Analysis of the Cognitive Network (graph) in Systematic Political Science Using
Zeta Function and a Clique for the Sermon on the Mount 

by
Dallas F. Bell, Jr. 

1. Introduction 

It is common for the earliest communications in children to reflect their displeasure with another child taking something of theirs and that someone having told them that they would do something that they did not do.  Those two thoughts are epistemological expressions of the Natural Law of Freewill (NLF) concepts of stealing and lying.  Children do not have to be taught the reality of those behavioral options nor do they have to be taught that they do not want those behaviors to be used toward them.  However, they do have to be taught not to use them toward other people though the innateness of NLF is widely evident. 

As people age, more input of words and images allow for more associations and subtlety of expression.  Prepositions, such as across, after, before, etc., describe space concepts.  Matter is usually a noun or pronoun such as I, me, you, etc.  Tenses indicate a time frame.  Causation is expressed in verbs.  Nouns, verbs and modifiers may be used to express the epistemological rationality of what is considered good and evil.  Concepts of good and evil are from the chosen theology developed from the innate options of systematic theology monads (e.g. love, justice, etc.) with compliance or noncompliance with innate NLF.   

Modifiers are adverbs (e.g. evilness, good, righteously, etc.) and adjectives (e.g. blessed, evil, good, righteous, etc.)   Punctuation marks in a written text can express epistemological rationality as can variations of tones in speech.  Nouns and verbs may also have an implied epistemology, such as murder, which can be both a noun and verb.  Most mentally healthy people do not want to be murdered and think murder is evil.  This is why the act of murder by murderers is often replaced by other words so as not to create a visceral negative reaction to their behavior (i.e. abortion, euthanasia, etc.)  This may give rise to so called Freudian slips, where the actual word of a thought is unintentionally expressed instead of another word that is less descriptive of the actual hidden thought.  

All human communication must use the aforementioned sentence components to express thoughts in theological monads and NLF--cognitive networks.  Propagandists in business and government know this structure and attempt to manipulate it by associating words or images favorable to their cause.  For example, conservative politicians may say that their liberal opponents want to raise taxes.  This is to stimulate the innate association of liberals to being enslaved.  Being enslaved is contrary to the NLF of not wanting to have your justly earned possessions stolen.  The association need not be true to create the desired negative effect.  Liberals could defend that conservative strategy by, among other things, changing their identity from liberal to another (temporarily) less viscerally negative term such as progressive. 

Untruth, unlike truth, has a problem in that the more associations or steps there are, the more likely will be the revelation of their untruth.  For example, a liberal politician may call their opponent a Nazi.  Nazi is commonly associated with lying, stealing and murder.  The voter may be inclined to not reject the lying or stealing accusations but would not likely accept that the opponent is a mass murderer.  Therefore, the triple association would likely be widely rejected.  Focus groups can and are used by business and governments to identify acceptable associations. 

Whether intentional or unintentional, speech can and does conjure up subconscious thoughts within the cognitive network. 

2. Analysis of the Cognitive Network (graph) 

Linguists know that humans are usually unaware of the complex network that cognitively governs their communication.  A network or graph with nontrivial features in network theory is called a complex network.  Nontrivial features may include a hierarchical structure, assortativity and disassortativity vertices, fat tail in degree distribution and a high clustering coefficient.  A dimension of a complex network can be a, ζ, zeta function. 

A well known example of a complex network is a small-world network such as voter networks, electrical power grids, etc.  This is a graph where most nodes or vertices are not neighbors, but most vertices can be reached by a small number of steps.  This would also include a clique where all vertices are connected by edges.  A fat tail occurs where there are many vertices with a high degree of connections.  Deletion of a random vertex may not dramatically decrease the clustering coefficient (or increase the mean-shortest path length of an edge) of a complex network.  On the other hand, a similar but random network would dramatically decrease the clustering coefficient. 

A graph is directed if its vertices are connected by directed edges from one vertex to another.  Graphs are undirected if the edges are not directed between vertices.  If V: = {1, 2, 3} and all are connected and undirected this would be a clique where E: = {{1, 2}, {2, 3}, {3, 1}}.  The clustering coefficient qualifies how close the vertex and its neighbors are from being a clique.  For example, if a vertex is near three connected and undirected vertices the clustering coefficient is C = 1, or if only two of the three neighbors are connected it would be C = 1/3, and if none of the three neighbors are connected it would be C = 0.   

3. Zeta Function and Clique for the Sermon on the Mount 

A semantic network is a graph in which all the vertices represent concepts.  In systematic political science, NLF forms a clique with 10 vertices and thus is a size 10.  The La and Lb categories generally reflect this size 10.  Specifically, a La clique is a size 4 from the vertices of the first four NLF and the Lb clique is a size 6 from the vertices of the fifth through tenth NLF.  Each individual 10 NLF can be a vertex or connected hub to its subsets such as the eighth NLF, not to steal, has edges to 8-D-1, 2, 3, 4 and 8-Dn-1, 2, 3, 4, 5, 6. 

The graph zeta function can be used to plot separate lines in a text(s) or contrast separate tests as to compliance or noncompliance with NLF and the monads of systematic theology. 

Before graphing techniques are employed, it is important to first break down the text to be analyzed into lines or verses by epistemological implication (R), individual and societal behaviors (B, W), theological and eschatological concepts and monads (T, E), and implicit/explicit compliance with NLF or noncompliance with NLF (*).  The Sermon on the Mount is a record in chapters 5 through 7 of the biblical book, Matthew.  They are the words spoken by Jesus around the summer of 28 A.D.  This speech is paralleled in Luke 6:20-49.  That famous example is broken down as follows. 

Example of a nonexhaustive cognitive network: the Sermon on the Mount

[KJV; Matt. 5, 6 and 7] 

Matt. 5

Verse; R; B and W; T and E; NLF

   3; blessed; poor; heaven; 1

   4; blessed; mourn; comforted; La, Lb

   5; blessed; meek; inherit; 5, La

   6; blessed; hunger/thirst; filled/righteousness; La

   7; blessed; merciful; mercy; Lb

   8; blessed; pure; see God; La, 1, Lb

   9; blessed; peacemakers; children of God; Lb

10; blessed; persecuted for righteousness; heaven; 1

11,12; blessed; reviled/persecuted/lied about; reward in heaven; 1, 9

13; do not; lost savor; cast out; 1

14; do; light; not hid; La, 1

15; do; light; give; La, Lb, 1

16; do; let light shine; glorify God; La, 1

17; do not; think not destroy law and prophets; fulfilled; La, Lb

18; do; law; fulfilled; La, Lb

19; do not; teach/break commandments; least in heaven; 1, La, Lb

       do; teach/do commandments; great in heaven; 1, La, Lb

20; do; exceed in righteousness; to enter heaven; 1, La

21; do not; kill; judgment; 6

22; do not; angry without cause; judgment; 6, La

       do not; say Raca; in danger; 4

       do not; say fool; hell; 4, 1

23, 24; do; gift at altar; reconcile with brother; Lb, 8

25, 26; do; agree with adversary; paid the uttermost; Lb, 8

27, 28; do not; lust; adultery; 7, 10

29, 30; do not; let the body offend; hell; 1

31, 32; do not; divorcement without fornication; adultery; 7

33-37; do not; swear; God's throne; 1, Lb

38, 39; do; smitten on cheek; turn the cheek; Lb

40; do; if sued; let him have cloak; La

41; do; if compelled; go twain; La

42; do; if asked; give; 10, Lb, 8

43-45; do; bless/love/do good to enemies; Father in heaven; Lb

46-47; do; love; reward; La, Lb

48; do; be perfect; Father is perfect; La, 1, Lb  

Matt. 6

Verse

  1; do not; alms before men; no reward/Father/heaven; Lb

  2; do not; do thine alms; hypocrites; 9

  3, 4; do; alms in secret; Father reward; Lb

  5; do not; pray as hypocrites; reward; 9

  6; do; pray in secret; reward; La, Lb

  7; do not; pray vain repetitions; heard; La, Lb

  8; do not; what is asked; Father knows; La

  9; do; pray in this manner; Hallowed Father in heaven; La

  10-13; do; pray/forgive other's trespasses; forgive; La, Lb

  14; do; forgive trespasses; Father forgives; La, Lb

  15; do not; not forgive others; Father not forgive; Lb

  16-18; do not; fast openly; reward; La, Lb

       do; fast secretly; be rewarded; La, Lb

  19; do not; make treasures on earth; thieves can steal; 8, 1

  20; do; make treasures in heaven; thieves can't steal; 8, 1

  21; do; where treasure is; there heart; 1

  22; do; light is eye; full of light; La

  23; do not; eye be evil; darkness; La

  24; do not; serve God and mammon; hate one and love other; 1, 2

  25; do not; take no thought for life; life more than meat; La, 10

  26; do not; fowls do not sow; Father feeds them; La

  27; do not; take thought; add to height; Lb

  28, 29; do not; thought for raiment; lilies do not toil; La

  30; do not; God clothe the grass; little faith; La

  31, 32; do not; take no thought; Father knows need; La

  33; do; seek first kingdom of God; all things shall be added; La

  34; do not; take no thought for tomorrow; evil sufficient unto today; La 

Matt. 7

Verse

  1; do; judge not; be not judged; Lb

  2; do not; ye judge; you shall be judged; Lb

  3-5; do not; consider mote in brother's eye; hypocrite; 9

     do; consider beam in own eye; shall see clearly; 9, Lb

  6; do not; cast pearls before swine; trampled/rend you; La

  7; do; ask, seek and knock; shall find; La

  8; do; ask, seek and knock; receive, find and open; La

  9-11; do; evil man can give good gifts; Father gives good things if asked; 5

  12; do; all things to men that should do to you; law/prophets; La, Lb

  13; do; enter in straight gate; wide gate leads to destruction; La, 1

  14; do; straight gate is way; few find it; La, 1

  15; do; beware of false prophets; they are wolves; 9, 8, 3

  16; do; know them; fruits; La, Lb

  17, 18; do; good tree, good; corrupt, evil; good and evil fruits; La

  19; do not; not bring good fruit; cast into fire; La, 1

  20; do; know; by fruits; La, Lb

  21; do not; not every one that says Lord enters; heaven; 1, La, Lb

        do; Father's will; heaven; La

  22, 23; do not; prophesied/cast out devils; never knew them/iniquity; 3, 1

  24, 25; do; hear and do sayings; wise man; La

        do; founded upon rock; fell not; La

  26, 27; do not; hear and not do sayings; foolish man; La

         do not; build upon sand; fall was great; La 

(Beatitudes, Matt. 5:3-12; The Lord's Prayer, Matt. 6:9-13; The Golden Rule, Matt. 7:12) 

4. Conclusion 

When analyzing the Sermon on the Mount it is obvious that monads of systematic theology are employed, as heaven in 5:3, or implied, as compassion in 5:4.  The alternative must be no heaven and no compassion which would reflect a T2 or T3 view of rejecting T1 beliefs.  All 10 NLF were covered and complied with, which also indicates a T1, R1, B1, 1W and E1 view when applied to the common individual and societal options.  The clustering coefficient is high in its association of vertices with its neighbors.  This explains why this speech has been innately accepted as true for nearly 2,000 years.  Its innateness also explains why even those with T2 and T3 beliefs have historically accepted much of the text in the Beatitudes and the Golden Rule. 

The text of the Sermon on the Mount can be contrasted (zeta function), as 5:42 saying to give if asked and its compliance with NLF 10, Lb and 8, to another text, as the line by Karl Marx "From each according to his ability, to each according to his needs!"  Marx's line was taken from part one of his 1875 writing Critique of the Gotha Programme.  We can see that Marx implies the violation of NLF 10, Lb, 8, La and 1.  This indicates Marx's writing has a T3 view.  That also implies the consistent monads of no love, no mercy, etc. which can form a clique of T3 symmetry.  

Even Darwinian evolutionists that follow Marx want to be treated with mercy according to Jesus' teaching though their belief implies no mercy.  In Matt. 7:28, 29, the people that heard the Sermon on the Mount first-hand were astonished at the perfect speech because Jesus taught with authority and not as a mere scribe.  That is why billions of people have logically accepted Jesus as the Messiah as He claimed and have rejected other figures that are at some point exposed as inferior frauds.  The basics set forth in this paper should aid in the ultimate pursuit of truth for all people that value that effort.  Since this process is mathematical and composed of finite sets it is, of course, easily computational. 
 

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