**Part**

**12**: Seldon’s

**--**

*Message Series**‘*

**Actual**’__Meta__finity

*versus***:**

*Fanciful*__In__finity
‘

__Meta__finite*’*,*‘‘‘***-**__Meta__**Dynamical**’’’*Change**and**Mathematical**“*.**Singularity**”
Dear

**,***Readers*
It is my

**,***pleasure***my***and***,***honor**as***officer of the***an***Foundation****[**__Encyclopedia Dialectica__**F**.**.**__E__**.] Office of Public Liaison, to**__D__**with***share***, from time to time,***you**as***are approved for public release by the***they***F**.**.**__E__**. General Council,**__D__*key**excerpt*__s__**the***from***i**__nt__**e**__rn__**a**__l__**,***writing*__s__*and***the***from***i**__nt__**e**__rn__**a**__l__**, of***sayings***o**__ur____co__*-*, Karl Seldon.**founder**
The

**such release in this***twelfth**new***is entered below [***series**Some***.**__E__**.**__D__*standard**edit*__s__*have**been***, in the***applied**version***below, to the direct transcript of**__present__ed**o**__ur____co__*-*’s**founder****].***discourse*

*This*

*instalment***the**

*addresses*

**Seldonian****of the relation between the bandying about of**

*view*

*fanciful*

*and*

*even*

*mystical**“*in

**”**__in__finit__ies__

*descendence**-*

**phase***“*

**pure**”

*mathematics*

*and***in**

*even*

*mathematical***,**

*physics*

*vis**-*the

**a**-**vis**

*Seldonian***of**

*concept**‘*.

**’**__meta__finity
For

**,***more information*__regarding__**for [***and***]***further**instantiation*__s__**, these**__of__*Marxian and Seldonian***, please***insight*__s__**--***see*

*and*
For ‘poster-ized’

**of***visualizations***of***many***--***these Marxian and Seldonian insights***of***specimen*__s__*‘*--**’**__dialectic__al art**:***see*

*ENJOY!*
Regards,

Miguel Detonacciones,

Member,

**Foundation****[**__Encyclopedia Dialectica__**F**.**.**__E__**.],**__D__
Participant,

**F**.**.**__E__**. Special Council for Public Liaison,**__D__
Officer,

**F**.**.**__E__**. Office of Public Liaison.**__D__**“**...leaving aside any extended commentary upon the contra-factual, ‘contra-actual’ axiomatics of Cantorian, “mathematical-Platonist”

**, and its deductively rigorous phantasies, for now, this is to register a few remarks regarding the mathematical “**

*mysticism*__in__finitism” that invades even the ostensive realism of mathematical physics.”

“The more-realistic,

**linear partial [integro-]differential equations that abound in modern mathematical physics are prone to predict --***non**precisely because of*their**linearity -- bouts of divisions by zero in real finite-time, divisions by zero which can be interpreted as representing***non*__in__finite values for key physical metrics and variables: so-called*“*.”**singularit**”__ies__
“Such conjunctures in the modeled
time/history of a physical phenomenon or system are rightly regarded as mathematically
meaningless by many of the more realistic physicists, and as marking physical
conjunctures for which the equations, and the “laws” that they formulate, “break
down”.”

“There are, of course, some “mush-minded”

*‘*among “physicists”, who want us to believe that, e.g., the gravitational collapse singularity of the Einstein General Relativity system of “simultaneous”**mystoid**’__s__**linear partial differential equations means that there is some kind of ‘“actual, physical***non*__in__finity*”’*at the**of every “black hole”, as well as at the “Big Bang” natural-historical «***core***»***arché***of***/core**our***as a whole itself.”***cosmos*
“However, in a metaphoric
manner, there is something meaningful about such a zero-division “singularity”
in an otherwise physically accurate, highly-predictively-valid equation or
equation

__s__-system. Instantaneous ‘‘‘__in__finite**itative’’’ change, from the very instant in which a denominator-resident dynamical factor-variable takes on the value**__quant__**0**in such an equation or equation__s__-system, and/or in its/their solution-function(s) [in the few cases in which such functions are known in “closed form” for**linear equations], might signify, and might be the only way to signify, a***non*__finite__but**itative change, e.g., an**__qual____ontological__change, within a mathematical language which is capable only of “purely”**itative expression(s).”**__quant__
“This kind of change is what we
call

*‘*finite change’, whereby the also__meta__*‘*dynamical’ character of an also**-**__meta__**system becomes manifest.”**__dynamical__
“And, indeed, we find that,
quite typically, zero-division singularities in the equations of physics and of
engineering occur at critical points in the cumulative course of at first
apparently only

**itative change, at which**__quant__**itative change, in the form of the**__qual____self__*-*expansion of the ontology of the phenomenon or system that the equations model, bursts forth. And this irruption of additional ontology typically also coincides with the*‘*dynamical’ transition from a predecessor dynamical system to its**-**__meta__**itatively,**__qual__*ontologically***-- ‘‘‘evolutely’’’ expanded -- successor system, that may also «**__different__**»***aufheben**-*‘‘‘contain’’’ and incorporate its predecessor system.”
“Division-by-zero singularities
typically mark, not [impossible] actual, physical

__in__finities, but transitions from a predecessor system to its successor system:**in natural history.”**__revolutions__
“Beginning with the seventh
system of dialectical mathematics in the “slow”, “training-wheels” version of our
solution to our ‘meta-equation’ for the system

__s__-progression of the axiom__s__-system__s__of dialectical mathematics, the “purely”-quantitative equations of mathematical physics become ‘[re-]qualified’, by fully-arithmetical, fully-ideographical, fully-algorithmic ‘mathematical qualifiers’. These comprise ‘metrical qualifiers’, that arithmeticize, e.g., the more primitive, “syncopated”, “dimensional analysis” expressions like ‘sec.’, ‘gm.’, & ‘cm.’, as well as ‘ontological qualifier’ mathematical ideograms. ... We say ‘__re__*-*qualified’, because these ideographical ‘mathematical qualifiers’ bear a psychohistorical resemblance to, and resonance with, the ‘**nad’ arithmetical qualifier ‘‘‘numeral’’’ of the psychohistorically pivotal ancient proto-algebraic work of Diophantus of Alexandria, entitled**__Mo__**, which launched modern, algebraic mathematics, while still evincing salient ‘psychoartefacts’ of the ancient Mediterranean mathematical «**__The Arithmetica__**».’***mentalité*
“Per a key axiom of that
seventh dialectical-mathematical axiom

__s__-system, and beyond, the multiplication, by ‘empty zero’,**0**, of a ‘‘‘[re-]qualified’’’, ‘quanto-qualitative’ mathematical expression, whether that expression be ‘metrically-qualified’ only, ‘ontologically-qualified’ only, or metrically and ontologically ‘co-qualified’, yields a new kind of arithmetical value and ‘meta-numeral’, which we call ‘full zero’.”
“Occurrences of that, ‘full
zero’, value, signify, in that axiom

__s__-system, and beyond, that a new successor system has emerged, starting from the moment of a sustained such singularity, such that the mathematical language of the old, finite equation(s), that may have “miraculously” well-described and predicted the finite development of the predecessor dynamical system, up to that very moment of division-by-zero singularity, is no longer adequate to describe the ‘new*of the successor dynamical system, that has «*__finite__-y’**»***aufheben**-*irrupted from out of the very heart of the predecessor dynamical system, as an expression of the very nature of that predecessor system itself; as an ultimate, immanent, ‘‘‘evolute’’’__self__*-*transcendence of that predecessor system, via the irruption of a new ‘qualo-fractal’ scale of -- still finite, but ontologically-expanded -- ‘cosmo-ontology’. ...**”**
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