## Mathematical Expressions for the Human Mind

Robert Howard Kroepel
Lakside Studios
New Durham, NH USA 03855-2107

The functions or operations of the human mind can be described by mathematical expressions.

An individual’s mind is his personal system of desires/fears/priorities which causes his behavior as his actions/reactions including his feelings as his reactions to his realizations of his desires/fears/priorities, his personality as his mind-in -action, as his behavior as caused by his desires/fears/priorities, his mental problems as his unrealistic [unachievable or/and inappropriate] desires, and his mental health as his realistic [achievable and appropriate] desires.

A desire is wanting a person, a thing, or an event.

NOTE: For the purposes of the observation and measurement required for an operational definition of ‘desire,’ scientists (and nonscientists) can observe and measure an individual’s approach behavior towards a person/thing/event as evidence of the presence and operation of a desire.

A fear is not-wanting a person/thing/event.

NOTE: For the purposes of the observation and measurement required for an operational definition of ‘fear,’ scientists (and nonscientists) can observe and measure an individual’s avoidance behavior away from a person/thing/event as evidence of the presence and operation of a fear.

NOTE: Desires and fears are interrelated by being opposites. The desire to live is the interrelated opposite of the fear of dying.

A priority is the importance of each desire or fear compared to (relative to) all other desires and fears.

NOTE: For the purposes of the observation and measurement required for an operational definition of ‘priority,’ scientists (and nonscientists) can observe and measure the effort an individual makes for his approach behaviors to desired persons/things/events or avoidance behaviors away from feared persons/things/events as evidence of the presence and operation of priorities.

NOTE: The term ‘desire(s)’ can be used for convenience to designate desires/fears/priorities.

An individual’s mind and his sense of ‘I’ and ‘me’ and ‘myself’ develop in the following process (sequence):

1. There is a material world of people/things/events comprised of matter/energy which exists objectively and independently of the individual’s opinions and in contrast to his ideas/dreams/fantasies/etc.

2. The individual perceives the material world through his (perceptual)  senses of (1) sight; (2) hearing; (3) touch; (4) smell; (5) taste.

3. Through his perceptions the individual learns which people/things/events achieve his desires/do not achieve his desires and avoid his fears/do not avoid his fears.

4. The individual develops desires for those people/things/events who/which achieve his desires/avoid his fears.

The individual develops fears of those people/things/events who/which do not achieve his desires/do not avoid his fears.

Thus, the bridge between the material world and the individual’s ‘I’/mind is his senses/perceptions.

5. The individual’s desires/fears/priorities, taken together as a personal system, (A) comprise his mind; (B) cause his behavior; and (C) is his ‘I’/‘me’/‘myself.’

Paraphrase: The individual’s ‘I’/‘me’/‘myself’ is his mind—his personal system of desires/fears/priorities which causes his behavior.

An individual’s self-esteem is (A) his perception of himself and (B) his reaction to his perception of himself. Thus, self-esteem involves a self-perception and a feeling which is a reaction to that perception.

If an individual has a desire, D (for a person/thing/event), and a realization, R (a person/thing/event achieved nor not achieved), of that desire, then as he achieves more of his desire his level of happiness increases, and if he achieves less his level of happiness decreases.

For example, if Sam wants to earn \$1000 next week, his level of happiness is 100% if he earns \$1000 (or more) and less than 100% as he earns less than \$1000—75% if he earns \$750, or 50% if he earns \$500, etc.

This can be expressed as —

SEi = Ri/Di x 100%

Where

SE = Self-Esteem
D = Desire [Wanting a Person/Thing/Event]
R = Realization of a Desire [Person/Thing/Event Achieved/Not Achieved]
i = Identification number, i

NOTE: Happiness = SET + 51% (or higher); Unhappiness = SET = 49% (or lower).
NOTE: The SEi expression describes a straight-line or linear function wherein increases or decreases in R/Realizations produce direct increases or decreases in an individual’s SEi;  the individual may not experience such direct linear functions, and, if so, then the SEi expression may require a function number that would produce a curvilinear (nonlinear) increase/decrease in SEi.

If D1 = \$1000; R1 = \$1000, then —

SE1 = \$1000/\$1000 x 100% = 100%

If D2 = \$1000 and R2 = \$750, then —

SE2 = \$750/\$1000 x 100% = 75%

If D3 = \$1000 and R3 = \$500, then —

SE3 = \$500/\$1000 x 100% = 50%

The SEi mathematical expression serves for one Desire, Di, and its Realization, Ri.

The SET mathematical expression accounts for all desires and realizations an individual might have.

SET = (R1/D1 x P1 x 100%) + (R2/D2 x P2 x 100%) + ... + (Rn/Dn x Pn x 100%)

Where:

SET = Self-Esteem Total
D = Desire [Wanting a Person/Thing/Event]
R = Realization of a Desire [Person/Thing/Event Achieved/Not Achieved
P = Priority [The Importance of Each D/Desire]
n = The last number, n, of a series

NOTE: All P/Priorities must sum up to (add up to) 1.00.
NOTE: Happiness = SET + 51% (or higher); Unhappiness = SET = 49% (or lower).
NOTE: The SET expression describes a straight-line or linear function wherein increases or decreases in R/Realizations produce direct increases or decreases in an individual’s SET;  the individual may not experience such direct linear functions, and, if so, then the SET expression may require a function number that would produce a curvilinear (nonlinear) increase/decrease in SET.
NOTE: The SET expression recognizes that an individual has a multitude of D/Desires (and F/Fears), each having its own P/Priority, and each having its own R/Realization.
NOTE: The SET expression also recognizes that as a result of changes in an individual’s physiology (body) and psychology (mind) his D/Desires, P/Priorities, and R/Realizations change, and, as a result, his SET changes from moment to moment, and yet, over a period of time, his SET is likely to maintain a average level.
NOTE: The SET expression suggests that an individual is not likely to achieve 100% of his D/Desires at R/Realizations of 100% and thus experience a long-term SET of 100%; but it also suggests that an individual is likely to achieve at least some of his D/Desires at R/Realization levels and thus never experience a long-term SET of 0%.

If Sam has has the following D’s, R’ and P’s, then his SET can be caculated by the SET expression.

D1 = 1; Sam desires to love and be loved by Suzy;
R1 = 1: Suzy loves Sam and Sam loves Suzy;
P1 = .50; Sam’s priority for Suzy is high.

D2 = \$40,000; To earn \$40,000/yr. as a professional musician playing the piano;
R2 = \$30,000; Sam earns \$30,000/yr. playing the piano;
P2 = .35; Sam’s priority earning money is not as high as his priority for loving Suzy.

D3 = 4; To fly his airplane at least four hours per month;
R3 = 2; Sam flies his airplane 2 hours per month;
P3 = .15; Sam’s priority for flying his airplane is not as high as his priorities for earning money and loving Suzy.

NOTE: Sam’s P/Priorities sum up to 1.00 (.50 + .35 + .15 = 1.00).

Running Sam’s numbers gives his SET:

SET = (R1/D1 x P1 x 100%) + (R2/D2 x P2 x 100%) + ... + (Rn/Dn x Pn x 100%)

SET = (1/1 x .50 x 100%) + (\$30K/\$40K x .35 x 100%) + ... + (2/4 x .15 x 100%)

SET = (50%) + (26.7%) + ... + (7.5%)

SET = 84%

Thus, Sam experiences happiness at a high self-esteem of 84%.

If Suzy should leave Sam, then his R1 = 0 and his SET is thus:

SET = (R1/D1 x P1 x 100%) + (R2/D2 x P2 x 100%) + ... + (Rn/Dn x Pn x 100%)

SET = (0/1 x .50 x 100%) + (\$30K/\$40K x .35 x 100%) + ... + (2/4 x .15 x 100%)

SET = (0%) + (26.7% + ... + (7.5%)

SET = 34%

Thus, Sam would experience unhappiness at a low SET of 34%.

Thus, if a scientist knew all of an individual’s desires/fears and priorities, and his realizations—his achievements of his desires and his avoidances of his fears, then that scientist could determine the individual’s self-esteem—how he perceives himself and his reaction to himself as a feeling, particularly as an emotion of happiness or unhappiness as sadness, anger or/and fear. An individual is his desires/fears/priorities.

In summary, an individual’s mind—his 'I' and his ‘me’ and his ‘myself’—is his personal system of desires/fears/priorities, and an individual functions according to (an individual’s self-esteem is described by) the SEi and SET mathematical expressions:

SEi = Ri/Di x 100%

and

SET = (R1/D1 x P1 x 100%) + (R2/D2 x P2 x 100%) + ... + (Rn/Dn x Pn x 100%)