Full Title:
Part 1 of
2.
‘Musean Convolute Hypernumber Qualifiers’ and
‘‘‘Dark Matter’’’ / ‘‘‘Dark Energy’’’.
Dear Reader,
Preface.
The predicted next phases of
the dialectic of Nature -- of the ‘self-meta-evolution’ of the cosmos in
general, and of its human[oid] species in particular, as predicted by the F.E.D. ‘Dialectical Theory of Everything Meta-Equation’
itself, and by the F.E.D. ‘Psychohistorical-Dialectical Meta-Equations’, which
zoom-in on the human and ‘meta-human’ components of that master ‘meta-equation’
-- all seem to presuppose the development of superluminal interstellar drive
capability in the coming years, among many other conditions and developments
that their fruition requires, if the possibilities that these predictions
identify are to be actualized.
In late September of 2011, this blog, and various internet forum threads,
featured a series of posts about an old F.E.D. hypothesis, addressing a potential pathway to a
superluminal interstellar drive --
The purpose of the present
post is not to
review the specifics of that old hypothesis as to a possible physical mechanism
that might be harnessed to engineer an interstellar drive, since that hypothesis has already been addressed in
those earlier blog-entries.
Rather, it is to share with
you a related new hypothesis that has emerged within the current work of the
Foundation research collective, regarding a potential solution to the greatest
mystery of contemporary cosmology, and of contemporary cosmological physics.
Many contemporary mainstream theoretical physicists are, in our observation, experiencing a deep sense of bankruptcy, of late, as a result of recent superb
and precision work by the community of experimental
and observational
physicists.
In particular, recent
observational work by astronomers, cosmologists, and other ‘‘‘observational
physicists’’’ has revealed that only
~ 4.9% of the mass-energy of the known cosmos is encompassed
by the “Visible Matter” upon which physical theorizing, to date, has been
focused almost exclusively.
The majority of that known cosmological
mass-energy -- ~ 95% -- is in the form of “Invisible” Matter-Energy: an estimated ~ 26.8% taking the
form of “Dark Matter”, and another ~ 68.3% taking the form of “Dark Energy”.
Much of the mainstream
theoretical physics community admits that it presently “hasn’t a clue” as to
the nature of these majority constituents of Nature.
Others have proliferated a veritable “Tower of Babel” of new,
mostly “ad hoc” theories, or, really, of theory-fragments, or ‘theoretessimals’,
isolated or scrambled in relation to the rest of physics, in attempting to
explain these still-mysterious ‘majority phenomena’.
Lacking scientific
explanations for the vast majority of the contents of the cosmos constitutes a
kind of “scientific insolvency” for modern theoretical physics.
This text is a summary record
of a “thought-experiment” by yours truly.
The question that that
“thought-experiment” addresses is this --
¿What
explanation of the nature of this ‘majority of Nature’ might emerge if the alternative, “hypernumber”, ‘qualifier’, [meta-]finitary solution
to the v = c singularity of the Einstein
Special-Relativistic Momentum Equation is “physical”, i.e., if it has empirical counterparts, rather than it being merely an ‘aphysical’, ‘anempirical’, “extraneous” solution?
This question turns out to be
related to another question: ¿What would result if we required
that the values of the square-roots involved in the evaluation of the Einstein
Special-Relativistic Momentum Equation, alike, for both subluminal and ‘‘‘luminal’’’ velocities, be ‘‘‘proper square roots’’’ [which are hypernumber-valued], as opposed to ‘‘‘improper
square-roots’’’ [which
are “Real-valued”], but required if and only if these hypernumber, ‘‘‘proper square root’’’ values turn out to
be “physical”?
Part 1. of this inquiry begins with the Introduction reproduced below.
Regards,
Miguel
Introduction.
A typical ‘qualo-quantitative’ phrase of the “natural
languages” of Terran humanity, e.g., in English --
...five kilos [of] apples...
-- has three principal components, in the Seldonian theory
of such natural language formations.
Seldon names these three components as follows --
‘five’ = a ‘metrical
quantifier’;
‘kilo(s)’ = a [plurality of] ‘metrical [unit-]qualifier(s)’;
‘apples’ = an ‘ontological qualifier’ [denoting an ‘‘‘ontological category’’’, e.g., apples].
Now, of course, we know that the [metrical, etc.] quantifier element of this common,
characteristic natural language ‘content-structure’ has undergone an enormous “symbolic”, i.e., algorithmic, ideographical, arithmetical, algebraical, and analytical development, in
humanity’s ‘engineered languages’, especially in the modern era.
The enormity
of this mathematical development has been, in part, conditioned by, and
stimulated by, the enormous,
unconscious-paradigmatic influence of what Marx called “The Elementary Form of
Value”, the very root, or “economic cell-form” [Marx], of the entire edifice of
his critique of the ideology of capitalist political economics, and a paradigm
which resides at the very core of ‘‘‘modernity’’’, of the
modern «mentalité»,
of the modern ‘Human Phenome’, including,
most assuredly, and
most inescapably, the
mentalities of modern scientists.
The habitual, habituating, incessant, intensive practice,
the daily
‘multi-repetition’ -- by ancient humanity, by pre-modern humanity, and,
especially, by modern humanity -- of this C-[M-]C’ paradigm,
has led, cumulatively, to today’s one-sidedly quantitative, “quant”
mentality: to the ‘Money Mind’ of "Modern Man" -- really, to the ‘Capital[-value] Mind’ of contemporary global
humanity, pervading all classes, bourgeois and proletarian alike.
That root Marxian value-form is, at its own root, the
ultimate abstraction of “The Reproduction and Circulation of the Total Social
Capital” [Marx, Capital, volume II,
title of Part III], of the mutual confrontations of “Commodity-Capitals”, abstracting from the mediation of those confrontations by “Money-Capitals”, in the markets of the Capitals-System, and eliciting a ‘‘‘psychohistorical’’’ ‘elision of the qualifiers’ -- a tendency to omit, to miss, to suppress, and/or to
ignore the crucial cognitive role of ‘qualifiers’ -- a tendency rampant in the modern mentality, in modern language,
including in modern mathematics and in modern scientific theories -- pervasively so, alike, in silent,
private cognition, in heard and written dialogue and monologue, and in other
kinds of discourse as well.
¡In
part, consequently, the
“symbolic” [ideographical] development, in our ‘engineered languages’, of the
other two principal elements -- of both the ‘metrical
qualifiers’ and the ‘ontological qualifiers’ -- has been retarded, to say the least!
¡The ‘metrical qualifiers’, or ‘metrical
units’, of that key
practical component of physics known as “dimensional analysis” are, still to
this day -- except, to our knowledge, in the work of Seldon and the Foundation
-- languishing at that most primitive algebraic-symbolic stage, the stage of
“syncopated” abbreviation, e.g., of “sec.”, “gm.”, “cm.”, “in.”, “ft.”, “lbs.”, “mos.”, etc., that, once, all of “symbolic”
[ideographical] algebra occupied -- at its inception -- in that circa 250 C.E. seminal Ancient Alexandrian proto-algebraic text by
Diophantus of Alexandria, entitled Arithmetica!
¡The
last time that explicit ‘ontological qualifiers’ -- “kind of thing” ‘qualifiers’ -- appeared in an occidental work of arithmetic,
algebra, or analysis -- of algorithmic ideography -- was, to our knowledge, in
that same work by Diophantus of Alexandria, Arithmetica, in the form of his ‘Monad qualifiers’, denoted by Mo, circa the Second Century of the Common Era, ~ 1800 years ago!
That is, until the
1867 + C.E. work of Karl Marx, in Capital, with its c [constant capital], v [variable capital], and s [surplus-value] ‘‘‘coefficient’’’ and subscript ‘qualifier’ tags, or labels, representing
dialectical-science-‘decensored’ qualitative
and dynamical distinctions
to which capitalist -- ideological -- false consciousness was blind, plus its C and M ‘quanto-qualifiers’, as
well as the later, circa 1996 + C.E. work of Karl Seldon and the Foundation -- the
dialectical discernment of whose ‘unquantifiable
ontological qualifiers’
was ultimately inspired by those ‘Marxian
qualifiers’, as well as
by the ‘Musean hypernumbers’ -- the last time that explicit ‘ontological qualifiers’ appeared in an occidental mathematical work, was, to
our knowledge, in that same source, the Arithmetica, almost 1800 years ago.
The “predicate letters”, “individual constants”, and
“individual variables” -- perhaps even the “logical quantifiers” -- of
“Symbolic Logic”; of first-order predicate calculus, and of higher-order
predicate calculi -- deductive-algorithmic, but not arithmetical -- and Boolean
algebra, whose ‘logical quantifiers’, denoting class ideograms, connote ‘class qualifiers’ as well, connoting ‘class quanto-qualifiers’ on the whole, stand as partial exceptions to the
situation as described by the statement immediately above.
The “pure”, unquantifiable
‘contra-Boolean’ ontological qualifiers
arithmetic of the NQ_ that Karl Seldon discovered constitutes a
contrasting, countervailing , ‘‘‘psychohistorically’’’ therapeutic
‘counter-elision’ -- an ‘elision of the quantifiers’ -- to the presently ‘‘‘psychohistorically’’’
prevailing ‘elision of the qualifiers’.
The NQ_ ‘unquantifiable
ontological qualifiers’
are of the species that Seldon terms ‘evolute qualifiers’, as defined via the following links --
evolute [versus convolute]
But there is also another kind of ‘arithmetical qualifier’, named, by Seldon, ‘Musean hypernumber qualifiers’.
This kind has emerged immanently, although not without
resistance, within the development of standard arithmetic and algebra, at least
since the Western European Renaissance.
Also, this kind has, predictably, proven to be more discernible,
for the ‘‘‘psychohistorically’’’ prevailing ‘Human
Phenome’, than the immanent
emergence of the NQ_ kind, the latter as a “Non-Standard Model of the Natural
Numbers”, from the N, because the former kind is not
so subversive of the prevailing, one-sidedly ‘quant-ic’, “Elementary
Value-Form” unconscious paradigm as is the latter.
This other kind is also termed, by Seldon, that of the ‘quantifiable convolute arithmetical qualifiers’.
These ‘qualifiers’ are neither ‘metrical qualifiers’ nor ‘ontological qualifiers’, by Seldonian definition.
Instead, they are [‘self-reflexive function’] number-space ‘trajectory-qualifiers’, or
“power-orbit” [Musès] ‘qualifiers’.
Their first exemplar, standardly today denoted by i, or “[the] imaginary unit[y], emerged explicitly into human
consciousness in the occidental Renaissance, during the 1500s C.E., in
the writings of physician, mathematics teacher, and general polymath, Gerolamo
Cardano, the first mathematician to systematically employ “negative” numbers,
and of hydraulic engineer Rafael Bombelli, the first writer to publish rules of
calculation for, and, thereby, to systematically employ, “imaginary” and “Complex” numbers.
The first ‘psychohistorical emergences’ of this first kind
of ‘convolute qualifier
hypernumber’ are recorded, e.g.,
(1)
in a letter from Cardano to Tartaglia, dd. 04 August 1539 C.E., noting “difficulties created by the
appearance of these new numerical entities” [Bortolotti], and asking Tartaglia’s
help, (2)
in Cardano’s treatise on arithmetic and algebra, entitled «Ars Magna» [“The Great Skill”],
published in 1545 C.E.,
wherein Cardano uses, but also complains bitterly about, these “subtle” but
“useless” and “sophistic” numbers, and the “mental tortures” attending to their
multiplication, and (3)
in Bombelli’s treatise, «L’Algebra», published in 1572 C.E., in which
Bombelli ‘rule-ifies’ and codifies key calculations using “complex” numbers.
The historically second exemplar of these ‘quantifiable convolute hypernumber qualifiers’ is, perhaps, per Charles Musès, first encountered,
implicitly, in the “mysterious” Pauli Spinor operators of quantum mechanics.
[FYI: The late
Dr. Charles Musès was one of Karl Seldon’s major mentors, especially in the area
of hypernumber theory, until they acrimoniously fell out regarding what Seldon
saw as certain ethically-deficient components of Dr. Musès character].
Musès denotes this historically second kind of “counter-imaginary”
hypernumber by e
[such that this underscored symbol represents, given the typography available here, the Greek letter epsilon, not to be confused with the '''transcendental-irrational Real number''' e that is the base of the "natural" logarithms], and contrasts it to the historically first kind of ‘quantifiable convolute hypernumber unit qualifier’, denoted i [Greek letter iota, per Musès], defined as “the proper
square root of -1” -- this second kind being defined as “a
proper square root of +1”, +1 itself being
the “improper” square root of itself, in the same sense that a set is an “improper”
subset of itself.
Thus, e2 = +1, so e
is ‘contra-Boolean’, as is i2 = -1, per Seldon, because both transcend Boole’s “fundamental
law of thought” for ‘Boolean,
formal-logical hypernumbers’, which is --
x2
= x, a
la 0B2 = 0B and 1B2 = 1B.
Indeed, both e
and i
transcend Boole’s “fundamental law of thought” in a strong
sense, since not only is it the case that e2 ~= e
and that i2 ~= i , in the sense of
purely quantitative
inequality, as in 22
< 5 or 22 >
3, but in
the far stronger sense of ‘non-quantitative inequality’,
i.e., of ‘qualitative inequality’:
neither is e2 >
e, nor is i2 >
i, nor is e2 <
e, nor is i2 <
i, nor, of course, is e2 = e or i2 = i,
thus transcending the "trichotomy law" that holds for the standard 'pre-Complex' arithmetics.
Note Also: We have e2 = ee,
so that 1/e =
ee/e
= e/1,
and, thus, that 1/e =
+e.
Also, 1/i =
iiii/i = iii/1
= iii = (ii)i = (-1)i = i(ii) = i(-1), so 1/i = -i.
Like the “Complex numbers”, based upon the unit i, the “counter-Complex numbers” [cf. Musès], based upon the unit e, have “Real powers” -- have “power-orbit” [Musès], and “exponential orbit” [Musès] ‘number-space trajectories’,
which are fused together in the case of the unit i, but which are split in the case of the unit e, involving a pair of orbits in a four-dimensional
number space for et [with t denoting Real[-number]-time, or a "continuously-varying" time-like parameter ], but a two-dimensional ‘number-space trajectory’ for eexAxt,
as with the two-dimensional number-space trajectory for both for it
and eix(pi/2)xt
[the latter, given certain “principal value
conventions”] [note that the base of the exponential here is the '''transcendental irrational Real number''' that conventionally uses the symbol e, but that the exponentiated e denotes the Musean hypernumber "epsilon"] --
it = r×cos((pi/2)×t)
+ i×sin((pi/2)×t)
= eix(pi/2)xt
-- and --
eexAxt = r×cosh(At)
+ e×sinh(Axt)
-- versus --
ent = r×cos2((pi/2)×t)
+ en×sin2((pi/2)×t) - (1/2)×in×sin2(pixt) - (1/2)×i0×sin2(pixt)
-- wherein we
have used visible light spectrum ordinal
color-coding to indicate the units of the ‘number-space dimensions’ / 'number-space axes' in
which the ‘number-space trajectories’ play out, in which r
denotes the unit[y] of the “Real” number-line, r = +1, and in which “cosh( )” denotes the hyperbolic cosine
function, and “sinh(
)” the hyperbolic
sine
function.
Perhaps the simplest species of the «genos» that Musès named
e, or en,
was designated by him as the unit e3,
and is mimicked by the “counter-diagonal” 2-by-2
matrix --
_ _
| 0
1 |
| 1
0 |
_ _
-- which, when squared, or self-multiplied, per the standard matrix
product rules, yields the “diagonal” 2-by-2
matrix --
_ _
| 1
0 |
| 0
1 |
_ _
-- which mimes [the] “Real” unit[y], r = +1.
Both of these species of ‘quantifiable
convolute hypernumber unit qualifier’ figure centrally in the hypothesis, to be presented
in the next section, regarding a possible unified explanation of “Visible
Matter”, “Dark Matter”, and “Dark Energy” alike.
More amplitude regarding the meaning of the Seldonian
epithet ‘convolute’ in the context of ‘contra-Boolean’ hypernumbers, and
regarding the distinctions in kind between the ‘Musean convolute hypernumbers’
and the Seldonian ‘evolute
meta-numbers’ of the NQ_, can be gleaned via the following links:
‘onto’
‘onto-dynamasis’
‘‘‘convolute’’’
‘convolute processes’
‘convolute meta-numbers’
‘convolute product rules’
‘singularity
semantification’ via ‘convolute re-qualification’ of singularity-harboring
equations’
