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A mathematical point is the simplest model for calculating psychological interactions. It is similar to a material point in physics, it is the same abstract object, that has certain properties and coordinates in space.
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A mathematical point is the simplest model for calculating psychological interaction (stimulus — response). Psychological interaction consists of two acts, separated by a certain quantity of time. The first act is the determination (measurement) of the quantity of irritation. The second act is the change in the intensity of the action being performed by a certain value, which corresponds to the quantity of irritation (reaction to irritation, response). The interaction is considered completed, when the intensity of action being performed has changed by a quantity, that corresponds to the quantity of irritation (complete excitation for a certain quantity of time). Technically, such a mathematical point is called a machine, where external irritation (stimulus and stimulation) is called incoming information, and the reaction to irritation (response to a stimulus) is called a change in the magnitude of work being performed by the executive mechanism. Accordingly, any living being in psychology is a technical device (machine), that was created by someone and has some kind of power source, because the work being done and the change in the work being done are impossible without energy expenditure (calories). An ordinary internal combustion engine is also a machine, it also converts energy into some kind of action, i.e. it also performs work, which has some value. But a living being, like a machine, is distinguished by the ability to adjust the magnitude of work performed through incoming information, which is a collection of incoming data for a preset algorithm. Incoming information is an instruction to the executive mechanism to change the magnitude of work performed. Since work is performed in a one–dimensional space, there are only two types of commands — to add or reduce relative to the actual magnitude of work being performed (current condition). In the elementary case, this is a command to turn on or off. In a more complex case, this is the magnitude, conducted to the executive mechanism, how much it is necessary to change the magnitude of work performed relative to the actual magnitude of work performed (current condition). Accordingly, the magnitude of work performed is a certain condition of the machine (and the creature), which remains unchanged, until there is incoming information (an order) to change this condition by a certain magnitude. Like any Newton's body, which is in an unchanged condition, until there is а force to change this condition by a certain magnitude. This value is set through incoming information, determined through the senses (or any other sensors). Accordingly, any living being in psychology is a technical device (machine), that has been created by someone and is capable of changing the magnitude of work performed through external irritation (stimulation), i.e. it is an executive mechanism, that has a control system. Since sensory organs (nerve cells) and executive mechanisms (muscle cells) can be external to a machine, the definition of such a machine can be simplified even more. In psychology, a living being is a computing device (machine), created by someone, which takes a value at the input, converts it into another value according to a predetermined algorithm and conduct to the output. It is difficult to understand, who exactly created a living being (in theology, the developers of all living beings are collectively called God), but it is not difficult to understand, why it was created. An ordinary internal combustion engine is also a machine, it also performs work, that has a certain magnitude. To change the magnitude of work being done, need a separate mechanism for regulating the work being done (to increase or decrease the turnovers of the internal combustion engine). And it also requires the presence of those, whom we collectively call God, in order to pull the control knob there or here (to increase or decrease the turnovers of the internal combustion engine). However, if the regulation of work, performed of the internal combustion engine, is tied to the external environment, then in order to change the magnitude of work being done (to increase or decrease the turnovers of the internal combustion engine), it is enough to show the internal combustion engine something, that it will perceive as a command to change the magnitude of work being done (to increase or decrease the turnovers of the internal combustion engine), and the magnitude, by which the magnitude of work being done should be changed (to increase or decrease the turnovers of the internal combustion engine). Convenient! Because God no longer needs to pull the control knob of the internal combustion engine, and therefore be present on this planet at all, the machine itself will see everything (hear, smell, etc.) and adjust the magnitude of work performed (to increase or decrease the turnovers of the internal combustion engine), what we perceive as the behavior of a living being (including our own behavior). On his planet, God has a slightly different culture, than humans, which is logical, because God is not a human being, including a different type of mathematics. However, the rules of geometry in this Universe are the same for everyone, which means we can describe a living being as a technical and computing device (machine) in the language of geometry, and translate it into the language of mathematics, that we understand. We will call an abstract model of such a device a mathematical point by analogy with an abstract material point. Its mathematical and geometric description boils down to several rules.
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1. Point A is the point of intersection of two straight lines and the origin of coordinates on both lines. Both lines are directed, point A divides both lines into two symmetrical halves, where one side comes from infinity and the other goes to infinity. Since the incoming side (it can be either of the two sides, depending on the direction of the straight line) is considered the space behind the back, only the outgoing side makes sense, where in relation to any other points on the outgoing side, point A is incoming (the first in the sequence).
In distilled psychology there is no sense in defining the initial position of point A, since its position is determined relative to point B on the outgoing side, and only if point B is present on the outgoing side, just as the position of point B is determined relative to point A, taken as the origin of coordinates. That is, only the coordinate difference of points A and B has meaning, regardless of the definition of their positions relative to the third point. Accordingly, to define the coordinate of point B, in distilled psychology the coordinate of point A is forcibly taken as the origin and the incoming point (this is a postulate of analytical geometry). In human culture, the initial position is set relative to an arbitrarily chosen center, these will be the points (Od) and (Ow) on each straight line. Accordingly, the position of point A will have coordinates (ds) and (ws) relative to the selected origin coordinates (Od) and (Ow).
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Comment. Straight line segments (OdA) and (OwA) and coordinates (ds) and (ws) are different things. Straight line segments are physical phenomena and their quantity, coordinates are a magnitude, that we have defined (measured) according to the selected units of measurement. Units of measurement may be different, but the principle of measurement in human culture is always the same, it is the ratio of the length of the segment and the length of the standard, so any coordinate is the quantity of such standards. For the segment (OdA), this ratio is with its reference (ld), accordingly, (ds = OdA / ld). For the segment (OwA), this ratio is with its reference (lw), accordingly, (ws = OwA / lw). Two standards are two different units of measurement, because straight line segments can reflect different phenomena. For physical quantities (with valid definition) these are physical standards — meters, kilowatts, Joules, degrees Celsius (or other methods of measuring temperature), etc. For psychological quantities (with abstract definition) these are non–existent, but accepted standards — units of measurement for danger, beauty, yummy, etc. For distilled psychology — this is not important, because in distilled psychology there are no standards (ld) and (lw), therefore, neither in distilled psychology, nor in the behavior of a living being, nor in its anatomy, we will never see the familiar digits. But this is important to us, because in our culture, the definition is usually expressed by a digit (coordinates (ds) and (ws)).
Therefore, the creation of a mathematical point begins with the creation of correspondences of units of measurement (standards) and coordinates, that are defined (measured) by such units. For units of measurement, this is the correspondence of the selected standards ((ld) >> (lw)). For example, one degree Celsius in the definition (meter, kilowatt, danger, yummy, and any other unit of measurement and the type of space, that we measure with such units) corresponds to one degree Celsius in the work performed (meter, kilowatt, danger, yummy, and any other unit of measurement and the type of space, that we measure with such units). One meter cannot be equal to one yummy, because these are different phenomena, so they only correspond to each other so, that the dimension of one step (standard) in both spaces corresponds. For coordinates, this is the correspondence of the coordinates of point A relative to the two coordinate centers at points (Od) and (Ow) on two straight lines ((ds) >> (ws)). For example, some value of degrees Celsius (meters, kilowatts, threat, yummy, and any other type of space) corresponds to some value of degrees Celsius (meters, kilowatts, threat, yummy, and any other type of space). Both coordinates reflect the creature's resting norm (the origin) in the incoming and outgoing spaces.
We will never see these correspondences in a creature, except in the form of an already installed constant, because in a creature the coordinates of point A are considered equal to zero, since point A is the origin of coordinates, and the correspondence of coordinates (ds) and (ws) is set at the design stage, i.e. their true correspondence is known only to the creators of all living, and without the creators of all living, such a correspondence is impossible in principle. Therefore, it may seem, that there is no such correspondence in a creature. However, determining the difference of values, where one value is greater or less, than the other, implies the presence of one (and constant) of the two values, with which any other values are compared (greater or less, than such a value), and therefore the determination of such a value. Since there are two coordinates ((ds) and (ws)), since these coordinates reflect the distance from the centers of coordinates (Od) and (Ow), since in front of us are two segments of straight lines OdA and OwA with a common point A, which is one of the ends on such segments, since two straight line segments have lengths, which may not be equal, then the coordinate accordance ((ds) >> (ws)) of the common point A on both lines are assigned forcibly. Even if the values of the coordinates and the type of space coincide, they cannot be equal (identical) to each other, because this is a violation of logic and a phenomenon, that is impossible in nature. The same applies to the correspondence of the length of the selected units of measurement ((ld) >> (lw)). We understand, that one meter cannot be equal (identical) to one degree Celsius, because these are units of measurement for the length of space and the quantity of heat, two different physical phenomena. But they can correspond to each other, as if two different physical phenomena still intersected at the same point A.
And one last thing. Geometrically, point A is the endpoint of two straight line segments (OdA) and (OwA), whose lengths may not be equal. Also geometrically, point A is also the endpoint of two more straight line segments AB and AB', whose lengths may also not be equal. Despite the fact, that point A is common to four straight line segments, the ratio (OdA) and (OwA) is not necessarily equal to the ratio AB and AB', one does not follow from the other. Through the lengths of two straight line segments (OdA) and (OwA), is installed the accordance of coordinates ((ds) >> (ws)) of point A relative to the origin at points (Od) and (Ow). And only. Further transformation of segment AB into segment AB' occurs through the correspondence of the dimensions of spaces ((ld) >> (lw)), where we (and creature) know only the length of the segment AB, which is determined through the senses as the magnitude of the deviation from the resting norm (ds). Since geometrically point A is not only the origin of coordinates for points B and B', but also has coordinates relative to the origins at points (Od) and (Ow), the final coordinates of points B and B' relative to points (Od) and (Ow) are calculated arithmetically. Except, if the lengths of the segments (OdA) and (OwA) are equal to zero (the resting norms (ds) = (ws) = 0), then the final coordinates of points B and B' relative to points (Od) and (Ow) are obtained pure without arithmetic. Accordingly, each being (living, electromechanical, etc.) operates with information not only about the length of the segment AB, which is determined through the senses (or any other control and measuring devices) as the magnitude of the deviation from the resting norm (ds). But also information about the proportionality of spaces ((ld) >> (lw)) to transform the position of point B on one straight line to the position of point B' on another straight line. And the function (formula) of such a transformation as information. A creature cannot receive information about the proportionality of spaces and the transformation function (formula) from the external environment, therefore, such information is contained in each creature initially as initial data. That's all, in distilled psychology, a being does not operate with information about the correspondence of the position of point A relative to points (Od) and (Ow), and therefore does not perform arithmetic operations.
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2. A mathematical point contains a definition space. Geometrically, the definition is a straight line segment AB, bounded by two points. The first end of the straight line segment is the position of point A (the origin), the second end of the straight line segment is the position of the irritant (point B), which is on the same straight line with points (Od) and A. Point B has a coordinate (x) relative to the origin at point A and a coordinate (xd) relative to the origin at point (Od). The coordinate of the irritant (x) relative to point A reflects the length of the straight line segment (dx) as the magnitude of the definition (difference in values), and therefore the magnitude of the irritation (stimulus). The simplest definition is the logical true or false, is there an irritant (stimulus) or not. A more complex definition is the magnitude of the definition (coordinate difference (dx)), which is the measured or calculated distance between points A and B. The difference in values (dx) can be determined only through another point (the second end of the straight line segment), otherwise the length of the straight line segment AB will remain undefined, since there is no second end of such a segment (point B). The difference in values (ds) between points (Od) and A is not a definition, it is an internal parameter of a mathematical point (the resting norm of a being).
At the top is distilled psychology, where the coordinates of point B are determined relative to the origin at point A. The (x) coordinate of point B is defined relative to point A as the difference in values (dx), the irritant (stimulus) on the left is defined with a minus sign, as is customary in human culture, but is placed after it, because it does not reflect a negative value, but a polarity, since the irritant (stimulus) on the left or right is defined by a separate name as a separate space. For example, there will be an irritant (stimulus) on the left, that is colder, softer, uglier, more disgusting, etc., than I am (my internal parameter and resting norm (ds)). And on the right there will be an irritant (stimulus), that is warmer, harder, more beautiful, tastier, etc., than I am (my internal parameter and resting norm (ds)). Can the opposite. Accordingly, the difference in values between will be defined as the coordinate of the irritant (x) relative to zero (my internal parameter and the resting norm (ds)), which is always positive, but differs in polarity to the left or right.
dx = x – 0
Below there is the human version, where the point coordinate is determined relative to the point (Od) (absolute zero — the property is not expressed). Accordingly, the creature acquires an internal parameter and a resting norm (segment OdA or coordinate (ds)), the value of which may not be equal to zero. Similarly, for the position of the irritant (segment OdB). The difference of the values (AB) in this case is calculated as an arithmetic difference.
dx = xd – ds
Where (xd) is the value of the irritant (stimulus) relative to the point (Od), (ds) is the magnitude of the internal parameter (the resting norm in the definition), (dx) is the magnitude of irritation as the difference between (the magnitude of the deviation from the resting norm in the definition). In distilled psychology, a being determines the difference in values (dx) through its senses relative to itself (its resting norm (ds)), so there is no need to calculate this value through arithmetic. However, the difference in values has a vector, that in one–dimensional space is directed to the left (minus) or to the right (plus) and is indicated after (because the difference in values (dx) is always a positive value). In the human version, the difference in values (dx) is calculated arithmetically, therefore it takes on a positive or negative value, depending on the magnitude of the irritant (more or less, than the value of the creature's resting norm (ds)). Accordingly, the position to the left (minus) or to the right (plus) is indicated before (positive or negative value).
Definition is the measurement of the difference in values (dx) between the irritant (stimulus) value (xd) and the set value (ds), the difference in values (dx) is the magnitude of deviation from the set value (ds). In psychology, such measurement is performed through the senses (sense of smell, hearing, vision, etc.), which are technical control and measuring devices, similar to other technical control and measuring devices — thermometers, voltmeters, rulers, clocks, etc. Normally, the magnitude of such a deviation is zero, i.e. there is no irritation (because there is no point B, from which a straight line segment can be formed, the length of which will be the value of the deviation). Psychology begins, when the deviation value (dx) is not zero, in this case the deviation value corresponds to the quantity of irritation. Since the definition is used as an incoming signal, the definition consists of at least one operation of determining the coordinate of point B (relative to points A or (Od)), at least one comparison operation of the coordinate of point B relative to the coordinate of point A, greater or less, than the subjective preset value (0 — zero) or objective preset value (ds), and at least one operation of calculating, how much greater or less (dx).
The internal value (ds) defines the subjectivity of the creature. If there is no internal hardness value (ds), then there are no phenomena or objects, that are softer or harder, than the internal value (ds) by the magnitude (dx), which means, there is no irritation (stimulation), which means, there is no reaction to irritation (response to stimulation), hard or soft phenomena or objects is not exist for the being. If there is no internal temperature value (ds), then there are no phenomena or objects warmer or colder, than the internal value (ds) by the magnitude (dx), which means, there is no irritation (stimulation), which means, there is no reaction to irritation (response to stimulation), cold or warm phenomena or objects is not exist for the being. If there is no caloric value (ds), then there are no phenomena or objects, that are tastier or more disgusting, than the internal value (ds) by the magnitude (dx), if there is no beauty parameter (ds), then there are no more or less beautiful by the magnitude (dx), than the internal parameter (ds). This means, that there are no delicious or beautiful things in this world, this is not provided by the developer, because it is not provided, relative to which value (ds) are they delicious and beautiful, to determine the difference in values (dx), far as delicious and beautiful they are relative to the value (ds). If there is no internal distance value (ds), then there are no phenomena or objects closer or further, than the internal value (ds) by the magnitude (dx), which means, there is no irritation (stimulation), which means, there is no reaction to irritation (response to stimulation). The creature will cease to orient itself in space and distinguish distances, closer or further, because there is no point A with a coordinate (ds), relative to which closer or further. Etc. The value (dx) may be logical (true or false, there is a difference or not), but without the value (ds), the creature will cease to distinguish the surrounding world, because the value, relative to which there is a difference, is not set. The opposite is also true, until there is a point B with coordinate (x) relative to point A or coordinate (xd) relative to point (Od), the creature will not know, how much harder, warmer, more calorific, more beautiful, closer, etc., because point A cannot form a straight line segment (dx) with self. This means, that the creature will not know, that it is hard, warm, high-calorie, beautiful, located in space, etc. at all, i.e. will not have subjectivity, which is not only definition the position (coordinate) of the irritant (stimulus) relative to own position (coordinate), but also definition own position (coordinate) relative to the position (coordinate) of the irritant (stimulus), because the length of the segment (dx) is the same at either end (AB = BA). The norm of rest (ds), the magnitude of which is different from zero, is not perceived by the being as a value, different from zero, since it is considered the origin (zero). Accordingly, any comparison is made relative to this norm and is perceived as a deviation from the norm.
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Explanation and examples. If the length of the straight line segment (OdA) is not zero ((ds) > 0), point B will lie to the left or right of point A at a distance (dx). The plus or minus signs simply indicate, where exactly point B lies relative to point A, on the left (minus) or on the right (plus). In this case, the length of the straight line segment AB cannot be greater, than the length of the segment (OdA), because in this case, point B will lie to the left of point (Od), which is nonsense. Point (Od) reflects the zero expression of a property (i.e., the property is not expressed) — zero temperature, zero voltage, zero work performed, zero abstract values, etc. In nature, there are no properties, that are expressed negatively (less, than absolute zero). If the line segment (OdA) is zero ((ds) = 0), then the positions of points A and (Od) coincide. In this case, there is no difference, relative to which of the two points the position of point B is determined, since the coordinates (x) and (xd) of point B relative to points A and (Od) will also coincide ((x) = (xd)). In this case, the coordinates (x) and (xd) will always be greater, than zero (((x) = (xd)) > 0), they will always be equal to the difference in values (magnitude of irritation) between ((x) = (xd) = (dx)), and therefore the difference in values (magnitude of irritation) will always be greater, than zero ((dx) > 0). For us, this is a special case, because in our culture, if the straight line segment (OdA) is not equal to zero ((ds) > 0), and the coordinate of the irritant (stimulus) is less, than the resting norm ((xd) < (ds)), then the difference in values will be less, than zero ((dx) < 0). Because of this, there is an illusion in abstract definitions, that each space assumes a pair (and a duality of feelings). For example, if there are beautiful ((dx) > 0) relative to the beauty norm (ds), then there are ugly ((dx) < 0) relative to the same beauty norm (ds). In fact, ugliness (like any abstract definition) is always defined as greater, than zero ((dx) > 0), relative to the norm of ugliness (ds). In other words, there is a beauty norm (ds) relative to which the quantity of beauty is determined (measured), and there is an ugliness norm (ds), relative to which the quantity of ugliness is determined (measured). If beauty and ugliness are associated with the same real space, if the values of the norms of beauty and ugliness coincide ((ds) = (ds)), then all phenomena and objects will be either beautiful (if (xd) > (ds)), or ugly (if (xd) < (ds)). Either–or. For example, if the resting norm (ds) of beauty and ugliness corresponds to zero degrees Celsius ((ds) = 0 °C), then objects and phenomena with temperatures above zero degrees Celsius will be recognized as beautiful, and objects and phenomena with temperatures below zero degrees Celsius will be recognized as ugly. If, for example, the space of beauty extends from zero degrees Celsius to infinity ((ds) = 0 °C +), and the space of ugliness extends from ten degrees Celsius to absolute zero (Kelvin, ((ds) = 10 °C –)), then in the range of ten degrees Celsius (0 ... 10 °C) objects and phenomena will be recognized as both beautiful and ugly at the same time. If the beautiful attracts and the ugly repels, as it usually does, then a beautiful and ugly object or phenomenon will both attract and repel simultaneously. Such a creature will not live long (this is an error in the design of a mathematical point and the creation of a living being, but no one forbids it, this is also possible). And what kind of objects or phenomena will be recognized, if their temperature is equal to the temperature of the resting norm ((ds) = 0 °C)? Neither one. Objects or phenomena with such a temperature will not be considered irritants, and therefore will not possess beauty or ugliness as a property (and its expression (dx)), because the length of the segment AB, as well as the magnitude of irritation (dx), are equal to zero. And they will not evoke any feelings.
On planet Earth, every being contains invisible resting norms (ds) — in physiology, this is the body temperature norm, the norm of something in the blood, and some other norm. In behavior and psychology, it is the norm of perception, what should be the surrounding reality (individual – environment interaction) or another individual (individual – individual interaction). Each individual defines an environment or another individual (including itself) relative to a certain norm (ds). Any deviation from this norm by a quantity (dx) is perceived as irritation (stimulation), which requires a reaction (response) to irritation (stimulation). And irritation is also a feeling. For example, if the ambient temperature (xd) is higher, than the ambient temperature norm (ds), then it is felt. Something is really hot. And if the body temperature (xd) is higher, than the body temperature norm (ds), then this is also felt. I have a fever, something is really bad. Can the opposite, the feelings will be different. And there are also distance norm (ds), which may also not be zero. Then the irritant (stimulus) coordinate (xd) in physical space may be greater or less, than the internal value (ds) by a certain value (dx). Some individual came too close or moved too far away in physical space relative to the distance norm (ds). This also evokes different feelings depending on the type of irritation (stimulation). For example, if the irritant (stimulus) is defined negatively, then approximation will evoke a feeling of fear and horror (and a desire to increase the distance between to a safe distance (ds)), while if it is defined positively, then distancing will evoke a feeling of fear and horror (and a desire to reduce the distance between to a safe distance (ds)). Can the opposite, the feelings will be different. Furthermore, in human society, if an individual has a property with a value (xd), different from the set norm (ds), this also evokes irritation (stimulation) as a difference in values with a magnitude (dx). Such an individual will evoke a feeling of fear, or contempt, or hatred, or disgust, or some other repulsive feeling with a magnitude (dx), but this is not, what should be (ds). Something completely disgusting. The opposite is also true, such an individual can evoke feelings of admiration, adoration, love, and other alluring emotions with a magnitude (dx), because this is not, what should be (ds). Something completely fine. Each individual has a different norm (ds), relative to which the environment or another individual is defined (including self-determination). Therefore, the definition of the environment or another individual can be different. For some, it is too cold, while for others it is perfectly normal, because the temperature norm (ds) is different, and therefore the temperature difference (dx) is different. For some, it is too close, what a horror, they need to move further away. And for others, it is too farther, what a horror, they need to come closer. Because the distance norm (ds) is different, the difference in positions (dx) is also different. And this is not only about bravery or cowardice, but also about the distance between individuals or phenomena at all. For some, it's too disgusting, while for others it's perfectly acceptable, because the abomination norm (ds) also varies in magnitude, and accordingly, the abomination difference (dx) also varies. In psychology, it's believed, that this is a character, the same phenomenon evokes different reactions in different individuals, because they have different character. In reality, this isn't entirely true, a living being is a machine, where reaction is a derivative of perception (definition), the same phenomenon is perceived (defined) differently, because the reference point (ds) is different for each individual. In other words, each individual has its own distinctive character, because each individual perceives (defines) the same phenomenon differently (relative to its resting norm (ds)). Finally, definition is also a measurement, where the magnitude of irritation (dx) is also measured through a certain measurement standard (lx), therefore (dx = AB / lx), where AB is a natural phenomenon and its quantity (or an abstract reflection of such a phenomenon and its quantity), (dx) is the result of measuring such a quantity, and (lx) is a unit of measurement. Since we are talking about the same space, the units of measurement of such a space must be identical to the units of measurement of straight line segments in such a space ((ld) = (lx)). For example, if we set the resting norm (ds) in degrees Celsius, then the deviation from the resting norm (dx) must also be expressed in degrees Celsius. If the resting norm is set in meters, then the deviation from the norm is also set in meters. If the resting norm is set in units of measurement of beauty or ugliness, then the deviation from the norm is also set in units of measurement of beauty or ugliness. Etc. Beauty or ugliness of one or another individual is a property and its expression relative to the norm of beauty or ugliness (ds), i.e., the difference in values ((dx) = (xd) – (ds)). Just like warmth or coldness (temperature) is a property and its expression relative to the temperature norm (ds), where such a norm is the set (but not the actual) temperature of our body ((ds) = 36.6 °C), i.e., also the difference in values ((dx) = (xd) – (ds)).
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