Mathematical Model of Happiness

MATHEMATICAL MODEL OF HAPPINESS.

Happiness for all, for nothing,

And let no one go offended!

A. and B. Strugatsky.

"Roadside Picnic"

INTRODUCTION.

The author of this article does not pretend to write any comprehensive work on one of the most complicated and ancient issues that occupy mankind. Moreover, the author is not even sure of the methodological justification of applying to such subtle emotional categories as "Happiness" and "Grief" of a dry mathematical apparatus. However, the author seems curious about the combination of such non-close categories (the emotional state of the individual and mathematics), and also the conclusions that can be drawn from such a combination are curious.

1. 1. TERMS AND DEFINITIONS.

To construct a further chain of reasoning, we introduce several terms that have long been widely known. Terms with a large share of voluntarism are accepted in the author's interpretation, despite their varied interpretation in various social and philosophical reference books and articles (from dictionaries of Marxist-Leninist ethics to religious and philosophical works). So, let us introduce three terms.

1. MOOD - the emotional state of an individual at a particular moment in time. This concept is certainly well known to any person and does not require further interpretation.
2. HAPPINESS is a momentary state of emotional upsurge, close to euphoria. This condition can be caused by various causes, but, regardless of the causes that caused it, physiologically it is approximately the same for every particular person. In different personalities, the physiological manifestations of HAPPINESS may differ somewhat.
3. GORE - a momentary state of emotional decline, close to depression. Causes may also be different. Manifestation in individuals is analogous and opposite to the manifestations of HAPPINESS.

We draw attention to the fact that MOOD, HAPPINESS, and MOUNTAIN in this context are states of momentary, instantaneous, variable in time, and have nothing in common with the interpretations of these concepts in the aforementioned scientific literature on this subject, where they are often described as prolonged states ("The Happiness of Labor "," The Happiness of Faith ", etc.).

1. 2. MATHEMATICAL MODELING.

Let's construct a speculative schedule for the individual's TIME. For clarity on the time scale, T, we indicate abstract events that affect the MOOD, for example: the praise of the leader (P), the loss of any valuable item or money (Y), the meeting with the loved one (B), the illness of a loved one (B) P. Let's take the calibration of the scale of the MOOD N: the average level of the MOOD is 1, the maximum achievable level of mood is 2, the minimum attainable level of mood is 0.

Let us explain the given graph. At the beginning of the T coordinate, the personality is in the neutral MOUNTAIN (N = 1). After the occurrence of event II (praise of the leader), N begins to grow and reaches a certain value N> 1. After a certain time, a new event Y (loss of a valuable item) results in a decrease in the MOOD to N <1. The next event B (meeting with a loved one) again changes the value of N and makes it greater than 1. The fourth event B (illness) again sharply worsens the MOOD to N <1. After a certain time, the following event, not indicated on the chart, may occur, which can again change the value of N, and so on throughout the life of the individual. It should be noted that the events shown on the chart are conditional and are intended only to illustrate the reasons for changing the MOOD.

Thus, we have a certain function of the MOOD from time:

N = F (T),

Describing the MOOD at a particular moment in time, depending on the circumstances in which the person enters.

Let's try to take the time derivative of this function. We obtain another function:

S = N '(T) = F' (T)

Let's depict the graph of this function against the background of the events applied in the graph of the function N = F (T) and try to give the parameter S a physical meaning.

Realizing that the physical meaning of the first time derivative of any function is the rate of change of a given function, we come to the conclusion that S is the rate of change in mood.

According to the personal experience of the author and on the basis of his long-term observations of the surrounding people, we dare to conclude that it is at the maximums of the graph of the function S = F '(T) that the state defined by us as HAPPINESS appears and at the minima of this function the state of HORE is manifested. Such a conclusion may seem speculative, but refer to your life experience: did not you, at the moment of mood change towards its increase, experience a state close to the definition of HAPPINESS that we defined, and, conversely, with a decrease in mood, the state we designate as a mountain? And is a change in mood not a necessary condition for the manifestation of these feelings?

Thus, we conclude that HAPPINESS and GORE are functions of the first time derivative of the MOOD.

The ranges of the values of the function S lying above the zero mark describe the state of HAPPINESS, and vice versa, the ranges of values of S below zero describe the state of the HOT.

The author quite admits that the conclusions drawn here are controversial and, perhaps, in the chain of his reasoning there are logical inconsistencies. However, he conducted a small sociological survey among his acquaintances (however, does not pretend to be any representativeness) shows that the majority of people experience similar feelings and agrees with the above interpretation of concepts.

1. 3. SOME CONSEQUENCES.

From the above, we can derive several consequences.

1. HAPPINESS and the MOUNTAIN can not be long enough, because We experience them only at the time of the change in the MOOD, and this process is always, firstly, finite, and secondly, as a rule, very short-lived. The attempt to present "Eternal happiness" does not correspond to the elementary theory of functions, because In this case, the function of MOOD should strive for infinity, which is impossible from a physiological and psychological point of view.
2. HAPPINESS and the MOUNTAIN are stronger the higher the rate of change of the MOOD. Given the finite nature of the absolute values of the MOOD (in our reasoning and graphs, the MOOD varies from 0 to 2 units), the higher the rate of change, the shorter the time interval of this change. Consequently, a stronger HAPPINESS and a grief is always more fleeting than their weaker forms of manifestation.
3. HAPPINESS and GORE concepts are differential, i.e. Independent of the absolute value of the MOOD. If we construct two identical graphs of the function N = F (T): the first with the change in the absolute value of the MOOD from 0 to 1, and the second with a synchronous change from 1 to 2, then the function S = N '(T) obtained from these two graphs, Will be the same.

Hence follows the political and economic conclusion: the level of happiness of the population does not depend on its welfare. For example, a prisoner in a camp receives the same full-fledged happiness from a pack of cigarettes given to him, as the oligarch who is buying a new yacht feels, because The mood change in them occurs about the same size. To illustrate this thesis it is possible to bring the sincere and strongest happiness of millions of people from the winning of the sports team, although for each of them this does not affect their material well-being and personal life, or the sincere grief of millions of people on the death of the dictator of their country (remember the funeral Stalin, Kim Jong Il, etc.). In addition, we can assume that people have come to the same conclusion about the independence of the level of happiness from well-being for a long time. As a supporting example, let us quote the English proverb: "To make a man happy take everything from him, and then return any half."

Here the author should make a small remark: he is far from an authoritarian ideology and his political worldview categorically does not accept the active use of this conclusion in practical politics in order to quickly achieve people's happiness by reducing their standard of living. Such approaches in the history of mankind have been used more than once, and it is well known that each time it ended.

1. With a sufficiently long process of the vital activity of the personality, the value of the integral of the function S in time tends to 0. In our figure, this is the total area bounded by the graph of the function S and the T axis: the area of the figures above the T axis (the total amount of HAPPINESS) is equal to the area of the figures below the T axis (the total amount GORYA).

In other words, for each person during life there is an equal amount of happiness and grief and this ratio does not depend on any external factors.

1. 5. CONCLUSION

The method of mathematical analysis of the emotional states of an individual used in this article is deliberately given only in a small part of the possible application. An inquisitive reader can independently continue research in this area. For example, it would be interesting for the author to introduce the term ADDICTION into the reasoning and analyze its correlation with the MOOD, HAPPINESS, and MOUNTAIN, or reflect on the possibility of artificial optimization of the graph of the function N = F (T) in order to achieve the most comfortable state of the person for a long period of time. However, when writing this article, the task was only to bring to the readers' judgment the very possibility of applying mathematical tools to the analysis of the emotional sphere of the individual.

The arguments given in this article and the conclusions drawn do not in any way claim to be true in any instance. Moreover, the author is not sure of the correctness of his reasoning and will be grateful for any criticism addressed to him. Also, in advance, the author accepts possible criticism of blasphemy from religious figures and organizations. Only the fact that it did not aim to question the religious feelings of people and treats with respect for any religion can justify its justification.