Dear Psychohistory Project Group Members,
Part I.
Prelude to the Psycho-Historical Equations --
A Model of the History of Nature
A New Model of the Universe.
Pre-Note: The model of our " kosmos " presented herein is an 'ideo-graph-ical'
model of the dialectic of the " physis " , in the ancient Greek and philosophical
sense of that term. A definition of that term thus seems useful at the very
outset of this exposition. For example, the Random House Dictionary of the
English Language, College Edition [1968], defines " physis " as follows --
"physis (fi'sis), n., pl. -ses (-sez). 1. The principle of growth or change in
nature. 2. nature as the source of growth or change. 3. that which grows,
becomes, or develops. ...".
Note also that this ancient Greek term, " physis " , in its "combining form", of
"physio-", or "physi-", resides at the [psycho-]historical and semantical roots
of modern English terms such as "physics" and "physiology".
Definitions of two key terms, invoked throughout.
" arithmos " = a Number OF THINGS; an assemblage, or a population, of
QUALITATIVE unities, of QUALITATIVE units, or of QUALITATIVE " monads " , all of
the same given KIND, or " Genos " ;
" monad " = a unity, or a unit; a constituent of an " arithmos " .
This exposition is based upon a new model of the universe set forth in writings
by Foundation Encyclopedia Dialectica [F.E.D.], mainly as drafts of a book
entitled Dialectical Ideography: A Contribution to the Immanent Critique of
Arithmetic, and posted to the following website --
www.dialectics.org
Introduction. Watch the " kosmos " , in a Process of "Continual Emergenc[e](y)",
Unfold Before Your Mind's Eye, in Simulation, via an Historical Dialectic of
Nature Model with a 3-Symbol Seed --
n^(2^t)
-- wherein n [underscored], or q|n ["q" underscored, with SUBscript "n",
subscript NOT underscored], denotes the primordial " arithmos "
[ = "number of qualitative " monads " , or units"; i.e., "assemblage of
ontological units"] and "ontological category" that has "pre-nuclear
"particles"" as its " monads " , or "units", taken as the "historical premise",
or " arche' " , of the total self-development of " Natur " , and where t -- the
Greek letter "tau" if the Symbol font were available -- denotes the discrete
epoch counting-number for the epochs of cosmological "[meta-]evolution" ["the
succession / progression of ontological self-evolutions punctuated by
ontology-expanding self-revolutions"].
This [underscored] n, or q|n [q underscored, with subscript n, subscript NOT
underscored]; this ontological category of "pre-nucleus, pre-nuclei,
pre-nuclear" "particles"; this fecund primordial " physis " " genos " of
cosmological ontology, this " arithmos " of " monads " -- the deepest and
earliest so far known to the consensus of the community of modern scientists,
hence our necessary starting point in formulating a theory within modern science
at present -- includes, among its monadic " species " , the " species " of
"photons", "neutrinos", "electrons", "quarks", etc., but does not include the
" species " of the " genos " of "proto-nuclear sub-atomic "particles" ", e.g.,
the protons " species " , and the "neutrons" " species " .
This formula instantiates the profound potential "semantic concentration" of
ideography as a "shorthand" written language; the enormous "semantic
productivity", the depth of intuitive, "connotative" per-symbol meaning, that
ideographic notations can achieve.
There is a theorem, deductively provable from the "Axioms of Dialectical
Symbolic Logic", posted here previously, and stated in detail in the
pictographic summary of the book Dialectical Ideography, available via the
following link, slides 9-11 --
www.dialectics.org . . .
-- which states that, for any k [NOT underscored] in the set of "Natural"
Numbers, N = {1, 2, 3, . . . } --
[ q|1 ]^k = q|1 + . . . + q|k
-- and hence that --
[ q|1 ]^(2^k) = q|1 + . . . + q|2^k.
Thus, "Seldon functions" of the form x^(2^t) for a generic " " arche' " -thesis"
ontological category denoted x [underscored], forming the Left Hand Sides [LHS]
of "Seldon Equations" such as the one immediately above, represent the "moment
of unity" in
such expressions of dialectical processes.
Their Right Hand Sides [RHS], such as the non-amalgamative sum-expansion, q|1 +
. . . + q|2^k, above, represent the "moment of multiplicity / diversity" in such
expressions of dialectical processes.
The "Seldon formula" < q|n >^(2^t) involves two levels of exponentiation.
Where adjustable superscript-height-level controls are available, only 3
ideograms -- only three ideographic "symbols" -- are required for this formula.
Above, 4 "symbols" are needed, because the caret, '^', is used to indicate the
second level of "superscription", i.e., 2^t means the same as [FORTRAN's] 2**t,
e.g., 2^3 = 2**3 = 8.
This dialectical model of the 'self-[meta-]evolution of the " kosmos " at
"taxonomy level 1", the most general level of ontological taxonomy, takes 5
symbols if you count the underscore -- which signifies the "contra-Boolean"
character of the symbol it underscores -- as a separate symbol, and 6 symbols if
you add 1 as a "pre-super-script", to signify the taxonomic level / location of
this model, thusly --
(^1)^(2^t).
Even Einstein's General Relativity model of the universe, reduced to its
"gravitic" and homogenized mass-energy aspects only, requires, in its tensor
formulation, 5 symbols --
G = 8piT
-- wherein G denotes the momentaneous [tensorially-formulated] Geometry of the
total cosmos ["curved" or "warped" locally in proportion to local
mass-energy-density], where pi = 3.14159..., and where T denotes the
"stress-momentum-energy Tensor" of the Universe, describing the total, detailed,
momentaneous distribution of mass-energy throughout the [finite] space-volume of
that Universe. If we ignore the "G =", and write just "8piT", then this model
requires only 3 distinct symbols, counting "pi" as one symbol since, given a
Symbol font, "pi" would be replaced by a single Greek character.
If we substitute the value of t that counts up to the cosmological epoch in
which humanoid "meta-societies" -- connoted by (^1)q|h -- are emergent, per this
version of the "taxonomy level 1" ontological-categorial taxonomy, namely t = 8,
and expand the formula in accordance with the rules stated in my earlier post
here, on the Axioms for Dialectical Symbolic Logic, we obtain a pure qualitative
"cumulum-sum" of inhomogeneous, non-amalgamative, " asumbletoi
arithmoi " [Plato: "unaddible numbers"] ontological category symbols containing
256 ontological category signifying terms --
^(2^8) = ^256 =
+ . . . + +
[--->
q|1 + . . . + q|255 + q|256
-- wherein the q|1, q|255, and q|256 ideograms represent generic /
minimally-interpreted "unquantifiable ontological qualifier meta-numbers", and
wherein 'x [----> q|k' means "maximally, intuitively, connotatively interpreted
"intensional / heuristic" symbol, x, is identified with, assigned to, or is
interpreted by, minimally-interpreted, generic symbol q|k", for k in N = { 1, 2,
3, . . . }, the set of "Natural Numbers".
We will explain the meaning of the "complex unit[y]", 8-subscript, "hybrid" term
"(^1)q|lbepmasn" a little later along, in the "Preliminaries" section, and
beyond.
The "Dialectical Ideography", or "Dialectical Symbolic Logic", employed here, as
"axiomatized" in my earlier post, together with the interpretation or assignment
of it -- the model -- specified in this post, in its sequel, together solve the
problem of the Marxian "Dialectic of Nature" [i.e., this model constitutes a
solution to that fundamental open problem of Marxian Theory. We do not assert
that this solution is the only possible such solution.].
In the sequel to this post, below, we will supply you with the interpretational
background preliminaries essential to your understanding of this model, followed
by a narrative exposition of the model itself.
You can then behold the glorious self-burgeoning of our " physis " " kosmos " ,
from its single, tiny seed -- herein denoted 1n -- simulated before your own
mind's eye, by thinking this model for yourself.
More about this "New Model of the Universe" can be found via the following link,
starting on page B-20:
www.dialectics.org . . .
Preliminaries Regarding the Generic Interpretation of Heuristic, "Intensional",
Dialectical Ideograms.
1. On the Generic Meanings of "Cross Product" Terms in the Model.
Suppose that the symbol '(^k)q|z', connotes a new, unprecedented
ontological category that has emerged in the latest iteration of an
historical-dialectical model of a self-expanding "Cumulum" of self-diversifying
ontology, an historical "Cumulum" initially located at the kth level of the
F.E.D. universal taxonomy.
Suppose that this historical-dialectical model can be expressed as follows, per
the Axioms posted here earlier:
(^k)C(t) = ^(2^t) = ^(2^t).
Suppose further that the ontological category connoted by (^n)q|y first emerged
into existence in a previous [self-]iteration of this model, i.e., for a lesser
value of the t "independent variable".
Then, by the " " aufheben " evolute product-rule", per the cited axioms, the
product of (^k)q|z, as "[sentential] subject", interacting with and operating
upon (^k)q|y, as ["sentential"] object, is as follows --
(^k)q|z "times" (^k)q|y = (^k)q|z "of" (^k)q|y = (^k)q|z< (^k)q|y > =
(^k)q|z x (^k)q|y = (^k)q|y + (^k)q|zy.
Given all of the above, (^k)q|zy will denote a new, qualitatively different
ontological category, qualitatively unequal to either of its "parent"
ontological categories, namely (^k)q|z and (^k)q|y.
The ontological category of new -- or "neo-" -- ontology connoted by (^k)q|zy,
residing at the kth level of the F.E.D. universal taxonomy, for k in N = {1, 2,
3, . . . }, signifies concepts which, per F.E.D., include the dialectical
"synthesis" of (^k)q|z, with (^k)q|y, the dialectical "complex unity" of (^k)q|z
and (^k)q|y, and the "conversion" of the " monads " , or "units", of the (^k)q|y
" arithmos " , into their "meta- " monads " , or "meta-units" -- the
"neo-units" of the (^k)q|z " arithmos " , also catalyzed by the " monads " , or
"units", of the (^k)q|z " arithmos " .
For example, if (^1)q|s connotes the ontological category of "proto-nuclear
sub-atomic particles" [i.e., the category which includes that of protons and
that of neutrons as among its sub-categories], residing at level 1 of the F.E.D.
universal taxonomy, and if (^1)q|a connotes the ontological category of "atomic
nuclei" [i.e., the category which includes "Helium atom nuclei" [a 'meta-unit'
of units of the (^1)q|s category, the atomic nuclei which, in the typical case,
are each composed of two proton units and two neutron units, tightly merged
together into a new, single, atomic nucleus,
"meta-unit", or "meta- " monad " '], then we can "particularize" or "instantiate"
the generic expression above as --
(^1)q|a "times" (^1)q|s = (^1)q|s + (^1)q|as
-- wherein the qualitatively new ontological category, connoted by (^1)q|as,
connotes the " arithmos " , or "number/assemblage of qualitative, ontological
units", of those cosmological and galactic units which, through "stellar
nucleosynthesis", progressively convert "proto-nuclear sub-atomic particle"
units-- mainly ionized Hydrogen atoms, i.e., essentially, "naked protons" --
into ever higher "atomic/nuclear species", or 'physio- " species " ' of atomic
nuclei "meta-units", or "meta- " monads " -- e.g., the nuclei of Helium atoms, of
Lithium atoms, of Carbon atoms, of Nitrogen atoms, of Oxygen atoms, etc., which
form sub- " arithmoi " of the "[meta-] " arithmos " " that constitutes the
ontological category of "atomic nuclei", connoted by (^1)q|a.
That is, (^1)q|as connotes the ontological category, or " arithmos "
["number/assemblage of qualitative " monads " /units"], which has the
first-generation stars as its "units"/ " monads " , i.e., which has as its units
those gargantuan cosmological processors which convert "proto-nuclear sub-atomic
particle" units/ " monads " into their "atomic nuclei" meta1-units /
meta1- " monads " , which we call "the first stars".
TO BE CONTINUED
Regards,
Psi_Sci
