__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 “**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”, ‘*__qual__ifier’,* *[__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 ‘__a__physical’, ‘__an__empirical’, “__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 *__sub__luminal and ‘‘‘luminal’’’ velocities, be ‘‘‘__proper__ square roots’’’ [*which are ***hypernumber**-**valued**]*, as opposed to ‘‘‘***im**proper
square-roots’’’ [which
are “__R__eal-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
**__quant__ifier’;

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

‘**apples**’ **=** an *‘***ontological **__qual__ifier’ [denoting an *‘‘‘***ontological category**’’’, e.g.,* ***apples**].

Now, of course, we know that the [metrical, etc.] __quant__*ifier* 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 **__Phe__nome’, *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 __quant__itative, *“***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 **__qual__ifiers’ -- a tendency to omit, to miss, to suppress, and/or to
ignore the crucial cognitive role of *‘*__qual__ifiers’ -- 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
**__qual__ifiers’ and the *‘***ontological **__qual__ifiers’ -- has been retarded, to say the least*!*

*¡*The *‘***metrical **__qual__ifiers’, 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 ‘__onto__*logical *__qual__*ifiers**’* -- “__kind__ of thing” *‘*__qual__ifiers’ -- 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 ‘__Mo__nad __qual__ifiers*’*, denoted by **M**^{o}, *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** [__c__onstant capital], **v** [__v__ariable capital], and **s** [__s__urplus-value] ‘‘‘coefficient’’’ and subscript *‘*__qual__ifier*’* tags, or labels, representing
dialectical-science-*‘*__de__censored’ __qual__itative
and *dynamical* distinctions
to which capitalist -- ideological -- false consciousness was blind, plus its **C** and **M** *‘*__quant__o-__qual__ifiers’, as
well as the later, *circa* **1996**** +** **C**.**E**. work of Karl Seldon and the **Foundation **--** **the
dialectical discernment of whose *‘*__un__quantifiable
ontological __qual__ifiers’
was ultimately inspired by those *‘***Marxian
**__qual__ifiers’, as well as
by the *‘***Musean hypernumbers**’ -- the last time that explicit *‘***ontological **__qual__ifiers’ 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 **__qual__ifiers’ as well, connoting *‘***class** __quant__o-__qual__ifiers’ on the whole, stand as __partial__ exceptions to the
situation as described by the statement immediately above.

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

The _{N}__Q___ *‘*__un__quantifiable
ontological __qual__ifiers’
are of the species that Seldon terms *‘*__e__volute** **__qual__ifiers*’*, as defined via the following links --

__e__**volute** [versus __con__**volute**]

But there is also another kind of *‘***arithmetical **__qual__ifier’, named, by Seldon, *‘***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 *‘***Human
**__Phe__nome’, than the immanent
emergence of the _{N}__Q___ kind, the latter as a “Non-Standard Model of the __N__atural
Numbers”, from the **N**, because the former kind is not
so subversive of the prevailing, one-sidedly *‘***quant**-ic’, “**Elementary
Value-Form**” __un__conscious paradigm as is the latter.

This other kind is also termed, by Seldon, that of the *‘***quantifiable **__con__volute arithmetical __qual__ifiers’.

These *‘*__qual__ifiers’ are neither *‘***metrical **__qual__ifiers’ nor *‘***ontological **__qual__ifiers’, by Seldonian definition.

Instead, they are [‘self-reflexive function’] number-space *‘***trajectory**-__qual__ifiers’, or
“power-orbit” [Musès] *‘*__qual__ifiers’.

Their first exemplar, standardly today denoted by **i**, or “[the] __i__maginary *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, “__i__maginary” and “__C__omplex” numbers.

The *first* ‘psychohistorical emergences’ of this first kind
of *‘*__con__volute __qual__ifier
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 **__con__volute hypernumber __qual__ifiers’ 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 __e__*psilon*, __not__ to be confused with the '''transcendental-irrational **R**eal number''' **e** that is the base of the "natural" logarithms], and contrasts it to the historically *first* kind of *‘***quantifiable **__con__volute hypernumber unit __qual__ifier’, 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 *“*__im__proper” square root *of itself*, in the same sense that a set is an *“*__im__proper”
subset *of itself*.

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

**x**^{2}**
= ****x**, *a
la* **0**_{B}^{2} **=** **0**_{B} and **1**_{B}^{2} **=** **1**_{B}.

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

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} **=** __e__ or **i**^{2} **=** **i**,

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

__Note Also__: We have __e__^{2}** **__=__ __ee__,
so that **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 “__C__omplex numbers”, based upon the *unit* **i**, the *“***counter**-__C__omplex numbers” [cf. Musès], based upon the *unit* __e__, have “__R__eal 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__^{t }[with **t **denoting **R**eal[-number]-__t__ime, or a "continuously-varying" __t__ime-like parameter ], but a two-dimensional ‘number-space trajectory’ for **e**^{ex}^{Ax}^{t},
as with the two-dimensional number-space trajectory for both for **i**^{t}
and e^{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 **e** denotes the Musean hypernumber "__e__psilon"] --

**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 “__R__eal” number-line, **r**** **__=__ +**1**, and in which “**cos**__h__( )” denotes the __h__yperbolic **cos**ine
function, and “**sin**__h__(
)” the __h__yperbolic
**sin**e
function.

Perhaps the simplest *species* of the «*genos*» that Musès named
__e__, or __e___{n},
was designated by him as the *unit* __e___{3},
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] “__R__eal” *unit*[y], **r**** **__=__ +**1**.

Both of these *species* of *‘*__quant__ifiable
__con__volute hypernumber unit __qual__ifier’ 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 *‘*__con__volute’ in the context of ‘contra-Boolean’ hypernumbers, and
regarding the distinctions in kind between the ‘Musean __con__volute hypernumbers’
and the Seldonian ‘__e__volute
meta-numbers’ of the _{N}__Q___, can be gleaned via the following links:

‘**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**’