The Anatomy of a Question and Time Khalookah[1]  
Using P Versus NP
Applications for ΔΔ[2] of Serial Crime

by

Dallas F. Bell, Jr.

Mark Schar,[3] at Stanford University's Center for Design Research, says the convergent mode of thinking primarily uses facts to close down questions and chooses a decision outcome in problem-solving.  The brain regions activated depends on the specific divergent task.  For example, different brain regions will be used for verbal logical syllogisms versus numerical deductive logic, if that brain only processes language in a different manner than numbers, per se.  However, it can be said that both of these tasks largely engage prefrontal cortical regions, almost exclusively.[4]

The divergent mode of thinking generally asks questions to converge for a problem-solving decision outcome.  The brain regions activated depends greatly on the defining of divergence.  If it is inductive inference, perhaps the cognition found in Raven's Matrices,[5] then it is a more complicated picture involving not only cortical areas but also areas largely associated with memory (hippocampus), fear (amygdala) and reward (ventral striatum).[6]  Perhaps risk and ambiguity are mediated by the orbitofrontal cortex as they are processed in different brain regions.  Ming Hsu's,[7] et al, paper shows this mediation of the amygdala and striatum by the orbitofrontal cortex in ambiguous decisions.

The question arises as to what consciousness controls brain mediation.[8]  Questions, like this, are an essential aspect to complex problem-solving.  They are linguistic expressions designed to find information to form answers, unless it is probing[9] or rhetorical.  Rhetorical questions are tools to give information and not pursue information.

The structure of a question begins with an indicator word(s) that a question follows, such as where, when, who, does, is there, etc.  That grammatical structure is punctuated with a question mark or a verbal heightening of the tone.  The body of the basic question involves finding the relationship between two (knowable) entities (set A and set B) to find an outcome from the set of possible answers.  For example, the question "How long is the board?" can be seen as the need to find the relationship between set A (all possible lengths) and set B (the board).  From the set of possible answers (A), the exact answer (C) is to be found.  The answer is the exact measurable length of the board from that set of possibilities, such as "Eighteen inches."  The answer could be expanded to restate, all or in part, the question, such as "The length of the board is eighteen inches."

That example shows that C is a subset of or equal to the category of A applied to the subject B.  Then C ⊆ A and A – X (all but the answer C) = C or X + C = A so B = C which forms the answer statement "the board equals 18 inches in length)."  Analysis of the question "What does 2 + 2 equal?" would include A (all possible numbers), B (2 + 2), and C (4).  Analysis of the question "Where have you been?" would include A (all possible places you could be), B (you), and C (school).      

The give and take of a question presupposes[10] a core of common beliefs and understanding between the questioner and the answerer.  There also needs to be an assessment of the motivation[11] of those involved.  The initial question may indicate how the answer is to be reached.  A philosopher (Kant, etc.) may ask "How ought I to behave?"  Meaning, he has an openness to all possible behaviors, whereas a biblical scholar may ask the same question designed to find a biblical law(s) that applies to the behavior implied by question.  Ludwig Josef Johann Wittgenstein (1889-1951) spoke of language games which exposed words as without significance unless anchored to a particular identifiable task.

If the relationship between subsets of a line of thought is not proven, a question is said to be begged.  This logic devise is used to restate the thought as a question to address the unproven statement as either true or false.  For example, the statement is sometimes made that "The reason the crime is so high in that neighborhood is due to low average incomes." That thought can be addressed as a question "If the reason there is high crime in that neighborhood is low average incomes, then why are their average incomes the same as the adjoining neighborhood which has low crime rates?"  By this restatement, the beginning statement is rebutted.

Zoroaster, in Gathas (Hymns), saw the human condition as the mental struggle between truth (good) and untruth[12] (ignorance[13] and evil[14]).  Expectedly, Friedrich Nietzsche (1844-1900) demonstrated the latter in his book Also Sprach Zarathustra: Ein Buch für Alle und Keinen.[15]

A question can be asked to create a false reality, such as an abortionist may ask "Who is to be saved the mother or her unborn baby?"  A late Knoxville, Tennessee, medical doctor stated on many occasions that in his 40 years of delivering over thousands of babies he never faced that choice.  He also made it a point to survey his peers at annual medical conventions for many years and none of them ever had to make that choice either, nor did they know of any other doctor that had to make that choice.  This does not exclude the possibility of any life threatening scenarios, just that the instance is much more rare than the question intends to suggest. It is obvious that the question is not a neutral pursuit of truth but is designed by the questioner to formulate an accepted scenario to legitimize the murder of unborn babies.

There are also irrational questions that pose sets with no relationship in reality and have no possible existent answer.  If someone asks "What is the color of the number seven?", there can be no answer because we realize that numbers are abstract and do not reflect a light spectrum and so can have no color.

There are also ignorant questions where the question sets demonstrate a lack of understanding of their meanings, such as "Who created the infinite God?"  Obviously, God being infinite, He must then have always existed and of course not need to be created, as He is the first cause of all effects.  Another question along those lines is "Can God create a problem too big for Him to solve?"  God is infinite and omniscient.  He would not need to play chess with Himself by fluctuating between inherent omniscience (at times chooses to not know something and is theoretical subject to error inconsistent with infinite holy omnipotence) and total omniscience (knows everything at all times).[16]  However, God is not something to impute all things we do not understand as atheists do with the invalid theory of genetic evolution.

Some questions have exact answers outside of the perception of man's ability and are in God's domain.  An overarching question might be "Why does God do all the things that He does?"  The inexact answer, from the set of man's perceived possibilities, could be that God acts from love, holiness, etc.  But an exact "why" for all circumstances can not be reasonably known by man.

Valid questions require an understanding and desire to find a logical answer.  This is not random and is designed with purpose by intellect.  This intellect is required to differentiate and narrow a matter.  It does not matter to a carbon atom if 2 + 2 = 4 or 1,004.  A relevant threshold from infinite numbers is reached immediately, by intellect, that 2 + 2 would likely equal a set of numbers from -99 to 99 of which 4 is accepted.  Omniscience is required to know if this is always perfectly true.  An open question is one where we have the ability to see that there may be a breakdown of truth due to a lack of understanding all associated things (e.g. the 3x + 1 problem).[17]

Flipping an equal two-sided coin has a 50% chance of ending up on one specific side and a higher order unknown is the chance of winning the lottery.  A proper question allows for the narrowing of possibilities.  Many people consider the set P is related to the set NP and can properly be answered by a set of equal to or not equal to relationships to each other.  In 1971, Stephen Cook and Leonid Levin formulated the P (easy to find) versus NP (easy to check) problem.

Generally, P is a set of somewhat relatively easy problems and NP is a set of difficult problems with somewhat relatively easy solutions.  N is the execution time of an algorithm which is directly proportional to the number of elements it is handling.  Most algorithms are complicated and inefficient with execution times proportional to N times the logarithm of N or N squared.  N's raised to powers are expressed mathematically as polynomials (the P in this problem).  P is the set of problems whose solution times are proportional to polynomials of N's.

An execution of N to the third power is slower than N squared.  NP (nondeterministic polynomial time) is a set of problems whose answers can be verified in polynomial time.  Many can be solved in exponential time.  If it takes a second to perform N, the execution time of N to the third power might take around three hours, while the execution time of 2N might be 300 quintillion years etc.

The question of "Does P equal NP?" is translated to "If a solution to a problem can be verified in polynomial time, can it be found in polynomial time?"  The majority of NP problems are solved in exponential time (NP-complete).  That means polynomial time solutions by one can be adopted to solve all others.  It has been intuitively argued by Scott Aaronson, a professor of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology, that if P = NP there would be no special value to create leaps or gaps between solving a problem and recognizing the solution once it is found (only Mozart could appreciate a symphony, etc.).  Many other experts caution not to be overconfident that P does not equal NP.

The question of P versus NP can be looked at as P ⊆ NP, P = NP – X, NP = X + P, or X = NP – P where X is a set of NP different from P, so P is not equal to NP.  On the other hand, NP ⊆ P could be NP = P – X, P = NP + X, or X = P – NP, so P is not equal to NP (if X is different from NP) or P = NP (if X is the same as NP).  It is argued that solving a NP-complete problem in polynomial time indicates NP ⊆ P or even P = NP.

Heraclitus (c. 535 BC – 475 BC) is quoted in Fragments[18] as saying "Time is a game played beautifully by children."  With God's omniscience, there is no gap in time of the ability to solve an issue.  It is already known.  Then finite man, as God's created children, must be communicated with by God in periods of time called dispensations (khalookah).  This prevents man's senses from being overloaded as time allows man to process Divine behavioral boundaries and freely choose his behavior.[19]  At pre-set times, more is revealed by God, thereby expanding and proving prior revelations as true.  Dispensation can be seen as addressing changes in man and his institutions as well as his relationship to God and His law.

Dispensation periods organize time and place.  In the fullness of time,[20] laws for individuals and institutions have been defined, geography is assigned,[21] the spiritual realm is explained,[22] and technology is brought to fruition.[23]  Before the Torah, Enoch and Noah walked with God.[24]  During the Torah, God walked before Abraham.[25]  After the Torah, man walked before God.[26]  The new covenant knowledge needs the old covenant knowledge to mature.  This puts Messianic Jew's genealogies, history, Israeli geography, theology and experience at the forefront of Christian leadership for the end times.

Increased Jews for Christ (Messianic Jews) today are considered to be a sign of the end times.  Jesus said to the Jews He was speaking to that they would not see Him again until they say blessed is He that comes in the name of the Lord.[27]  In 2011, it is reported that there are 150 Messianic Jewish congregations in Israel.  The number of believers has grown from 12 in 1948 to 3,000 in 1987 and 5,000 in 1997.  Today, it is estimated that there are over 20,000 believers.[28]  Knut Høyland, director of the Caspari Center, points out that there are problems in collecting exact data on converts.  For example, was a convert considered a Jew genetically or maternally and paternally or both etc.[29]  Rabbi David Rudolph, at Tikvat Israel Messianic Synagogue, recommends the (1999) book titled Facts and Myths About the Messianic Congregations in Israel, Mishkan 30-31.[30]

The Messiah was both to suffer for sin (must be God, as Jesus claimed, to be the perfect sacrifice) and ruler of all nations (nations still operate on the behavior of Jesus and in His Second Coming He will physically rule from Jerusalem).[31]  The set time is now.[32]  The Yigdal[33] is a peeyoot[34] often used after the Shema[35] in synagogue services.  Its lines 6, 7, 8, 12, and 13 address the dispensations and the Messiah.

Aristotle (384 BC – 322 BC) said "Time crumbles all things; everything grows old under the power of time and is forgotten through the lapse of time."  Dispensation shows time has periods of relevance and questions and their answers have entropy.  This is the strategy of code making in cryptology.  It is believed by code practitioners that it must and will take longer to decode something without the key than the content of the codes importance to the code users.  This is reflected in the belief surrounding the P versus NP problem.

The above principle also means that given enough time and appropriate resources all codes that can be developed can be decoded without the key.  Behavior is somewhat like a code.  Serial crimes exhibit the same criminal behaviors or codes over and over.  It seems logical that given enough time and appropriate resources their behavioral code can be broken and the crimes stopped.  Scott Aaronson points out that computer science concepts are not always useful for crime-solving due to the "information-theoretic" nature of criminals.[36]

Aaronson makes a good point regarding complexity.  The complexity of a crime can increase exponentially if more than one person is involved and committing different types of crimes, as David Canter recognizes.  His book titled Investigative Psychology explains how complex the issues can become.[37]  Oddly, decision analysis scientists (neuroscientists, physicists, behavioral economists, etc.) are usually excluded from behavioral science organizations by people educated in law practice.  Gary Bauer, member of the Board of Advisors at the Foundation for Defense of Democracies, thinks that people with law degrees often seem to have more expertise on foreign policy issues and national defense than scholars in other fields.[38]

Differential diagnoses[39] (DDx, ddx, DD, or ΔΔ) implement various aspects of the hypothetico deductive method.[40]  This begins with looking for the simplest answer first and only after this is ruled out then more complex diagnoses can be considered.  The lower set of odds of occurrence can be induced from the evidence to a set of possible answers and those can each be deduced to an outcome set until the correct answer is found.

The move by most societies today toward omniscient technologies[41] is dramatically increasing data available for government employees.  It is believed that universal government surveillance of its citizens against their will is a greater threat to future freedoms than those for whom they are providing protection from.  Kofin al midat S'dom[42] means that if A has a legal right and the infringement of that right by B will cause no loss to A's right but will benefit B, then the infringement will be allowed.  This rule[43] can be used to examine the abuse of rights.

Crime can be expected to increase in the last days.  The BBC (British Broadcast Company) on 8 January, 2003, noted the soaring crime rate of Vatican City.  According to Vatican Chief Prosecutor Nicola Picardi, calculations of the 455 population in 1992 had 397 civil offenses (87.2%) with 608 penal offenses (133.6%).  In 2012, Nancy S. Jones (chief disciplinary counsel for the Tennessee Board of Professional Responsibility) reported a marked increase of Tennessee lawyers facing discipline for stealing or misusing client funds.[44]

Conversion syndrome (mass hysteria) is the term used to describe the outgrowth of physical symptoms that arise without clear explanation.  In 1692 Salem, Massachusetts, teenage girls were bitten and pinched by unseen agents after a séance.  Some of the girls became dumb while others limbs contorted as reported by a witness, Rev. John Hale of Beverly.  Other outbreaks have occurred; uncontrolled laughter in Tanzania (1962), fainting in Blackburn England (1965) and the West Bank (1983), rashes and dizziness in Portugal (2006), nausea in Mexico City (2007), fainting in Tanzania (2008), screaming and shaking in Brunei (2010), and Tourette's-like symptoms[45] in LeRoy, New York, (2011-2012).

Laszlo Mechtler, DENT Neurologic Institute in Amherst, and Gregory Young, Acting Associate Commissioner and Medical Director of New York, are looking at changes in blood flow in the brain with fMRI testing to determine if there is any observable neurological reason for the episodes in LeRoy.[46]  In the last days, there is to be an increase in demonic influence and possession,[47] as was recorded in the Bible.[48]

The uncertainty principle states that there is a limit on accuracy of things, such as position and momentum, being simultaneously known.  The more precise we measure one area the less precise we may be in another area.  On some level, this may be applied to human behavior profiling.  Serial criminals are by definition successful at not getting caught.  It can be expected that the higher the intelligence the more likely is the adjustment of that behavior to confuse profiling or measuring.  Profiling changes the reality of the crime as adjustments are made.

The anatomy of a question is complicated by time and dispensation.  Using P versus NP we can see the structure to a complex question.  These ideas can often use differential diagnoses, as applied to future serial criminal activity.

(Appreciation is extended to the following people for their email exchanges with Dallas F. Bell Jr.; January 2012, Colin Ross, a psychiatrist at the Institute for Psychological Trauma, regarding dissociative disorders in serial crime; Anil Nerode, a professor of mathematics at Cornell University, regarding serial crime application of P and NP; Philippe Jaming, Institut de Mathématiques de Bordeaux, regarding uncertainty principles and serial crime; Steuard Jensen, professor of physics at Alma College, regarding doubled geometry applications; Bascom Talley, Intelligence Analysis Programs at Johns Hopkins University, regarding mathematical applications to behavioral analysis; February 2012, Chongfu Huang, president of China's Society for Risk Analysis and is the director of the Research Center for System Simulation and Disaster Modeling, Academy of Disaster Reduction and Emergency Management Ministry of Civil Affairs and Ministry of Education and professor at Beijing Normal University, regarding uncertainty in decision analysis.)

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