Abstract: META game theory is the Manifold Equation of Theological Asymmetry. It combines the primary and secondary variables, factors, and elements or subsets of systematic political science, theology, epistemology, psychology, sociology, and eschatology. Within these academic disciplines emerges a dynamic system. Through the singularity of theological belief, the epistemological vector is created. That vector produces the parametrics of decision making for individual behavior and subsequent societal behavior based on the eschatological magnitude set forth in the chosen theological singularity. This provides the min max or area of the function where both individual and nation-state decision-making behavior can be predicted stochastically. In this domain behavioral arcs are plotted three-dimensionally. The arcs combine to form waves. The x axis records the time, and the y axis annotates behavior in relation to compliance with or defection from the anchor of natural law. The I and IV quadrants of the z plane registers the problem-solving ability in reference to the ability to invent tools and use them to manipulate the environment in the achievement of the common hierarchical needs; survival, economic security, love and affection, status and self-esteem, and self-actualization. The dynamic and stochastic decision-making behavior formulae for individuals and nation-states are presented. This holonomic approach should enhance the forecasting abilities of decision-making analysts from all scientific fields.

1. Introduction

The holonomic approach to decision-making formulae must first include an understanding of systematic political science—Manifold Equation of Theological Asymmetry (META) game theory. It basically projects that a theological singularity must be chosen from either an infinite God or not. If it is the latter, a finite god who complies with some natural law or finite gods who comply with few natural laws must then be chosen. These three options are used to synthesize input from senses into the rationale for what is considered good and evil. Those three epistemological vectors set the min max for behavior in achieving the common individual needs. In ascending order, the parametric needs are survival, economic security, love and affection, status and self-esteem, and self-actualization. The process of pursuing needs causes the formation of groups that have similar need levels and the same theological singularity. The corresponding individual need level creates a parametric societal level of either a First, Second, or Third World political system. Each system has an eschatological magnitude based on the original chosen theological singularity.

Additionally, factors and variables exist that must be included in this analysis. To prevent confusion in the meaning of terms, symbols in equations unique to systematic political science are in red font.

The subject of natural laws has been introduced briefly. Natural laws are the anchors of META game theory. Other game theory scenarios may choose a correct outcome by accident since they are posed on how players may react to each other without regard to an anchor formed from cooperating with or defecting from a natural law through the epistemological vector of a chosen theological singularity.

Finite beings are composed of atoms that compose the molecules of deoxyribonucleic acid (DNA). Natural Law of this Physical dimension (NLP) is the dynamic mechanism that provides the order for existence concerning mass, energy, and velocity. All matter is subject to those natural laws and the violation of which by individuals produces inefficiency in achieving needs and hastens physical death (e.g. gravity, heat, and cold). Law must have authority attested to by negative sanctions for violations, a justice component, and positive rewards for compliance, a benevolent or love component. The second aspect of law is the Natural Laws of the Free-will (NLF). This dimension provides the dynamic mechanism for decision-making order and is equally real as and important as the NLP dimension.

Steven Pinker has pointed out that children are born with the ability to recognize verbs and nouns. We also know that children recognize truth at birth and only later reject it. If adequately modeled parentally, a common behavior for a child is to avoid eye contact and gulp when confronted with the truth that exposes their lie. Thomas Aquinas observed that truth is self-evident and known to all. It is axiomatic that two plus two equals four. This can be demonstrated by holding up two fingers on the right hand and two fingers on the left hand. A conscious effort must be strategically made to deny that four digits are being held up and to choose an untrue sum that is other than four. The stress resulting from the cognitive dissonance of being confronted with a lie will be physical manifested.

William Blackstone and John Locke believed that good comes from God's laws and bad from rejecting those laws. That view is opposed to John Stuart Mill's belief that whatever behavior makes one happy is good. Thus, a child knows at birth by mean and extremes of concepts like love and justice etc. that there must be an infinite God of love whom they justly trust until they choose otherwise. At a point in all childhood experiences, specific questions of purpose arise that address past, present, and future realities. This is when the authority/standard of the infinite God is consciously chosen or rejected by freewill for a belief in a finite god or gods, resulting in loss of efficacy in achieving needs and hastens physical death. The epistemological vector from that chosen faith becomes the substance of things hoped for and will calibrate the behavioral boundaries for achieving individual needs unless a conversion is made to another theology.

All NLF natural laws for finite beings with freewill fall into two core categories. First are those that direct behavior regarding the infinite or holy God: one, there should not be any other gods; two, do not make images of those gods; three, do not take God's name in vain; four, keep His day holy. The second category includes the last six laws that direct behavior toward others, which are necessary for a societal Q1 trust quotient. Law number five is for children to honor parents; six, not to take innocent human life; seven, not to be unfaithful to your spouse; eight, not to take the property of others; nine, not to lie; ten, not to desire the possessions of others. Those are negatively stated with the acknowledgment that their truth is foreknown by all humans. This is to say, for example, that we know from birth to be truthful and the laws only reinforce compliance with what we know is efficient.

It has been said that if the infinite God of grace upon whose shoulders the government rests is chosen, He will be loved and the neighbor will be treated as one would like to be treated. This highest or all-encompassing law indicates compliance with or rejection of the other laws. Those laws provide the basic anchors for plotting decision-making behavior. Technically, if a violation of such laws is thought, brain activity occurs, and behavior has taken place. But mapping can take place only if the thought is acted upon. Conversely, a thought to conform to a law does not mean that behavior will be compliant. Then neither is it possible for finite humans to comply with all natural laws in thought or deed. If a thought is entertained long enough, it will be acted on. When any law is violated, the min of infinite or righteous perfection is exceeded, and all law is technically violated. Obviously, then, all finite beings fall below this infinite threshold, but the plots here are concerned with compliance or violations as they are seen to occur.

2. Individual Decision-Making Formulae

2.1 Dynamic (Macro) Equation

Solve for the sum of individual behavioral possibilities.

The y axis, I and IV quadrants, equal the plots from either 1, a subset of 2, a subset of 3, a subset of , 4, a subset of 5, of the parametric B, behavioral levels, achieved from a B1, B2, or B3 behavioral track, which equals to or is less than the corresponding epistemological rationality of R1, R2, or R3 vector of NLP, known natural laws of the physical dimension and NLF plus the subsets of known natural laws of the freewill dimension. The R1, R2, and R3 vectors are a subset of the corresponding theological singularities of belief of T1, min 0 max 1 lim to infinite compliance NL, natural laws, or T2, min -1 max 0, or T3, min -2 lim to physical death from noncompliance with natural law using FA, fuzzy analysis. The T1, T2, and T3 course is verified with LSA (latent semantic analysis) of the T belief and its subset of eschatological magnitudes of the corresponding E1, E2, and E3 beliefs.

And

The x axis equals min 0, which is the birth year and max of 140 years or time of death that plot time gradients in years or generations where a generation is 20 years.

And

The z, I and IV quadrants, equal the usually static plot of I, intelligence of lo, lower problem-solving ability min 0 max 95, av, average problem-solving ability, min 96 max 139, and gi, gifted problem-solving ability min 140 max less than 300.

And

Then the xy plots are joined to the plot on the z plane. Those plots are joined to other xy and z plots by interpolation.

Therefore, the area of the function is extended to indicate the sum of possible changes in behavior considering the gravitational pull toward the T track of the societal majority, P1, and specifically known STI (stimuli) and the need levels achieved and to be achieved by O, probability of occurrence; O1, 90% to absolute certainty, O2, 75% to 89% certainty, and O3 50% to 74% certainty. The min max of the x axis is extended by past time patterns considering the corresponding S category or average tolerance to moderate persistent stress; S1, 15 to 30 years for T1, S2, 7 1/2 to 15 years for T2, and S3, 3 1/2 to 7 1/2 years for T3. The min max of the y axis is extended by past compliance with or rejection of NL, all known natural laws. The z plot usually remains unchanged.

Given that all factors and variables of SPS, systematic political science and DS, deception strategies have also been considered, the xy and z predictive plots conclude the dynamic formula input.

Thus, the dynamic individual decision-making equation of META game theory is completed.

2.2 Stochastic (Micro) Equation

Solve for the sum of individual behavioral probabilities.

The y axis shifts the same dynamic plots from the I and IV quadrants to the respective II and III quadrants, which form the H, history. The I and IV quadrants now plot the specific compliance or noncompliance with NL, all known natural laws.

And

The x axis shifts the same dynamic plots from the I and IV quadrants to the II and III quadrants of a min 0 of the date of the last need level achieved and a max of the birth date in negative years and less than -140 years. The I and IV quadrants now plot time in days, weeks, or months with a min 0 and max of the date the next B need level is achieved.

And

The z plane's axis plotted from the dynamic I data usually remains unchanged.

And

Then each xy plot is joined parallel to the plot on the z plane by interpolation. Therefore, the new plots in the I and IV quadrants of the xy plane create a Barc, behavioral arc. The min max of that Barc and the min max of the II and III quadrants form the area of the function to be extended to indicate where the sum of probable behavior change is likely to occur in relation to compliance with or rejection of NL, known natural laws expressed in the affirmative as either a Barc1, O1 of T1 arc momentum; Barc2, O1 of T2 arc momentum; or Barc3, O1 of T3 arc momentum, given that the same information and analysis techniques used in the dynamic model have been considered.

Thus, the stochastic individual decision-making equation of META game theory is completed.

3. Nation-State Decision-Making Formulae

3.1 Dynamic (Macro) Equation

Solve for the sum of nation-state behavioral possibilities.

The y axis, I and IV quadrants, equal the plots from either 1, an element of 2, an element of 3, an element of 4, an element of 5, of the parametric W, behavioral levels, which are derived from the polarization of individuals with the same T1, T2, or T3 singularity of beliefs, corresponding R1, R2, or R3 vectors of rationality, in achieving the same B1, B2, or B3 parametric track of 1, 2, 3, 4, or 5 levels of individual behavior. They form either a P1, 51% or more, P2, more than 24% and less than 49%, or P3, more than 2% and less than 24%, group with a T1, min 0 max 1 lim to infinite utopic compliance with known NL, natural laws, or T2, min -1 max 0, or T3, min -2 max -1 lin societal collapse from noncompliance with natural law and can be categorized using FA, fuzzy analysis. Each of those demographics influence the four societal institutions of Fa, family, Ch, church, Bu, business, and Go, government to form and support a corresponding 1W, First World, 2W, Second World, or 3W, Third World political system. They can be identified with tools such as polling using LSA, latent semantic analysis of the T belief and its subset of eschatological magnitudes of corresponding E1, E2, and E3 beliefs.

The 1W1 has a P1 of T1, a P2 of T2 and a P3 of T3; the 1W2 has a P1 of T1, P2 of T2 and a P3 of T3, with Q1 trust all are equal under the law, C1, and free, F1, to pursue their needs productively at 75% to 100% average capacity, A1; the 1W3 experiences a min max shift to a P1 of T2, a P2 of T1, and a P3 of T3 , and now don't trust Q2, two tiers of legal classes C2, and average productive capacity of 50% to 74%, A2; the 1W4 min max shifts to a P1 of T2, P1 of T2, and a P3 of T1 , and F2 with a O1 of M2, projection of power; the last level 1W5 shifts the min max to a P1 of T3, a P2 of T2, and a P3 of T1, now with three tiers of legal classes C3, fear Q3, slavery F3, and average productive capacity of less than 50%, A3 ending the cycle with a ST, societal transition, either of STr, rational transition to another 1W system by STrr, reformation of the L2, or higher level of crisis/change affecting 50% to 74% of the population, to a T1 belief; or a Strw transition to a 1W system by victory in a war for independence over T2 and T3 opposition. The second transition option of STir, irrational transition leads to a 2W or 3W system by either STird, dominated by another society with T2 or T3 beliefs; or STirr, revolution resulting in military victories over other T beliefs; or STirc, catastrophic crisis from famine, disease, war, etc., leading to the extinction of societal structures and mass migration to other societies.

The 2W1 has a P1 of T2, a P2 of T3, and a P3 of T1, with two tiers of legal classes, C2, the elite ruling class has F1 freedom to pursue needs with Q1 confidence but the worker class is F2, Q3, and A2. The 2W2 has a min max shift of the P1 to a T3, the P2 to T2, and P3 is T1, now is C3, Q3, F3, and A3. The 2W3, 2W4, and 2W5 levels are not collectively achievable because of noncompliance with natural laws—lim. The ST options are the same as for a 1W system.

The 3W1 has a P1 of T3, a P2 of T2, and a P3 of T1., with three tiers of legal classes, the elite has F1 freedom to pursue needs with Q2 confidence but the worker class is F2, Q3, and A3 and the slave class is F3, Q3, and A3. Noncompliance with natural law prevents a 3W2, 3W3, 3W4, or a 3W5 level being collectively achieved—lim. The ST options are the same as for the 1W system.

And

The x axis of 1W, 2W, and 3W systems equal min 0 max end of the cycle plots of time in years or generations.

And

The z plane's I and IV quadrants plot by hundred thousands, ten millions, or billions the I, intelligence min max of lo, av, and gi demographics of either I1, 85% to 90 % av, 5% to 7% gi, 5% to 7% lo; or I2, less than 85% av, more than 7 1/2 % gi, less than 5% lo; or I3, less than 85% av, less than 5% gi, more than 7 1/2 % lo.

And

Then the xy plots are joined to the plot on the z plane. They are joined to other xy and z plots by interpolation.

Therefore, the area of the function is extended to indicate the sum of possible O1, O2, or O3 changes in behavior considering the gravitational pull of geographical neighboring nation-states, G2, with the same T track or, G3, with a different T track; the supply of natural resources, N1, requiring 10% or less on imports, N2, requiring 11% to 30% on imports or, N3, requiring more than 30% on imports; and specific STI, stimuli. The min max of the x axis is extended by past time patterns considering the corresponding S category of S1, S2, or S3. The min max of the y axis is extended by past compliance with or rejection of NL, natural laws, and the corresponding level of 1W, 2W, or 3W system template of P1, P2, and P3 based T demographics. The z plane is also projected with special interest to the L factor involving immigration and migration.

Given that all factors and variables of SPS and DS deception strategies have been considered, the predictive xy and z plots conclude the dynamic formula input.

Thus, the dynamic nation-state decision-making equation of META game theory is completed.

3.2 Stochastic (Micro) Equation

Solve for the sum of micro nation-state behavioral probabilities.

The y axis shifts the dynamic plots from the I and IV quadrants to the respective II and III quadrants that form the H, history, and may include more than one cycle. The I and IV quadrants now plot the specific compliance or noncompliance with NL between societal levels.

And

The x axis shifts the same dynamic plots from the I and IV quadrants to the II and III quadrants with a min 0 of the date the last level was achieved and a max when the cycle(s) began in negative years or generations and less than -1,000 years. The I and IV quadrants now plot time in days, weeks, or months with a min 0 and a max of the date the next W level is achieved.

And

The z plane plots in quadrants I and IV the same I data as in the dynamic model.

And

Then each xy is joined parallel to the plot on the z plane by interpolation.

Therefore, the new plots of the I and IV quadrants on the xy plane create a Warc, behavioral arc. The min max of that Warc and the min max of the II and III quadrants form the area of the function to be extended to indicate the sum of probable behavior change is likely to occur in relation to compliance with or rejection of NL, natural laws expressed in the affirmative as either a Warc1, O1 of T1 arc momentum; Warc2, O1 of T2 arc momentum; or Warc3, O1 of T3 arc momentum, given that the same information and analysis techniques used in the dynamic model have been considered.

Thus, the stochastic nation-state decision-making equation of META game theory is completed.

4.Conclusion

The dynamic and stochastic formula template of both the individual and nation-state decision-making models reflect a topographical equation with asymmetrical theology—META game theory. A global formula is constructed in the same manner as the nation-state template where as all P1, P2 and P3 groups combine worldwide from each 1W, 2W, and 3W system to create a global 1W, 2W, or 3W world dynamic model and stochastic model expressed in the affirmative as either a global arc, GLarc1, O1 of T1 arc momentum; GLarc2, O1 of T2 arc momentum; or GLarc3, O1 of T3 arc momentum. Forecasting accuracy at all levels lies in the skill of the analyst to use these tools in applying data.

Obviously, only the infinite God has the infinite data necessary to predict behavior perfectly. It is not the nature of those with free will to be epistemological nihilists, so man is likely to continue to study decision making for prudence sake. Hopefully, the holonomic approach presented will be of assistance to this worthwhile strategy.

References

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Bell, Dallas F., Jr., How Theology Dictates Political Systems. Presented at the conference hosted by Mid- America Baptist Theological Seminary in Memphis, TN, 2002.

Bell, Dallas F., Jr., The Primary and Secondary Precursors to Mathematical Formulations in Dynamic Games. Presented at the New 2004 Economic Windows conference hosted by the Department of Economics and Statistics at the University of Salerno, IT, 2004.

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Pinker, Steven. The Language Instinct: How the Mind Creates Language. William Morrow. 1994.