Seldon Speaks: ‘Contra-Boolean Computers’, ‘Singularity Semantification’, & ‘The Nonlinearity Barrier’.
Dear Reader,
It is my pleasure to share with you, from time to time, seminal
selections from the sayings, shared by him among we of F.E.D.,
by F.E.D.’s co-founder, Karl Seldon,
such as the following [E.D.
standard edits applied] -- in this case,
said recently, during one of the induction seminars for new F.E.D.
recruits:
“As we have so
often noted before, the greatest mathematical, scientific, engineering,
cognitive, intellectual challenge facing Terran humanity today, across
essentially the entire spectrum of the sciences, is what we of F.E.D.
have come to call -- somewhat in keeping with the similar phrase coined by
Ladis D. Kovach [in his article entitled “Life Can Be So Nonlinear”] --
‘The Nonlinearity Barrier’.”
“This epochal obstruction to human progress, this ‘Barrier’,
often comes to attention by way of the contemporary, and longstanding, inability to solve “law
of Nature”-expressing nonlinear differential equations -- in many cases after
centuries of efforts in attempts to do so, including by some of the greatest
masters of mathematics in mathematics history -- an inability to solve due precisely
to their nonlinearity. This unconscious
ideological, psychohistorical disability began with the beginning
dynamical model of modern science, that of the Newton gravity equations for
more than two gravitationally-interacting bodies, e.g., for more than two
planets, or even for the, "three-body", Moon, Sun, Earth sub-system of our Solar System. ... as well as in more quotidian loci, such as the epidemic
unconscious inability, in modern society, in our natural languages, e.g., in
modern English, for many of us to sensibly formulate comments/descriptions that
involve totalities within which we ourselves, the ‘commenter’s’/‘describers’, are
also included. ... .”
“The NQ
arithmetic for dialectics -- despite its [relative] utter simplicity, as the
[meta-]systematically first explicitly dialectical arithmetic in our
presentational progression of dialectical arithmetics -- already exhibits, in embryo,
the solution to one of the most essential symptoms of ‘The Nonlinearity Barrier’: “infinite”
singularity in one or more of the metrics, the “vital signs”, of the dynamic
system modeled by a nonlinear differential equation, irrupting at a real finite
time
parameter value, let’s call it t*, of that nonlinear differential equation model of that
dynamic system.”
“The Foundation
has recently published an account of our proposed solution to this aspect of ‘The
Nonlinearity Barrier’, in the realm of such nonlinear differential equation
models, as 're-qualified' using our 'quanto-qualitative' Mu arithmetic for dialectics, and using its 'quanto-qualitative' successor arithmetics for dialectics --
-- as a further development of earlier work [see pages A-6
to A-14]
--
-- when such equations are «aufheben»-elevated into the context
of the seventh system for the mathematics of dialectics in our presentational progression,
via the ‘metrical-qualifiers re-qualification’ of such equations.”
“Such ‘re-qualified’ classical dynamical differential
equations can, at best, describe the state of affairs that arises at/after their
singularity, as/by
‘·’, the axiomatically regulated value which we call
‘full zero’.”
This value, ‘full zero’, ‘·’,
a value far different from, although deeply related to, the traditional ‘empty
zero’ value, 0,
means that the ontologically new/different state of affairs that arises, at/after/as, singularity, cannot be described within the terms
and via the other ‘ideo-resources’ available within the de facto model
specification of the nonlinear differential equation model, given the implicit,
or explicit, ‘‘‘ontological commitments’’’, the implicit, or explicit, ‘‘‘ontology’’’,
of that model specification -- its ontology-descriptive limits.”
“That is, the ‘full zero’ value expresses the inexpressibility
of the post-singularity state of affairs by/in the language of the pre-singularity
model.”
“For example, in a dynamical model of a three-body -- e.g., of
a three-planet -- gravitationally-interacting dynamic system, for which the
initial conditions are such that two of the planets are predicted to collide,
and since collisions take the form of division-by-zero, “infinite”-force
singularities in Newton-equations models, this model cannot describe the
coalescence/disintegration
process of the interplanetary collision, in part, because this model is
committed to the existence of the two planets as integral parts of its ontology,
and cannot describe processes that result in their ‘dis-existentiation’, or a
state of affairs after their ‘dis-existentiation’.”
“Likewise, a “purely-quantitative” nonlinear differential
equation model of a main-sequence, Hydrogen-burning star, might “go singular”
at the point of the exhaustion -- or of the complete conversion into Helium --
of the star’s core Hydrogen “fuel”, so that the core Hydrogen concentration has
abruptly dropped to 0,
as a result, not of any
action upon the star, from its exterior, by other [ev]entities, outside of it,
but as a result of the self-gravitational/implosive versus thermonuclear self-explosive
‘intra-duality’, and of the self-interactive ‘‘‘self-activity’’’, of this star
itself.”
“The NQ dialectical ideography,
despite its rudimentary descriptive capabilities, can describe,
connotatively, the new ontology that arises at/with/after/as such a singularity.”
“If the ontology, ‘pre-singularity’ -- just prior to the t = t* moment of that singularity/- division-by-0 -- is denoted by the
ontological-quality-connoting ideographical qualifier, X, or,
equivalently, by qX,
then the incremental new ontology that irrupts with/as/after the
[ontological] singularity is denoted by qXX.”
“This new symbol, generated by the symbolic representation
of the self-interaction
of that which is denoted by qX, or by X [a ‘‘‘self-action’’’ represented by
the self-juxtaposition of its symbol, or by that symbol’s “squaring” or
self-multiplication, via the operation denoted by ‘*’] --
XX = X * X = qX *
qX = qX + qXX
-- ‘‘‘solves’’’ for that singularity,
“purely”-qualitatively, and ontologically, to the extent that the connotations
of qXX
can be aptly identified with the ontology, and consequent phenomenology, known
to manifest, or expected to manifest, after such a singularity. More advanced systems of dialectic mathematics,
and the more advanced mathematical models that they can express, are needed to ‘‘‘compute
past singularity’’’ in quantitative detail.”
“Our typical interpretation of the connotations of a term/‘categorogram’
like qXX,
is that it connotes a category for “individuals” which are ‘meta1-individuals’
in relation to the individuals constituting the meaning of the category denoted
by qX.”
“Thus, in the context of our second example, if qX
connotes the star in question, as a whole, but emphasizing the composition of
that star’s core as, initially -- in its qX ‘meta-state’, or
‘ontology-state’ -- consisting principally of Hydrogen
atoms/nuclei
as its defining “individuals”, then qXX could be
‘‘‘solved-for’’’ as connoting the dialectical, or «aufheben», negation/conservation/elevation
of that core content, into a core content that, ‘post-singularity’, consists
principally of those ‘meta1-individuals’, relative to the Hydrogen atoms/nuclei as its former defining
“individuals”, called Helium atoms/nuclei, in that
each individual Helium nucleus is created by a
process involving the fusion
of two Hydrogen nuclei/protons --
XX = ~X = qX[qX] = ~[qX] = qX2 = qX + qXX
-- interpreted/ ‘‘‘solved’’’ as --
HH = ~H = qH[qH] = ~[qH] = qH2 = qH + qHH = qH + qHe = H + He
-- so that the category He refers to the ontologically
different composition of the -- now Helium
-- core of the star, after the singularity.
The carried-forward category, H, now refers to the possibility
or actuality of H type “individuals” remaining inside the star, e.g., in
(a) concentric layer(s) surrounding the now-Helium
core.”
“Then, the next singularity-bounded epoch, whose description
is generated by means of the ‘‘‘self-interacting’’’, or “squaring”/‘dialectical self-negating’,
of the description of the result of the first singularity, (H
+ He) --
~(H + He) = (H
+ He)(H
+ He) = (H + He) * (H + He) = (H
+ He)2 =
(H +
He
+ qHeH +
qHeHe) [--> q1
+ q2 + q3 + q4
-- describes, via, qHeH,
the processes and loci of the continuing conversion of Hydrogen ‘‘‘individuals’’’ into Helium [meta1-]individuals, e.g., in concentric
outside-core layers of the star, &, via qHeHe,
describes the new,
second singularity,
of the irruption, e.g., transiently and intermediately, of the [locally] new
ontology of Beryllium atoms/nuclei, of atomic number 4 [e.g., "PPII" variant of "p-p process"]
-- i.e., with two pairs
of protons in
their nuclei, each resulting from processes involving the effective fusion of two Helium atoms/nuclei -- and thus as ‘meta1- meta1-individuals’,
or ‘meta2-individuals’, in the core of the star.”
“Because the NQ dialectical ideography
is aptly describable as a ‘contra-Boolean algebra for [dialectical] logic’, and since
the [revised] Boolean algebra models the logic of today’s digital
computers, one might well wonder what capabilities might especially and
uniquely accrue to a computer architecture whose core logic was that modeled by the NQ ‘contra-Boolean
algebra’.”
“F.E.D. has not, to-date, made
public much of our ‘‘‘wondering’’’ on this topic, in the context of this era
of, e.g., the Watson supercomputer, the internet, “Big Data”, etc.”
“For today, we will leave the solution of this topic to you,
our newest members, as an “extra credit” assignment, to enable you to test your
mettle on an issue which may be even of the very greatest importance.”
“Apparently, such a computer might be capable of ‘‘‘computing
past singularity’’’,
i.e., of ‘computing post
singularity’’’ [including, in particular, of computing
up to, and beyond, the ‘‘‘Singularity’’’ of our predicted irruption of the
android robotics, second species of the ‘meta-humanity’ that we foresee],
its calculations not ‘‘‘losing their way’’’ at the t* point of singularity; of
division-by-zero ‘‘‘explosion’’’.”
“Also, albeit in a “purely”-qualitative,
“purely”-ontological way, the NQ way
of modeling such veritable progressions of nonlinearity-induced [‘‘‘self-reflexivity’’’-induced] singularities, also captures, if, again, only
in a “purely” non-quantitative way, the other of the most essential symptoms
of ‘The Nonlinearity Barrier’, namely, the ‘irrepetitivity’
of the behavior of, e.g., nonlinear dynamical systems’ total differential
equation models; their phenomena of causal, deterministic, exact, but never-repeating order.
“This kind
of order -- little recognized as such within the prevailing «mentalité» -- is akin to the
never-repeating order
of the decimal expression of an algebraic or transcendental “irrational” “Real”
number, i.e., the exact determinism that determines each digit in the decimal
sequence of digits representing that “irrational” number, as determined by the
individual nature/definition
of that “irrational” number, coupled with the non-repeating character of that
sequence of digits, which many are wont to -- quite mistakenly -- call “chaos”,
or “randomness”.
“Consider, for example, the ‘‘‘deterministic non-periodic flows’’’ -- the
never-repeating state-space trajectories -- generated by the approximate,
“numerical” solutions of the nonlinear, “total-differential” equations that
model such nonlinear dynamical systems, and that constitute “attractors”, or
‘dynamical solution-geometries’, that are unique to non-linear
differential equations, not
found among linear
differential equation models, e.g., “limit-cycles” and “strange attractors”.
“This trajectorial ‘irrepetitivity’
is most obvious in the case of the so-called “strange” attractors, which are
the most “normal”, the most ubiquitous ‘dynamical solution-geometries’ for
nonlinear total-differential equations.
These “strange” attractors are ‘‘‘asymptotically aperiodic’’’.”
“However, the “asymptotically periodic” attractors, e.g.,
the “limit-cycles”, also exhibit, though not so obviously, this phenomenon of
trajectorial ‘irrepetitivity’; their
actual trajectories never, ever actually “cycle”, i.e., “until” the “limit”, of
the |t| in W
“moment”, a “moment” which can never, ever arrive.”
“For all such strictly ruled, determinate, determined,
deterministic trajectories, however “non-periodic”
-- however ‘irrepetitive’ -- “chaos” is an ideologically, psychohistorically misleading misnomer.”
“Those who want you to believe that “shit [ just ] happens” are those who do not want you to
notice that they are the real source of the “shit” that is happening to you, as they “pull
the strings”, from “behind the scenes”.
“The dyadic or triadic ‘self-iterative’ ‘self-reflexion’, and
consequent «autokinesis», of an initial, initiating population of
“individuals”, as represented by the «arché», or “starter”, ontological category, in an NQ ‘meta-model
meta-equation’ that generates an NQ-algebraic categorial progression, is also qualitatively, ontologically never-repeating, is qualitatively
different for
each and every value of its self-iteration parameter, e.g., for t in W.”
“For each value of this historical, epochal time-representing
parameter, a unique ‘cumulum’ of ontological category-symbols is generated, as
representing possible existences during that epoch -- qualitatively,
ontologically different from those for all other epochs -- and is asserted as
being representative of the ‘ontology-state’ of the modeled Domain during that
epoch.”
“True, each such cumulum, from t = 1 onward,
does «aufheben»-include
the representation of the possibility of the continued existence of the content
represented by the ontological categories irrupted in all preceding
‘self-iterations’, for preceding values of t, i.e., corresponding to earlier,
smaller values of this ‘self-iteration parameter’, or ‘‘‘time-like’’’
“independent variable”.”
“This «aufheben»-inclusion
represents the ‘‘‘self-similarity’’’ aspect of the content represented by such
ontological-categorial progressions, an aspect whose representation is provided
for via the ‘second
conservation’
moment of the ‘double-conservation
«aufheben» evolute product rule’, axiom §9.”
“However, each such ‘self-iteration’ also includes [one or]
more new, unprecedented possible ontological categories --
representing possible new qualities, new kinds of «arithmoi», or of populations, made up out
of new kinds
of [meta-]«monads»,
i.e., new kinds
of individuals
-- that make that cumulum, as a [sub-]totality, ontologically unprecedented, unique, and, as a whole, never-to-be-repeated -- irrepeatable.”
Regards,
Miguel
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