevant, since he measures from the irritant, the distance has increased or decreased, and how much, which makes it possible to calculate in the usual way through subtraction. But in psychology, the practice of an external observer is not applied (a living being is full automation), therefore. To the irritant.
Total distance traveled (s) = Distance (r) – (Distance (max) – Reflected difference of values (y))
From the irritant.
Total distance traveled (s) = Reflected difference of values (y) – Distance (r)
Since all the initial data are known in advance or calculated in fact, a living being knows at a glance, how many meters to walk and in which direction. If it knows this, then we can also know it, having calculated in advance, how far a living being will move away or approach. And if we do not know the original data, then we can calculate them by measuring the distance by which the distance has changed, thus calculating the magnitude of the difference in values or initial settings that the creators of all living things have set.
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Let's draw a small line. There is a certain space of values, where between the position of a living being (the expression of its property relative to absolute zero) and the position of the maximum allowable difference in values is the value of the irritant. In psychology, this is a control parameter. He, like a slider, sets the position of a living being by his position between two points. And there is a certain coordinate space, where a living being is located between the position of the irritant and the position of the maximum permissible position. In psychology, this is a controlled parameter. In this case, we control the position of a living being relative to the irritant. By moving the slider in the space of values, we move a living being. There is a certain distance (s), to which we move a living being through the influence of an irritant. With this distance, we set the beginning and end of the interaction. Not necessarily (although often) the end point means zero speed, this is the place, where need to stop. With two points we lock the space for interaction. What does the imitation of energy interaction have to do with it? If we mentally declare that the total path traveled is the quantity of irritation, if we establish, that there is some conductivity, that regulates the quantity of time required for the complete passage of this path (the number of definition calls), then we will know not only the distance, to which a living being will approach or depart, but also for what time and at what initial speed. And if we draw an analogy further, then the movement of a living being will be similar to the conduct of excitation, i.e. imitation of energy interaction. But with the correction, that it is not the value in the space of values that moves, but the carrier of the value in the coordinate space. But, alas, in psychology everything is a little more complicated.
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Speed control is a change in the traveled path in three-dimensional space (or coordinate space). It does not matter, where a living being moves, but it always moves at a certain speed, i.e. it goes some way in one call of consciousness. Even if this path is zero (the living being is at rest, i.e. it is not moving anywhere). There is also some space inside which the speed (the value of the distance traveled) should change. Such a space can be represented as a straight line segment, where there will be two speeds at the ends — the initial and the final.
We are not yet interested in the distance Av1Av2, where the speed should change, so we will skip it. We are interested in the speed difference, which is considered as a difference.
dv = v2 – v1
Since one value can be greater than the other, then (dv) can take a positive (if a living being is accelerating) or a negative (if a living being is slowing down) value. If we want the final number to be zero (the command to stop at some point), then the speed difference will correspond to the initial speed.
The speed difference is the difference in the distance traveled in one call. The space in which the speed changes is the distance traveled in one or more calls. The reason for this discrepancy lies in the different way of accounting for changes in coordinates. The segment Av1Av2 is a certain space, within which the traveled path will change. That is, it is a space, where a certain value will be added to the initial speed (if we are talking about an increase in speed) or subtracted (if we are talking about a decrease in speed). The point Av1 is the point, from which we begin to add or subtract this value, here this value is thought to be the maximum. The point Av2 is the point, where we finish adding or subtracting this value, at this point this value (dv) is zero (well, almost). Coordinates are calculated in different ways.
s(c) = (v1 +/– dv / r * e)1 + (v1 +/– dv / r * e^2)2 + (v1 +/– dv / r * e^3)3 + … + (v1 +/– dv / r * e^с)с
The value (s) is the number of calls. There may be many of them, there may be one (although then why do we need psychology). But, no matter how many of them there are, each call is a separate summand, the sum of which is equal to (s). And with each iteration, the value of the path traveled in one call decreases or increases. Similarly, for the value of the path traveled in one call, which will also change towards the final value.
v (c) = (v1 +/– dv / r * e^c)
When calculating the coordinates of the total path traversed, there can only be the sum of the private paths traversed per call. In other words, the total path traveled consists of parts. But each part may not be equal to the other, they may differ, be larger or smaller than each other. Therefore, the magnitude of their differences can be either a sum or a difference, it all depends on "more or less". In psychology, such a difference in (dv), by which the value of the particular path traveled changes, is the quantity of irritation, that needs to be reduced to zero for a certain number of calls. So that after a few calls of consciousness, the initial speed is completely similar to the final one. Accordingly, the magnitude of the difference at the end should be zero (well, almost). But we understand, that, on the one hand, we have to meet a certain number of challenges, on the other hand, a certain distance. The general path traveled is known to us, it is set by the irritant through the difference in values. The speed difference is also known, it is set by the irritant through the difference in values (the same, or some other, it does not matter). We only don't know the number of iterations (c).
If a living being does not change its speed, it will pass the common path for some time. There is no time in psychology, there is consciousness, but the meaning is the same.
Number of calls initial (c1) = (total distance (s) / initial speed (v1))
In other words, if a living being does not change its speed, then the total distance traveled will be the sum of such speeds. And we are interested in, how many such segments fit into the total traveled path. We won't get an integer, but we can round it up to an integer. If a living being changes its speed immediately, it will pass the common path in a different quantity of time (this will be a different number of parts, that make up the whole).
Final number of calls (c2) = (total distance (s) / final speed (v2))
Thus, there is some difference in the number of calls, which we need. This is the difference between two speeds, but not in space, but in time. In other words, there is a change in the distance traveled in space, and there is time that is needed to change the speed. And one must correspond to the other. The easiest way is the average value.
Total quantity of calls (c) = c1 * c2 / 2
In a more complex case, the quantity of time may also be the quantity of irritation, in this case it will not be the total quantity of calls, that will change, but the quantity of time between two calls, i.e. the frequency of calls. We will skip this moment.
In this case, we consider the pure case and its physical meaning. In this case, the quantity of irritation is the speed difference (dv), and the quantity of excitation is the change in the speed difference by a certain magnitude of excitation. With each iteration, the excitation will decrease, and in each iteration a new value of irritation will be returned. If the velocity drops to zero, then the values will be different, but the meaning is the same, we will subtract (v1) from the initial velocity until the velocity becomes zero. In this case, the quantity of irritation is not a part of the speed, but the entire speed, that needs to be reset to a given point for a given number of calls. If the speed increases, then we add to the initial speed until it is equal to the final one. The quantity of irritation is not a speed, it is a virtual quantity, that needs to be brought into correspondence with the distance, how many units of distance are contained in one unit of irritation.
For acceleration in the space of values, everything will be exactly the same, only in the other direction, the same for the coordinate space. What is it for? Sometimes it is important to know, what the speed of a living being will be on the fifth challenge? On the tenth? Sometimes it is important to know, how far a living being will have time to go by the fifth challenge? By the tenth? But it's not just that. A living being needs to be controlled, it is a machine, that requires an operator. But such an operator can be the environment, physical properties and their expression. Accordingly, the environment without an operator should set the direction (to itself or from itself), the distance (how far to itself or from itself) and the speed (how fast to itself or from itself). All this is set through the difference of values between the value of a living being and the value of the environment, which a living being defines through its senses. But there are two subtleties. Firstly, the difference in values does not set the speed, but the speed difference, the same segment (dv). Secondly, the difference in values does not set the speed directly. Alas, but in psychology everything is somewhat more complicated.
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Since we are dealing with technology, a living being does not have the physical phenomenon of speed and the path traveled in its pure form. There is some work being done, the value of which corresponds to the speed and the distance traveled. It can be the quantity of muscle tension, that corresponds to the path traveled, or the quantity of engine revolutions, anything, that we collectively call the work being done. Which is further converted into physical work — is the movement of a living being from one point to another (i.e. the work being done has some efficiency, which we will skip). Thus, we have two spaces, the dimension of which must correspond to each other, i.e. one unit of work performed corresponds to one unit of the path traveled. The magnitude of the work performed is set by the magnitude of the difference in values, this is an external signal to increase or decrease the quantity of work. An increase or decrease in the distance traveled is a consequence of a change in work. We remember, that there is a certain acceptable range of definitions, and there is a certain range of work, above which a living being simply cannot.
The conversion is performed according to the same templates, only the orientation differs, relative to which origin we reflect point B.
(max D) / (x) = (max A) / (y)
From right to left, the maximum definition will correspond to the minimum work, from left to right, the maximum definition will correspond to the maximum work. Only the parameter A(r) will be new, this is the actual work, that corresponds to the current speed (v1), that needs to be changed. The segment AB is the quantity of irritation, that needs to be reset, i.e. turn the segment OA into the segment OB. If otherwise, this is the difference of the work being done (dA), where one unit of work being done corresponds to some kind of speed. Fortunately, the developers of all living things were not morons, so everything is directed from left to right.
Now we can generalize. Any living being determines the difference in values (coordinate (x)) through its senses. It can be a difference in temperature (warm or cold), a difference in beauty (attractive or ugly), any other difference, that sets a living being in motion. The coordinate (x) is converted to the coordinate (y), this is the reflected difference of values. A living being is already doing some work, there is a value of the work being done, even if it is zero. But this is also a position in the space of values, the position of a living being (A1) and the reflected position of the irritant (y) may not coincide, they may form a position difference (dA). The value of the work being done changes to a new one.
A (c) = (A1 +/– dA / r * e^c)
Since the side effect of the work being done is movement, the living being will move, i.e. change the speed of its movement. This is the distilled conducting of excitation in the space of values, when the magnitude of the work performed (dA) is defined by the magnitude of the incoming signal (x). And we may ask, why do distances in psychology (and indeed a living being in general) need? We can simply adjust the speed by adjusting the incoming value difference. We can simply adjust the speed by adjusting the incoming value difference. A living being saw something, it was a command to stop, it stopped. But where exactly should it stop? And that's where distances are needed, where coordinates are already considered differently. Any living being, that moves from one point to another, does physical work. Yes, this is the work, that the engine does, which needs energy costs (fuel), but nevertheless. Any engine has an actual magnitude of the work performed, which can be changed relative to itself in the past (more or less, faster or slower, etc.). Such a change in the magnitude of the work performed (dA) is called psychological work. It also has a physical meaning, as does the definition, that sets the magnitude of psychological work. The irritant sets a certain deviation value.
But the same irritant sets a new resting position (zero), where the magnitude of the irritation will be zero. At this point, the value will freeze, and it will not change anymore, the psychological work is finished. When conducting excitation, everything happens exactly like this. The irritant even suggests, which zero is the real one, between which the value of a living being is locked. We've seen it somewhere before. In the same way, a living being is trapped between two zeros in the coordinate space. Each zero is a place, where a living being should stop in three-dimensional space relative to the position of the irritant (i.e. indicates a new distance, which should be between). If the difference in values is maximal, then the living being should stop either near the irritant, or at the maximum distance from the irritant.
If we ignore the method of changing coordinates, then the movement of a living being in the coordinate space to the irritant or from the irritant is completely similar to the conduct of excitation in the space of values. Because the same techniques are used, this is the modus operandi of the creators of all living things. We can say, that the movement of a living being in the coordinate space is the conduct of excitation in three-dimensional space. Or in other words, conducting an excitation in the space of values is the movement of a living being in the space of values. There is a difference in the work done (dA), and there is a difference in positions (total distance traveled (s)). If the difference of the work performed (dA) is the psychological work done by the applied force (irritant) in the space of values, then the difference of positions (the total path traveled (s)) is the psychological work done by the irritant in the coordinate space. The comparison is not very correct, but still, the living being has changed its position relative to the position of the irritant, it has increased or decreased the distance. If this happens in a straight line, that is drawn through the living being and the irritant, then the path traveled (s) will be the difference between the initial and final position of the living being relative to the irritant. But in psychology, not everything is so simple, we live in a three-dimensional space, where can move not only in a straight line, which is drawn through a living being and an irritant.
A living being has performed physical work by moving from point A to point A1 or A2, these segments are the same. If we assume, that psychological work coincides with physical work, then the segments AA1 or AA2 are also psychological work, this is a common path (s). But then what is considered a coordinate space? Then we must assume, that the irritant indicates a certain position, and the line is not drawn through it, but through a living being and the indicated point, i.e. straight AA1. But what about the distance between the irritant and the living being? We can imagine moving in a circle around the irritant, when the distance between does not change, although the living being is in motion. If we assume, that the coordinate space is a virtual straight line, then we must admit, that a living being performs physical work, but does not perform psychological work, because the distance between a living being and an irritant does not change. And if it changes, then not completely. When moving to point A2, the distance between the living being and the irritant will be a straight line segment BA2, and when moving to point A1, the distance between will be a straight line segment BA'1. In other words, when moving to point A1, the psychological work will not be complete, the physical path traveled is the segment AA1, and the psychological path traveled is the segment AA'1. Knowing the distance before and after, we can calculate the magnitude of such work.
АА1 = AB – BA1
If a living being moves to point A2, then such an equation will return us full work, if to some other point, and the distance does not change, then such an equation will return us zero, if a living being moves in the other direction, then such an equation will return us a negative value. If we fill this equation with a physical meaning, then the physical path traveled (segments AA1 or AA2) is either the speed (the path traveled in one call), or the complete path traveled, consisting of several parts. Segment BA is the initial distance between the irritant and a living being, which is defined through the senses, and segments BA1 or BA'1 is the final distance between the irritant and a living being for one or more definitions. The value A'1A2 is part of such work. It can be less than zero, only if the movement is made from the irritant. But in general, point A'1 is locked between points A and A2. This means, that its coordinate cannot be greater than one (the distance traveled in physical space), and cannot be less than zero (the distance does not change), because less than zero is an increase in distance, i.e. the work being done, only in the other direction. It may seem, that the coordinate of point A'1 is a derivative of some angle. But, alas, even here in psychology, not everything is so simple.
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The irritant and the living being form a straight line, that is drawn through them as through two points. This straight line sets the zero angle, relative to which any third point has an angular coordinate other than zero, if it does not lie on such a straight line. The living being and the irritant themselves have zero angular coordinates relative to each other, since they lie on such a straight line. If we recall, that such a straight line is carried out anew in every act of consciousness, then we can say, that a living being and an irritant always have a zero coordinate relative to a straight line, that is drawn through a living being and an irritant, because they always lie on such a straight line in every act of consciousness. If we draw a circle around a living being, then such a circle will intersect the straight line at two points. Any point, that lies on a circle, has coordinates other than zero (if it does not lie at the origin). Thus, to denote such a coordinate, we need to choose the origin of the coordinates. We have two points, where the circle intersects with the straight line. We can choose any of these points as the origin. Accordingly, any point on the circle will have some angular coordinates other than zero relative to one of the two points. Since two points divide the circle into two semicircles, we will stop at one semicircle (any one), which we will straighten into one-dimensional space for clarity.
A living being has its own angular coordinates. This is true for any living being, whose angular coordinates have the position of the body, which can be rotated around its axis. We remember, that everything is relative, so the proper angular coordinate must be relative to something. If the direction of the body position coincides with the straight line between the subject and the irritant, then there is no question, it is time to adjust the speed. But as a rule, the body of a living being has an angular coordinate relative to the straight line between it and the irritant, which is not zero. A living being also has a head, which can also be turned, may just look at the irritant. Such an angular coordinate is the eigenvalue of a living being relative to the irritant. This is the position of a living being relative to the irritant, not on a straight line, that is drawn through the living being and the irritant, but on a virtual circle relative to a straight line. Since the origin of coordinates may be different, then the angular coordinate may also be different.
A living being turns its head (body, tank turret, something else) not just somewhere (clockwise or counterclockwise relative to the position of the irritant), but also to some limits (by some degrees relative to the origin), where need to stop, stop turning head, otherwise can wring neck. We remember, that the definition has a certain maximum, above which to twist the head (body, tank turret, something else) it doesn't make sense anymore. And we see, that the change in the angular coordinate also has limits, these are points O1 and O2, which makes no sense to cross.
Here a lot depends on what exactly we transform (maximum or minimum expression, i.e. the directivity of the definition space) and what we transform into (maximum or minimum angle from the irritant, i.e. clockwise or counterclockwise direction), i.e. from the polarity of the spaces. But the meaning will be the same.
(max A) / (x) = 180° / (y)
A(max) is the maximum allowable definition. Since we measure the length of the semicircle in degrees, then the coordinate (y) will return in degrees. For example, in the left part it is the ratio of someone's beauty to maximum beauty, in the right part it is the ratio of the angle to the entire length of the circle in degrees. But the circumference of a circle can be measured not only in degrees, but also in minutes, seconds, etc., so it makes sense to refresh in memory, that the length of a semicircle is a derivative of the radius of a circle.
Semicircle length = p * Circle radius
It also makes sense to refresh the pitch of the angular space.
Arc length in 1° = p * Circle radius / 180°
Accordingly, the part of the arc of the circle is the number of such steps.
Arc length = p * Circle radius * Quantity of degrees / 180°
This is far from the only correspondence, that needs to be reached. Wherever we reflect point B from the definition space into the angular space, but if its position does not coincide with the position of point A, then we will get the difference in values (the difference in angular coordinates (df)). This means, that a living being in one or more iterations of consciousness must change its angular coordinate at point A to the angular coordinate at point B. Such an arc (or the distance between) can and should be considered as the quantity of irritation, that needs to be reduced to zero. Accordingly, the quantity of irritation will decrease in portions of excitation depending on the excitability parameter. The size of the excitation portions is defined as follows.
Quantity of excitation (c) = Quantity of irritation / r* e^c
To calculate the angular coordinates directly, it is necessary to correspond, to what quantity of irritation and excitation 1 degree corresponds. But if we ignore the dimensions of spaces, then the portions of excitation will be some quantity of degrees.
df (c) = df / r * e^c
A living being will smoothly turn its head to where it needs to, or the hull, or the turret of the tank, or not smoothly, but the turn takes place in a certain quantity of time. There is no such thing in psychology, there is a call of consciousness, so the turn will happen in a certain quantity of calls of consciousness. If there is no consciousness (the deceased), then there will be no turning.
We have two angular coordinates of a living being, there are two origin coordinates, and there are two directions, where a coordinate can be added or subtracted (the quantity of excitation converted to angular coordinates). No matter how hard we try, but here the change and calculation of the angular coordinate fully corresponds to the change and calculation of coordinates in the value space. If we count from point O1, then …
f (c) = f1 +/– df (c)
If we count from the point O2, then …
f (c) = f2 +/– df (c)
There are no more differences. Both cases will return the current angle f(c), where exactly here and now (at the time of the call (c)) a living being is looking, or where the hull, tank turret or something else is directed. The difference in angles (df) can be set by any difference in values, for example, the difference in speeds (dv), or the difference in temperatures (dt), or the distance between the irritant and a living being. But we must remember, that these are the difference in magnitude and different spaces, that need to be brought to conformity. And that the direction of such a space can be different, as well as the direction of conversion.
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