APPENDIX
STUART C. DODD Department of Sociology, University of Washington
Seattle, U.S.A.
Summary
Let cosmos = Uo = I = the universal set of all nameable elements, n in number, and let them be called "actants". Hypothesis 1. If n actants interact, reiterantly, randomly, and ceaselessly, then they will always be forming and unforming compound actants, each in its own life-cycle, by trying out all their nnpossible combinations, or permutations, or repetitions, and thus operating the cosmos and all its parts largely by the "key" self-reiterant processes (i.e. 2n, n2 , 2n, nn, uncreated creators of all that was, or selfmade makers of all that is, forever working towards greater fulfillment (= nn) of what may be. More exactly: if all n actants thus interact, they form the cosmos overall at a fixed creation rate, C, in 8 levels of organization, each a normal distribution with its average life-cycle in one eon or log century of time - all as more fully hypothesized in the epicosm model.
The specifications for this epicosm model of the cosmos are as follows. The model tries to state the following:
(A) A semiotic system which describes, extensionally in terms of sets and elements, man-symbol-thing systems. So some of the model's symbols (concepts, scales, operation signs, etc.) become some of its substantive variables. (See Rows A and B of the Reiteratings Matrix appended as Exhibit D.)------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
(page 393)
(B) A stochastic system which explains probabilistically how each state yields the next by reiterant operations.
(See Row B of Exhibit D.)(C) A self-reiterating system which predicts continually its own self-creating (= 2n), and self-fulfilling (= nn)
(See Row C of Exhibit D.)(D) A testable system which controls, by indices above 99%, (1) its reliability in descriptive reobserving, (2) its reproducability from explanative antecedents, and (3) its agreement with predicted outcomes. (See last section, Exhibit D).
The features of the epicosm model in five versions (A) - (E) follow herewith.
(A) Popularly stated, the core
epicosm hypothesis helps to describe the cosmos thus (in either four or
eighteen words).
If all n ACTANTS' INTERACTS occur in nn ways, then they con-
tinually ORGANIZE COSMOS and all its parts.Here:
cosmos = the set of all things namable;
actant = any thing namable as its element;
interacts = any repeatings, combinings or permutings of actant elements or sets of them;
to organize = to interact = to build;
continually = ceaselessly = without start or stop;
occur = happen = reiterate;
parts = pieces = samples = aspects(n is estimated by the model as Cn7=1077 = 2256 real and rising primal
actants in the 7-level universe, so nn = 2 raised to the power of 2264
(B) Algebraically stated,
the epicosm equation helps explain cosmic growth thus:
Uo = 1 = a/ct(C) Geometrically stated, the Mass-Time Triangle (MTT) graphs the epicosm model in Exhibit A.
This says: "The universal set of cosmic actants is unitary (Uo = 1). It builds up to level t as the number of actants at (in logs), which equals the constant creation rate, C ( = lg2 10 = 11), if multiplied by the time taken, t (= 1, 2, 3, 4, 5, 6, 7, 8), so c = a/t."
It shows cosmic self-control, or complexity, H, as an area or product of actants x interacts, of abscissa x ordinate, of(page 394)
A x lg A, of n x lg n (so H = n lg n = lg nn = a self-power or fulfilment of possibilities in bit units).Exhibit A pictures the cosmos (i.e. the n actants) if organized, or built up, as self-products, into seven real levels and one top imaginary level. This top level measures all symbols or speech acts of society. This integrates all communicated mental activity with all other cosmic activity - perhaps the first non-mystical mathematical model to achieve operationally such integration of mind and matter. (See Exhibits A and B for details.)
Four inductive steps discovered the MTT as follows.
(1) Plotting masses of actants found the interlevel quantum jump (Cn = 10±11 tons).(2) Plotting these against their time sequence, t, found high correlation (rnc.t = ±1.0 ).
(3) Plotting masses against levels found their constant log creation rate, (= log Cn = c/1 = 11).
(4) Plotting ± c found the isosceles triangle (MTT) or normal-curve-in-logs, which the central limit theorem proves to synthesize all distributions of means of actants in the cosmos.
By deductive steps, one can read off averages from the MTT for each
level in turn, its smallest mass and size, frequency
and age, number of actants and interacts, degree of organization and complexity,
and rate of cosmic evolution and devolution. All these are hypotheses deduced
from the epicosm system, a/ct = 1, ready for further empirical testing.
(D) Technically stated, the Epicosm theory helps cosmic predicting as follows (see EpiDoc 128).
If all n actants, or things namable, interact(page 395)
= the core hypothesis
and do so randomly, reiterantly and ceaselessly,
= 3 postulate hypotheses
thus forming and unforming in life-cycles
= the universal cyclic hypothesis
all combinations, permutations or repetitions
= the combinatoric hypothesis
in all their possible nn ways.
= the fulfillment hypothesis
Then they form the cosmos and all its parts
= the core consequence hypothesis
as a vast normal probability distribution,
= the normal consequence hypothesis
organized in 8 levels of complexity, at = ct
= the 8 levels consequence hypothesis
at a creatant rate, c, of actants c = log Cn = lg210 = 11.03522
= the creatant consequence hypothesis
organized one level per eon or log century of time, t,
= the eon-century consequence hypothesis
by compounding self-reiterant processes, Ks = 2n, n2, 2n nn
= the Key reiterants hypothesis
- all as spelled out further in the epicosm modelling
= the residual epicosm hypothesis.
(E) (1) Statistically stated,
the Epicosm modelling applies the theory of stochastic processes to the
cosmos, if cosmos is defined as the unit universal set, Uo =
1, of all things namable.
By this definition, or semiotic operation, everything in the cosmos reappears as a fraction of one. Then in the future tense, everything can be, in principle, measured as a probability or proportion of unity. Every science then seeks to discover the precise amounts and relations and systems of compounded probabilities of its actants (or "phenomena-viewed-as-sets"). Since every probability density function adds up to one by definition, these stochastic functions express alternative and specifiable ways of analyzing the infra-structure of any set up to, and including,, the cosmos. Stochastic formulas then portray cosmic phenomena as the probable acts of cosmos.
(2) Thus the binomial and normal distributions arise from the simplest
intra-acting of a set of n elements (= no
= 1) with itself n times when structured
into its two half-lives:
(no)n = (1/2 + 1/2)n= (p + q)n = 1n = 1 = (nn)0= 1 set.
(3) In polar co-ordinates,
eøi = cos ø + i sin ø = e2pini (= 1n = 1 = Uo for interger n). This on-going unitary cosmos, Uo= 1, is analyzable into cycles of a cohort of actants. Thus as e2pinti = 1nt = 1, the eon cycles are of size or radius n, = 1/t, and t = 8 in number, so nt = 1. This is here hypothesized to measure cosmic activity as n actants, and cosmic time as t cycles, in general.*
Then their product, activity x time (in erg seconds), or A x
t or n x lgn (= H) can measure the complexity of the universe as
an area in the mass-time
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* n and t are ordinarily taken as finite,
representing a finite slice, or sample, of a potentially
infinite number of interacts. When n and t are
infinite, one is then talking about "the eternal cosmos", and not about
the current finite slice of its constant and ceaseless on-going.
(page 396)
triangle, defined by any specified n and t (such as "the spatial universe", "the material universe", "the living universe", "the mental (i.e. verbal) universe", etc.).
(4) All this stochastic interpretation of the unit cosmos, Uo = 1, may go far towards explaining the cosmos causally by combinatoric processes, themselves products of reiteratings, Ks, of actants. If this semiotic hypothesis holds up, man can say:
"Reiterant interactions of actants seem to describe the content of the cosmos, as Uo= 1 = a/ct; and explain their continual creation as the characteristic function of a single random process, i.e. E e2pini, and predict their future as the Gompertz entropic growth and decay curve of cosmic evolution and devolution, i.e. pt = 1 - q2t.All these and other stochastic submodels are semiotic hypotheses, that spell out the epicosm modelling in detail - which is largely awaiting exploration.
IMPLICATIONS
The implications of the epicosm model, too manifold for full discussion here, may be suggested by the notes below.
(1) The whole epicosm modelling has been formally systematized in a tight semiotic theory of 32 hypotheses, for eventual publication and wider testing, (See EpiDoc 42.)(page 397)(2) Over a hundred tests of fit, averaging above 99.5% of agreement, have
been run between the model's formulas and major constants of mathematics
and the physical sciences. e.g. G of gravity, C, light, F, Faraday's constant,
in one series; e = 2.7182, cy = .5772, i = sq. root of -1, 0, 1, 2, 4 in another series, etc.(3) Lists of many further testable fits await funding to execute.
(4) Two technical hypotheses of high promise seem to be: "If the reiterating matrix (see Exhibit D) is systematically explored and tested, cosmologists will gain measurably in explaining and predicting cosmic activity."
(5) "If the key periodic table for generating cosmic constants (EpiDoc 144) were similarly expanded and fitted, cosmologists could measurably improve cosmology."
(6) Two highly controversial, yet important, physical hypotheses are: "Epicosm theory is more able than current physical theory to account for negative entropy whereby the cosmos, with no external source of energy, yet builds up the stars, galaxies, and all other organized entities to their current state."
(7) "If antilog time scales, at, were appropriately substituted for the present standard sidereal time scales, ts, where atdef = ets or lnat = ts, then the universe would reappear as non-expanding consistently with the red shift and all other empirical facts. This calls for semantic, not hardware, testing. This antilog time hypothesis seems not only to produce a constant universe but it also seems fully to solve the problem of creation, whether gradual or sudden bang, by predicting and postdicting an eternally existent, and overall constant, on-going.
Five hunches, for example, expect that epicosm modelling might help
(8) to explain anomalies of quasars,
(9) to systematize subatomic particles,
(10) to develop a unified field theory,
(11) to predict fission of photons into gravitons,
(12) to generate curved space and gravity from a random state of completed entropy; etc.
Note four Epicosm hypotheses of human import:
(13) One hypothesis expects that on our Earth total evolution will accelerate in verbal and mental ways more than in physical or physiological ways.This leaves great freedom for men to hasten or hinder, to redefine or alter such fulfillings as they desire. The design of the cosmos and all its parts including man seems to tend toward mutually compatible self-fulfillments.(14) Another hypothesis expects that inner-directed or self-governing systems whether in atoms or cells, persons or nations, tend to gain compared with outer-directed systems.
(15) Based on the physicists estimate of 1078 particles in the universe, the mass-time graph expects well over a hundred billion, 1011, Earth-like planets with conditions suitable for humanoids to have evolved on them.
(16) Finally, a summarizing hypothesis expects that human systems, in common with all systems, will tend with sufficient time towards fuller trying out and consequent greater fulfillment ( = nn) of their potentialities.
APPENDIX 1: EXHIBIT A EXPLAINED
Exhibit A graphs the cosmos overall as a unit isosceles triangle or normal curve on log co-ordinates. Its internal structure is pictured (by these loglog units) as a hierarchy of eight nested triangles with a common apex. Their eight base lines represent the eight levels of increasing complexity into which cosmic activity (i.e. phenomena) seems currently organized. These ascending levels seem to evolve in eight successive log-time periods. They go from the state of completed entropy at the bottom (Level G) to the mental activity of
(page 398)
The Mass-Time Triangle Diagram (linked gif diagram)
(the MTT is also available as two separate, unlinked pdf files on this website):
http://people.clarityconnect.com/webpages3/jag8/mtt90.pdf (vertical)
http://people.clarityconnect.com/webpages3/jag8/mtt180.pdf (horizontal)
(MTT diagram courtesy of Dick Spady and Niche Press)
(page 399)
symbols used by society at the top (Level Ai). The graph therefore shows
the evolving of cosmic action (or phenomena measured in erg seconds) within
each first half-life of every cohort of cosmic action elements (called
"actants").
The co-ordinates in the graph of this mass-time triangle are in units of common log cycles. The abscissa is measured in metric tons (convertible into erg seconds). When generalized, it represents the amount of activity, a, or number of actants at any level, t. Then the ordinate simultaneously represents (a) the rank in complexity of the level from 1 to 8 (in units of the creatant, c = lg210 = 11.03522 =11); (b) the degree of organization (as a log of the activity); (c) the amount of interaction of the actants (in log cycles of self-products); (d) the correlated time, t (in logs of centuries ago).
Then the equation for the two sides of the mass-time triangle in logs is -ac = ± ct. This says that the cosmic activity (at) or number of actants at level t equals the creatant, c, or rate of organizing that activity, times the period (t) it took. This equation for the cosmos, = Uo = 1 = a/ct (when the cosmos is extensionally defined as the universal set (= Uo) of all namable elements) summarizes the epicosm model.
The mass-time triangular distribution can be interpreted when re-graphed as a log transformation of the normal probability distribution of' all actants
in the cosmos. To show this, take natural logs of the normal equation, transforming it to a parabola, i.e. ln(y) = ln(e |- X2/2|) = - x2/2 and then take bits-logs transforming the parabola into the MTT's straight-line sides, i.e., lg lny = lg |-x2/ 2| = 2 lg x - 1 or T = (± )2M - 1 where T = lglny = time and M = lg x = mass.
Viewing the cosmos or universal set of all actants (or phenomena)
as a normal distribution is supported by the central limit theorem and
the binomial theorem. The former says in effect that properly adding all
distributions of actants in the cosmos together must yield a normal distribution.
The binomial theorem says that n rounds of full interacting, or self multiplying
of the rising and falling halves* of the cosmos (as (p + q)n
= 1n = 1) will also yield a unit normal distribution.
Thus, the cosmos, if built of randomly interacting primal elements (or
like elements at any level) will organize itself continuingly as a normal
distribution if looked at through these symbols or concepts of randomly
interacting halves.
Thus, an extensional and semiotic re-viewing of the cosmos opens up
vast vistas for science and for human understanding of everything around
and
___________________________________________________________________________________________________________________
* Or halves of any set where p = q = .5 and
no = (no/2
+ no/2)
= p + q = 1 .
(page 400)
within us. For this normal cosmos entails for every properly specified actant, or compound of them, a unique and computable and absolute probability of occurrence. Every science is then seen as the re-search on how best to specify actants in its field by the most fruitful empirical techniques of observation and semiotic* techniques of symbolizing. The epicosm modelling is largely a semiotic inquiry to find more fruitful concepts - such as "actants", "interactants", and "reiterants", etc., seem to be.
A dual interpretation of the mass-time triangle - in its static versus dynamic aspects - should be well understood. Just as the formula for the circular circumference, 2pin, can be graphed either as one circle of radius n or as n circles of unit radius, or just as "a set of elements" should be seen both as a unitary set and as a plurality of elements, just so the epicosm formula, a = ct, and its graph (the MTT) should be viewed both as a static picture at one date of eight cohorts of actants varying over eight different phases of their life cycles#; and also as a dynamic picture at eight dates of one cohort of actants evolving through eight successive phases of its life-cycle.
Further interpretations of this normal cosmos when viewed through log units are tabled as readings from the full mass-time graph. These estimates, for each of the eight levels of cosmic organization, its probable minimum, median, and maximum of equivalent mass, time span, age, length, number of actants (= A), degree of organization (= lg A), degree of complexity (= A lg A or lg AA), fulfillment (= AA), and rate of organizing (= A/lg A) or average speed of evolving and devolving.
Thus, the epicosm model's induction of a normal cosmos seems fruitful for many important deductions - all as hypotheses to be tested, of course.
APPENDIX 2: EXHIBIT B EXPLAINED
Exhibit B plots all material entities in the cosmos by their mass, cross-classified against their rank in organization. It tells how the epicosm model was developed by inductive steps. When actants were listed by increasing weight, an important periodicity emerged. Equal intervals of eleven log cycles, 1011, a factor of one hundred billion, were observed between the smallest entities at each of the four most observable levels of organized actants. (See the four dots in Exhibit B.) The threshold actants at the successive levels of matter, life, man, and society fitted well to the straight
_____________________________________________________________________________________________________________________
* Semiotics is the science of man-symbol-thing relations or systems.
# Or first, and rising, half-life cycles, more exactly.
(page 401)
(image page 401 here - EXHIBIT B (under construction))
(page 402)
diagonal line, C. (See Exhibit B.) This line measured a constant rate of organizing 1011 actants per level or per log century of time (since sequence in organizing showed a perfect rank correlation with log intervals of time). This rate of organizing is interpretable as the cosmic speed of evolving, i.e. a creation rate of a hundred billion (= Cn = 1011) actants organized per level or eon of time, if reckoned back from the present.
This "rate of evolving" hypothesis (that expects a constant ratio between interlevel jumps in organization of actants and their correlated time periods) was then explored further. It was dramatically found to hold if extended in this mass versus time graph both upwards and downwards and even sidewards in a symmetric and complementary downslope taken to measure a rate of devolving from an apex.
Details of these extensions, as hypotheses generalizing the rate of evolving index, C, to all levels of cosmic activity or phenomena, are developed in the 160 EpiDoc mimeographs or working notes prepared to date for checking and eventual publishing. Here these exhibits will simply sample these semiotic hypotheses which claim that better symbolizing can make better relations among actants, and systems of them more observable and testable.
Glimpses of fruitful consequences of extending this constant creation
rate*, C, upwards, downwards, and sidewards in
the mass time graph may be seen through the following four sentences
that state four "extension hypotheses".
(1) If the constant creation rate, C, is extended upwards (by using complex numbers) through Level Ai in the mass time graph, then all society's speech activity and consequent mental life will become more observable and testable as that special case of the epicosm formula, a = ct, for all cosmic activity, or phenomena, when t=1 (i.e. the ever-current present century).(2) If the constant creation rate, C, is extended downwards (by equaling C to the speed of light) in the mass-time graph, then all the physical phenomena and laws invoking radiant energy, or gravity, or completed entropy will become more observable and testable as those three special cases of the
epicosm formula, a = ct, for all cosmic activity when t = 6 or 7 or 8 (i.e. their formative period between ten billion and ten quadrillion years ago).(3) If the constant creation rate, C, is extended downwards and rightwards from an apex (by using its opposite sign) in the mass-time graph, then the upper limit of actants in each level and the nature of all cosmic on-going as the concurrent life-cycling of all its actants, in cohorts by levels, will become more observable and testable. This is the reversed or devolving case of the epicosm formula, a = ct, for all cosmic activity when t rises from 1 to 8, measuring increase of positive entropy, or "heat death", or disorganizing of each cohort of actants in its second half life.
(4) If the constant creation rate, C, is extended by rotating it 90 degrees in the mass-time graphing, then all cosmic activity becomes more observable and testable as a vast, normal, probabilistic and stochastic process which, as t varies from 8 to 0, varies from purest chance or least predictability (with p = (10-2c)8 = 10-176 = 0 at Level G) to perfect law or complete predictability (with p = (10-2c)0= 100 = 1 at Level A).
Exhibit C is entitled "The mass-time triangle extended through the radiation spectrum". This graph enlarges and fills in the mass-time graph from the Level F for gravity through the energy Level E and up to the matter Level D. It shows that the action or phenomena of radiant energy and gravity in their varying degrees can be viewed as a special case (when t = 5, 6, 7 in a = ct) or representative sample of overall cosmic action and laws. One can either generalize to (i.e. induce) the cosmic law, a = ct, from this graph, or particularize (i.e. deduce) this graph in physics from the larger law of cosmic activity, a = ct.
This radiation spectrum graphs the wavelengths plotted against their frequencies for waves of radio and radar, visible light, X-rays, gamma rays, and cosmic rays, up to the electron or threshold of matter.
The slope of the graphed line represents the speed of light which is C = 3 x 1010 cm/sec.This becomes Cn = approx. 1011 mm/third-of-a-second when translated into millimeters and third-of-a-second in the simplifying and systematizing terms standardized throughout the epicosm modelling. For then, Cn = 1011 becomes approximately the cosmic creation rate or ratio of actants organized one level upwards per eon of time, throughout the mass-time graph. Then, the graph measures the rate of organizing photon actants into
(page 404)
(image page 404 here; EXHIBIT C (under construction))
(page 405)
particle actants and the rate of organizing or creating photons (of about 1 mm wavelength) from the hypothetical gravons (of about Cnmm wavelength),
A useful consequence of equating the creation rate to the speed of light (in appropriate units of length and time) seems to be that the mass-time graph, if amplified as in Exhibit C, can be used to read off or predict the results of clean fission or fusion between photons and particles. Thus, when a laboratory's clean fission of a proton and its paired anti-proton into a pair of photons of exactly the same mass was published, the wave length and frequency of those resulting photons was read off correctly from the mass-time graph interpreted by Exhibit C.
Furthermore, the mass-timc graph enables predicting clean fission and fusion between specified photons and the hypothesized lower levels of gravons as elements of gravity at Level F and entropons as elements of the state of completed entropy at Level G.
Thus, the epicosm modelling seems to offer powerful symbolic tools for analyzing the activity of gravity and entropy where hardware tools are not at present adequate.
APPENDIX 4: EXHIBIT D EXPLAINED
Exhibit D is entitled "The reiteratings matrix, Rrc, for cosmists". It tells broadly how scientists, starting from scratch without even a language, can build models for the past, present, and future cosmos. Row A of this 4 x 4 reiteratings matrix tells how every symbol that man ever uses is built by the trio of acts called "reitering". Reitering is operationally defined in Row A as the intersect or product of three acts, namely combining a name and a thing named; repeating that naming among people, occasions, and contexts; without permuting or changing it. This trio of combinatoric speech acts seems to create every standardized and socialized and recurring symbol known or knowable to man.
Then Row B tells how four successive and cumulative rounds of reitering produce the four "key operators" and operations of all mathematics, logic, and language. Compounding these operations builds all syntax. Syntax in turn relates all symbols together producing all language and the communicated knowledge of man.
Row C, next, tells how the simplest and most probable self-reiterings of the four Key Operations form the four "Key Processes". These, when mixed
(page 406)
and blent as sums and products, etc., seem to produce the regular entities and their formulas of whatever exists or happens around us and within us.
Finally, Row D organizes cosmic on-going or
phenomena in four submodels by tenses. These try to help explain the past
causation of the cosmos; to describe its present contents; to predict its
future consequences; and to control more and more of its compounding at
any time. The synthesis of these submodels produces the epicosm model.
This tells how the n cosmic actants, interacting in their nn
ways
that tend to fulfil all their possibilities, continually organize the cosmos.
Its summarizing epicosm equation, Uo= 1
= a/ct, asserts for testing that the unitary cosmos, if defined as the
universal set, Uo, of all things namable,
is organized in eight levels or subsets of random and reiterant actants
(at=8 )which are ceaselessly and constantly formed and unformed
by the creation rate (c) and the time taken (t).
(Comment by JCG) : Refer to the four operations of Table D, row C, and take n = sq. root 3 . We then have: 1) 3.46 (r); 2) 3; 3) 3.32 (h); and 4) 2.59 (f); all rounded to nearest hundredth, and in what follows the "fit" is approximate not exact:r lg r! = lg h2 = 2 lg lg 10 = 3pii/e.
h lg 10 = 2 sq. root 3 , so lg lg 10 = sq. root 3
f = lg 6 = anti lg k where k = Boltzman's constant /100, or log k = k/ 10
*******************
Or take n = t, where tt = 2, then(page 407 - 408: Dodd's 4x4 matrix))2t = 3.16 = sq. root 10; t2 = 2.50 = u, where uu = 10,
2t = 3.00 and tt = 2. One could go on with other equally remarkable equations, for the set of operations in row C is basic, being a special case of the generator:
(1 + n-1)n
whose upper limit is e. Sets are the basis of Dodd's general system theory which suggests that all sciences are isomorphic, capable of being reduced to these functions, provided we can find the "natural" units.
Dodd's 4x4 matrix - page 1 of 3 (jpeg)