Tuesday, October 22, 2013

Part 1 of 2. Musean Hypernumbers and '''Dark Matter/Energy'''.


Full Title: 

Part 1 of 2.  

Musean Convolute Hypernumber Qualifiers and ‘‘‘Dark Matter’’’ / ‘‘‘Dark Energy’’’.





Dear Readers,



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 “InvisibleMatter-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 theMoney 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-Formunconscious 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 e[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
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/ConvoluteReQualification/ConvoluteReQualification.htm






TO BE CONTINUED.


Next

Conjecture -- 

‘Epsilonicity’ of “Visible Matter”; ‘Hybridicity’ of “Dark Matter”; ‘Ioticity’ of “Dark Energy”.









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