EpiDoc 450April 30, 1976Seattle, WA

PAN-ACTS COSMOS

By

STUART C. DODD, PhD

And

BURT WEBB

“Personal immortality seems to be highly probable and largely proportionate to one's influenceon living persons and their memories, when extended through records.”

Stuart C. Dodd, PhD 1900-1975

COPYRIGHT © 1976 by BURT WEBB

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I Culture, Model and Science

All human cultures have a model of the universe. Primitive societies embody theirmodels in mythology and modern societies define their models with science. Such modelsserve important psychological and social functions.

1) They define the origin and structure of the world.2) They provide the basic framework for social relations.3) They explain the stages of life which most people experience.4) They reveal the relationship between normal consciousness and altered states of

consciousness.

Models can be compared for complexity, coherence, processes, structures, and thesocial systems which result. Such models are essential to human society regardless of theirexact content.1

These cultural models have several common features. The universe is thought tohave different levels. There may be only a few levels or there may be many. Distinction isoften drawn between the realm of the living and the nonliving. The world of everydayobjects is often contrasted with another level where the ordinary distinctions of space, time,and identity dissolve. Another common feature is a set of key processes including creation,destruction and balance. Perhaps the most important similarity is the concept of unity indiversity. All the levels and all the processes are seen as parts of an integrated whole.

Two examples of such models are the Tarot and the Holotheme. The Tarot is a deckof cards which represent pieces of a complex system. Its origins are lost in antiquity but itdefinitely existed in Europe during the 14th Century. It contains a system of 10 levels whichreach from a transcendental Source through various cosmic realms to the mundane Earth.It also contains four suits which represent four basic processes operating throughout the 10levels.2 The Holotheme was developed by J.L. Jolly and published in 1968. It contains 8levels which extend from abstract patterns of information through space, energy, matter,life, creatures, societies and nations to the planetary level. It emphasizes four keyprocesses which operate within each of the levels.3 Both of these models ultimately viewthe universe as an integrated whole.

My field is sociology and much of my career has been devoted to the application ofmultidimensional scales to modeling sociological phenomena. Early in my investigations, Iassigned different dimensions to actions, actors, times, places, and values. By placingthese dimensions at right angles, I constructed a matrix. The cells of the matrix representpossible occurrences. In time, I extended this matrix to eight dimensions for comprehensive-sociological analysis. I also developed other matrices for explanation, prediction andcontrol.4

I have made considerable use of statistical concepts in my modeling. Statistics formsa bridge between continua and discrete entities. The Normal curve is quite well known. Thenorm defines a class of entities while the spread of the curve allows the inclusion of thevariability between the entities. The Entropic growth curve is less well known. The curvehas an s shape and represents processes which first accelerate and then decelerate. TheHelix curve is a useful method for dealing with cyclic changes. The Combinatoric curvedeals with combinations and permutations of entities which are the result of numbers and

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relationships. These four curves appear to be important tools for understanding theactivities and nature of entities.

I am a scientist and I follow the four aims of science. The first aim of science is thedescription of our world. Science seeks a system of categories which will capture theessential aspects of the entities under study. The second aim of science is the explanationof the origin of the entities. Science seeks to know the causes of the entities under study.The third aim of science is the prediction of the future. Science searches for accuratemethods of predicting future events and structures of interest. The fourth aim of science is ageneral understanding. Science attempts to find basic structures and processes whichmodel the behavior of entities at all levels and times. These four aims of science have beenguides for my work in cosmic modeling.

The foundation of my model is an abstract point space of randomly interactingelements which I call primons. These random bits evolve through eight levels oforganization. The first level is that of pure organization in terms of binary choices and itselement is the curvon. The second level is that of empty curved space and its element isthe gravon. The third level is energy and its basic element is the photon. The fourth level ismatter and its element is the neutron. The fifth level is life and its basic element is the cell.The sixth level contains all multicellular creatures and plants and the element is an entity.The seventh level is society and its element is the social group. The eighth level is that ofculture and its element is the concept. This level contains the symbolic representation of allthe other levels.

Physicists have found action to be more basic that energy, space or time. I define anactant as any entity under scientific study. As actants of any level interact, they build up theentities of the next higher level. The Gompertz growth curve represents the way that suchgrowth proceeds in time. The actants brought into existence by this process displayvariability which converges on a normal distribution for large numbers of actants. Asconditions of such growth recur, the growth will recur. Such cycles of recurrence can berepresented by a helix. The basic behavior of such interacting actants is always covered bythe ideas of combination including permutation and repetition. These can be represented bythe Sterling combinatoric curve. As the actants evolve up through the levels of organization,there is a simultaneous devolving back down. These processes balance each other and thewhole universe can be seen as a balanced whole. I call this integrated sphere of activity theCosmos or the total of all things being studied by science.

This paper is organized into six sections. The first section has been devoted to somebackground ideas and an exploration of the basic levels and elements of my theory which Icall the Pan-Acts model of the Cosmos. The second section will deal with describing thepresent nature of groups of actants through the normal curve. The third section will explainthe past origins of the actants by the Gompertz curve of growth and decay. The fourthsection will deal with predicting future cycles of behavior by the Euler helix curve. The fifthsection will cover the understanding of interactions at any time through the Sterlingcombinatoric curve. The sixth section will contain some thoughts on the significance anduses of the Pan-Acts model. Thus the four aims of science will be linked with the four coreprocesses that govern the interactions of actants through out the Cosmos.

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II Describing the Present

A. Hierarchic Periodicity

In his attempts to describe the universe, the scientist struggles to go beyondqualitative differences into quantitative relationships. A set of eight levels is mentionedabove. Many models converge upon this basic set, but no other model attempts todefine the quantitative relationship between levels.

As the Pan-Acts model was being developed, the typical actants of the differentlevels were ranked according to their masses. It became evident that there existed aconstant step between levels, such that each higher level exceeded the previous levelby a ratio of 1011 on a scale of tons.

The primary determinant of the eight levels was not mass, but ratherorganization. Each level is more complex than the preceding level. A two dimensionalgrid is needed to represent complexity versus mass.

When graphed in Cartesian coordinates, order of complexity is the ordinate andmass is the abscissa. If semi-log scales are used, then a straight line appears whichshows a constant rate of changing organization versus changing mass. This line iscalled the Creatant in Pan-Acts.

(Plate 1)

B. Trials Confirmed

This periodicity of mass versus organization was originally observed with respectto the material and biological actant. Extending the Creatant line downward into smallerand simpler actant yielded a unit actant for curved space which was named the gravonbecause of its connection to gravity. Below the space level lays some sort of pre-space.The actant of this level was called the curvon because the basic process of this levelconsists of the emergence of order out of randomness through rotating vectors.

Ultimately, there is a primordial zone of un-patterned random activity whoseactants are called primons.

Extending the Creatant line upwards yields the social group as an actant and atcultural level, humanity is the actant. Both of these levels are more complex and moremassive than the biological level of cells.

This system was developed by the empirical observation of a regular jumpbetween actons representing a set of commonly recognized levels. When the standardinterval is marked off along the Creatant line, the resulting masses fit the empiricalobservations quite closely.

(PLATE 2)

C. Nested Curves

If the Creatant is pivoted around the point representing the cultural level, then aninverted "V" shape is formed. Then, as mass increases, organization decreases. This

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represents the levels of astronomical activity. As size becomes larger, the actantsbecome simpler and more elemental. Ultimately, the stage upon which the entireuniverse rests consists of primons in random constant motion.

Taking common projections of the age of the various actants, a relationshipbetween time and organization emerges. Basically, older actants are simpler. Both massand organization are seen to increase from the remote past to the present. However,when the cultural level of the present is passed, the pattern inverts and organizationdecreases as the future is entered. In the far reaches of the future, the most elementalactants are found.

At a particular level, the actants are distributed over a normal curve with respectto variation. The normal curve emerges at each level as the basic form. If the normalcurves for all the levels are nested and rectified, a triangle figure appears which is calledthe Mass Time Triangle.

(PLATE 3)

D. MTT Graph

This Mass Time Triangle (MTT) is an excellent graphic device for compactexpression of the Pan-Acts model. It makes the important relationships visual and is agreat aid in understanding the model.

The sizes of actants of various levels are ranked on a scale which ranges from10-77 tons to 1099 tons. The kinds of actants represented include primons, curvons ofpatterning, gravons of space, quanta of energy, atoms of matter, living cells,multicellular entities, communities of entities and symbol-using cultures.

The span of time reaches 1018 centuries into the past and future, covering a totalspan of 1036 centuries. The range of organization reaches from the totally randomprimon level to the totally ordered unit symbol for the whole universe, (U0 =1).

Special stages of time, which represent two level jumps, are the Motional,Material, Vital and Verbal. Special zones of organization are the Spatial, Material,Human, and Real Universe. These zones interpenetrate to a great degree.

(PLATE 4)

E. Key Periodic Table

Scientists have pinpointed a number of key constants. These include i (squareroot of a minus one), γ (inverse of the Euler-Maseroni constant), r (statistical constant), h (one half of the coefficient of Planck's constant), and π (ratio of circumference of a circle to the diameter). Pan-Acts has shown that these five constants can be derived asbasic functions of the Creatant line, C.

Four basic combinatoric formulas have been found to be useful in deriving furthercore constants for scientific use. These four formulas are 2n (self-sum), n2 (self-products), 2n (set-powers), nn (self-powers).

The result of applying the four formulas to the five key constants yields asystematic table of major cosmic constants including the Speed of Light, Gravitational

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Constant, Faraday’s Constant, Fine Structure Constant, Planck's Constant and manymore. The fit of the generated constants to the commonly accepted values is within .4%.It is such a close fit that this system of generation must be an important insight into thenature of our universe.

This periodic table of constants helps to predict the spectrum of radiant energy,the periodic table of the elements, the DNA double helix, .stochastic processes andother important scientific concepts.

(PLATE 5)

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III Explaining The Past

A. Pair Permuted Interacts

In order to explain the origin of space, the Pan-Acts model postulates a cloud of1077 infinitesimal bits of energy 10-71ergs each. These primons are in constant randommotion. Any unit vector drawn from any origin point establishes an ordering of theprimons through which it passes. Given the random motion, the order and hence thevector will be reversed in a finite period of time, (t). In a time equal to 2t, the order andthe vector will reverse again and return to the original orientation with a probability ofunity. Thus, a cloud of random primons will generate an oriented vector space.

When the unit vector is reversed, each pair of points is transposed and thus theprocess can be expressed in terms of the gamma function for permutations, Γ(n) = n!/n. The reversal represents a half cycle which can also be expressed in radians, Γ2(1/2) = π radians. Upon full reversal, the expression becomes π + π = 2π. Repeating c cycles forms a super cycle of radius c equal to 2πc. If the new unit radius is taken to be c, then the new cycle is 2π. Taking the self product of the cycle (c = 1) gives 4π 2 which is equalto the Gravitational constant, G = 4π 2.

Thus, randomly interacting primons will generate an oriented vector space andself products of the vector space generate a curved space with gravity.

(PLATE 6)

B. Entropic Processes

The first levels of the Pan-Acts model are seen to be connected by cyclic self

products. The general equation y = e-2 |t|develops the entropic curves of growth and

decay as studied by Gompertz. This ∫ shaped curve illustrates the accelerating and decelerating change found in self-related growth and decay of biological systems.

The Pan-Acts model states that each successive higher level is the result of pair-permuting or entropic growth process from the preceding level. Taking eight stages ofoperation, the eight levels of the model are developed. This process is reversible andhigher levels are seen to devolve into lower levels via the same equation with a reversalof sign in the exponent.

This model explains the origin of a given level as the operation of the Gompertzentropic process at work on an adjacent level. Lower levels organize into higher levelsby negentropic growth and higher levels disorganize into lower levels by entropic decay.

(PLATE 7)

C. Reiterings Matrix

The four rows of the Reiterings Matrix develop, respectively, symbols, syntax, keyprocesses and cosmic laws. The first row explains the origin of symbols throughrepetition of any actant; combination of the actant -with a name; permutation of the order

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of the name and the actant; and interacting these operations in the activity of speech.The second row explains syntax through listing into sets; adding into sums; multiplyinginto products; and self-multiplying into powers. The third row explains four keyprocesses in terms of self-sums or pairs; self-products or squares; pair-powers ornorms; and self-powers or fulfillments. The fourth row yields four cosmic laws ofpredicting the future; describing the present; explaining the past; and understanding theoperation of the Cosmos.

The four columns of the Reiterings Matrix develop, respectively, prediction,description, explanation and control. The first column deals with predicting futureconsequences through repetition of actants; listing into sets; self-summing into pairs(2n); and creating a helix of future cycles [(eπi)2n]. The second column deals withdescribing present contents through combining actants with names; adding into sums;self-multiplying into squares (n2); and creating a normal distribution of present

probabilities [(e-.5)n2]. The third column deals with explaining past causes through

permuting the order of actants and names; multiplying into products; pair-powering into

norms (2n); and creating entropic-curves of past growth [(e)2n]. The fourth column deals

with controlling changes through interacting of speech elements; self-multiplying intopowers; self-powering into fulfillments (nn); and n creating combinatoric curves of self-

governing [(e)nn].

The log factors of 2n,n2,2n,and nn in row three reveal the profound connectionbetween past, present, future and eternity. Rows and columns are developed fromprevious rows and columns by definite operations.

(PLATE 8)

D. Unit Cube

The Unit Cube is an aid to visualization of the Pan-Acts model. The three axes ofthe Unit Cube are Activity, Organization, and Time. The Activity axis extends over 10100

primons. The Organization axis measures in bits the nine levels of cosmic phenomena.The Time axis is 1032 years. Each axis in log terms is taken to be unity with any positionon any axis dividing it into fractions P and Q which add to equal unity,(P+Q=1).

With each edge as unity, each face diagonal is equal to √2_

and the cube diagonal

is equal to√3_. These three root numbers (√1

_,√2

_,√3

_) build up the key constants. In a

general n-dimensional, √n_

represents the n-dimensional diagonal of the unit rectangular,rectilinear polyhedron.

The graph is illustrated by the Unit Cube to be an integrated whole. Action isseen as organized energy (c) in time (t), (a/ct=1). This compact model explains theevolving and devolving of the Cosmos in terms of three related axes and fractionalratios. Any particular phenomena whatever can be represented by a point or region inthe Cube.

(PLATE 9)

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E. Gambit Benchmarks

The diagonal of the Unit Cube is √3_ which will be designated as γ1. When γ1 is

self-multiplied to an integer power m (m=1, 2, 3, 4), the result is called a gam ( γ 1m). This

power series of √3_

yields 1, √3_

, 3, 3√3_

, 9.When gams are exponentiated to the base 2, a series of single gambits is

generated, (2γ1m

). The first gambit is 2√3

-- 0

= 2 and represents the basic bit or binary

choice. The second gambit is 2√3

-- 1

= 3.32193 and is called the Root Creatant (h) which isthe bits log of 10 (h=lg 10) and measures the relation between base 2 and base 10

number systems. The third gambit is 2√3

-- 2

= 8 which shows the number of real levels inthe Cosmos as well as other phenomena which contain octaves. The fourth gambit is

2√3

-- 3

= 36.651 called the Cubit which is the cube of the Root Creatant (h3) and equal tothe creation rate expressed in bits which measures the inter-level quantum jump

throughout the hierarchic Cosmos. The fifth gambit is 2√3

-- 4

= 512 which is the bits log ofthe real spatial universe of seven levels.

When gambits are exponentiated to the base 2, a series of double gambits isgenerated. The first double gambit is 22=4 which is the simplest unit of the Gompertzgrowth and decay curves. The second double gambit is 2h=10 which is the root of thedecimal number system. The third double gambit is 28=256 which measures the TopAtom or the bits log of the half-universe; the real and rising spatial universe. The fourth

double gambit is 2h3

= 1011 which is the speed of light in the standardized Pan-Acts units

of millimeters, tons and thirds of a second. The fifth double gambit s 229

=10154 which isthe size of the spatial universe.

Thus the gambits generate with rising powers of m, ten constants or benchmarkson a rising log gradient of bits or organization of Cosmic action. The single gambits dealwith logs, systems and sets. The double gambits deal with natural numbers, subsystemsand elements of sets.

(PLATE 10)

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IV Predicting the Future

A. Polar Versus Rectangular Coordinates

The classical Cartesian coordinate system expresses interacting variables interms of two perpendicular axes. Coordinates and curves can be translated into thesystem of polar coordinates by the formula e2πirt= cos 2πrt + i sin 2πrt. One dimension becomes a set of concentric rings measuring angle and the other dimension becomes aset of radiating lines measuring distance.

When the Creatant line is restated in polar coordinates, it becomes a cycle. Thiscycle can be expressed as 2πr where r is the radius. It can also be expressed as 2π times r unit cycles. Now the Creatant line is a helical coil where each turn represents alevel of Cosmic action. Thus we arrive at a projection system where recurrence ofconditions brings recurrence of patterns of action.

The relationship between polar coordinates and rectangular coordinates parallelsa number of interesting relationships. One such relationship is that between logarithmsand integers where a curve line on an integer plot becomes a straight line on a log plot.Other interesting relationships include the curval versus the linear, multiplication versusaddition, sensation versus cognition and log time versus antilog time.

(PLATE 11)

B. Schwarzschild Dimensional Ratios

Mass, length and time are fundamental to our understanding of physics.Schwarzschild derives these concepts from a set of constants including the Gravitationalconstant (G), the speed of light (C), and Planck's constant (h).

The unit of free mass is Mu = √Ch/G = 5.45707 X 10-5. The unit free radius of Mu

is Lu = √Ch/G3 = 4.04989 X 10-33. The Shuster period of Mu with Lu is Tu = 2π√Ch/G5 =8.48795 X 10-43.

Taking the ratios of Mu, Lu and Tu yields powers of unit free velocity (Vu

m). In

section III-A, G was shown to be equivalent to 4π2. Vu1

= Lu\Tu = (GhC5/C322π2Gh).5=

(C/2π)1. Vu

2= Mu/Lu = (ChC3/GGh).5 = (C/2π)2. Vu

3= Mu/Tu = (ChC5/GGh22π2).5 =

(C/2π)3. Vu

4= MuLu/Tu

2= Fu which is force. Vu

5= MuLu/Tu

3= Pu which is power. Thus we

can represent velocity, force and power in unit free dimensions as a power series of Vu

m

, (m =1,2,3,4,5).

A three axis matrix can be formed where Mum

, Lum

, and Tum

are the axes. Sinceevery formula of physics can be re-expressed in unit free dimensions and since thissolid matrix MIII has a cell for every possible integer dimensional formula, the matrix canbe seen as a periodic table for physical formula.

Taking a log unit cycle (e2πi =1) as the sun time, Tu can be equated to 1. Solving

the Schwarzschild ratios as a set of simultaneous equations, then Lu = Tu2

. Solving for

Mu, Mu= Lu

3. The log relationship of length to time is logLu = 2logTu. A series of binary

powers can be associated with these log relationships so that 1 is time (20), 2 is length

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(21), and 8 is mass (23). These binary numbers can be used to calculate a binarynumber N (2N bits) for each logarithm dimensional formula in physics. These binarynumbers can be associated with each cell in the three axis matrix, MIII in the same waythat the atomic numbers fit in the periodic table of elements.

By shifting our language, all formulas of physics can be freed of the number andnature of their particular units by being re-expressed as dimensional formula. The newformulas can be re-expressed again in interdimensional units of set theory andcombinatoric algebra as the power set 2m. For large m, 2m measures the area under thebinomial and normal curves. Forming normal curves begins to organize law and orderout of random actants at every level of the Mass-Time Triangle which measures Cosmicevolution and devolution.

(PLATE 12)

C. DNA Helix

The structure and function of living beings are defined by the chromosomes in thenuclei of their cells. The chromosomes contain genes which are composed of DNAmolecules. These molecules are shaped like ladders twisted into double helical coils.The sides of the ladder are alternating deoxyribose and phosphate units. The rungs ofthe ladder are pairs of four bases which are adenine, thymine, cytosine, and guanine. Itis the sequences of these four bases which forms the genetic code. When taken intriplets, these bases select a particular amino acid from the set of 20 amino acids whichare the building blocks of all proteins. Although there are 64 possible triplet codes, thereare only 20 amino acids. More than one code sequence can designate the same aminoacid.

RNA is the translation mechanism which reads the DNA code and then organizesamino acids into the proper sequences to form the proteins which act as structures andorganic catalysts called enzymes in the living being. Each protein has its own uniquesequence of amino acids and the average protein contains 100 amino acids. Anaverage DNA molecule in a bacterium can contain codes for 330,000 amino acids whichcould specify 3,300 different proteins. The possible number of different proteins is 20100

which is a number so great that the universe does not contain enough matter to form oncopy of every single possible protein. The actual number of biologically useful proteins isbetween 5,000 and 10,000. This is, of course, an estimation based upon our knowledgeof Earth biology. The possibility exists that other planetary environments might utilizeother sets of proteins. The estimated number of possible proteins and possible planetsis so great that one is forced to conclude that life is a universal and diversephenomenon in the universe.

(PLATE 13)

D. Staggered Cohorts Hypothesis

The concept of feedback' is extremely important to the understanding of dynamic

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processes where the output of the process influences the functioning. Feedback plays avital role in automation engineering, ecology, biology, psychology and many other fields.

A set of actants in subsets called cohorts are defined by successive periods inwhich they start a set, of sequenced acts called phases within a set of time periodscalled a cycle. Interacts in one period of more mature cohorts upon less mature cohortsdefines feedback in the Pan-Acts model. Interacts in one period of less mature cohortsupon more mature cohorts defines feedforward. Interacts in one period of equallymature cohorts upon each other defines feedin. Thus sets of N randomly interactingactants in time sequences will naturally organize orderly stochastic laws in reiterantpatterns, measurable in bits of action.

The staggered cohorts hypothesis predicts the cybernetic processes of feedbackand feedforward which are so important in understanding time dependant processeswhich are self-influencing.

(PLATE 14)

E. Pan-acts-theism

Pan-act-heism is an attempt to provide a scientific basis for religious concepts.Religions deal with some ultimate power, usually called God, which organizes andmaintains the Cosmos.

The Pan-Acts model states that all actants interact randomly, ceaselessly andreiterantly, forming and unforming in their overlapping cohort life cycles all their nn

possible combinations, permutations and repetitions. They continually organize theCosmos and all actants therein as hierarchic normal distributions at nine levels. TheCosmos is self built by vast stochastic processes at a Creatant rate C = lg210 = 11

during each cohorts life cycle of 1032 or er'r' years. Pan-act-theism equates the ultimate

God with the Cosmos itself.This view of the Cosmos contains the following implications. The Cosmos is self-

creating by the past interacting of actants through successive self-products in Gompertzcurves of ± entropy. The Cosmos is self-maintaining by present combinatoric interactingof actants as described by binomial and Gaussian normal probability curves. TheCosmos is self-directing by future cycles of actants as predicted by ruler's helix curve.The Cosmos is self-fulfilling by anytime reiterant organizing of actants as controlled bySterling's combinatoric formula. The Cosmos is self-sufficient as summarized by Dodd'srectified Pan-Acts equation, a/ct= 1=U0

It is hoped that Pan-act-theism can assist the integration of religion and sciencein the service of humanity. Science could become the intellectual research about what ismost important to man while religion becomes the emotional motivator of all man'sactive decision making for a positive future.

(PLATE 15)

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IV Predicting the Future

A. Combinatoric Interactions

The behavior of all actants at all levels in the Cosmos follows a small set ofregular processes. These processes have been described in III-C under the ReiteringsMatrix. The general behavior of the Cosmos can be understood in terms of these self-reiterings.

Self-sets deal with all counting and all ordered pairs of actants,(n0). Self-sumsrepresent the simplest combining of Cosmic infrastructure, (2n). Self-products yield thetransition formula between levels of the Cosmos, (n2). Pair-powers produce the set of allcombinings of n things or the family of subsets of a set of n actants, (2n). Self-powersexhaust the fulfilling of all combinatoric possibilities of a set of n actants, including allcombinations, permutations, and repetitions, (nn).

Self-cycling of the log of base eπi produces the helix of n coils in the DNA of allliving creatures, (eπi)2n. Self-squaring of the log of base e-.5 produces the standard

normal curve which can be rectified into the MTT graphing all Cosmic actants, (e-.5)n2.

Successive self-squaring e explains the Cosmic evolution and devolution of each cohort

of actants, (e)2n. Self-powering the log of base e produces a self-governing model which

fulfills all the nn combinatoric possibilities latent in any n actants, (e)nn.

Therefore, nn represents the fulfillment or design of the Cosmos. All Cosmicactants interacting at the Creation rate through four stages of time measure, make andmanage the Cosmos.

(PLATE 16)

B. Constant Features

Science has discovered four important constants of the materialuniverse. The number of particles (Nu) in the universe is estimated to be 14 X 1078. Theforce constant (Fu), which is the ratio of the nuclear strong force to the gravitationalforce, is estimated to be 2.3 X 1039. The age of the universe (Tu) in atomic time units(1022 = 1 second) is estimated to be 3.2 X 1039. The Gravitational constant (G) is equalto 39.4784 in astronomical units. These four constants seem to be fundamental to thenature of the universe we inhabit.

The Gravitational constant (G) seems to be of central significance in this group ofconstants. The logs of the other three constants are as follows; log Nu = 39.5682, log Fu

= 39.3617, log Tu = 39.5051. The average of these logs is found to be 39.4783. Thisaverage is only one part in one million different from 39.4782 which is the value of G. Inview of the fact that these numbers are based on accepted estimates, it is interesting tonote such a close fit.

These four constants can be translated into combinatoric terms of the Mass-TimeTriangle. The square root of the number of particles can be represented as the numberof material actants (AD) at level D measuring Cosmic action. The force constant can berepresented as the bits-log difference between Phase D and Phase H which is a

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measure of Cosmic organization (OrD). The age of the material universe can berepresented as the time interval between the present and the beginning of the materialuniverse. The Gravitational constant can be represented as the Cosmic Quantum ofhierarchy (Q) which measures the interlevel interval in the MTT. Thus, the stochasticevolutionary gravitational process is tightly related to the total content, organization andage of our universe as explained in the Pan-Acts model.

(PLATE 17)

C. Social Modeling

The Pan-Acts model of the Cosmos can be translated into sociological terms foruse in social modeling and planning. The symbolic level becomes symbolic records. Thesocial level becomes valuation in all preferences and policies. The human levelbecomes the people involved. The life level becomes activities. The material levelbecomes all equipment and materials. The energy level becomes the timing ofschedules and sequences. The spatial level becomes all locations. The curval level isreserved for residual circumstances not covered by the other categories.

A community can be analyzed in terms of eight institutional groups. The familyconcerns itself with populations. Education utilizes media in shaping opinions.Economics covers industrial activity. Politics involves intergroup relations, includingmilitary. Religion includes ethical and philosophical questions. Health reveals thephysical welfare of the population. Recreation covers entertainment and the arts.Science is the domain of technology. These eight institutional sectors permit acomprehensive approach to community.

The set of personal transacts translated from the Cosmic levels can be arrayedon an axis. The set of eight institutions can be arranged on an axis perpendicular to thefirst axis. A third perpendicular axis can be constructed from a division of time into foursections. The past section is dedicated to explanation. The present section is dedicatedto description. The future section is dedicated to prediction. The final section extends toall time and is dedicated to control. The resulting matrix permits the analysis of thebehavior of a society in detail.

(PLATE 18)

D. Applications of the Power Parameter

The transcendental log factor m seems to measure the power parameter of theCosmos. M grows by integers to 4 (m=0, 1, 2, 3, 4) and denotes the first five powers orthe successive self-products of its basal actant (A). This measures the successivestages of organizing all Cosmic interactions, (log A). The Pan-Acts model contains adozen domains that have been analyzed in terms of the log factor m.

This subsection deals with some of those domains and the order of factorsmentioned will follow the sequence of powers of m. In terms of moments of frequencydistribution, the sequence yields the frequency or area, the mean or central tendency,the variance or dispersion, the skewness or asymmetry, and the kurtosis or unimodality.

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With respect to categories of systems theory, the sequence yields qualities, quantities,relations, systems, and supersystems. In scientific disciplines, the sequence found ischaos theory and cybernetics, geometry and astronomy, physics and chemistry, biologyand psychology, social science and semiotics. In the sphere of societal ideals, thesequence can be freedom, progress, equality, justice and unity. The power series of mcan be crossed with the dozen domains to yield a matrix of 60 cells of systemic crossreference.

M seems to be a simple integer exponent governing the universal development ofeverything namable. M measures broadly the steps in evolving and devolving of everycohort of actants in the Cosmos. It implies that logarithms measure Cosmic organizationor that the Cosmos seems logarithmic.

(PLATE 19)

E. Testing the Model

It is explicitly understood that the models of science are continuously being testedand improved. No model is seen as being ultimate or complete. When two or moremodels cover the same phenomena, they can be distinguished by relative accuracy,elegance and utility. Throughout the development of the Pan-Acts model, it has beencomprehensively tested in a number of ways.

Consistency tests measure the internal logical agreement in the statements of themodel. The Pan-Acts model contains a high level of internal consistency which revealsan elegant set of relationships between Cosmic processes. Correspondence testsmeasure the external empirical agreement between expectations of the model andexperimental results. The Pan-Acts model has been shown to be accurate in manypredictions to a few parts in a million. Concordance tests measure the agreementacross time between the model's performance and the aims of science. The Pan-Actsmodel provides many useful tools for explanation, description, prediction and control.Convergence tests measure the percentage of full agreement among all the tests of themodel. The Pan-Acts model scores well on all the tests.

The Pan-Acts model of the Cosmos goes beyond all other published models ofthe Cosmos. It has specified more empirical quantities more accurately. It has revealedmore principles of operation and their interconnection. It has formulated more usefulapplications. It has been stated in more forms and in more levels from overview todetail. In general, the Pan-Acts model has been critically tested in depth by its creatorfar beyond any other comprehensive model of the universe.

(PLATE 20)

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IV Pan Acts Culture

The last four sections of this paper have dealt with the four aims of science. In thesecond section, an attempt was made to describe the present nature of the universe interms of normal distributions. In the third section, the past development of the universe wasapproached in terms of exponential growth and decay. In the fourth section, the futureevolution of the universe was projected through helical cycles of recurrence. The fifthsection covered the combinatoric principles that govern all universal processes throughtime. Thus, the four aims of science were connected to specific mathematical tools.

The first section of this paper discussed the four social functions of a Cosmic model.With respect to the four aims of science, the model must serve these four aims in each ofthe four social functions. The universe must be described, explained, predicted andcontrolled. The social fabric must be described, explained, predicted and controlled. Thedevelopment of the individual must be described, explained, predicted and controlled.Finally, the integration of waking consciousness and altered states of consciousness mustbe described, explained, predicted and controlled. The last section of this paper will developthis integration of the aims of science and the functions of a Cosmic model.

Any functional society must have some model of the actual world in which it exists.As a society increases in complexity, size and technology, the model must develop in asimilar fashion. In a huge industrialized society, the model of the universe must be a veryaccurate representation. Science serves as the universal model for industrialized nations.

The Pan-Acts model of the Cosmos is an extension of science. It covers allphenomena studied by the sciences and employs a rigorous mathematical foundation. TheCosmos is described in terms of nine levels of activity. On each level, large numbers ofactants yield a normal probability distribution with respect to a particular characteristicunder study. The origin of the present systems is explained as the integration of actants intohigher level actants or the disintegration of an actant into lower level actants. Theseprocesses are governed by entropic growth and decay curves. The future behavior of theCosmos is predicted in terms of helical cycles of repetition where repeating circumstancesyield repeating effects. Throughout past, present and future, the behavior of the Cosmos iscontrolled by the laws of combinatorics. Actants combine, permute, and repeat in theexploration of possibilities inherent in a group of actants.

Pan-Acts modeling sees the Cosmos as a continuously evolving and devolvingwhole which covers all possible combinations of actants. The Cosmos is self-governing,self-creating and self-fulfilling. This model is sufficiently comprehensive to permitinterdisciplinary integration of the sciences and simultaneously sufficiently detailed enoughto permit further development of specific technologies.

A society is partially defined in terms of the role structures and interaction patterns ofits members. As societies grow in complexity, more roles are required and interactions mustbe developed in greater detail. The big nations of the earth employ a variety of socialsystems. Some are the result of historical tradition and some are the result of historicalaccident. All have been shaped by the efforts of those in power to redesign the role systemto permit necessary social change. There is no agreed upon framework for an optimum oreven satisfactory social framework.

The Pan-Acts model contains a submodel for sociological systems as given in

Pan Acts Theism

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subsection V-C above. No particular social role system is given by the Pan-Acts model. Theframework of transacts which mirrors the nine Cosmic levels and the eight institutions whichdetail a community are parts of a methodology for exploring any societal system. Anydescriptions of a social system will include normal probability distributions of characteristicsacross individuals and institutions which preserves the variability inherent in the Cosmos.Explanations of existing social systems will reveal entropic growth and decay processeswhich create and destroy social organizations. When a particular social situation isrepeated in great detail, the model predicts that the results will be repeated also. All socialsystems and situations are influenced by combinatoric processes which explore variouspossibilities inherent in them.

Perhaps there exists no optimum or universally acceptable social system. The Pan-Acts model provides the basis for analysis and synthesis of any number of different socialsystems. It also permits cross comparison of different systems. The greatest benefit of thePan-Acts model for sociology lies in its ability to facilitate the exploration of different socialsystems in an ongoing effort to discover better ways of organizing human societies.

The integration of the individual into society is another function of a societal model.In simple small societies, such integration is easy and effective. As societies increase insize and complexity, such integration becomes a growing problem. As each individualdevelops, a sequence of important changes marks off different stages of life which involvedifferent roles. These changes include birth, puberty, marriage, membership and death. It isvital for the mental health of the individual that these stages are clearly understood andaccepted in terms of the societal model.

The Pan-Acts model describes individuals in terms of characteristics which are foundto form normal distributions across large numbers of individuals. This reveals individualsvariability as a natural consequence of the function of the Cosmos. The origin of theindividual is explained in terms of exponential growth of cells under the guidance of DNA.The death of an individual could be an entropic decay of cellular processes. The Pan-Actsmodel predicts that the same developmental changes will usually result in the same stagebeing reached. Throughout the development of an individual, combinatoric processes guidethe working out of the potential of the individual. The basic principles of interaction in themodel are reflected in such personal interactions as marriage and membership in familiesand other social groups.

The Pan-Acts model provides a rich framework for the individual's personaldevelopment and integration into society. It permits the individual to see the function ofCosmic laws in personal development and social relations while preserving that individual'sunique nature and fulfillment of potential.

Most societies recognize the existence of different states of consciousness. Mostsocial interaction takes place in the ordinary waking state. Important personal and socialevents can take place in other states of consciousness. Dreaming, delirium, drugged andcontemplative states of consciousness are linked to creative insights in the arts, sciences,philosophies, and religions. The last important function for a societal model is the revelationof the relationship between ordinary consciousness and these altered states.

Pan-Acts modeling provides unique opportunities for consciousness explorationthrough a framework which includes all physical and psychological entities and events.Detailed description of states of consciousness with respect to different variables will yield anormal distribution across time and individuals. This approach will emphasize the variability

Pan Acts Theism

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of consciousness in a particular state. Explanation of personality integration anddisintegration can be approached as growth and decay of particular connected sets ofconsciousness variables. The model predicts that recurrence of a constellation of variableswill lead to a recurrence of a particular state of consciousness. Across time, thecombinatoric approach suggests that consciousness is the ability to be aware of a particularpattern in a Cosmos which contains many potential patterns.

The Pan-Acts model contains nine levels of Cosmic phenomena. Ordinaryconsciousness is that state which focuses upon the local actants of the nine levels and thesocially approved manner of dealing with them. Altered states of consciousness rangebeyond this local orientation to explore other patterns in the Cosmos. Such exploration maybe of ultimate benefit or harm to the world of ordinary consciousness but such exploration isvital for the evolution of society in a changing world. Pan-Acts modeling is well suited todirecting this exploration in a comprehensive and coherent manner.

The growing movement in General Systems modeling is extremely important tohumanity in this era. Only comprehensive models such as the Pan-Acts system have thenecessary scope and integration to serve as the framework for a planetary social system. Itis the belief of the authors of this paper that Pan-Acts modeling can make valuablecontributions in all areas of social function for the development of a humane, ecological andevolving planetary society.

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PLATES

Pan Acts Theism

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Plate 1: How Arraying Masses Discovers Cosmic Periodicity,

Log Cn = c =.. 11

SD: 69-26R by S.C. DoddEpiDoc 154R Univ. of WashJune 1973 Seattle, 98105

This graph discovers a periodicity, or "quantum-like" jumps of 11 log cycles of mass(called "Cn") between smallest entities in the 4-level range of material organization from

minimal at the electron (10-33 = Cn

-3) to maximal in society (100 to 1011 or Cn

1)

This Cn - factor seems to measure the inter-level jumps in average organization ofcosmic actants. It seems to represent one eon or log century of Earth years interpreted so it

produces a constant cosmic Creation Rate Cn=10c= =.. 1011 of actants organized per level or

eon. Then ±c defines the slopes or 2 sides of the Mass-Time Triangle.

At the Electron Point (D' in the MTT) this Cn=1011 translates into the Speed of Light (in

mm per third of a second units) by Einstein's formula E/M=C2, expressing a transition ratio

between radiant energy and the threshold unit (called an "acton") of mass.

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Pan Acts Theism

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Plate 2: Plotting Material Entities by Mass vs. Organization Rank

SD: 69-27 by S.C. DoddEpidoc 155 Univ. Of W ashJune 1969 Seatt le, 98105

This develops :

1) A cardinal scale of cosmic organizat ion (in bi ts lg a), the ordinate;2) Extendib le to an 8 leve l un ive rse (where t=8, as below) ;3) Correlated wi th past t ime periods (or ages, t , to date);4) Yielding a constant log growth rate, c, (= log cn= lg210=11.03522);5) Their synthesis in the epicosm equation, a t = ct, which says: cosmic

activi ty, α, at any level t, equals i ts growth rate c, x t ime taken, t.

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Plates 3 & 4: The Mass-Time Triangle (MTT) Model of the Cosmos = U0 =1

Dimension of Cosmos

25

Plate 5a: The Key Periodic Table, sks, Generating Cosmic Constants”

By Stuart C. Dodd, Ph.D., Emeritus Research Professor of Sociology,University of Washington, Seattle, Washington 98105

A paper for the International Congress of Cybernetics and Systems at OxfordAugust 28 – September 3, 1972

If cosmos is defined as the universal set, U0 = 1, of all things-namable, called “actants,”and if each actant is viewed as an item of organized Action(= Energy X Time, dimensionally),then the resulting Key Periodic Table, sKs, (see below) describes the current contents of thecosmos in a 5 X 4 matrix (within a half percent tolerances of discrepancies in fits), Its 20 cellssystematize the major cosmic constants (e.g. e, π, i, γ; G(gravity), C(light), F(Faraday’s constant), α (Fine Structure constant), h (Planck’s constant), etc.).

This matrix generates invariant combinatoric patterns of interactants (called “constants”)as explained by the set-product or intersect of:

5 input Key constants, i.e., Ks = { γ, π, h, r, I }; and

4 thruput Key operations or cycles of cumulative reiterating, i.e. Ks = { Self-sums, 2n;Self-products, n2; Set-powers, 2n; Self-powers, nn }; with

20 output cells recording 20 “core” constants -- and systematizing many more.

This Key Periodic Table, bounding four periods of cosmic evolution in every cohort ofactants, helps to predict (in cells, arrays, or compounds):

a) the physicist’s spectrum of radiant energyb) the chemist’s periodic table of atomic elements,c) the biologist’s double helix in the DNA chain molecules of all living cells,d) the statistician’s random stochastic processes,e) the semanticist’s complex number algebra for speech and consequent mental

activity.

These Key constants are basic functions of the Creatant Rate, c.

(i.e., c = 41/y0 = π π_

= h'

2= 2

r' =.. i-16r = logCn = 11.03522)

c controls continual creation and perpetual cybernetic operating of the cosmos by the“Epicosm Equation”, U0 = 1 = a/ct (a = log of the number of actants at the tth period).

Plate 5b: Scientific Aims

Plate 5c: Derivation

SCIENTIFIC AIMS of this “Epicosm Modeling”These semiotic keys, k, may help scientists in:Describing cosmos, u0 = a/ct = 1, as selfExplaining cosmic, as self-powers: nPredicting mind & matter, as selfControlling cosmos more, as self

5 Key constants bound 5 stages of cosmic evolving

5 stagesin cosmicevolving anddevolving

Their rankincomplexity

HVerbal StageSymbol Level AiSociety Level A

a

I

Vital StageMan's Level BLife Level C II

Material StageMatter Level DEnergy Level E III

Motional StageGravity Level FEntropy Level G

IV

Infinitesimal StagePrimal level H

V?

parameters of5 binomial curvesare shown in 5stage rows

Org bits

Dimension of Cosmos

26

Plate 5b: Scientific Aims

of this “Epicosm Modeling”semiotic keys, k, may help scientists in:

= a/ct = 1, as self-sums: 2n

powers: n2

matter, as self-powers: 2n lg n

Controlling cosmos more, as self-fulfillings: nn

stages of cosmic evolving

Their rank

complexity

Theirage inYears

T

Min. actionin ton

equivalents

M

5 SKey Constantsas syntactic predictors

Names Formulas Converters

b100

102

104

c1011+11i

1011

100

d

i

e= imaginary= √-1= eπi/2

•106

108

•

10-11

10-22 r= “crux”

= lg C= lg c= 3.46404

1010

101210-33

10-44 h= root-"creatant"= lg 10=3.32123

1014

101610-55

10-66 π = Pi= Γ2

(1/2)

=3.14159

101810-77

2256 γ -2

=Euler’sconstantssquared

3

Org bits

TimeCycles

Actant sets

Keyconstantsboundingstages

Name,formula andsize of key, K

Key Constantsas syntactic predictors

Names Formulas Converters

= imaginaryf real to iimaginaryCartesian to polarcoordinates

“crux”

= lg C =.. √12

= lg cL /h3.46404

creatantto bitsnumbersto δ

-"creatant"= lg 10

3.32123

tens totwos orbits, lg2

(1/2)

=3.14159

negative topositivediameter tocircumference

Euler’sconstantssquared

Continuous todiscrete

Name,formula andsize of key, K

Domainconverters frombase B1 to B2

Dimension of Cosmos

27

The 5 Key Constantsbelow can all be derivedfrom the enumerativegenerator: EG

DERIVATION: This TABLE IA shows a set product of 5 “keyconstants”, SK, x 4 self-reiterant “key operations", KS, as simplestcombinatoric processes if m = 2 in repeating (mn& mm), permuting(nm), combining (mn).

4 Key Operation, KS

EG = ((n+1)/n)n

As belowIf n is largeEB = e = 2.71828

self –sumsPairings

2n

self-productSquarings

n2

pair powersNormings

2n

self powersFulfilling

nn

If n = -.5EG = ((-.5+1)/-.5)-.5 i

=1/i

g2i

= paired image.= 2i= (1+i)2

h12

= sq. image.= -1=√1

Ii2i

= polar bit=2= 1 “i-bit”

jii

= fulfilled= e- π/2

= ci=ii(-16)=ce

If n = +.5 rEG = ((+.5+1)/+.5)+.5 r=√ 3 = γ, 2γ =r

2r="paired crux”= 6.92808=lgc2=lg4r

r2

=rectangularvariance ratio=12= lg2c

2r=crux-bits.

= c=11.03522

cn=102r= c102

h

=c , 2h

rr

=fulfilled r=73.96387=lg cn

2=2h3

If n = +.5EG = ((+.5+1)/+.5)+.5 h=√3 = γ, 2γ = h

2h=Planck’sconstant= 6.64386

hp 2h

h2=”creatant”= c=lg2 =11.03522

=cL=10 h2= 10c

2h

=ten-in-bits=10.00000=2lg10 =10

h h

=fulfilled h=53.95409=10√2 =√2 rh

If n = +.5EG = = γ,= γ-1 ππ/3 = γ3/3 + γ5/5- γ7/7

2π = circumference= 6.28318=ce =e2π * 4

π2

= sq. circle= 9.86960= π2=πΓ2(1/2)

2π

= 1/10 log ofcomplete univ.= 10.00000=2 lg 10=10

π π

=fulfilled π = 36.46023cL/3 h3

If n = +.5 (i.e. minimal)EG = ((+.5+1)/+.5)+.5 γ=√ 3 = γ

2γ-2

= paired squaredgamma= 2 * 3 = 6= r √ 3

γ-4

=discreteconverter -4

= 3 2 = 9= (r / 2) 4

2γ-2

=inv. γ 2 bits=23 = 8

=2(γ/2) 2

γ--2γ-2

=fulfilled γ—2

= 33 = 27

= (lg2h) lg2h

If n is -1 EG is 00 11 2-2 4

Threshold ofeach stage“quantums”

Variance ofeach normalcurve

Areas undernormal curves

Fulfilled cyclesof N actants

Dimension of Cosmos

28

Plate 5d: Social Uses

SOCIAL USES of this man-symbol-thing system:These keys may help society to unlock better know-how re n actants interacting in nn waysdepending on their internal organization levels & external relevant context from past tofuture & on better symbolizing to help fulfill man: nnp

KeyCon-stants

How simplest* compound keys fit# empiric constants*2 out of 100+ now known #with 99.6% + agreement

2n2

= paired squares=stage meanings

4n2

= squared pairs=stage ranges

e5 key constantsas empiric predicteds

Names % misfits Exact values of eK

ik

2i2 = -2= speech bit

l4i2 = -4

= speech bit bit

m n o p

0 % Δ : =def.

4i2 = -4, a bit bit= I = knowledge unit constant=naming a name.

r2r2 = 24log 2N0

N0= Avogadronumber

4r2 = 48(also lg Ffaraday'sconstant= F)

--- +.08% Δ =F = lg Faraday’s Constant

h2h,2 = 2c=

“macro-crux”=f(log(2c)!)=22.07044

4h,2 = 4c=4 log (rate ofcreation) =44.14088

+.32% Δ = c-c, c,=11= lg 1011

=Cn = Speed of Light in mm/sec/3

π2π2

=2Γ4(1/2)

=19.73921

4π2

=universalgravitational constant=39.47842

+0% Δ = 4π2= (2 π)2= u4

=G= Gravitation Constantin astronomical units

γ2γ-4

= 2√ 3=18

4γ-4

= 3r2

(γ =.57721) = 36

-.02% Δ = .57721 =1/√ 3

=γ, = Euler- Mascheroni Constantaverage of 5 Δ’s . 0 7 % or 99.93% agreement

2n2 =prin.Quant. No.in AtomicPeriodic Table

4σ2 =Range in binomialdistribution

5K5 subsystems show: 5 c isomorphs in 5diagonal cells in column h,i: Kh –Kl = I; Kh–Kh-

1

Where C = 2 π(π /2) = h2 = 2r = i1(-2 π ). 5sums of 4K2S = Products of 3 K’s = powers oftop K = Size of Universe –γ2 + π2+h2+r2= π * h * r = 36 = r4/4 = ¼ log

Cn13 entropons

Dimension of Cosmos

29

Plate 6a: The Permutive Gravity Hypothesis, G = [2r2(U0/2)] = 4π2

SD: 72-14 by S.C. DoddEpiDoc 244 Univ. of Wash.Seattle 98105 Apr. 11, 1972

How the total Energy of the Universe U0 , when analyzed down to a set of n near-infinitesimalsnn possible ways total Energy of the Universe, U6, when analyzed down to a set of n near-(called "primons"), each 10-71 erg, if resynthesized by permuting' within their (as specifiedbelow) could constantly form a curved space and action of gravity.

The GRAVITY SYSTEM

"PRIMONPERMUTINGSORGANIZEGRAVITY"

as 1 of 4 subsystems orstages of a cosmo-cycleby the Mass-TimeTriangle or EpicosmEquation

a/ct=1= U0

[INPUT

HYP: If thecosmic set of nprimons, in mstaggered cohorts,at t phases of theirlife cycles...

U0/2=1/2

Each half-universe...

THRUPUT

...permute, internallyand externally andsuccessively (asspecified below)...

[2r2(1/2)]2

...if permuted in &between halves…

OUTPUT]

...then theyconstantly form adynamic curvedspace &gravitational action.

4π2=G

...produces the Gconstant.

STEP 1: OrderingRandomness forms avector length n = n

STEP 2: Reversing an orderingforms a half circle (or a permutedhalf set of radius n

2

Γ(1/2)n = πn

π

STEP 3: Repeating areversal forms a full cycleof diameter 2n

πn+ πn=2 πn

π

Dimension of Cosmos

30

π

STEP 4: Repeating t cyclesforms a supercycle of radius

r = 2πrt

n=rt, all integers

STEP 5: A Self-product of a cycleforms its square or the gravitationconstant G

G = 2π x 2π = 4π2 (2π2)

STEPS 5+ : (Furthersteps)t successive self-productsform the t levels of cosmicorganization(See Mass-Time Triangle)

y = (2π)2 t

Dimension of Cosmos

31

Plate 6b: The Permutive Gravity Hypothesis Explained

SD: 72-14A EpiDoc 244

This page tries to tell in simple prose and equations (like 0 = 4n2) how random primalactants, or near-infinitesimals of energy, can (simply by permuting or rearranging themselves)continually form and maintain a dynamic curved space and gravitational interaction (and latercompound into all other levels of cosmic interaction or organization).

Step 1 – Order randomness forms a radius-vector, n

From any random point in a randomly moving set or "swarm" of actant-points, or near-infinitesimals of energy (hereafter called “primons”) pass a randomly directed radius-vector, n.The n actant-points falling along this vector at any one instant fixes a random permutation ororders of those n points. If this baseline random ordering is identified by naming its n points bythe natural numbers 1 to n, then changes in the ordering, called “permutings” can be measuredin units of pair-interchanges called “transpositions” (as when two marbles roll around eachother and change their AB order to BA.

Step 2 - Reversing an Ordering forms a half cycle, π n

A reversal of the ordering of n points in a line can be measured in transposition units(i.e., pair-permuted units) by the gamma function Γ (n) = n!/n = (n-1) (n-2) (n-3)--3•2•1 (for integer n). It can be graphed as if each point moved along a semi-circle of radius n, i.e., as π n; or as a vector rotating thru an angle of 180° or π radians. Its formula for all actant-elements inthe cosmos, U0, is Γ(U0/2) • Γ(U0/2) = Γ2(1/2) = π. This π stands for a half-cycle, a transition from an active randomness in a period to an aligned and reversed ordering at one instant, areversal of sign, a 180° rotation (among many other meanings of π ).

The cosmos is here operationally defined as the universal set (U0 = 1) of all thingsnamable, called "actants". This includes both itself and the null set since these are namable. Itincludes anything non-existent at least as an existent act of speech whether its referent is nullor not. Primal actants are the prime or unorganized subset of actants.

Step 3- Repeating a reversal forms a full cycle, 2 π n

Step 3 repeats the internal permutings of Steps 1 and 2 in the other half of the cosmos.This doubles the semicircle's reversal (2π) of a random permutation (or ordering of n elements (=πn)). It thus forms a full "cosmo-cycle", measured and expressed in algebraic letter and number symbols, as 2πn or 2π U0. In word symbols, 2πn translates into "the measure of the circumference of a circle" (where "the measured of" means "compared with a multiple of astandard unit" which goes back to the natural numbers which in turn can be derived from, orbuilt up by, the reitering rule of speech behavior). 2πn can also be viewed as a permutation of n things (which are reversal operations or n's here) when taken m at a time by the formula, nm,for permuting (with repetitions allowed) in the starting case when n is minimal at 2 and m at 1

Dimension of Cosmos

32

so 21 (πn) = 2πn. Its numerical value is 2 x 3.14159n = 6.28318n. Step 4 - Factoring the radius. n forms t subcycles. each of radius r. if n=rt. (2πr)t

Step 4 continues these permutings by repeating t times the cycle of radius r. If n isfactored into r • t (all integers), this "generalized cycle" formula, 2πn = (2πr)t, can be graphed either as 1 cycle of radius r (where both r and t are natural numbers) or as t cycles of radius 1.This factoring flexibly develops cycles into subcycles and supercycles. These can representalmost any set of actants, its subsets and elements, all as circles in a curved, or totally circular,space.

Dimension of Cosmos

33

Plate 6c: The Permutive Gravity Hypothesis Explained (Con.)

SD: 72-14A EpiDoc 244

Step 5 - Squaring the cycle forms the Gravitation Constant (2π)2 = G

If the permutings thru Step 4 (forming a cycle) are repeated they will form:a unit cycle squared (2π)2 = 4π2 , ora self-product of actants, 2πn in number, or a pair-permuting, orthe universal gravitation constant G = 4π2 in astronomical units as a

dimensionless pure number, the squared circumference of a circle.

G represents the summarizing and invariant interactions called "gravitational action."Gravity includes its many subforms called "spinning," "orbiting," "circling," "cycling," "rotating,""falling," "accelerating (toward a center)," "attracting (between 2 masses)," "escaping fromorbit," "forming waves (in large sets by alternating semicycles)," and other consequences ofdynamic curved space.

This curved space in turn becomes further organized by simple permutings of "gravons"into photons, particles, atoms, molecules, DNA helices, etc. (as spelled out in the Mass-TimeTriangle).

Further Steps, #6 -Successive self-products form all higher cosmic levels (of actant cohorts,continually organized by negative entropy, in due life-cycles, anddisorganized by positive entropy)

Further cumulating of t successive pair-permutings or squarings forms the higher levels

of cosmic organization, (2π)2t

t successive squarings, or t serial self-products, of any n set of actants, n2t

, as started inStep 5, develops the Gompertz growth and decay curve. This is the law of negative entropy, orinformation (H = Σpi lg pi, or n lg n = lg nn = the self-power in bits = the fulfillment" of allcombinatorial possibilities in any n-set of actants.

Negative entropy can, according to the Mass-Time Triangle, account for the furtherorganizing of the next three stages in cosmic evolution within every cohort's cosmocycle ofactants. (See the Cosmosphere graphed in EpiDoc181R).

Dimension of Cosmos

34

SignificanceA first trial version of this descriptive semiotic formulation here called a "Permutive

Gravity Hypothesis" is:

[2Γ2(U0/a)]2 = [2Γ2(1/2)]2 = (2π)2 = 4π2 = G = the universal gravitation constant in naturalastronomical units. This series of algebraic formulas asserts as one of several alternativeprose versions:

"If all n primal actants* interact permutively as spelled out# by the gamma function and tsuccessive self-products (i.e., squarings or pair-permutings), in y = [2Γ2(U0/a)]2t, then theycontinually form a curved space and the consequent interactions of gravitation."

* These "primons" of Action or near-infinitesimals of energy-in-time (where A=ET=ML2T-1) are

estimated by the Mass-Time Triangle (MTT),& Epicosm Equation, a/ct=1, (where c =.. 11= log

"Creatant" rate) to be each 10-71 erg in mass and 10+77 in number within the real and risinghalf-cosmos.

# As usual in combinatoric algebra, other alternative derivations or formulations are possibleand confirmatory. Note that:

1) π/2 = Π (4n2/4n2-1).2) or π/4 = 1 - 1/3 + 1/5 - 1/7 + 3) or arctan x = x - x3/3 + x5/5 = x7/7 + .................. -1 ≤ x ≤ 1. (If x = 1, 1 results) 4) If x = 1/√ 3, π is exact to 70 decimals.

Footnote: By the Gregory series (1971) p. 92, History of Mathematics by H. Eves, 1969, Holt,Rinehart, and Winston.

Dimension of Cosmos

35

Plate 6d: Hypotheses about Sub-Gravity Levels Explained

How many levels best specify the cosmic hierarchy of actants? Do 8 or 9 levels, oneCreatant apart, best describe the present structuring of cosmic activity, or best explain its pastgenerating, or best predict its future functioning?

Towards answering this question as to whether the bottom (or also the top).of the Mass-Time Triangle is open closed (and if closed, at what boundary?) at least two hypotheses, A andB, are sketched herewith.

The earlier Hypothesis A uses 8 levels (see EpiDoc301) starting at Level G in the MTT.It assumes a curved space as the start of the stochastic organizing of everything. Curvedspace is measured by the unit-cycle (=2π) or half-cycle (=π) as its elemental actant.

The later-developed Hypothesis B (see EpiDoc306) uses 9 levels, starting one levellower at Level H in MTT. It assumes the randomly acting set of primons, or near-infinitesimalsof energy, as the start (and also the end) of every cohort's cosmocycle. The gamma function ofany random half set, Γ2(U0/2)= π measures the reversal of any random ordering. But let Table 5 compare their specifications further:

(See table 5 below)

Both Hypotheses A and B support the entropic, or permutive, submodel for the cosmos,

y=e2t. This explains all cosmic organization from level to level by its n actons equably forming(and unforming in their life cycles) all their pair-permutings or self-products called "successiveparings" (shown in Table 5), as graphed by the Gompertz S-shaped growth and decay curve,pe1-go •

Its first derivative or rate of organizing in bits is dptidt=4c2qtlgqt=-.48046 lg expressing inbits a self-power or fulfillment of its actants.

The 8-levels Hypothesis A predicts, better than B, this binary numbers system ofexponents (=2n) in that it neatly subdivides each cosmocycle into 2 half-lives, 4 eras, 8 stages& 16 eons (=the 16 levels of organization), predicting their recurrence in every recurring cohortof octants.

The 9-levels Hypothesis B explains, better than A, the start of each cosmocycle byanalyzing the curved space (assumed as the given in Hypothesis A) still further as a permutingwithin and between halves of the random primons as measured by the gamma function of anyhalf-set (=U°/2),

Namely 1-2(00/2)4(1/2) = n. Thus Hypothesis B explains how the orderly permutativeorganization of the whole cosmos perpetually arises from randomness at the nadir that bothends and begins every cohort cosmocycle (with the continuous creation of curved space andthe consequent interactions of gravity).

Any Universe, U, within the cosmos can be specified by its subscript, stating by anumber how many half-cycles it includes and by letters its top and bottom levels--thusU7AG=the real and rising spatial universe, while U18AiH = the whole 18-half-levels of the complexrising-and-falling universe. (See EpiDoc26)

Dimension of Cosmos

36

Table 5 The Lowest Level SpecificationsLetter

ofLevel

Its Acton'sMass equiv.in tons

ItsFormerName

ItsNewName

ItsNewActon

ItsPrimonPower

Its NewPhase..t

Its Key Constant in terms of Its AssumedStart or Base

ItsFormula

π h,r y'

F 10-55 Gravity Gravity Gravon Cn

2= 102c 2 4π2=G r2h

22y'

22

y' Squared, or

Pair-permutedcurvons.

G=(2π)2

G 10-66 Entropy Curvity CurvonCn

1= 101c 1

2π r√h 2y

'2

y'/2

Curved Space,or Pair-per-muted primons.

2π=Γ2(1/2)

E10-77

(2-256)(none) Primity Primon Cn

0= 100

= 1

0√2π √r√h

√2y'2

y'/2

Random Energyinfinitesimals, E N=σzέ

2 = Σσ6

2

Fixed byprojectingCreationlinedownwards

Hyp. A.=8-leveluniverse

Hyp. A.=9-leveluniverse

The"-on"flagsthethreshold actantata level

C = 11.03522π =

.. √3h

'= y

'√2

y' = 3.14159n = pi

= h'

2= lg2 10

h'= 2

y' = 3.32193 = the “Root-Creatant”

2r =.. (r+1)

r'

= 2y' = 3.46410 = √12 = lg c= lg Cn = the “Crux”

π π_

, π_

=3.51 = “co pi”y'= √3 = 1/.57721 ± .02%

22y

' = 4y' = “Life Constant” (DNA)

Cn = 10C = the Creation Rate in tons organized per eon or log century= the interlevel quantum jump in the Mass-Time Triangle

=.. the speed of light in Epicosm standard and simplifying units of millimeters, tons & thirds of a second.=graphed as the slope of the left side of MTT

Dimension of Cosmos

37

Plate 7a: Four Cosmic Laws of Organization as Stochastic ProcessesName of thelaw anddiscoverer

a

Its formula.and equationnumber

b

Its Key, Ks,process orself-reiter-ant loggovernor c

Aim ofscientistsserved

d

Tenseofcosmicactivity

e

InputtransfactorActors X

P X

f

ThruputTransInteractingsA g

factorsx Timingsx T

h

produce

i

Outputproduct,End-States

Vj

Euler'sHELIXLaws

1

y=ei(2πn) = 1= cos2πn +isin2πn Eq 33a

2n•π a self-sum of πn

predicts theorganizing of

futurecosmicactivity

asnrandomactants

Interactingbycombining& permutingin unit life

In tSuccessiveCycles ofradius r(rt=n)

Forms (ifn isaninteger)

the helix of tcoils

Gauss’NORMALlaw

2

y=1/ue.5(x2

)

un = √2πn Eq 33b

x2a self-product of x

describesthe organ-izing of

Presentcosmicactivity

asn

all-or-noneactants

Interactingjointly

t timesas in(p+q)t

forms (ifarea= σ = 1)

The normalcurve

GompertzENTROPICLaw

3

y=e2t

Eq 33c

2t

a pair-power,the Power set

explains theorgan-izing of

cosmicactivity

asn

ceaselessactants

interactingas self-products orsquarings

tsuccessivetimes as

e(2t)

forms theentropicgrowth (anddecay)curves

Stirling'sCOMBINATORIC law,

4

y = e(nn)

lny=nn=enn!/uEq 33d

nn

a self-powercontrolsthe organ-izing of

anytimecosmicactivity

asn

reiterantactants

interactingbycombiningpermuting &repeating

Simul-taneously

as in e(nn)

forms Thecombinat-oric of self-fulfillingcurves

Dodd’sSelf-Reiterantlaws,

5

y = e(Ks) = eθ

or A=Ct

in C and tunitsEq 33e

Ks

(2n,n2,2n,nn)= the 4 “self-reiterants”

Models theorganizing of

All timecosmicactivity

asn

actants orthings -namable

Interactingin up to nnways

simul-taneously

as in e(Ks)

forms The Mass-TimeTriangle(log scales)

Dimension of Cosmos

38

Plate 7b: Four Theses in Epicosm Modeling

SD: 70-34A by S.C. DoddEpiDoc195A Univ of WashJune 1, 1970 Seattle,98195

The four theses (below) in Epicosm modeling may be tentatively asserted for trial andtesting as hypotheses at first. Ultimately any confirmed hypotheses become asynthesis or model which is an operationally defined integrative theory of the cosmos.The "Epicosm Features Matrix" below orders the chief terms in these theses by increasingcomplexity or completeness downwards and rightwards. The matrix lists and orders (inCol. 1) the set of four terms in the theses composing the Epicosm theory, with their newdefinitive and summarizing concepts (in Col. 2) together with the associated aims ofscientists (in Col. 3) and the chief submodels or means thereto (in Col. 4). The four rowsexpand the four theses in correlated terms.

(See Table 1)

The four theses can be jointly summarized in one sentence that states (see EpiDoc195) a semiotic version of the Epicosm theory for the material and mental universes asfollows:

"If one describes cosmic activity in terms of CONCURRENT CYCLES of INTERACTSby ACTANTS, then one explains and predicts it better than in other terms."

The Epicosm Model's formula, at = ct, where at = actants at Level t; c = Creatant constant;t = time -- all as graphed in the Mass-Time Triangle.

Dimension of Cosmos

39

Table 1 16 Epicosm Features (out of 64 in full matrix)

=cosm

os

8 Features of Cosmic Activity 8 Features of Cosmists' Activity

4T

he

ses

4 AXESof the cosmos

4 CONCEPTSnew in Epicosm

Modeling

4 AIMSof Cosmists

by tense

4 SUBMODELSor hypotheses

by tense

of

act

an

ts

ACTIVITY, AAbscissa inMass-Time

TriangleUnit=1•Actant

ACTANTS = A

=def.

any thing -namable2=unit of actants,1 bit, a pair, an

interacting

DESCRIBINGthe present

NORMAL probabilitydistribution

(Gauss' formula)

y = e-.5x2 a

Actants

inte

ract

s

ORGANIZATION, θθ = lg A = a Unit = 1 bit

REITERANTS = R= all "reiterating"

operationsy'= √3=means,

standard actant=constant oforganizing

EXPLAININGthe past

ENTROPICgrowth and decay

(Gompertz' formula)

y = e2t

/c

inte

racts

cycl

ic

TIMING, tt = ±lg A

Unit = 1 Cycle= 2π • 1

CREATANT = cc = 1g210 = log C

= 11.03522= constant logCreation Rate

π=the half-cycle, unit of time

PREDICTINGthe future

HELIX cycles(Euler's formula)

y = e2πit

tcyclically

Con

curren

t

COMPOUNDS:Complexity:

H = A lg A = AtCreation Rate:

Cn = 10c =... 1011

CRUX = r

= lg r! =.. lg c

= 3.46 =.. √12

r = N/σN =.. 2π/√h

r is where uniquelycombinations =permutations

2πy, = πr=standard cycle

22Y,=c=creatant=cosmic level

CONTROLLINGat any time

COMBINATORICinteracts

(Stirling's formula)n n = en!n√2πn

= self-power= "Fulfillment"

of actants

=1

&co

ncu

rren

tly

Dimension of Cosmos

40

Plate 8: The 4 X 4 Reiteratings Matrix

Row 1fo rms every symbo l man uses;

and so helps to descr ibe the cosmos interact i vely

and and defines a unit called a

4 F ac t o r s i n

a r e i t e r i n g

R EP E A T I NG

of any

thing-namable,

An actant

C O M B I N I N G

it with

a name,

PE R MU T I N G

In any

order

INTERACTING

In three

speech acts,

S Y M B O L , S,

the element of

all language

= “re-“ = “reit-“ = “reiter-“ = ”reitering-“

Row 2f orms al l syntax men use;

and so helps to exp lain the cosmos re la t ive ly

4 R o u n ds i n

a r e i t e r i n g

L I S T I N G

into

SETS,

,,,,

A D D I N G

into

SUMS

+

MU LT I P L YI N G

into

PRODUCTS

X

SELF_MULTIPLYING

into

POWERS

|X

Produces all

SYNTAX

i.e., all language

& math

and so he lps to pred ic t the cosmos quant i ta t ive ly

4self-reiteratings

SELF-SUMS

or

PAIRS

2n

SELF

and so helps to cont ro l the cosmos systemat ica l l y

4LOG

REITERNGS

Predicting

as

HELIX

future cycles(eπ2)2n

Describeas

NORMAL

presentprobabilities

(e-.5

Dimension of Cosmos

41

Row 3f orms 4 KEY processes;

and so helps to pred ic t the cosmos quant i ta t ive ly

SELF-PRODUCTS

or

SQUARES

n2

PAIR-POWERS

or

NORMS

2n

SELF-POW ERS

or

FULFILLMENTS

nn

Row 4f orms 4 submodels ;

and so helps to cont ro l the cosmos systemat ica l l y

Describe

NORMAL

presentprobabilities

2.5)n

Explaining

as

ENTROPIC

past growths

n

(e)2

Controlling

As

COMBINATORIC

Anytime

Self-governings

n

(e)n

Produces

4 KEY

Processes

Produces

4 KEY LAWS

of the Cosmos

(by tense of time)

Dimension of Cosmos

42

Plate 9: The Unital Cosmos

EpiDoc 267 by S. C. DoddMar. 6, 1973 Univ. of Wash.

Seattle 98105

Graphed as a unit cube on 3 axes (a/ct = 1/1.1 = 1)

This page builds on the Mass-Time Triangle and aims to unify that modeling:A) by defining cosmos as the universal set of all things-namable, called "actants," each

taken as an item of compounding Action or organized Energy in Time, so A = ET, orA/ET = 1.

B) by symbolizing cosmos, like any set, in units of itself so U1/U1_

= U1-1 = U0 = 1. Thisderives the zero exponent notation for any set or intersect. Thus X0 as a factorqualifies its products without changing any quantity. Words of any sentence qualify

each other, forming better specified units of thought. Πi=1

1=n

(Xi

0) = X

n

0= 1. This zero

exponent could outdo zero digits in making man's qualified thinking more exact.C) by graphing the cosmos as a unit cube (below) with 3 axes and 9 Levels (overleaf)

wherein each Edge = √-1__

= ±1; Face diagonals = √2_

; and Cube diagonals = √3_

= y,. These 3 simplest Root-Integers build up the Key constants, Periodic Table,

etc., etc. Thus y, = √3_

= 1/y, = 1/.5772; arctan y, = y, - y'

3/3 + y

'

5/5 - y

'

7/7 ---; h = 2

y'; r

= 2y'; c = 22

y, 10 = 2h; and 4π2 = G (Gravity); 2h2 = C (Light); 4r2 = lg F (Faraday),

etc.D) by testing formulas via unital equations, like a/ct = 1, formed by dividing, by one side,

any equating of hypothesis to fact, of possible factors to their product, of predictionto outcome, etc., in order to measure fits as a % of 1.

E) by every Acton (= smallest actant at a level) splitting its unit axis into 2 proportions orcumulative probabilities, such that p + q = 1.

Dimension of Cosmos

43

Dimension of Cosmos

44

Dimension of Cosmos

45

Glossary:Actant = any thing-namableActon = smallest actant at a Level (=Ai---H)

Primon = acton at H=10-77 =.. 2-256 ton equiv.

Cohort = coeval set of actonsReiter = combine, permute, repeat

Creatant=log Creation Rate=log Cn= c = lg210=h2=2r=π π_

=4y =.. 11

Spatial Univ. = 8 Levels Ai-H p + q = 1 = U0

Rising portion + Complement = Whole Axis

4 unital subprocesses, if viewed from Now, generate 4 stochastic Cosmic Laws, thus:a) In the present, cosmic contents, as structured by actants

interacting in their 2 half-lives, are described by theBinomial and NORMAL Probability Laws: (p + q)n = 1n = 1

b) In the past first half-life, cosmic causation, as t successiveself-products, or squarings, with a growth and decay ratemeasured by bits of fulfillment, nlgn=lgnil, is explained by theENTROPIC Law of cosmic evolving and devolving: ∫ lg pp dt = 1

c) In the future tense, cosmic consequences, reitering underreitering conditions, are predicted by the single (and doublefor DNA) HELIX Law as: at = (e2πira)ts = 1rt = 1

d) At any time, cosmic on-going, as all n actants interact, equably,reiteratingly, and ceaselessly, forming and unforming in theircohort life-cycles, all their possible na fulfillments is controlled

by Stirling's SELF-POWER Law: enn!/nn√2πn___

=.. 1

These 4 unital laws, fulfilling the 4 aims of scientists (underlined above) analyze andexactly resynthesize cosmos as a vast stochastic and ergodic process which (whatever itsinternal fluctuations) seems overall cyclically constant, self-creating, and eternally existent.

Dimension of Cosmos

46

Plate 10a: How Gambits Organize Cosmos

thru the m-powers of Root-3 acting as bits, or exponents, fixing bench marks for surveying thecosmos

Let: "Actant" = anything-namable (in erg-seconds)"Cosmos" - universal set of actants (=U° = 1)

Let: m = 0, 1, 2, 3, 4; γ 1= /T = 1.73205; y'm

= “a gam”

Y'= 2y

'm

= lg Y2 = "GAMBIT1sub-one " Y2 = 2

2y'm

= 2y' = "GAMBIT2

sub-one "

The Gambits hypothesis by analyzing the cosmos into "Curvons" of Action, A (each 10-

71 erg-seconds) and resynthesizing its Organization, 0 = lgA, via powers-of-gamma bits (called"gambits" here) expects system-metric "indices" to describe and explain, to predict and controlcosmic acts better than rival models do. In this Y matrix read up and rightwards just as actants

interact in permuting or forming self-products by at = u,2t (u, =√2π•1____

= 2.50662.)

This Gambit generates, as the power, m, rises, 10 constants, Y, or cosmic bench-marks ona rising lg gradient of bits of Organization, (=1gA) of cosmic Action, A, (= no. of actant's) in theMass-Time Triangle defined by a/ct = 1 = U0 which is the "Pan-Acts" formula for the cosmos.

Dimension of Cosmos

47

The Real Spatial Universe (of t - 7 Levels, A-G) within cosmos omits the extended topand bottom levels in MTT, namely: the Imaginary Level, Ai, of Speech Symboling and thesub-spatial Level H of unorganized, or random, primal actant-elements (each C-8 = 10-88 erg-ton-sec.)

Mass-Time Triangle (of 9 levels)

Spatial Univ. t = 7(Imaged Level: Ai and Subspatial Level H omitted)

H

C

D

E

F

G

B

Ai

A

Ai

H

0=

25

6

A = 2 512

Dimension of Cosmos

48

Much as in Pascal's Triangle, each matrix cell here is formed from the cell below it, as a"gambit" or first move, by raising m, the power of y, 1 unit; and from the left hand cell byexponentiating to the base 2.(Roman column numeral denotes tier of logs)

mPowers

y'm

Powers of√ 3

Cosmic Bench Marks5 Single Gambits 5 Double Gambits

Formulas Y1 Names Formulas Y2

Names

4 y'

4= 9

2y'4

512

512

29 h3y

'

Bits in theUniverse

22

y

'4

10154

U

229

22

y

'4

SpatialUniverse

Ma

cro

Un

its

3

5/9

y'

3 = 3√ 3

2y'3

36.651

h'

3

23√3 8y'

CreatantRate

22

y

'3

1011

C

2h'3

22

y

'3

Speed ofLight

2 y'

2= 3

2y'2

88

23 hy'

No. ofReal Levels

22

y

'2

256256

28

22

y

'2

TopAtom M

eso

Un

its

1

1.73205

y1

1 = √ 3

2y'= r

'=

3.46

2y'1

3.32193h

'

2√3 2y'

Bits in Ten2

2y

'1

101

10

2 22

y

'1

TensModulus

Mic

roU

nits

0 y1

0= 1

2y'0

2.02

21 Bits

22

y

'0

44

22

22

y

'0

Bitbits

Five OrganizationBench Marks

= θ = lg A = bits

Five OrganizationBench Marks

A = Actants

Dimension of Cosmos

49

Plate 10b & c: Explanation of the Gambits Bench MarksThe Pan-Act Model, a/ct = 1, as Background

The Gambit Formula, Y„ presented in the matrix overleaf, defines 10 bench marks, orconstants of the cosmos serving as reference points for surveying briefly all cosmic Action(=A), its Organization (= 8 = lg A) and Timing (T = Σ|θ|) according to the Pan-Acts Model reviewed herewith:

Let "actant" = any thing-namable, viewed as an item of action or Energy x Time (so A =ET = ML2T-1 dimensionally).

Let "cosmos" = the universal set (= U° = 1) of all actants. (Let the zero exponent denote"the set of ---" (whatever its base stands for).)

Then the Pan-Acts Model, or system of testable hypotheses, states: "If all n actantsinteract in all nn ways, then they fulfill all their possibilities and so form the cosmos and all itsparts." More briefly: ACTANTS' INTERACTS ORGANIZE COSMOS.

This Acts model for the cosmos is graphed and specified in more detail in the Mass-Time Triangle (=MTT) and summarized in the Pan-Act formula, a/ct = 1, where a = actants atLevel t, c = the Creatant Rate C. 11), and t = any of the 9 levels of cosmic organization.

When m = 0, Y, =

2y'0

2 0

221

BitA bit of organization is a dynamic unit ofBecoming, i.e., 2 possibilities becoming 1outcome.

In 2n = N or lg N = n, n stands for the number of bits, the log; capital N stands for theantilog which is also the number of combinations of n things taken 0 to n at a time. N = the totalfrequency or area under the binomial curve (or a normal curve for n large). N = subsets in ann-set.

Let "a bit of information" denote two possibilities becoming one outcome when in thepast tense with outcome known--like work energy in physics;

Let "a bit of decision" refer to that unit of becoming in the present tense while theoutcome is in the process like kinetic energy currently flowing;

Let "a bit of uncertainty" stand for the bit in the future tense where the outcome isunknown, or potential, paralleling potential energy that has not yet happened;

Let "a bit of complexity" denote, regardless of tense, the formula H = lg -Σ1

m

pi where any

unit set (= S0 = 1) is divided into m subsets each of any size or number of elements;Let "a bit of organization" denote the regular case where the m subsets are equal with

n/m elements and so that each of these unit subsets is 1/mth of the set and each element is1/nth of the set. Here H = lg n = θ = "Organization."

Dimension of Cosmos

50

When m = 1, Y, =

2y'1

3.32193

h'

2√3 2y'

Bits in Ten

h'= 2

y' = 2√3- = 3.32193 =

.. π

_

! =.. Γ(u

') =

..

σ2π

2 = √c = √π π

_

= 2 r / 2 = lg 10, = the

"Root-Creatant"

This Root-Creatant is the Square root of the Creatant constant, c (= 11.03522) = h2; =

2r' = r

'! = 2π+1/ π = 4

y'. It is also the bits log of ten (h

'= lg 10 or 2

h'= 10) and so converts all

man's cultural custom of computing in tens (because of our 10 fingers) into nature's practiceof combining mostly in pairs. The Creatant, in turn is the empirically observed interlevel ormacro-unit of cosmic organization. c is the slope in MTT and is the constant rate ofcontinual self-organizing of the cosmos.

When m = 2, Y, =

2y'2

8

823 h

y'

No. of RealLevels

8, the Octave = 2y'2

= h'

y'

= number of the real levels in MTT,= a basic unit of organization.

e.g., the 8 x 8 Mendelyev Table, the octave on the piano, the Buddhists' Eight-FoldPath, the B cosmic levels, etc., etc. (see Genesa). 8 is the maximal value of t, the number ofeons of time, in the Pan-Acts log formula for the real cosmos, namely, a=ct, or in unital form,a/ct=1. These eight eons as 1 full cycles comprising their 16 rising and falling half-livesconstitute the real cosmocycle of 2 half-lives, 4 "eras," 8 "stages," or 16 "eons" of time, T. The

cosmocycle T16 then equals 10 2 • 16 = 1032 = er'r' = years by MTT readings. Note that this

cosmocycle measures in nits the self-fulfillment, r'

r', of the universal or standardized actant, r

'.

(i.e., r, = √12 = 3.46410 is the actant in standard deviation terms since in a rectangular distribution of actants σ A = A/r

'so A/σA = A /A/r

'= r

'.)

When m = 3, Y, =

2y'3

36.651

h'3

23√3 8y'

CreatantRate

h3 =2y'3

= 8y' = 2

3y' = 36.651

"the Cubit." This bench mark in cosmicorganization is the cube of the Root-Creatant. It is thus the cubed bits in 10and named for short a "cubit."

This revives an archaic unit to use as modern technical measure of the log number of actants

Dimension of Cosmos

51

in 1 cosmic period of Action, A, (= 1 Level of Organization, θ (= lg A); or 1 eon of Time, T (Σ | θ

|). Note that a cubit in bits equals a Creatant in "decits" or common logs, i.e., 2h3

= 2hc = 10C =

Cn = 10lg2 10 = 1011.03522, the Creation Rate. So the Creation Rate expressed in bits is lg en = h3

= 1 cubit = 36.651 bits (of erg-seconds of Action).

When m = 4, Y, =

2y'3

512

512

29 h3y

'

Bits inUniverse

29= 512 = 2

y

'

4

= h3y

' = 83

= the lg U14, the bits logs of the real spatialuniverse of 7 levels or 7 full eons.(Levels G thru A in the MTT.)

This real spatial universe does not include the top or imaginary Level of Speech Acts (Aiin MTT) nor the bottom pre-spatial, or unorganized, Level H of Primons. Primons (=Level H)are the randomly acting ultimate elements of energy, each estimated at 2-256 or 10-71 equivalenterg-seconds at the nadir.

The Gambits Sub-Model Y'= 2

y'm

with y' = √3 as Core Element

The square root of 3 = y'= √3 = 1.73205, is the inverse (within .02%) of the Euler-

Mascheroni constant, y0 = .57721 =.. 1/y

'. The English letter y, is here used to stand for the

root of three, √3(1) to distinguish it from the Euler constant(2) to be more typewritable, and(3) to denote the basic unit-log or unit of exponent along the vertical ordinate measuring

the degree of Organization in the Mass-Time Triangle.

It can be derived from the Enumerative Generator, (n+1n )n

= EG at the minimal limit when n =

1/2, EG = √3. y'serves as a log converter between discrete and continuous variables, between the finite and

the infinitesimals, by the formula: Σn-1 = In (n + .5) + y0 .

(a) One (permutive) operation--self-multiplying y, to an integer power m (= 0, 1, 2, 3, 4)--defines a "gam" = ym.

(b) A second (combinative) operation--exponentiating any gam to the base 2--defines

the Single Gambit, Y'= 2

y'm

.

(c) A third (repetitive) operation--repeating that exponentiating--defines the Double

Gambit, Y''

= 2Y'.

These 3 forms of interacting build the Gambits model, Y'.

The explication of the five Double Gambits, Y''

= 22y

'm

in a paragraph each (as exhibited

Dimension of Cosmos

52

here for the Single Gambits, Y'= 2

y'm

= lg Y'') is omitted here in the Second Printing of this 64

Exhibits Booklet) to make way for the newly developed EpiDoc 305:11, page 4, on the"Gambits Grid Cylinder."

Dimension of Cosmos

53

Plate 11: The Permutive Gravity Hypothesis, G = [2r2(U0/2)] = 4π2

SD: 72-14 by S.C. DoddEpiDoc 244 Univ. of Wash.Seattle 98105 Apr. 11, 1972

How the total Energy of the Universe U0 , when analyzed down to a set of n near-infinitesimals nn possible ways total Energy of the Universe, U6, when analyzed down to a setof n near- (called "primons"), each 10-71 erg, if resynthesized by permuting' within their(as specified below) could constantly form a curved space and action of gravity.

The GRAVITYSYSTEM

"PRIMONPERMUTINGSORGANIZE GRAVITY"

as 1 of 4 subsystemsor stages of a cosmo-cycle by the Mass-Time Triangle orEpicosm Equation

a/ct=1= U0

[INPUT

HYP: If the cosmicset of n primons, inm staggered cohorts,at t phases of theirlife cycles...

U0/2=1/2

Each half-universe...

THRUPUT

...permute, internallyand externally andsuccessively (asspecified below)...

[2r2(1/2)]2...if permuted in &between halves…

OUTPUT]

...then they constantlyform a dynamiccurved space &gravitational action.

4π2=G

...produces the Gconstant.

STEP 1: OrderingRandomness forms avector length n = n

STEP 2: Reversing an orderingforms a half circle (or a permutedhalf set of radius n

2

Γ(1/2)n = πn

π

STEP 3: Repeating areversal forms a full cycleof diameter 2n

πn+ πn=2 πn

π

Dimension of Cosmos

54

STEP 4: Repeating t cyclesforms a supercycle of radius

r = 2πrt

n=rt, all integers

STEP 5: A Self-product of a cycleforms its square or the gravitationconstant G

G = 2π x 2π = 4π2 (2π2)

STEPS 5+ : (Furthersteps)t successive self-productsform the t levels of cosmicorganization(See Mass-Time Triangle)

y = (2π)2 t

Dimension of Cosmos

55

Plate 12: Bits Seem Inter-dimensional Units

EpiDoc 401 by S.C. DoddNov. 25, 1974 Univ. of Wash.From EpiDoc 294R Seattle 98195

Or = n = lg N = lg 2n== “Or” = Organizational index

= ordinate in Mass-Time Triangle

I. Unit-free Dimensions (i.e., Schwarzchild’s) Mu, Lu, Tu, Du (density) are defined by :

A. Mu = √Ch/G = 5.45707 x 10-5 = the unit-free mass (“cosmo-mass?)B. Lu = √Gh/C3 = 4.049895 x 10-33 = the unit-free Schwarzchild radius of Mu

C. Tu = 2π√Gh/C5 = 8.48795 x 10-43 = the Shuster period of Mu and Lu

D. Du = 3C5/4πG2h = 11.96128 x 1092 = the mass density of a sphere of massMu and Lu

II. Their Rations, permitting relative solutions, yields power of unit-free velocity, Vum

, thus:

A. Lu/ Tu = (Gh•C5/C322π2Gh).5 = (C/2π)1 = Vu

1= First power (or moment?) of Velocityu

B. Mu/ Lu = (Ch•C3/G•Gh).5 = (C/2π)1 = Vu

2= Second power (or moment?) of

Velocityu

C. Mu/ Tu = (Ch•C5/G•Gh 22π2).5 = (C/2π)1= Vu

3= Third power (or moment?) of Velocityu

D. Vu3

• Vu1

= Mu • Lu/Tu • Tu = MuLu /Tu2

= Vu4

= Fu = Forceu , as a Fourth power of Vu

E. Vu

4• Vu

1= MuLu • Lu/Tu • Tu = MuLu /Tu

3= Vu

5= Pu = Poweru , as a Fifth power of Vu

Vu

mm = 1, 2, 3, 4, 5

III. The 3-Axis Matrix , MIII is the Vum

array when bordered in turn by its products with

integer powers of Time, Tu

t; of Length, Lu

land of Mass, Mu

m, so MIII = Tu

tx Lu

lx Mu

m.

Since every formula of Physics can be re-expressed in dimensional formula (with loss ofinformation as to the nature and number of units) and since this solid matrix, MIII has acell for everypossible integer dimensional formula, this 3-axis matrix seems to become a PeriodicTable for Physical Formulas.

IV. A Binary Number, N (= 1, 2, 4, 8, 16, 32, etc.) = (20, 21, 22, 23, ---) = 2n = the Power Setof all possible subsets of any set of n elements), or a number of bits, n, can beassociated with each cell of this matrix, much like the atomic numbers (of protons)associated with each cell of the Periodic Table for the Chemical atoms. Thus by taking alog unit cycle, e2πi = 1 (of unspecified radius, called "the unit cycle") as the "Sun Time"unit, Tu = 1, and 2 as the log relation of Length to Time, i.e., L = T2 so log L = 2 log T(see Feynman, et al, The Feynman Lectures on Physics, Addison-Wesley Pub. Co.,1964, p.5-1 the log Mass will be 23 = 8 by II. B. & C. above. Then the Binary Numbersare 1 for Time, 2 for Length (4 for area, L2) and 8 for Mass. Then every log dimensionalformula, being a product of integer powers of these three, will have a binary number, N

Dimension of Cosmos

56

(= 2n bits) associated with it.V. Bits can Re-express All Dimensional Formula in Timeless Terms

Thus in the unit-free Schwarzschild formula, (C/2π)m = Vum

(Eq. 1) for alldimensional formulas of Physics, let C be expressed in "Alpha-meters, αm ," defined byC/e8π = αm/2. So Eq. 1 becomes (e8π2π)m in alpha-meter units of length, each7.29188698 mm (=α + 7.49 ppm).Then translating this atom-time term, e8π, into its sun-time equivalent transforms Eq. 1 into bits thus:

Vum = (C/2π)m = (e8π/2r)m in αm units (8π/2π)m = 4m = (22)m =

(2m)2 = N2.The m in 2m is the number of bits in the binary numbers, N (= 1, 2, 4, 8, 16, 32, etc.).Thus by shifting our language, or symbolizing customs, all formulas of Physics whenfreed of the nature and number of their particular units by being re-expressed asdimensional formulas, can be again re-expressed in interdimensional units of set theoryand combinatoric algebra as the power set, 2 , and its square, 4m. 2m has a dozenmeanings including being the measure of the area under the binomial and normalcurves (for m large). Forming normal curves begins to organize law and order out ofrandom actons at every level of the Mass-Time Triangle that graphs the continuous andperpetual evolving and concurrent devolving of the whole cosmos. See EpiDocs 310, pp2-3; 311; 312.

VI. Bits offer a semiotic Unified Field Theory, the MTT, for all sciencesNote that this self-power or "fulfillment," formula (22)m, semantically unifies, or

offers a semiotic unified field theory, for:A. All formulas of Physics or Levels D, E, and below in the Mass-Time Triangle (which

graphs the Pan-Acts Model, a = ct, for the cosmos);B. All DNA cell nucleotide patterns of heredity in Biology or Levels C & above in MTT.

Dimension of Cosmos

57

Plate 13: The Helix Submodel

The HELIX SUBMODEL or Col. 1 in Row 4 of the Reiterating Matrix.

When the self-sum, 2n, is exponentiated to eπi (= -1) as base it becomes, e2πin = +1, theformula (if n is an integer) for either the helix of one cycle or coil with radius n, or a helix of ncycles each of unit radius. (The i factor in the exponent converts rectangular to polarcoordinates.) The helix also expresses the single random process and since it equals unity, aconstant, it also represents a stochastic process wherein each total state, or set of subsets,probabilistically determines the next total state however much shifting may go on among thesubsets. If one assumes the cosmos to be compounded from a random set of all elements ofenergy, as the Epicosm model does, then the helix predicts perpetual recycling of the totalrandom cycle of permuting.

Readings of the Mass-Time Triangle tentatively assign a cosmic cohort cycle of C7 =

1077+1 =.. 2256 primon units of real activity and a total cohort life cycle of 1032 (=10

25

= 10e

r

=..

104u

; u1 = √2π__

= 2.50) earth years, i.e., a log half-life of ten quadrillion years (= 1016). Thus thehelix applied to a cosmic cohort cycle predicts the perpetual recurrence of such cycles as itsfuture tense or long run prospect for the cosmos as a whole. This pictures a perpetually self-renewing constant cosmos with no sudden creation ever. (This non-expanding cosmos is harmonizedwith the red shift by the semantic hypothesis of antilog time scaling.)

Note that the helix formula formulates the start of each of the four eras, or quarterphases, in the cosmocycle of every cohort of actants. Its coils can reflect the essence of everylaw of science, namely: that the particular action asserted by a particular law will recur (orcontinue) under recurring (or continuing) conditions. This "axiom of the uniformity of nature" asit has been called, implicitly underlies all scientific laws. It might also be called the law of alllaws as it represents the principle common to every empiric law--"under like conditions, expectlike results." Each coil or recycling of the helix measures such recurring.

Thus the formula for the single random stochastic process, E = eitx, in polar coordinatescan be re-expressed in helix form. The formula for the double helix of DNA moleculesdescribes in every living cell its inheritable patterns. So the helix represents the start of theinorganic and organic eras within the first and the second half life of every cosmocycle, assystemed in the Pan-Acts model.

Dimension of Cosmos

58

Plate 14: Time Axis, T of the cosmos (= U0 = 1) in Epicosm Models

SD: 71-30 by S.C. DoddEpiDoc 230 Univ. of Wash.August 1971 Seattle 98195

graphing 4 cosmic cycles of an actant cohort, on rectangular & polar coordinates,subdividing cycles into 2 Half-Lives, 4 Eras, 8 Stages & 16 Eons as _t = 1,2,3,4 in 2-t

3 Versions of the EPICOSM Model:

Prose version: All n actants in nn interacts organize cosmos & all therein

Algebraic version:

a = actants at tc = Creatant Rate = lg210t = time taken (from Now)

Geometric version: See Graph of the Mass-Time Triangle (-MTT) for cosmos

Operational Definitions:

Actant, A = any thing-namableApex = max. θ; tip of MTT; the "Now" point Atom-clock time = at = antilog of usual sun-clock timeCohort = a set of like-aged actantsCosmos = the set of all actants = U0 = 1Interacts = all nn combinings, permutings, or repeatingsNadir = min. θ; start of θ cycle Organization = 8 = lg A = bits of actantsUsual sun-clock time, to = ts log in at = ets

a = ct 1

Dimension of Cosmos

59P

ositiv

eE

ntro

py

=D

iso

rga

inza

ting

Ha

lf-Life

II

Ha

lf-Life

IO

rga

niz

ing

=N

eg

ativ

eE

ntro

py

Ino

rga

nic

Era

2

Org

an

icE

ra1

Org

an

icE

ra1

Ino

rga

nic

Era

2

Mo

tion

IV

Ma

teria

lIII

Vita

lS

tag

eII

Ve

rba

lS

tag

eI

Mo

tion

IV

Ma

teria

lIII

Vi ta

lS

tag

eII

Ve

rba

lS

tag

eI

Eo

ns

FG

Eo

ns

DE

Eo

ns

BC

Eo

ns

Ai

A

Eo

ns

FG

Eo

ns

DE

Eo

ns

BC

Eo

ns

Ai

A

NOWNOWNOWNOW

TIME

2 Half-Lives = 4 Eras = 8 Stages = 16 Eons

Cycle 1 Cycle 2 Cycle 3 Cycle 4

TME = a count ofstandard cycles, ts,e.g. years

Logs converteternity of ts to finite

at

Dimension of Cosmos

60

NEW HYPOTHESES GENERATED:

1. Antilog Time Hypothesis: at = ets

A constant, non-expanding universe, consistent with the red shift, seems nowtestably specifiable by means of the antilog time scales, at

2. Cyclic Combinatorics Hypothesis:

Continual self-renewal by cyclic, combinatorial interacting of random actants canreplace sudden creation theories. This seems now testably specifiable by single anddouble helix formulas. These broadly predict future action of an eternal cosmos.

3. Permutive-Gravity Hypothesis: Γ 2(p) = π Random permutings measure the circlings, orbits, spins & similar cyclic action called

"gravity"--making curved space.

FORMULAS INVOLVED:

1. Axes: A=ML2/T; θ = IgA; T = Σ | θ | 2. Euler's Helix, eθi =cos θ +I sin θ = ± 1; ± I as θ = 2π, π; π/2 , 3 π/2 3. The stochastic single random process has Φ (u)=E(eiux) as characteristic function4. Note: 2πn=1 circle of radius n, or n circles of radius 1 or if n = rt (both integers) 2πn = t

circles of radius r.5. Compare time spans: ts at

Observed at Apex: 0 1vs at. Nadir (Start) - ∞ 0

Past cosmic span = - ∞ 1

6. In C=L/T, red shift implies:Expanding universe in suntime, tsConstant universe in atomtime, at

7. 0 exponent means "a set of-" n0/2 = half-sets of n elements The gamma function measures Γ(p)Γ(q) = π cscπp; (p+q=1) Γ2(n0/2) = π (csc π/2 = 1) 8. Eon boundaries (see MTT) of 16 levels (each a log-century of organizing or

disorganizing cosmic actions) are at ±(102) t years from Now (t = 1,2,3 --- 8)

Dimension of Cosmos

61

POLAR COORDINATES:

A cosmic helix showing 4 cosmic cohort cycles e2πi4, each = to 1032 years (from MMTgraph) or 10 quadrillion years, - & + from Now.

As all points on AB permute, reversing their ordering, AB rotates π radians, (a half cycle) thus becoming BA. 2nd permuting = unit cycle = 2π. This graphs the PERMUTATIVE GRAVITY HYPOTHESIS

Dimension of Cosmos

62

Dimension of Cosmos

63

Plate 15: Ultimate Cosmic Questions and Pan-Act Answers (Abstract)

EpiDoc 403A by S.C.DoddJan. 1975 Univ. of Wash300 Words Seattle, 98195

Perennial issues in philosophy and Cosmology can now be answered better thanhitherto with the emerging semiotic sciences, studying man x symbol x thing relations. Theseinclude set theory and systems theory, combinatorial and stochastic statistics, dimensional andtransactional analysis, operational and holistic synthesis. This assay in semiotics presentsanswers to some ultimate questions as seen thru Pan-Acts Modeling compared with othermodels.

Definitions: "Cosmos" = all actants (= U° = 1); "Actant" = any thing-namable, viewed as anorganized item or energyISSUEQUESTIONS OLDER

mythicalanswersfrom the Past

MODERNscientificanswersin the Present

NEWERhypothesized Pan-Actanswersfor Future Testing

ISSUE

WHO?made

God,theCreator

Natural forcesanthropomorphicallypersonified

Cosmos (=Pantheist's God)continually and cyclicallyrenews itself.

Person-ificationor God

WHAT? makesall things go?

GodRulesAll.

Law-abiding processesmaintain everything

n actants interacting in allpossible nn ways

Agency

WHY? GodWilledIt

Towards evolving ofeverything

Towards actants' cyclicfulfillment of their nn

possibilities

Destiny

WHERE?was cosmosmade

WithinManssight

Within man'sInstrumentedobservability

Wherever actants pair-permute, thus building

Location

WHEN?Was Cosmosmade?

In seven days Some 1010 years ago Thruout every cosmocycle,

T =1032 = err

years --ru=√12 (so In Tu = rr

= the standardized actantfulfilled)

Timing

WHICH?MaterialsMake upcosmos?

Earth,Water,Air,Fire

1078 sub-atomicparticles

Every phase's actants,pair-permuted,stochastically generate laterphases

Substance

Dimension of Cosmos

64

WHICH?Symbolsmake cosmosknown toman?

Genesis Iterms

Operationally-definedscientific terms

Pan-Actant termsmeasurablyimprove cosmic explanationand prediction

Knowledge

HOW ELSE?(beyond#1-7above)

Ignoredin myths

Further Unknownphenomena exist

Unknown causation ismeasured by k2 in(r2 + k2 = 1)

Unknowns

1 word 2 words 4 words 8 words

The answers here expand as the binary numbers (1, 2, 4, and 8) with time, becoming moreexplicit.

Dimension of Cosmos

65

Plate 16: The Pan-Acts Model In Set Theory Terms*

A semiotic** theory of the cosmos translated from its particular language into the universal language of sets.

THE PAN-ACTS MODEL. a=ct, STATED ITS RESTATING IN EXPLICIT TERMS OF SETS

Let the word "cosmos" stand for "all things namable." #1 Let "cosmos" denote the universal set (= U°) of allnamable elements

Let the word "actant" stand for "any thing-namable." #2 Let "actant" (= A°) denote any namable element or subsetof the cosmos Note that this implies any element may betaken (i.e., re-viewed or further analyzed) as a subset oflower order elements

-------------------------------------------------------------------------------------------------------IF all n actants interact (= the Hypotheses) #3 Insofar as all n actants interact (i.e., intersect)

randomly, #4 Equably, i.e., with equal and independent abilityceaselessly and #5 in perpetual cycling (observed as finite samples, or time

slices)reiterantly #6 and in four subsets of elemental operations, namely:

by LISTING (= itemizing) elements into sets (="re-")or ADDING (= counting) elements into sums (="-it-")or MULTIPLYING (= re-adding sums into products)

(="-er-")or EMPOWERING (= re-multiplying) products intopowers (="-ant")

#7 (Note that this union, or sum, of the set of 4 alternative andcumulating operations is here named "reiterant.")

in all their possible nn ways of #8 In all their superset of n combinatoric possibilities ofinteracting

combining i.e., by combining n elements into m subsets,= mn (=nn if m n)

permuting or i.e., by permuting n elements taken a subset m at a time, =n (=nn if m=n)

Dimension of Cosmos

66

repeating i.e., by repeating m elements interacting in subsets of m,= mm (=nn if m=n)

while continually forming #9 while perpetually organizing and disorganizingand unforming compounded actants in every cohort (i.e., coeval subset of

in cohort life-cycles, actants) in the first and second half-life phases (or subset oftime elements) within each cosmocycle,

THEN (= the conclusions)ACTANTS' INTERACTS #10 in just so far

ORGANIZE COSMOS elements or subsets of the universal set form that whole setand all its parts called "the cosmos."

(Note that the verb "form" here could be replaced bysynonyms like “organize," "shape," "formulate," or "inform.")

as a HIERARCHY of subsets #11 This hierarchy describes exactly (i.e., measures) thecosmos in the present tense as to its contents or structuring

of nine complex levels (8 real & 1 imaginary), at nine cumulative complex number (=a+ai) levels orone Creatant constant, c, a part subsets of actants

each a normal distribution of its i.e., 8 real levels of things-named (=a) (See MTT) andactants, individually called: Primity, Curvity, Gravity, Photity,

Massity, Biolity, Personality, Society, Symbolity withthreshold actants here called Primons, Curvons,Gravons, Photons, Massons, Bions, Persons,

Societons, Symbolons and 1 imaginary toplevel of their names (= ai) which comprises all the setof symbolizing actants, i.e., all speech andconsequent communicable mental activity. Each levelbeing a normal distribution of its mean actants (by theCentral Limit Theorem)

#12 The threshold actants called actons are one c apart.formed at a CREATANT RATE, c, that is overall #13 This Creatant Rate (of actants organized one

constant, c (= lg 10)2 = 11.03520 level per eon or log century) explains the cosmosalso c = h2 = lg2 10 = 3.321932 in the past tense as to its causes or genesis

=.. 2

r' = 2

2y' = 4

y' =.. r

'! where as nine successive rounds of self-products, i.e., intersects,

c = standard actant squarinqs or pair-permutings, n2. These together in

Dimension of Cosmos

67

= √12___

= 3.46410) sequence as(((q.) ) )"' 2 t = q2 E. , define the Gompertzgrowth and decay curves of negative and positiveentropy which measure all cosmic evolving anddevolving cycles.

during each COHORT COSMOCYCLE of time #14 This Cohort Cosmocycle measures the cosmos in the futuretense as to probable, cyclic, cohort, sequences ofstochastic Changing within each cosmocyclee, Tu, estimated

by MTT at T = 1032 =.. 10

er

= err

years i.e., In Tu = r'

r' = the

fulfilled standard actant, r, √12 = 3.46410 =.. lq c =

.. lg r! = 2√ 3 = 2y)) by converting some of the potential supersets intothe actual set of actants.

each cycle trending with time towards fuller #15 This trend to fulfillment controls the cosmos in any tense asself-FULFILLMENT, nn to its inferred design, or destiny, of eternal cycling that

seems required if one assumes conservation of energyand no creation from nothing.

--all as algebraically formulated in the Pan-Acts #16 --All this is restatable in algebraic versions as the reiterantEquation a = ct compounding of elements in a universal set as specified

where a = actants at level t overall by the Pan-Acts Equation, at = ct, (graphed by MTT)

--and as geometrically graphed by the Mass-Time #17 --All this is restatable in geometric versions as the Mass-Triangle (=MTT) as a nest of 9 rectified normal Time Triangle, scaled on a "Gambit-Grid" of unitprobability curves equilateral triangles of side 21 (= bit) altitude √3 (= 1

"gam" = y, = 1.73205), perimeter 6 (= 2y,2 = r, • y,) and area y. = √3 = lglq 10 or any constant multiple of these.

IN SUMMARY #18 The system called "COSMOS" is here defined as:A SYSTEM is here defined, universally& operationally, in Set Theory terms as:a) a set of elements with specifiable a) the universal set (U° = 1) of all namable elements called

"actants" (110'b) subsets and b) with its nine subsets, called "levels" (#11, 12)

Dimension of Cosmos

68

c) supersets, their c) and supersets of actants that are potential (i.e.,coming after) the present actual cohorts (#15)

d) intersects and d) with a major intersect, or subset in common, as thegrowth rate, c, called "the Creatant" (#13)

e) sequences e) all sequenced within their cosmocycles (#14)

*This prose statement should be read with its graph (called the Mass-Time Triangle, "MTT") alongside.** Semiotics is here defined as the science of man x symbol x thing systems.

Dimension of Cosmos

69

Plate 17a: How Arraying Masses Discovers Cosmic Periodicity,

Log Cn = c =.. 11

SD:69-26R by S.C. DoddEpiDoc 154R Univ. of WashJune 1973 Seattle, 98105

This graph discovers a periodicity, or "quantum-like" jumps of 11 log cycles of mass(called "Cn") between smallest entities in the 4-level range of material organization from

minimal at the electron (10-33 = Cn-3

) to maximal in society (100 to 1011 or Cn1

).This Cn - factorseems to measure the inter-level jumps in average organization of cosmic actants. It seems torepresent one eon or log century of Earth years interpreted so it produces a constant cosmic

Creation Rate Cn=10c=10lg

210

=.. 1011 of actants organized per level or eon. Then ±c defines the

slopes or 2 sides of the Mass-Time Triangle.

At the Electron Point (D' in the MTT) this Cn=1011 translates into the Speed of Light (in

mm per third of a second units) by Einstein's formula E/M=C2, expressing a transition ratio

between radiant energy and the threshold unit (called an "acton") of mass.

Dimension of Cosmos

70

Dimension of Cosmos

71

Plate 17b: Plotting Material Entities by Mass vs. Organization Rank

SD: 69-27 by S.C. DoddEpiDoc 155 Univ. of WashJune 1969 Seattle, 98105

This develops:

I) a cardinal scale of cosmic organization (in bits lg a), the ordinate;2 ) Extendible to an 8 level universe (where t=8, as below);3 ) Correlated with past time periods (or ages, t, to date);4) Yielding a constant log growth rate, c, (=log cn= lg210=11.03522);5) Their synthesis in the epicosm equation, at = ct, which says: cosmic activity, α, at

any level t, equals its growth rate c, x time taken, t."

Dimension of Cosmos

72

Dimension of Cosmos

73

Plate 17c: The Mass-Time Triangle Extended Through the Radiation SpectrumEpiDoc 66 SD:63 – 107

A Trial at Charting Levels D, E & F of Matter, Energy and Gravity

Rad

ioW

aves

Rad

ar

Infra

red

Ligh

tX-R

aysGam

ma

Cos

mic

Theco

nsta

ntve

locity

ofLigh

t

C=

10

mm

/1/3

sec

11

f,F

requency

incycle

sper

1/3

second

Cosm

icA

ge,

Eons

inLog

Centu

ries

1013

10

10

11

9

C = 1

10

10

10

10

10

10

22

18

14

11

6

3

C =1

C =2

0

Line

of

Qua

nta

, Wavelength in millimeters

10 10 10 10 1011 9 -3 -6 -9

10 10 106 3 0

Kilometer Meter

C-1mm

E'

F'

D'10

trill

ion

yea

rsago

100

brilli

on

years

ago

1bill

ion

years

ago

Level D of Matter

Level E of Energy

Level F of Gravity

(Mass Dominates)

(Time factor Dominates)

(Curved space factor Dominates)

E = MC2

= fhp

C = λf E = EnergyM = Rest massC = Speed of Light = 2.9979 x 1011mm/secλ = Wave length in mm f = frequency in cycles in 1/3 second

“Mid-Photon”? Wave length, λ = 10

0= 1 = C

0mm

Frequency, f = 1011 = C’ cycles/ 1/3secMass equiv. = 10

-44tons

ElectronDiameter = 10

-11mm = C

-1mm

Mass = .91 x 10-33 tons

“Gravon”

Diameter of Earth’s magnetic field = 8 x 1.27 x 1010

mm = 1.016 x 1011

=.. C

1mm

Frequency λ, = 100= C

0= 1 cycle/ 1/3 second Mass equiv. = 10

-55tons

Dimension of Cosmos

74

Plate 17d: Distribution by Mass of Smallest Living Entities

SD: 69-28 by S.C. Dodd

EpiDoc 156 Univ. of Wash

June 1969 Seattle, 98105

of fact = mean of 100 studies, published up to 1983 :1022.25 tonsTesting the fit

vs. theory = mass-time graph of a=ct, the Epicosm equation, :1021.96 tonswhere a =lg210 =11.03522; t = 1, from origin at electron, :10-33 tons

----------------10-29 = 1.4%

The discrepancy was .29 of a log10 cycle or 1.4% in logs, 98.8% agreement between expected & observedlogs (of masses of smallest living entities). .

—

Discovering good fit of the observed boundary between the living vs. non-living actants & the prediction of itby the mass-time triangle, graphing the Epicosm model of the cosmos, U0= 1 = a/ct.

Dimension of Cosmos

75

Mean of non-living Mean of Quasi- Observed Mean Mean of LivingEntities (proteins) entities (viruses) of all entities entities (cells)

Data N Mean σ

Group A, Living Cells NA = 27 10-20.23 1.13

Group B, Quasi-Living Cells NB = 66 10-23.02 1.02

Group C, Non-Living Cells NC = 7 10-24.32 0.09

Over-All No =100 10-22.27 0.01

Expectedthreshold oflife by MTT

Dimension of Cosmos

76

Plate 18a: Dimensions of Societal Planning, S

SD – 72-15 by S.C. DoddEpiDoc 245 Univ. of Wash.April 11, 1972 Seattle, 98105

A Conspectus of the “ACT/S” Matrix building macro-sociology(a sub-matrix of the Epicosm Model, a/ct = 1 for the Cosmos)

This matrix of ACT/S (=1) in 3 axes can record the data for macro-Sociology to helppredict and control the acts and value-systems of society, in dimensional form, as:

[A8 ; C8 ; T4 ;] = S0256 = Society = all Activity, A within a Culture, C and Time T.

Planners seek to analyze and resynthesize present society (in desired ways that help to buildon its past, predict its future, and improve its self-direction) measurably better.

This transact data model, or methodological theory for systematizing sociologicalbehavior hypothesizes that: Insofar as an earlier Transact Tr1 matches a later Transact Tr2,

feature for feature, in just so far Tr1 correlate with and predict Tr2. If changes in their featuresare also matches, when all else is unchanged, then Tr1 also controls Tr2. This ACT/S modelseems widely applicable, practical, testable in principle, and flexible for specific cases, thrusubdividing into sub-matrices and condensing into super-matrixes as needed and insertingindices as desired in the cells.

Dimension of Cosmos

77

=Tra

nsfa

ctor

sin

plan

ning

:

=Sym

boliz

ing

inall r

ecor

ds

=Valui

ngs,

pref

eren

ces,

polic

y

=Peo

ple

from

staf

f to

polle

e

=Mat

erial e

quip

ing

&bu

getin

g

=Res

idua

l Circ

umst

ancing

Trans

act a

bove

=so

cial

plan

Family-Popul.

Education-Media

Economics-Indus

Political-Military

Religion-Ethics

Health-Welfare

Recreation-Art

Science-Tech

All=Community

Pa

st,

Cau

se

s,

Exp

lan

atio

n

Pre

se

nt,

Decis

ions,

De

scri

ptio

n

Ne

ar

Fu

ture

,P

rogra

ms,

Pre

dic

tion

Sym

bolic

Acts

Va

luin

gA

cts

Pe

ople

Acts

An

ima

lA

cts

Ma

teri

alA

cts

Tim

ing

Acts

Loca

tion

alA

cts

Re

sid

ua

lA

cts

inC

on

text

+

S V P A M T L R =Tr

A Transact = S V P A M T L R = Tr = a "recorded-act-in-full-context" as ordered in matrices

Indices & Sub-matrices mustfill out t hese 256 cells (=162 =44 = 28 ) in reiteraed wayswhich can build rules in this8x8x4 solid matrix recordingprobable acts of people in time

Personal Transact Axis, A

Cu

ltu

ralA

xix

,C

Time

Axi

s,T

Societal Indices(here in eightinstitutionalgroups)Interatctingtogether recorda community

S =

=Actsof

plan

ning

&ex

ecut

ing

=Tim

ings

, sch

edul

ing,

sequ

ence

=Loc

ating

offic

es, d

istri

cts

Th

ese

four

pe

riod

sca

npro

duce

scie

ntific

exp

reim

en

ts,

testin

gh

yp

oth

ese

,w

hic

h,

from

pa

sttr

en

ds

&m

an's

desir

es

ca

np

red

icts

futu

res

goa

lsan

dcon

tro

lo

utc

om

es

tow

ard

hum

an

fulfill

me

nt.

Thetim

eax

isre

cord

s;da

tes

&du

ratio

ns, s

peed

san

d

acce

lera

tions

, cha

nge

of

beha

vior

, seq

uenc

eof

acts

,

rate

sof

actio

n,pr

oces

ses

&fo

rces

, sta

gesin

plan

ning

, etc

In these 8institutional,universal yet variant,people act, interact,m and role-act to get,or to keep most ofwhat they want mostof their lives.

People act asa person = P0=1 ina 1-cell matrix: orPlurals = PI, a 1-array matrix, ofone sub-axis orGroups= PII in a 2-axis matrix; orOrganization= PIII

in 3 axes.

Powers of “transfactors”,or categories called“dimensions” of everytransaction are:

1) Factors, not addends;2) Necessary by the“vanishing intersect”test:3) Sufficient (i.e.accounting for 100 percent of the variance) bythe “multiple r-near-1”tests: and4) translatable into 8levels of the organizedcosmos.

Dimensional Powers=cumulative reiterings:X0 = a set, a list of elements: A QualityXI = a sum, a count of sets: A QuantityXII= a product, repeated sums: A RelationXIII=a power, self-product: = A SystemTransact-systems 3 “features” : Output8-“Transfactors”, modified by :Input4=”facets” or corner-scripts: Thruput

s

sXs

s, all connected by 4 “functors” or reiterant

“Thruput” operators like (+/=)(;), i.e.

X

Listings=SETSQualities S

Addings S=SUMSQuantities

Self-multiplying= POWERSS = Systems

S Multiplyings= PRODUCTSRelations

Dimension of Cosmos

78

Plate 18b: Social Transfactors Equated to Cosmic Levels

EpiDoc 342 by S. C. DoddApril 11, 1974 Univ. of Wash.

Seattle 98195Equating of 8 Cultural Transfactors in the Transact Model for Human Society

to 8 Cosmic Levels in the Pan-Acts Model for the Cosmos

The 8 TRANSFACTORSor factors of culturehere taken to analyzeman's activity aslearned by interaction withfellow men andall else.

The 8 cosmic LEVELSof cumulating inter-action or increasingorganization, hypothesizedto build up continually in 8eons of time.

The 8 newly emergingdimensions, eachcreated as self-products or squarings,of the Level below it, in"negentropy."

Rank, R, of Levelin Complexity,H, of interaction.

Name and Letter Name and Letter Name and Letter RH

Symbols S Symbolic Action Ai "Symbolons" S 1

Values, cultural V Societal Action A "Familons" V 2

Persons P Man's (Physiol.) B Persons P 3

Acts A Life Action C "Animons" A 4

Materials M Material Action D Mass (Electrons, etc.) M 5

Time T Energial Action E Time (Photons) T 6

Space L Gravitational F Space ("Crayons") L 7

Residual CCircumstances

Entropic Action G(at completion)

Number ("Cyclons") N 8

Dimension of Cosmos

79

Plate 19a: Twelve Applications of the Pan-Acts Model of the Cosmos-----------------------------------------------------EpiDoc 294R by S.C. DoddDec.1, 1973 Univ. of Wash.

Seattle 98195

A quantic matrix for testing the Pan-Acts Hypothesis a = ct = θ, mand discovering the “Power Parameter”, m, of the Cosmos.

ABSTRACT (in 50 words): This Quantic Matrix, mθ1, discovers the governing andtranscendental log factor, m. m seems to measure the power parameter of the cosmos. m alsomeasures cosmic time in eons (= log century factors). m is isolated for further testing by indicesof consistency, correspondence to fact, and concordance with scientific aims.

DERIVATION of mθ: The 60 cell entries in this Quantic Table were both induced and deduced as an

intersect, or set product, of two factor sets, θ and m. θ is the set of 12 column domains (below)measured in bits (=θ = lgX) when cross-classified by m, the set of 5 row powers, measured by integer bits (much like the mantissa and characteristic of common logs).

The power parameter, m, is here both a constant and a variable. It is a constant over the12 columns below that sample domains of human knowledge as named in the columnheadings and formulas. m is a variable with five values over the five rows of this QuanticMatrix. m thus appears here as constant within rows and variable between row, while θ is oppositely a constant between row and variable within rows. m grows by integers—m=0, 1, 2,3, 4. m denotes (1) the first five powers, or (2) the successive self-products of its basal actant(=A), or (3) the cumulated rounds of "the interacting of actants that organizes the cosmos."(This quote is a brief statement of the Pan-Acts Model, a=ct (=θm here)--see expansion below).

m seems thus a simple integer exponent governing, as a central tendency, the universaldevelopment of everything namable. m is a ± log broadly measuring the steps in evolvingand devolving of every cohort of cosmic octants. It implies the proposition, testable in principle,that: "Logarithms measure cosmic organization," or, more loosely, "Cosmos seemslogarithmic."

Note that the empirical induction here of log periods (or integer powers or quantumjumps of exponent) is supported in another dozen domains that have been similarly analyzedand resynthesized. Further support for this "log-periodic" view of a hierarchic cosmos appearsin the direct observing of periods in the Mass-Time Triangle.

U0 = 1 = a/ct [tc = mθ1]

The Pan-Acts Hypothesis The Quantic Matrix Subhypothesis

Dimension of Cosmos

80

USES of mθ: Towards UNDERSTANDING the cosmos this Quantic Table, mθ, may be used

as a broad operationally-defined guide to help order and systematize human thinking about a

unitary World View or Cosmology. It produces 22 versions, or symbolic ways, for analyzing

and resynthesizing everything-namable—which defines the cosmos here. This produces

improved understanding of the cosmos by modeling it with the excellence of that modeling

measured by "system-metric" indices likes improved reliability, precision, comprehensiveness,

lawfulness, ordering, testability, etc., etc.

This Quantic Matrix ISOLATES for testing the power parameter, m. This seems to

measure (in ordinal steps at least) the successive stages of organizing (=θ=lgA) all cosmic

interactions. It also seems to measure the Time sequences of eon subcycles, or 8 phases of

the ordered cosmocycle (estimated as 1032 = err

years). This, in universalizing dimensional

form that is free, of arbitrary empirical units, expresses all cosmic on-going or existence along

three axes called Action(=A=number of actants-Energy X Time so A=ET), Organization (θ=lgA

in class intervals of c), and Timing (=T=ΣIθI.= m here). So a=ct=θm.

THE TESTING of any model, or symbolized system, should measure is system-metric indices

of the internal consistency--(eg What % of its parts are interconnected by equations?); external

correspondence to fact (eg What of its parts are equated to facts?); and general concordance

with the aims of science (specified below) (eg What is its %- of maximal fruit-fullness—by a

specified set of system-metric indices?). The aims of science are taken as: "To describe

currently whatever is studied so as to explain its past, to predict its future, and to control it ever

better for man's ends." (Note that the qualifying limits needed in the above seem unknown still.

(Editor’s Note: The following pages contain a table that was difficult to read in the original

which was printed in landscape mode on a single sheet of paper. I have expanded the original

by taking the first 6 columns plus the last column of the original as the first set and then taking

the first column and the last 6 columns as the second set. The first and last columns are

general explanatory columns so they were needed for both sets of columns.)

Dimension of Cosmos

81

DOMAINSof the 12formulas

SYNTACTICOPERATIONS

"Reiterings."defining thecategories

MOMENTSof frequencydistributions(discrete &central)

CATEGORIESof knowledgeorganized byoperationsof Col. 1 & 2

SYMBOLING,the MENTALparameters,i.e. Imaging

DIMENSIONSof Mechanics

Schwarzschildsphere system

COMBINA-TORICpowers ofbitbits,22m = 4rn mgLIFE formula

GENERALFORMULASFOR ROWS

In bits ofOrganization

= θ = lg xm

FORMULASAntilogsBits-log2s

Col. 0

Sm

m lg SCol.1

Xm

m lg XCol. 2

Am

m lg ACol.3

Jm

m lg JCol. 4

(C/2π)m+1

(m+1) lg (C/2 π )Col. 5

4m = (22)m

m lg4 = 2mCol. 6

Xm

θ = m lg XCol. 13

Descendinglevels oforganizationθ = lg A

4

4

SIV , Sss

= "TIERING”into LOG-TIER

eg e2m

πi = 1

X4

FOURTHMOMENT

KurtosisUnimodality

AIV

SUPER-SYSTEMS

Parameter i.e.Compounds

of Cpd units

i4 = i1 • i3 = 1NAME and

THING-NAMEDexplicitintersect

(C/2π)5

= M0L

0

2

/ T0

3

= P0

= V0

5

= POWER

44

= 256= BITBIT

FULFILLED

X4

θ4 = m lg X4

A FOURTHPOWER

3

SIII , Ss

= SELFMULTIPLYINGInto POWERSeg (e2πi)t = 1t

X3

THIRD MOMENTSkewnessAsymmetry

AIII

SYSTEMSparameter

i.e. Cpd units

i3 = -i = 1/iTHING-NAMED

onlyi.e. Referent

(C/2π)4

= M0L

0/ T

0

2

= F0

= V0

4

= FORCE

43

= 64= BITBITCUBED

X3

θ3 = m lg X3

A THIRDPOW ER

2

SII , Ss

MULTIPLYINGinto

PRODUCTSeg a/ct = 1

X2

SECONDMOMENTVariance

Dispersion

AII

RELATIONSparameteri.e. Syntax

i2 = -1NAME of a

NAMEMetalanguage

Parameter

(C/2π)3

= M0

/ T0= V

0

3

= MASSCHANGE

42

= 16= BITBITSQUARED

a Self-product

X2

θ2 = m lg X2

A SECONDPOW ER

1

SI , sS= ADDINGinto SUMSeg Σpi = 1

X1

FIRST MOMENTMean Central

Tendency

i AI

QUANTITIESparameter

i.e. Mathematics

1 i = √1_

NAMEonly

(C/2π)2= M

0

/ L0

= V0

2

= POTENTIAL

41

= 4 = BITBIT= Fulfilled bit

4 = (2,2) = 2+2=2 2

X1

θ1 = m lg X1

A FIRSTPOW ER

0

S0 = 1 , sS = 1= LISTINGinto SETSeg U0 = 1

Universe

X0

ZEROTHMOMENT

Frequency, NArea Unit

A0

QUALITIESparameter

i.e. language

i0 = 1A SYMBOLName and

Thing –namedmerged

(C/2π)1= L

0

/ T0

= V0

1

= VELOCITY

40

= 1=A BITBIT SET

= A foursomeunit, quarter

X0

θ0 = m lg X0

A ZEROTHPOWER

Dimension of Cosmos

82

DOMAINSof the 12

formula

BINARYNUMBERS

Bits asDimensions of

mechanicsNORMALITY

COSMICCONSTANTS

“the Crux"Power Series

COSMICACTION

In STAGES &HIERARCHY ofSCIENCES by

size of Acton A

COSMIC TIMEPERIODS

as Fractionsof a log

cosmocycle, TU

(TU =1032

years)

COSMICORGANIZATIONin nit cycles

SOCIETALIDEALS

measurable bysix moments fdesiderata Cf

US Constitution

GENERALFORMULASFOR ROWS

In bits ofOrganization

= θ = lg xm

FORMULASAntilogs

Bits-log2s

2m

m lg 2 = m2

Col.7

r'

mh

'm l g r + I gh

Col.8

Cn

2m= 2

mrr

m (lg Cn

2) = mr

r

Col.9

%Tc = 2m-4

m-4

Col.10

eθi=e2m

πi

= E = 1in log cycles

lg lnE =m+lgπCol.11

vm

__

m (lg v4)

Col.12

Xm

θ = m lg X Col. 13

Descendinglevels oforganization

θ = lg A

4

24 = 16= 4 BITS

= FORCE0

= MOMENTUMif L0 = 2, T0 =1

0

r'

4h

'=

478.3576458=U13 -.378 %Δ

=SIZE OFUNIVERSE13

4rr

Stage I296 bit primons

Level Ai =SEMIOTICS

Level A =SOCIALSCIENCE

TU = 24-4 = 1COSMOCYCLE

=1032

years

= 102

5

= 10e

r

= er r

2πi • 8 m = 4 = EON

= 1 STAGE= 8 natural

cycles

m = 40 Kurtosis

No bimodality= UNITY

X4

θ4 = m lg X4

A FOURTHPOWER

3

23 = 8= 3 BITS= MASS0

if L0 = 2, T0 =10

.

r'

3h

'=138.0399578= α

-1 - .767% Δ = FINE

STRUCTURE

3rr

Stage II222 bit primons

Level B =PSYCHOLOGY

Level C =BIOLOGY

TC = 23-4

= 1/21st HALF-

LIFE= 1016 years= 1

st& 2

ndEra

2πi • 4 m = 3 = EON

ln Ce = 8π SPEED of

LIGHTin mm/sec/3

m = 3

0 Skewness= JUSTICE

X3

θ3 = m lg X3

A THI RDPOW ER

2

22 = 4= 2 BITS

= Fulfilled bit= POTENTIAL0

= PRESSURE0

if L0 = 2, T0 =10

r'

2h

'=39.86313715

= G -.975% Δ = GRAVITYconstant

2rr

Stage III148 bit primons

Level D =CHEMISTRY

Level E =PHYSICS

TU = 22-4 = 1/41st ERA

= 108

years= 1

st& 2

ndStage

2πi • 2 m = 2 = SEMIEON= 2 natural

cycles

m = 2N

2=0:EQUALIT

Y ofopportunityr12 = 1: LAWand ORDER

X2

θ2 = m lg X2

A SECONDPOW ER

1

22 = 4= 2 BITS

= Fulfilled bit= POTENTIAL0

= PRESSURE0

if L0 = 2, T0 =10

r'

1h

'=11.50749648

= CL -.042%Δ = SPEED OF

LIGHT (in mm)

1rr

Stage IV74 bit primons

Level F =ASTRONOMY

Level G =GEOMETRY

TU = 21-4 = 1/81st STAGE

= 104

years= 1

st& 2

ndEons

2πi • 2 m = 2 = QUADREON

= 1 natural cycle

m = 1ΣV

1/N=0:MEA

N ofopportunityr12 = 1: LAWand ORDER

X1

θ1 = m lg X1

A FI RSTPOW ER

0

20 = 1= the SET

of BITS.= TIME0 as

the unit ofDENSITY0

r'

0-h

'3.32193 lg 10

ROOTCREATANT

constant

0rr

Stage V0 bit primons

=RANDOMNESSof ENTROPY

at nadir ofcohort cycle

TU = 20-4 = 1/16= 1

stEON

= 102

years=1

st& 2

nd

semieon

πi m = 0 OCTEON

= ½ natural cycle= Permutive

unit of reverseorder

m = 0Σv

0/N = N/N = 1

Frequency ofAlternativesN-1 degrees

of FREEDOM

X0

θ0 = m lg X0

A ZEROTHPOW ER

Dimension of Cosmos

83

KEY to new SYMBOLS:

m = integer "Powers"= (0, 1, 2, 3, 4)A="actants" defined as things-namable

= (Hyp) Action = Energy x Time = ML2/Ty'= "Root-3"= √3 = 1.73205 = r/2

h'= "Root-Creatant" = lg 10 = 2

y' = 3.32193 = √c =

.. σ2(2π)

r'= “Crux" constant = lg c = √12 = 3.46110 = lg r

'!

C = Speed of Light = 3 x 1010 mm/sec/3Cn = Creation Rate = 10c mm/sec/3S = any symbol1q = Schwarzschild system10=."Zero exponent" denotes a set, a quality, a kind

The PAN-ACTS M0DEL for the cosmos develops the sixty cells values above. This modelstates in a 4-word version: "ACTANTS' INTERACT ORGANIZE COSMOS”. More fully in 40words it claims for testing: "If all n actants interact in all their possible nn ways, then they

produce the cosmos and all its parts--at a Creatant of √c =.. 11 = 2

2y' in 8 normal “space”

levels within each cosmic cohort cycle (of 1032 years). This model is spelled out in the Pan-Actsequation a/ct = 1 (where a = log actants, c = creatant rate and t = Time) and is graphed in theMass-Time triangle.

Dimension of Cosmos

84

Plate 19b: Fruitage by Fields

EpiDoc 316:4R by S. C. Dodd

Univ. of Wash.

A GUIDE TO USERS OF THESE EXHIBITSSpecialists in the fields below may find the Conspectus pages cited below of most interest

(Editor’s Note: This table and the page numbers are from another volume in the Dodd Memorial Library series: Dimensionof Cosmos. This table is included here for consistency, thoroughness and to show the breadth of application of Dodd’stheories.)

Field Exhibit A Page Exh ib i t s B Page1 Mathematicians: Rectifying Distributions 365 Rectifying Normal Curve 372

2 Astronomers: Permutive Gravity 292 Lowest MTT Levels 297

3 Physicists: Bits = interdimensionalunits

324 Radiation Spectrum 3124 Gravity Physicists: Permutive Gravity 294 Perm. Grav. Exposition 294

5 Chemists: Key Periodic Table 272 Key Periodic Table 273-275

6 Biologists: Fit of Living Cells 313 Serial Squaring 3577 Psychologists: Organization is

Logarithmic300 Motivating Conditions 379

8 Social Scientists: Transact Matrix 381 Momental Models 338

9 Statisticians: Random Organizing 326 Building the Moments 340

10 Sociologists: Counteractance 336 Transact Organization 305

11 Political Scientists: Synthesizing Self, etc. 393 US ConstitutionPreamble

37012 Semanticists: Zero Exponent 346 a + bi = Any Symbol 355

13 Linguists: TILP 414 Cosmic Units 26014 Journalists: Logistic Diffusion 334 Creative Fulfillment 392

15 Religionists: Pan-act-theism 264 What is Liked Most 26816 Social Actionists: Future Molding Game 362 Societal Planning 377

17 Methodologists: Testing Consistency 399 About the Modeling 321

18 Measurers: 3 Axes & 9 Dimensions 355 Testing a Fits 401

Dimension of Cosmos

85

19 Graphists: Unital Cube 252 Cosmosphere 24620 Chronologists: Anti-log Time 327 Time Axis 328

21 Hierarchists: Periodicity Tested 308 Creatant Line Found 310

22 Isomorphists: Trans factors & Levels 380 Transition Equations 394

23 Set Theorists: Pan-Acts in Sets 368 Pan-Acts in Sets 36924 Structuralists: Explanation. of Gambits 382 Explanation of Gambits 383

25 Functionalists: 4 Stochastic Laws 302 4 Theses in Pan-Acts 303

26 Evolutionists: Ultimate Questions 266 Gambits Grid Cylinder 286

27 Systemists: 3-Axis Cosmos 319 64 Features 31628 Metaphysicists: How Actants Unify 258 Cosmic Hypotheses 242

29 Ontologists: Gambits Chart 278 Mass-Time Triangle 24130 Cosmologists: 15 Versions 248 Epicosm Theory

Restated238

31 All Scientists: Consequences 396 Pan-Acts Theory 31732 Philosophers: 12 Applications 405 Fruitage by Fields 411

Dimension of Cosmos

86

Plate 20: Testing Epicosm Models of the Cosmos

EpiDoc 196by S. C. Dodd

June 16, 1970Univ. of Wash.

Seattle

98195

(Table 1*). This page reports: A Consistency Test on the 4 real Key Constants, K (= r, h„ n, 3)showing them

interconvertible within .1% (as tabled below).

A scientific model (or operationally specified theory) of some activity, A, is here called "atheory of A," or just "Model A." The Epicosm models study the activity (i.e., phenomena) of thewhole cosmos. The cosmos is operationally defined as the universal set (= U° = 1) of allnamable elements (called "actants"). The cosmist tries to analyze the cosmos in such termsthat their re-synthesis, if by operationally specified formulas, will restore the mole unitarycosmos, fully and exactly.

To assure and measure this resynthesis, four sorts of tests are used as follows:

1. Consistency tests measure the internal logical agreement in the statement of Activity Aamong its symbols whether concepts or sentences, units or scales, relations oroperators, a system and its sub- and super-systems, etc.

2. Correspondence tests (called "validity") measure the external empirical: agreementbetween the theory and the facts, between the supposed vs. the actual referents of thesymbols, between expectations by the model vs. experimental outcomes.

3. Concordance tests measure the telic agreement across time between the model'sperformance and the prior aims of scientists (to so describe as to explain, predict, andcontrol better).

4. Convergence tests measure the percentage of full agreement among all the tests of themodel's analysis and resynthesis of the cosmos.

In this Table 1, the Key constant in each row is converted into the Key constant of thecolumn by a formula involving only: the 4 Key constants, the 4 Key operations on them, and apercentage discrepancy called the "slip." This slip measuring the approximation to the rowconstant is the third entry in each cell. In exploring the Epicosm submodels, slip up to .4% istolerated. The average slip in this Table is .1% or one part in a thousand. One might say: TheKey constants appear to be 99.9% interconsistent by this interconversion test.

For fuller specifying of theory testing generally and scientific methods used in Epicosmmodeling, see S. C. Dodd, "Scient-Scales for Measuring Excellence cf Research Methodology,"American Behavioral Scientist, June,1966 , Vol. IX, No. 10.

Dimension of Cosmos

87

sK

Key ConstantFormula Name

cy

-2

Euler's Constant

π

Pi

h'

"Root Creatant"

r

"Crux"

r = 3.45986

=def

N/σN=N/N/r

= r = √12

r = 2cy

-1

+ .00424 or.1% r

= 2π/√h = π +1/ π + .01250 or

.36% r

r = 2 lg h'

+ .00418 or.1% r

r = N/σN =___N

√12=

√12 + .0000 or

.00% rh

'= 3.32193

=def

lg 10

h'= 2c

y

-1

+ .00100 or.03% h

'

h'= r lg3 / lg π

+ .00145 or.04% h

'

h'= lg 10

+ .00000 or.00% h

'

h'= 2

r/2

+ .00481 or.14% h

'

π = 3.14159

=def

Γ2

(1/2)

π = 3r/h

'

+ .00159 or .05% π

π = Γ2

(1/2)

+ .00000or .00% π

π = r√h'/2

+ .01141or .36% π

π = 3r/h

'

+ .00159 or .05% π

cy

-2= 3.0

=def

ln-2

y

cy

-2 = Γ d(1)*

+ .00000 or

.00% cy

-2

cy

-2 = π

h'/r

+ .00100 or

.03 % cy

-2

cy

-2= (lg h

')2

+ .00010 or

.003 % cy

-2

cy

-2= (r/2)2

+ .00734 or

.2 % cy

-2

* Illegible in original

Dimension of Cosmos

88

REFERENCES1. MYTHS TO LIVE BY by Joseph Campbell, Bantam 19732. BOOK OF THOTH by Aleister Crowley, Weiser 19443. DATA STUDY by J.L. Jolly, McGraw Hill 19684. THE TETRAMATRIX FOR MODELING MACRO SOCIOLOGY by Stuart C. Dodd, PhD,

1970

Dimension of Cosmos

89