Mathematical Psychology in Broad Strokes

Mathematical Psychology
In Broad Strokes
By
Peter Anyebe
Mathematical psychology subsists in the precise quantitative treatment of
psychological problems. Unlike physics where a clear cut distinction is made
between theoretical and applied physics however, it may not be accurate to
describe mathematical psychology as theoretical in the same sense. It has
adopted the same scientific principles of empiricism like all the other subjects,
to approach the formulation of theories from the inductive perspective.
Theoretical physics has thrived on the deductive approach, where broad strokes are made on the canvas,
followed by details. But it could be argued that this was possible only after certain fundamental features
of the course were laid out, inductively. Psychology may have arrived at the same point, where the
theoretical component has sufficient stuff, on which to thrive.
Sufficiency of basic postulates for broad strokes would be evident in the shift from the what, to the why
questions. While what questions are basically descriptive and merely define the system, the why
questions seek to diagnose, for the purpose of corrective interventions. This work is therefore based on
the following premises that attempt answers to the what, why, and how questions in psychological
analysis, respectively:
Humans are souls, S which is becoming
They need to create value, S and to reduce same into wealth, ROIApp
To do this they are endowed with certain abilities, A as well as the attitudes, L to optimize same;
which disposition has to be motivated, F
This means that given the factor-F the other
two, 2 would be determined, including L and A
in that order. Formally, F = f (L, A). This is a
typical formulation, based on the waves
principle, following which a phenomenon, F
would be adequately defined by the two, 2
features that include location, L and size, A. In
addition there is a connectivity factor that links
all three, 3 items, which in this case would be humans, the concept that is formalized. Forms
operationalize the quantum wave function collapse, QWFC according to the natural order, N-O which has
been derived from the four, 4 strategic principles that govern the universe. The typical form would
therefore be a unique expression of the waves principle, where all three, 3 features are linked; to
distinguish between the human and physical phenomena, which are characteristically continuous and
discrete, respectively.
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Recall the behavior model, R = f (P, S) following which the response, R to stimuli, S would depend on
the interpretation that the person, P makes of the stimuli. This puts the focus on interpretation, according
to the abilities, attitudes, and motivation; which define the quality of the person’s endowments and
wiring, for P → 1. Then responses would be appropriate for R = S, when interpretation is correct, for P =
1. This requires that the response performance is discretized, which discretization would be achieved
when the quantum wave function collapse, QWFC is adapted to the humanities, via the forms principle.
Like the endowments and wiring, the need to create value and to make wealth creates two, 2 possible
platforms from which to interpret stimuli, in fulfillment of conditional probabilities that influence
psychological choices. While creativity is spiritual, wealth is material; both of which would be
mathematically equivalents, being logically analogous. Then to link the broad strokes presented above as
answers to the what, how, and why questions respectively, the person would be quantified uniquely, to
betray their wiring, according to the observed location from which stimuli are interpreted. Moreover the
basic statistical requirements of probabilistic uncertainties would have been satisfied, to enable
diagnoses against the back drop of normality, whether the curve of the observed data is left or right
skewed.
For a demo of the continuity character of the forms principle, which demo strikes at the heart of
psychological research, the distinction is made between knowledge, which involves the mere awareness
of phenomena; understanding, which requires knowledge of the system’s operations; and wisdom, where
the process by which the system was made has to be understood. To link the three, 3 concepts in real time
the process would have to at once define the system operation, to adequately describe it. In this way, all
three, 3 aspects that characterize the information that is required for the interpretation of stimuli including
knowledge, understanding, and wisdom would be accounted for. This has been made possible with
quantum wave function collapses, where infinity, ∞ and a unity, 1 collapse to become equals, for 1 = ∞.
Recall that the adoption of the quantum wave function collapse, QWFC is achieved at the derivation of the
natural order, N-O from the four, 4 fundamental principles that govern the universe. Following the duality
series in operations research therefore, the N-O comprises four, 4 items, to operationalize the idea of
discrete performance levels, in psychological research. Three, 3 other principles combine with the N-O to
conceptualize creativity by the four, 4 strategic features including forms, which would be adequately
discerned by three, 3 features; waves, which are defined by two, 2 features; and the standard procedure
series, SPS that comprise six, 6 items. The perception model of mind, PMM is the common thread that
underlies this QWFC conception of creativity. Thus the mind that functions optimally, would reduce
phenomena into the five, 5 essential elements. Each of these numbers, from a unity, 1 to 2, 3, 4, 5, and 6,
represent discretized performance levels uniquely; according to the concept under investigation.
In this case the infinite number of features that comprise phenomena are collapsed into the handfuls, to
evaluate performance as a discrete function, which otherwise is actually a continuous phenomenon. This
doubles at once, to fulfill conditional probabilities, which is another principle that runs commonly in
psychological research. Discretization enables predictability, to open the doors to segmentation. Then
Luce’s choice axiom, which is actually a reference to the basis for psychological choices; could be
categorized into two, 2 according to the waves principle to include materiality and spirituality.
Spirituality is operationalized in the conception of learning, also in wave features, to include signal
detection or sensitivity, and choice reaction or focus. These are evaluated as the factors Sn and Fc,

respectively. The evaluations are made from the measures of the factors Pc for phenomenological
compression, and Rn for rationality. Then materiality would be restricted to meaning, as a wave function
of memory and logic. They are evaluated from the measure of the factor-√n, as the capacity to perform at
task by the standard procedure. Together, learning and meaning are wave functions that describe the
performance levels at which stimuli are interpreted. Then the expected responses would differ, to record
better scores at the higher level of spirituality, for operational excellence.
Thirdly given operational excellence, OE the performance at task would fulfill the statistical requirement
of probabilistic uncertainty, by which the data would be normal. A classic demonstration of this
conception is observed in the evaluation of the bill of health index, BHI. Thus the measure of value
creation, VCI is a function of the cost of materials, CM and the monetized return on investment, ROI
which are supposed to be inverses. Statistically therefore they ought to return a correlation coefficient, r
of a negative unity, -1 for r = -1. However at the optimum, the observed correlation would be a zero, 0 for
r = 0. This would be when both features are normally distributed, so that the data cancel each other out,
in a typical quantum wave function collapse, QWFC.
At optimum performance, which would be discrete according to the expected number of items, the subject
would have made choices from the axiomatic position of spirituality, as evident in the normal curve. This
is expressed in the first, 1st
law of performance. The second, 2nd
and third, 3rd
laws describe growth, as
evident in a curve that is left-skewed; and decay, for a curve that is rigt-skewed.
For the establishment of these broad strokes, the form of the human person is reduced into the three, 3
features that include the factors S, F, and C for soul, personality, and character respectively. Then given
the factor-C, the factors S and F would be determined, according to the requirements of the wave
function, for C = f (F, S). But F is actually the unit of analysis of S, so that given F, the factor-S would
also be determined.
So the establishment begins with the conceptual reconstruction of C, to
derive the character model, from which the identity kit, Id-K is
calibrated, to measure the factors Pc, Rn, and √n. Then S is reconstructed
mathematically from first, 1st
principles, to derive it. Following which the
appraised return on investment, ROIApp is derived, also from the first, 1st
principles. The factor-ROIApp is actually a measure of the power to make
wealth, POW while S measures the capacity for value creation. Then both
would be analogues, to present C as the conversion constant; which at a
unity for C = 1 would result in the relation, ROIApp = S. This becomes the
exhaust feature, with which to keep track of the establishment process.
Next the factor-F is reconstructed to predict the F-Score, FN which score discretizes performance into a
definite number, N of items, Nu. For instance productivity is evaluated as the capacity to reduce an idea
for Nu = 1, into the four, 4 strategic objectives for Nu = 4, that need to be fulfilled, for actualization.
Three, 3 other measures of F make up the four, 4 strategic variants of the factor, to suffice the
establishment. The factors Fb and FQ measure spirituality and materiality respectively, to fulfill the Luce
choice axiom, for the segmentation of humanity. As the lower limit of the spirituality-materiality
continuum, FQ would be stable for all humans and at all levels of performance, as evident in the observed
equality with the factor-F for FQ = F. But Fb would vary with operational excellence, OE as evident in

Fb > F when operations are below optimum. For distinguishing between choice platforms, Fb and FQ
present understanding as sufficient to effect segmentation. And FN discretizes, to make knowledge
suffice for predictions. Then the factor-FM which is the measures faith would be diagnostic, typifying
wisdom.
FM is optimum at 0.75 for FM = 0.75. This is when the measures of self-containment, ScT and the
performance index, PfI are optimum at 0.5 and 0.25 respectively for FM = ScT + PfI. At growth therefore
the score on FM would be less than the optimum, for FM < 0.75; and at decay, FM > 0.75. The factors ScT
and PfI serve for detailed diagnoses.
By the forms principle entrepreneurship is reduced into three, 3 schemes that include, to start a business,
to run the business, and to scale same. Then two, 2 capacities would be required including domain
expertise, for creating value; and strategy, to link the organization’s products with the end users. The
capacity to discern forms is a skill that is evaluated as the measure of faith, FM to at once put a value on
domain expertise. ScT measures the capacity for strategy, and together with PfI, they are both measures
of competency. Thus a mental skill, FM is split into two, 2 behavioral competencies, ScT and PfI to
facilitate the prediction of behavior, Po from thought, f0 for f0 = 2Po – 1. The prediction fails however,
when the relation that connects behavior and thought is not sustained. This would be observed in the
variants of the scores on ScT and PfI, whether they are less or greater than the optimum. This means that
at an FM score of greater or less than the optimum for FM <> 0.75, the person would be a hazard and
business transactions with them would be risky. The measure of FM is corroborated by the measure of
DNA, both of which are human versions of the fine structure constant, α. It is α that determines intelligent
life in the universe. It is valued at 0.007298. Like FQ therefore, FM and DNA are constants for all humans.
The diagnosis is corroborated by a measure of consistency. Recall the human-power resource quality
model, HpRQM as follows:
BHI’ = 2ScT x √2
ROIApp = S
C → 1
This model puts the right workforce, ScT in the right environment, BHI delivering profitable business
growth, ROIApp when the factor-C is constant, for C = 1. Recall that ScT is optimum at 0.5, and ROIApp is
optimum at √2 = 1.4142. By this model therefore, ScT / 0.5 and ROIApp / 1.4142 would be equal, for ScT /
0.5 = ROIApp / 1.4142. Any observed inequality would indicate inconsistencies in the measures, subject to
the measure of efficiency presented below.
To evaluate the performance index, PfI the factor-C is set at
a unity for C = 1. Then the predicted factor-√n would be a
unity for √n’ = 1, so that the index is evaluated as the
observed inconsistency in the measures of √n, for √n / √n’.
But the actual measure of the √n’ turns out to be 1.03, which
means that the √n is predicted at an efficiency level of 0.97,
for 1 / 1.03. Similarly, ScT would be evaluated at an
efficiency level of ScT / 0.5. So that at C = 1 when ScT =
0.46, the optimum score would be 0.46 / 0.5 = 0.92 for

EFF = √ (0.97 x 0.92) = 0.95. Then in general, the model efficiency, EFF would be evaluated at EFF = √ (1
/ 1.03 x ScT / 0.5).
Recall that FM is evaluated as the sum of ScT and PfI, for FM = ScT + PfI. Note also that the measure of
efficiency varies with the score on ScT. This means that the observed inconsistency on the HpRQM could
be adjusted by the measure of efficiency.
In summary three, 3 broad strokes have been presented, in the attempt to answer the what, why, and how
questions of psychology research. Then the three, 3 recurring concepts in psychological analyses were
recalled. Thirdly the forms principle has been presented as an appropriate research methodology to
investigate the concepts presented by the broad strokes. In kernel, the quantum wave function collapse
is imported from physics, and adapted to the humanities as the forms principle. Thus while the waves
principle handles discrete phenomena, its adaptation as the forms principle is suited to continuous
phenomena. This continuity principle runs through the work, to define the common and binding cord.
Then in conclusion, recall that the factor-S has been
presented as a measure of the capacity for value
creation, Vc. Recall also the second, 2nd
law of
thermodynamics, following which nature is in flux,
from a higher order to a lower order. This makes Vc
an up-hill task, to define S in real terms as a measure
of momentum. Then ROIApp would be the locational equivalent, so that given momentum, S location,
ROIApp would be determined, for ROIApp = S. Secondly by the human resource model, given size, ScT
location would be determined via the prediction of the BHI. This means that location, ROIApp would be
adequately predicted from momentum, S and size, ScT to put labor on the shelf according to the
capacities for value creation, S and wealth making, ROIApp.
This opens the flood gates for entrepreneurship, to make deliberate and objective decisions with respect
to the workforce. By the Pareto 80 – 20 Principle therefore, it would be sufficient to have a workforce in
which 20% is self-contained, for ScT → 0.5. Then given an organizational culture, OrgC in which the
knowledge bank and the ROI appraisal model are installed, the rest of the 80% would have the
opportunity to play catch-up, for profitable business growth.
Moreover this would ensure a steady supply of Arnold Toynbee’s creative minorities, for sustained
civilizations.
Other links that give more details on the concepts presented in this document include:
1. Relativity
2. Dimensions
3. Normality
4. Duality
5. The Natural Order
6. The F-Scale
7. The Identity Kit
8. The Business Case
9. The Path to Soul
Relevant Videos:
Learning: https://web.facebook.com/shopandgrow/videos/221041808367902/
Self-Creation: https://web.facebook.com/shopandgrow/videos/199293003876116/
Path Integral: https://t.co/2MqabDCMC4
Waves Superposition: https://t.co/EzS5NMr3Tm
Tesseract, the cube in 4 Dimensions: https://web.facebook.com/shopandgrow/videos/200611710410912/
Image: https://web.facebook.com/shopandgrow/photos/p.234548093683940/234548093683940/?type=3

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