__Full Title__:

**Part 1 of 2**.

‘

**Musean**

**Convolute**

**Hypernumber Qualifiers**’

**and**‘‘‘

**Dark Matter**’’’

**/**‘‘‘

**Dark Energy**’’’.

Dear Readers,

**.**

__Preface__
The predicted next phases of

**-- of the ‘self-meta-evolution’ of the cosmos in general, and of its human[oid] species in particular, as predicted by the***the*__dialectic__of Nature**F**.**.**__E__**. ‘Dialectical Theory of Everything Meta-Equation’ itself, and by the**__D__**F**.**.**__E__**. ‘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**__D__**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.***superluminal interstellar drive*
In late September of

**2011**, this blog, and various internet forum threads, featured a series of posts about an old**F**.**.**__E__**. hypothesis, addressing a potential pathway to a superluminal interstellar drive --**__D__The purpose of the present post is

**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.**

__not__
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

**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***theoretical***and***experimental***physicists.***observational*
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

Others have proliferated a veritable “Tower of Babel” of new, mostly

*“ad hoc”*theories, or, really, of theory-fragments, or*‘*, isolated or scrambled in relation to the rest of physics, in attempting to explain these still-mysterious ‘majority phenomena’.**theoretessimals**’
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”, ‘*,**’**__qual__ifier*[*__meta__*-*]*finitary solution to the***v****=****c****singularity**of the Einstein Special*-Relativistic Momentum Equation is “***”, i.e., if it has**__physical____empirical__**, rather than it being merely an ‘**__counterparts__**physical’, ‘**__a__**empirical’, “**__an__**” solution**__extraneous__**?**
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*[__sub__luminal and ‘‘‘luminal’’’ velocities, be ‘‘‘**square roots’’’**__proper__*which are*]**hypernumber**-**valued***, as opposed to ‘‘‘*[which are “__proper square-roots’’’__**im****eal-valued”]**__R__*, but required if and only if these***hypernumber**,*‘‘‘***square root’’’**__proper__*values turn out to be “*__physical__*”***?****Part 1**. of this inquiry begins with the

**reproduced below.**

__Introduction__
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**’__quant__ifier
‘

**kilo**(**s**)’**=**a [plurality of]*‘*[**metrical***unit**-*]**(**__qual__ifier**)’;***s*
‘

**apples**’**=**an*‘*[denoting an**ontological**’__qual__ifier*‘‘‘*e.g.,**ontological category**’’’,**apples**].
Now, of course, we know that the [metrical, etc.]

__quant__*ifier*element of this common, characteristic natural language ‘content-structure’ has undergone an**“symbolic”, i.e., algorithmic, ideographical, arithmetical, algebraical, and analytical development, in humanity’s ‘engineered languages’, especially in the modern era.**__enormous__
The

**of this mathematical development has been, in part, conditioned by, and stimulated by, the**__enormity__**, unconscious-paradigmatic influence of what Marx called “**__enormous__**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*‘‘‘*, of**modernity**’’’**«***the modern***», of the modern***mentalité**‘*,**Human**’__Phe__nome*including**,*,**most assuredly****,***and most inescapably***.***the mentalities of modern scientists*
The habitual, habituating, incessant, intensive practice,
the

**‘multi-repetition’ -- by ancient humanity, by pre-modern humanity, and,**__daily__*especially*, by modern humanity -- of this**C**-[**M**-]**C’**paradigm, has led, cumulatively, to today’s one-sidedly*itative,*__quant__*“*mentality: to**quant**”**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,

**, volume**__Capital__**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**-*, and eliciting a ‘‘‘psychohistorical’’’**System***‘*-- a tendency to omit, to miss, to suppress, and/or to ignore the crucial cognitive role of**elision of the**’__qual__ifiers*‘*-- a tendency rampant in the modern mentality, in modern language, including in modern mathematics and in modern scientific theories --**’**__qual__ifiers**so, alike, in silent, private cognition, in heard and written dialogue and monologue, and in other kinds of discourse as well.**__pervasively__**In part,**

*¡***, the “symbolic” [ideographical] development, in our ‘engineered languages’, of the other two principal elements -- of both the**

*consequently**‘*and the

**metrical**’__qual__ifiers*‘*-- has been retarded, to say the least

**ontological**’__qual__ifiers

*!***The**

*¡**‘*or

**metrical**’,__qual__ifiers*‘*of that key practical component of physics known as “

**metrical**’,__units__**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 ‘**

*¡*

__onto__*logical*__qual__*ifiers**’*-- “

**of thing”**

__kind__*‘*-- 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,

**’**__qual__ifiers**, in the form of his ‘**

__Arithmetica__**nad**

__Mo__

__qual__ifiers*’*, denoted by

**M**,

^{o}*circa*the Second Century of the Common Era,

**~**

**1800**years ago

*!*
That is,

**the**__until__**1867****+****C**.**E**. work of Karl Marx, in**, with its**__Capital__**c**[**onstant capital],**__c__**v**[**ariable capital], and**__v__**s**[**urplus-value] ‘‘‘coefficient’’’ and subscript**__s__*‘*__qual__ifier*’*tags, or labels, representing dialectical-science-*‘*censored’__de__**and**__qual__itative**distinctions to which capitalist -- ideological -- false consciousness was blind, plus its***dynamical***C**and**M***‘*, as well as the later,**-**__quant__o**’**__qual__ifiers*circa***1996****+****C**.**E**. work of Karl Seldon and the**Foundation**--**the dialectical discernment of whose***‘*was ultimately inspired by those**’**__un__quantifiable ontological__qual__ifiers*‘*, as well as by the**Marxian**’__qual__ifiers*‘*the last time that explicit**Musean hypernumbers**’ --*‘*appeared in an occidental mathematical work, was, to our knowledge, in that same source, the**ontological**’__qual__ifiers**, almost**__Arithmetica__**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

*‘*as well, connoting**class**’__qual__ifiers*‘*on the whole, stand as**class****-**__quant__o**’**__qual__ifiers**exceptions to the situation as described by the statement immediately above.**__partial__
The “pure”,

**quantifiable ‘contra-Boolean’**__un__**arithmetic of the***ontological*__qual__ifiers_{N}**that Karl Seldon discovered constitutes a contrasting, countervailing , ‘‘‘psychohistorically’’’ therapeutic ‘counter-elision’ -- an**__Q___*‘*-- to the presently ‘‘‘psychohistorically’’’ prevailing**elision of the**’__quant__ifiers*‘*.**elision of the**’__qual__ifiers
The

_{N}__Q___*‘*are of the species that Seldon terms**’**__un__quantifiable ontological__qual__ifiers*‘*__e__volute__qual__ifiers*’*, as defined via the following links --

__e__**volute**[versus

__con__**volute**]

*‘*[

**double**-]«

**»**

*aufheben*

__e__**volute product rule**’

**http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/AufhebenEvoluteProductRule/AufhebenEvoluteProductRule.htm**

But there is also another kind of

*‘*, named, by Seldon,**arithmetical**’__qual__ifier*‘*.**Musean hypernumber**’__qual__ifiers
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

*‘*, than the immanent emergence of the**Human**’__Phe__nome_{N}**kind, the latter as a “Non-Standard Model of the**__Q___**atural Numbers”, from the**__N__**N**, because the former kind is not so subversive of the prevailing, one-sidedly*‘*ic’, “**quant**-**Elementary Value-Form**”**conscious paradigm as is the latter.**__un__
This other kind is also termed, by Seldon, that of the

These

Instead, they are [‘self-reflexive function’] number-space

*‘*.**quantifiable**’__con__volute arithmetical__qual__ifiersThese

*‘*are neither**’**__qual__ifiers*‘*nor**metrical**’__qual__ifiers*‘*, by Seldonian definition.**ontological**’__qual__ifiersInstead, they are [‘self-reflexive function’] number-space

*‘*’, or “power-orbit” [Musès]**trajectory**-__qual__ifiers*‘*.**’**__qual__ifiers
Their first exemplar, standardly today denoted by

**i**, or “[the]**maginary**__i__*unit*[y], emerged explicitly into human consciousness in the occidental Renaissance, during the**1500**s**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, “**maginary” and “**__i__**omplex” numbers.**__C__
The

**‘psychohistorical emergences’ of this first kind of***first**‘*are recorded, e.g.,**’**__con__volute__qual__ifier hypernumber**(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

**exemplar of these***second**‘*is, perhaps, per Charles Musès, first encountered, implicitly, in the “mysterious” Pauli Spinor operators of quantum mechanics.**quantifiable**’__con__volute hypernumber__qual__ifiers
[

__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

**kind of “counter-imaginary” hypernumber by***second***[such that this underscored symbol represents, given the typography available here, the Greek letter**__e____e__*psilon*,**to be confused with the '''transcendental-irrational**__not__**R**eal number'''**e**that is the base of the "natural" logarithms], and contrasts it to the historically**kind of***first**‘*, denoted**quantifiable**’__con__volute hypernumber unit__qual__ifier**i**[Greek letter*iota*, per Musès], defined as “the**square root of**__proper__**-****1**” -- this**kind being defined as “a***second***square root of**__proper__**+****1**”,**+****1**itself being the*“*proper” square root__im__*of itself*, in the same sense that a set is an*“*proper” subset__im__*of itself*.
Thus,

Indeed, both

neither is

thus transcending the "trichotomy law" that holds for the standard 'pre-

__e__^{2}**= +****1**, so**is ‘contra-Boolean’, as is**__e__**i**^{2}**=****-****1**, per Seldon, because both transcend Boole’s “fundamental law of thought” for ‘**oolean, formal-logical hypernumbers’, which is --**__B__

**x**^{2}**=****x**,*a la***0**_{B}^{2}**=****0**and_{B}**1**_{B}^{2}**=****1**._{B}Indeed, both

**and**__e__**i**transcend Boole’s “fundamental law of thought” in a**sense, since not only is it the case that***strong*__e__^{2}**~=****and that**__e__**i**^{2}**~=****i**, in the sense of purely**itative inequality, as in**__quant__**2**^{2}**<****5**or**2**^{2}**>****3**, but in the**sense of***far stronger**‘*, i.e., of**-**__non__**itative**__quant__**equality’**__in__*‘*:**itative**__qual__**equality’**__in__neither is

__e__^{2}**>****,**__e__*nor*is**i**^{2}**>****i**,*nor*is__e__^{2}**<****,**__e__*nor*is**i**^{2}**<****i**,*nor*, of course, is__e__^{2}**=****or**__e__**i**^{2}**=****i**,thus transcending the "trichotomy law" that holds for the standard 'pre-

**omplex' arithmetics.**__C____Note Also__: We have

__e__

^{2}

__=__**, so that**

__ee__**1/**

__e__**=**

**e****e****/**

~~e~~**=**

__e__**/1**, and, thus, that

**1/**

__e__**= +**

**.**

__e__Also,

**1/i**

**=**

**iii**

~~i~~

**/**

~~i~~

**=**

**iii/1**

**=**

**iii**

**=**

**(ii)i**

**=**

**(**

**-**

**1)i**

**=**

**i(ii)**

**=**

**i**

**(**

**-**

**1)**, so

**1/i**

**=**

**-**

**i**.

Like the “

**omplex numbers”, based upon the**__C__*unit***i**, the*“***counter**-**omplex numbers” [cf. Musès], based upon the**__C__*unit***, have “**__e__**eal powers” -- have “power-orbit” [Musès], and “exponential orbit” [Musès] ‘number-space trajectories’, which are fused together in the case of the**__R__*unit***i**, but which are split in the case of the*unit***, involving a pair of orbits in a four-dimensional number space for**__e____e__**[with**^{t }**t**denoting**R**eal[-number]-**ime, or a "continuously-varying"**__t__**ime-like parameter ], but a two-dimensional ‘number-space trajectory’ for**__t__**e**^{ex}^{Ax}**, as with the two-dimensional number-space trajectory for both for**^{t}**i****and e**^{t}^{ix(}^{pi}^{/2)xt}[the latter, given certain “principal value conventions”] [note that the base of the exponential here is the '''transcendental irrational**R**eal number''' that conventionally uses the symbol**e**, but that the exponentiated__denotes the Musean hypernumber "__**e****psilon"] --**__e__**i**

^{t}**=**

**r**×

**cos**

**((**

*pi***/2**

**)**×

**t)**

**+**

**i**×

**sin((**

*pi***/**

**2)**×

**t)**

**=**e

^{ix}

^{(}

^{pi}^{/2)xt}

-- and --

**e**

^{ex}

^{Ax}

^{t}**=**

**r**×

**cosh**

**(**

**A**

**t)**

**+**

**×**

__e__**sinh(**

**A**x

**t**

**)**

**--**versus --

__e__

_{n}

^{t}**=**

**r**×

**cos**

^{2}**((**

**pi**

**/2**

**)**×

**t)**

**+**

__e__**×**

_{n}**sin**

^{2}((**pi**

**/**

**2)**×

**t)**

**-**

**(1/2)**×

**i**

**×**

_{n}**sin**

^{2}(*pi*x

**t)**

**-**

**(1/2)**×

**i**

_{0}**×**

**sin**

^{2}(*pi*x

**t)**

**--**wherein we have used visible light spectrum

**o**

**r**

**d**

**i**

**n**

**a**

**l**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 “

**eal” number-line,**

__R__**r**

__=__+**1**, and in which “

**cos**” denotes the

__h__( )**yperbolic**

__h__**cos**ine function, and “

**sin**” the

__h__( )**yperbolic**

__h__**sin**e function.

Perhaps the simplest

**of the «***species***» that Musès named***genos***, or**__e____e__**, was designated by him as the**_{n}*unit*__e__**, and is mimicked by the**_{3}*“***-diagonal”**__counter__**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] “

**eal”**

__R__*unit*[y],

**r**

__=__+**1**.

Both of these

**of***species**‘*figure centrally in the hypothesis, to be presented in the next section, regarding a possible unified explanation of “**’**__quant__ifiable__con__volute hypernumber unit__qual__ifier**Visible Matter**”, “**Dark Matter**”, and “**Dark Energy**” alike.
More amplitude regarding the meaning of the Seldonian
epithet

*‘*in the context of ‘contra-Boolean’ hypernumbers, and regarding the distinctions in kind between the ‘Musean**’**__con__volute**hypernumbers’ and the Seldonian ‘**__con__volute**meta-numbers’ of the**__e__volute_{N}**, can be gleaned via the following links:**__Q___
‘

**onto**’
‘

**onto**-**dynamasis**’*‘‘‘*

__con__**volute**’’’

*‘*

__con__**volute processes**’

*‘*

__con__**volute meta**-

**numbers**’

*‘*

__con__**volute product rules**’

‘

**singularity semantification**’*via ‘*__con__**volute 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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