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QUANTUM NETWORKS, STRUCTURE, AND RELATIVITY
Towards a New Mathematics
Integrating Quantum Mechanics, Complexity, Chaos, and Relativity
Editors and Chief Contributors
M. Dudziak, K. Sharpe, V. Sanyuk, L. Brizhik
Volume 1
Foundations
Preface
We are approaching the centenary of Einstein’s remarkable shift in thinking about simultaneity
and measurement that resulted in Special and General theories of Relativity. Never far removed
from any discussion of cosmology or fundamental particle physics, even from the outset in 1905,
was the question beneath the covers of both quantum mechanics and relativity. How is one to
reconcile the two seemingly contradictory models, both of which work and both of which appear
critical for any fundamental physics, in a manner that makes things simpler, more efficient, and
closer to the age-old goal of William of Occam and others even from the time of Parmenides?
How can there be a comprehensive and integrated theoretical understanding of physics that
connects from the Ur-Grund of space and time upwards to the macroscopic scales of
macromolecules, organisms and brains, and a cosmos full of stars and galaxies? The quest has
produced many different suggestions and directions of research, not the least of which are variant
algebras and the increased dimensionalities of string and superstring theories. The stream of
work in noncommutative spaces and geometry is most promising and interesting from the
perspective of developing both a mathematical foundation that can be used in common as a
language for quanta and gravity, however the translation of this approach into both experiment
and for extension into other scales and orders of magnitude is still very problematic. Resolution
of the fundamental problem seems to be elusively close but sometimes this closeness also seems
deceptively near, after almost a century.
Our goal is from the outset neither to claim having that complete and quintessential theory of
everything nor to argue for an avoidance of the issues. Perhaps in the course of writing and
reading these volumes, by progressing stepwise and in parallel through the whole century of
different theories and attempts, we will reach some unique clarification that brings us closer to
what we believe is the essential ingredient for a unified quantum relativistic theoretical physics.
This ingredient we believe to be namely a new foundational mathematics that is able to better
describe analytically the relationships between deterministic events and processes at one scale of
measurement with non-deterministic events at other scales and that provides a language more
appropriate than that of steps and limits, the classical calculus foundations of velocity,
acceleration, and movement, for describing and predicting processes that are inherently global,
massively interconnected, geometrical, and relational. It is quite possible that the tools of
noncommutative algebra and geometry will be very important in these descriptive tasks since the
processes of interest may be treatable as something similar to a space or a space-like object.
Perhaps there is such a thing as a fuzzy noncommutative manifold, an entity arising out of a
network of actions, and giving rise to what under conditions of experimental measurement, in the
observer-subject relationship, appear to be continuous spaces. 1
The nature of these three volumes, a comparatively monumental undertaking in a field that
extremely dynamic and full of different language constructs and interpretations, is somewhat
encyclopedic. We are embarking here to provide a type of centenary revisiting of quantum and
relativistic foundations and to create some perspective with which to understand and correlate
different models and theories that have been introduced, many of which we find to have, after all,
some powerful common threads and currents. From this encyclopedic foundation, starting in this
first volume and completing in the second, we intend to accomplish, as authors and coordinators
of this research stream, and also as members of the reading and interacting community, a basis for
what we believe to be a new mathematical form and language. This new or more ideal language
should be one that allows more cogent talk and analysis of complexity and coherence in spacetime. It must be a language that better describes the conceptual framework whereby one process
(quantum or cosmological) is generated and sustained and destroyed by virtue of the
interrelationships of all surrounding processes, giving rise to phenomena that appear particle-like,
and wave-like, and that obey principles of relativistic behavior under some measurements and
quantum mechanical behavior under others. It is a mathematics that must communicate with the
mathematics of points and vectors but that originates in thinking and reasoning about processes
that are neither points, nor lines, nor planes, nor spaces, where time is a construct of process,
change, and coherence but not a fundamental entity, and where space itself is recognized as also
being a derived entity, the common source of space and time being the indivisible timeless whole
of What-Is,  (physis).
Within this work there are some very unusual histories, events, and acknowledgments. This is the
culmination of many half-started and discarded papers, notes, and fragments. Nothing was done
in the ordinary and typical manner of academic physics and mathematics. An inordinate amount
of time was spent in other directions and in fact on what appeared and still appear to be unrelated
topics of research, not the least of which was time spent by one of the authors (M. Dudziak) on
matters that seem to be more in the sphere of computer science and applied mathematics. The
massive undertaking recently completed by V. Sanyuk in the form of an Encyclopedia of the
Physical Sciences (publisher xyz, Moscow, Russia, 2000) was both a practical launching pad as
well as an inspirational motivation for taking this approach of a three-volume restatement of the
problems and proferred solutions, as part of leading out of the problem and into a new theoretical
framework, that constitutes this work.
So many things are different here from the ordinary way in which things are usually done in
physics. Perhaps in the process, a different and valuable illumination has emerged. We believe so
and hope that it is shared by readers and students. As for the acknowledgements to those that
have assisted significantly, this list would be too long if it were to be anywhere approaching
completeness. We will defend ourselves in the spirit of Gödel and hope that we have not
forgotten too many of the most important individuals. Those who are scientists and researchers,
their names are mentioned by way of reference and discussion within these volumes. In addition
we must give credit to other special individuals.
[some list here, to be determined as we go along]
Introduction
The seemingly intractable problem of quantum relativity may not be a problem for the theoretical
physicists alone to solve. The long-sought key may be less a matter of twisting and rotating the
fundamental field equations and dimensionalities and more a function of bringing into the picture
a different conception of relation and interaction among fundamental processes and events, some
of which happen to be measureable in terms of E, p, and t. While intuitional leaps are looked
upon disparagingly in late twentieth century science, post Russell, Carnap, and a long-gestating,
long-stewing tradition of positivism and materialism, this was not always the case, and it may be
that in the twenty-first century a new light of value is found burning within the right hemisphere
of the brain, to complement the algorithms and algebras of the left.
Our intuitive leap comes in the form of a suggestion that this problem of integrating quantum
mechanics and general relativity is somehow not dissimilar and not unrelated from the problem of
reconciling complexity and nonlinearity with stability, structure, and self-organization. There
appear to be some common roots and perhaps some missing right language for bringing together
quantum theory and relativity that also apply to the mystery of how coherent organisms like
atoms, macromolecules, cells, and humans even exist in the first place, much less sustain
themselves over lifespans. Further, we are inclined to suggest that this critical and aggressive
problem in physics has implications that are intimated but not yet – before the solution can
manifest itself – evident and accepted as definitive implications for biology and intelligence. Our
suggestion is that some of the insights for the solution of the quantum relativity conundrum may
come from precisely these seemingly disparate phenomena in complex and organic systems. 1
This approach is quite unlike many of the speculative approaches that have emerged during the
middle to late twentieth century for drawing together quantum theory, biology, and in particular
the brain. We are not looking to extend merely an interesting analogy but are looking toward
something that may best be called a radical general covariance principle wherein the coordinate
system is not one of points in a grid but concepts and relations in an ontological space.
By way of one simple example, we can consider the simplest form of a solitary standing wave, a
soliton of a type described by the elementary Sine-Gordon equation
 2v  2v

 sin( v)
x 2 t 2
m.n
The complete mathematical vocabulary for these phenomena is in the traditional formalism for
describing waves and rates of change; i.e. differentiation of a variable in terms of one or more
others. This is straightforward PDE mathematics and grows out of the substrate of the calculus
since the time of Leibniz and Newton. However this type of expression is not in a formalism
made expressly for representing stability and structure first and foremost and rates of change
second. The language of differentiation is a language for expressing change – in position, over
time, or abstractly between one or more values in terms of one or more other values. This is
important and essential to any physics that is also a physis. However, there are other qualities and
their quantitative representations may lose something in the translation to a primarily
differentiation-oriented mathematic – relationship, stability, morphology, coherence, dependence
and interdependence are just some of those qualities. We are endeavoring to establish a set of
tools that can show relationships and changes within and among waves such as that depicted by
the S-G equation above. How else can we describe that form when it interacts with other entities
that cause it to be reinforced or to dissipate, to maintain itself with some quantitative degree of
certainty or confidence even, or to be transformed into a qualitatively distinctive other form? The
direction in which this work moves is one of a process algebra built from primitives that include
operators for topological and network-relational transformation.
A(, ,,) may be …
Can such a new language, or a new description of the ur-phenomena at least – perhaps
understanding the “particle” as a dynamic pre-space-time confluence of a network of events in a
hypercrystalline vacuum, not as an object at all in its own right (leading to the implication that
there are no objects or point-centered masses at all in the universe) – lead to a better theory.2 We
keep coming back to that complex and multi-faceted question - why at one end of the dimensional
scale everything seems both quantized and fuzzy, while at the other end there are these relativistic
descriptions demonstrated left and right by experimental observation, and in between is a fuzzy
region of a different sort altogether, where quantum effects appear to be at work in
macromolecular energy transport and biological information processing, yet having no apparent
causal link with the “classical” quantum mechanics.
It is not only the qualitative side that is of interest, but the ways in which the qualitative
differences between objects under transformation in a massive and complex population (particles,
waves, molecules, people) can be quantitatively measured and classified. It seems to be a new
type of number that is the goal, and with it a new type of geometry…
Within Volume One our objective is to examine some basics of physics and mathematics and to
do so in the new light of this search for a geometrical language that better fits and describes what
goes on at the quantum scale and at the relativistic scale. This examination is not intended to be a
standard recapitulation or summary but a re-opening, a dis-covering, in the true sense of the
original science of  (aletheia).3 This is more challenging than it may seem, since to be
in a proper sense phenomenologically open means to be free from preconceived interpretations
and theories. This is basically impossible yet we must try all the same.
Volume Two is oriented to a deeper explication of complimentary and also quite orthogonal
theories that have been developed, particular during the latter quarter of the twentieth century, for
answering the dilemma of quantum relativity. We believe that this may be the first effort to
analyze the different views and interpretations together in the virtual forum of one book. Unlike
a collection or compendium that provides different papers and chapters in relative isolation from
one another, except perhaps for the customary introduction and editors’ comments, and unlike a
singular exposition that advances only the one interpretation over several others, we are
attempting a true synthesis. The presentation and advancement of one view or another is done in
the context of others. Perhaps this is an attempt to perform counterpoint in physics and
mathematics and perhaps it will seem in the end to be less like Bach and more like Berg. It is for
the reader to decide how the harmonics turn out.
Volume Three is for the formulation and expression of the synthesé and the synergy that we
believe emerges naturally and, like the Tao, well-flowing-together from all of the preceding work.
It is at once the outcome and the beginning. In Volume Three we aim to lay out the groundwork
of this new organic, synergetic physis that can explain better how there is continuity across the
scales of Nature that is more than merely some interesting analogy.
Conventional Quantum Theory Revisited
Key points in QT, but each is examined in the context of the
impact or problem or dilemma with respect to GR.
Intro concentration upon Wh-Dew MWI and Bell MWI, also Bohm-Hiley
Ontolog. Interpret. and some MWI variations therein. But most of
this is reserved for Vol. 2.
Wave-Particle Duality and Complementarity
The wave-like and particle-like dual nature of light and indeed of all particles and matter is both
the conundrum and the doorway into understanding a more fundamental aspect of all reality.
Continuity, flow, and cycle are basic qualities of any wave, regardless of any wavelength or
frequency. Singularity of location, discreteness, finiteness of dimension are basic qualities of any
object that can be loosely called a particle, no matter what its size or shape.
What does it mean for something to be a particle at all
Double-Slit Experiment
[Basic description]
Heisenberg Uncertain Principle
The typical form of the uncertainty principle stating that both position and momentum of a
particle cannot be measured simultaneously to an arbitrary precision is
m.n
xp  h 4
where h is Planck’s constant. What is often misunderstood is that this is an uncertainty relation
describing an instantaneous measurement, not a statement of being unable to measure one or even
both of the values x and p with significant precision. A key point is that eq. m.n refers to two
kinds of measurement performed at the same time. Moreover, there are analogous relationships
for other values, such as energy and time,
m.n
Et  h 4
that refer to a precision of measurement of one value, namely energy, at two different instants of
time (separated by some interval t).
…
Why No Macroscopic Superposition
There is an anecdote that Einstein once asked, “Why is it that we do not see two moons?” This
kind of question should be a diving board into a pool of exploration. Surely there are no evident
macroscopic phenomena where location is superposed. Yet at the Planck scale locations are best
described as a fuzzy cloud. What happens when things get bigger, or rather, when things
aggregate and form something much more massive and thus (being careful here) occupy more
space and take more time to move?
All of the particles of the Moon are as superposed as they can be, examined and measured on an
individual basis. However there is no coherence to these individual particles. Their
superpositions are with respect to themselves, not in some order that is imposed from without.
The Moon is a statistical ensemble of all these quadrillions of particles and there is a new set of
relation that exists among all the particles now by virtue of being all-together in a certain spacetime framework at the scale of the Moon’s diameter. The mass of all the other contiguous
particles now plays a role in the determination of the activity of all of the particles in that vicinity,
and specifically any particle that is within some distance of any other. Suddenly there is a
dominating presence – the Moon! – that has a control and influence which is precisely a coherent
phenomena, even though it did not emerge from anything other than the statistical ensemble of all
these particles being within some general closeness of certain other members of the set.
…
EPR Paradox
The basic experimental situation
Why EPR appears to be a problem for quantum mechanics
An alternative viewpoint
To what extent is EPR not a paradox after all?
The problem is because of thinking of one uniform space-time that must be the same
configuration for both photons and in all places and times of measurement. We assume that any
system of particles - in order for a signal to transmit in some measurable period of time, not faster
than the speed of light and therefore implying nonlocality or superluminal transmission – must be
observable and measureable the same way by all observers.
What if this is not the case?
Consider the photons with opposite spin that have been generated by the experiment. Call them a
and b. Let us assume that a and b can communicate by virtue of being somehow part of the same
photon a’ and that there is no separation in space between them. There is no signaling problem to
be reconciled. But what does this mean to the observer of the entire experiment, who clearly is
measuring a and b as being meters or more in distance from one another?
The suggestion here is that there is no uniform space even for this rather localized environment of
the experiment and the observer and his instrumentation. In effect, the space is warped and
knotted such that my 3m is only 3m from my perspective but for a and b in terms of spin it is
something altogether different. That is the key – “in terms of spin”. On some other basis, a and b
are still moving meters and kilometers apart. But for certain things in which conservation applies
in the face of change through measurement of one part of the system a’, there is a different
distance metric.
Schrödinger Equation – TDSE and TISE
We want to consider some of the issues surrounding the relationship of the fundamental quantummechanical energy equation

2 2

( x, t )  V ( x, t )( x, t )  i ( x, t )
2
2m x
t
m.n
with the concept of a space and time measure that is dependent upon the energy E.
…
Nonlinear Schrödinger Equation as a Simple Soliton
Let us consider how a basic linear wave function can be modified by nonlinear variations in the
background medium. Amplitude can be modified slowly over time and space in a manner that
does not distort the essential stability over larger time or space measurements. This would be the
case, hypothetically, for a topological soliton that is able to absorb a variety of defects and
modulations in its structure without losing a fundamental integrity and identity. We can study an
example in the general form of the nonlinear Schrödinger equation (NLS)
a  1
2a
2
 a
i  vg    kk 2  [(    0 )    a 2 a ]a  0
x  2
x
 t
m.n
which has soliton solutions. Such a wave has an envelope about it that remains constant, and it is
the envelope of the wave that perhaps is most interesting and relevant to the notion of stability for
a wave of n-dimensions that is generated and sustained by a set of p other waves which are in turn
interactively defined.
Generalized Eigenvalue Equations and Operators
Scattering Theory and Born Approximation
Measurement and Hidden Variables
General Relativity
Ditto, looking at main developments since Einstein in light of QT.
Some discussion of Hawking’s approach, also Guth and Inflationary Universe.
Complexity, Chaos, and Stability
Distictions between compexity and complication, chaos and chance, stability and form.
Fractal and p-adic concepts (Freund, Pitkannen, N.)
Complexity vs. Complicatedness
Formal systems and machines as a special case can be simple or complicated. A large computer
program can be complicated to write, to validate, and to maintain.
Chaotic vs. Stochastic Behavior
Attractors and Strangeness
Chaos and Turbulence in Massively Parallel Systems
Solitons and Self-Organization
What is a classical soliton? An abstract soliton in n-dimensions?
Basic models and explorations in self-organization. Not only purely physical.
Simple Universal Nonlinear Waves
Korteweg – de Vries (KdV)
The simplest possible unidirectional wave equation is expressed in the general KdV form
u
u  3u
u

0
t
t x 3
m.n
and provides for two significant properties of dispersion and nonlinearity while at the same time
there is no dissipation. A common solution for u is given by
1
u  3 sec h 2  1 / 2 ( x  t )
2
Sine-Gordon
Balance of Dispersion
Formation of Coherent Structures
Stable Forms from Near-Equilibria States Perturbed by Nonlinear Effects
SONON and SOMA Models
Solitons in 2-D, 3-D, and n-D
Topological Solitons
m.n
Volume 2
Approaches and Investigations
Introduction
Twistors and Spinors
Concentration on Penrose models and his recent-era explorations into gravirtational collapse
Algebraic Models
Penrose-Hameroff QR model
Algebraic Formulations
Distinctions and pros/cons between Heisenberg and Schr approaches to QM, and new
developments aimed at QM QR resolution, esp., latter-day Hiley and students
Wheeler-Dewitt
A range of MWI models
Non-Existence of Time
Barbour, Gödel primarily
Fractal Space-Time Scales
Including p-adic models
Local Time
Hitoshi Kitada and others pro/con in the attempt to resolve QM and GR by virtually separating
them ontologically. Also counter-args like Lee Smolin and others.
Quantum Sets and Networks
D. R. Finkelstein
Volume 3
Organic Topological Networks
Introduction
We introduce the concept of an organic universe, that is to say, a universe characterized by the
whole that acts as an attractor for all disturbances and deflections, each of which manifests as a
unique system state, the sum of which are a quantum superposition of coherent activities over all
possible space-times. The universe is itself thus understood to be an organism in the sense of
which member entities within it are organisms but not all such member entities.
(Is the universe alive, therefore? It would seem so.)
Geometry Inside-Out
We have traditionally been taught a world viewpoint that places all objects of the world into a
geometry that exists by and of itself, a coordinate system that is abstract and shaped by its own
inherent mathematics. Then with GR we opened ourselves up to the idea that the shape of our
space and our universe is modulated by the masses of objects that are in space-time and thus to a
geometry that changes according to the presence or absence of masses.
Now we want to introduce that the entire geometrodynamics of the universe is influenced, even
so far as to say created, by the dynamic behavior of objects and their relations to one another, not
only a factor of mass and energy in the classical sense, but far beyond that, the relations of how
these objects interact with one another affects the shape of space and the duration of time for both
the most microcosmic local space-times of subatomic particles and the complete macroscopic
extent of the universe as a whole.
If the universe is alive it breathes and if it breathes then its geometry changes as it breathes each
breath.
[quote from Bradak-Upanisad]
The Point as Intersection of Spaces
We look at first the abstract point as a geometrical entity that comes into existence not of its own
prima facie but as a mathematical operation x that occurs simultaneously and in parallel among a
set S of adjoining points, lines, planes – something akin to projective geometry and as taken
further by George Adams, Nick Rosen, and others.
And this operation x occurs of course for the definition of each point and element in the set S.
So it is self-referential and recursive. And parallel.
Space Defined by the Whole
The Importance of Coherence for Structure and Organization
Space-Time as a Consequence of Local Coherence Scaled Upwards
Energy Defined Self-Referentially
Apply the geometry to energy now. A new meaning altogether to calculating what IS the
Hermitian of any system.
Time as Coherence and Consistency
Thought experiment – space travel and the case of Special Relativity.
Time Defined by Configurations in Space
Space Configured by Dynamic Time
A Soliton-like Model of the Generic Particle-Object-Cosmos
First Photon
The idea of First Photon is that the big bang never occurred because there was no ultradense
compact form of the universe to explode and inflate. We go back to the notion of a
hypercrystalline vacuum that is fundamentally and simultaneously a perfect solid and a perfect
space, through which as an enfolded or implicate potential order all possible paths exist and are
followed. In this super-vacuum which is both Plenum and Void there emerges a pure spark of
direction and individuation, the A of creation, which can be understood as the First Photon. The
big bang, no matter how one conceives of the process thereafter that first instant, occurs not in a
superdense packed matter but in pure vacuum, so pure and total that there is no "room" for a
particle to differentiate or individuate. However, the First Photon creates this possibility and
thenceforth the vacuum cracks and splits in billions and trillions of paths, this process being
otherwise measureable and describable as the Big Bang that initiates an inflationary, rapidlyexpanding universe.
Pure vacuum as pure energy, light
Empty space as solid energy
Mass as defect, hole, a pit or peak extending out of the Plenum
Mass is a perturbation, an irregularity, NON-LIGHT
The black void is pure light
Nothingness of empty space is fullness of the hypercrystalline matrix
The Speed of Light is ZERO - everything else is slower (or perhaps faster) but zero is the speed
of the Void
Light is not "bright" - that is the reaction with the measuring apparatus, which might happen to be
a proton, a wall, a face, a sky
Pure light is timeless, and so is pure vacuum
There are streams or currents in space which are similar to black holes but not of matter but of
pure light and these are zero-time and could be used as time portals and time tunnels.
Virtual Free energy (VFE) is not an impossibility but something that could be achieved by
'tuning' to the right probabilistic frequencies of regions of the vacuum and creating perturbations
that result in the formation / condensation of matter (mass) as a defect-reaction within the Void.
The result is the formation of a "virtual free photon" that lasts and stays - i.e., it has TIME and
this is because it is no longer part of the timeless hypercrystalline vacuum matrix. Where it
comes from, this energy? It is not entirely "free" - it comes from somewhere. That somewhere is
at the end (source) of a quantum stream - an improvement/evolution over the concept of a string.
a string is just an incomplete rendering of a quantum stream.
The stream leads to the particle that emerges. Something like a black hole in reverse, also is
another way to think of it.
Mind as Reflective of the Monad-Cosmos
Starting Material:
Our aim is to develop a new pathway of understanding and speaking about quantum physics, selforganization and the development of structure in space and time, and the manifestation of
relativistic processes in the universe that results from our observations and measurements.
We propose that in order to succeed in this process it is necessary to step back from the
conventional models and mathematics and to examine the Ur-phenomena by which natural events
are experienced and by which they become the subject of abstract conceptualization.
It is necessary to ask first what are the types of questions that have not been asked, what are the
perspectives that have not been used, and why our mathematics is the way that it is in respect to
describing events and processes at the quantum and cosmological scales.
We begin with the idea of a formless void free of dimension and call it .
Let there be one transformation , defect, disturbance and it is a topology that is describable only
as being the whole. There is at first no separation or discrimination between parts of .
[see my unfinished prelude manuscript to all this, First Photon]
How a part is defined from the whole. Convergence. Coherence. Where we get space actually
as well as time. We measure coherence and consistency and come up with separation and
distinction and a flow of one process to another. Eventually we call them states and define
objects as some type of things that ex-ist in one or another state at given “times.” Then we
complain that there is this weirdness called superposition because it seems that when we examine
some kinds of processes, our measuring apparatus forces us to recognize that these “objects” are
apparently in more than one “state” at the same “time”. We end up with Heisenberg’s
Uncertainty and then look for a way out.
But why did we get caught in the trap in the first place?
There is apparently no superposition because there are no states, no defined places for things to
be in, no defined instantons of time for things to occur in and from which to disappear.
In the end, there is not only no time, there is no space. What can this mean and how does it affect
life and the Universe? Obviously things still “go on.”
And something of the sort like this, only we have to make the leap from words and the
Wittgensteinian, Heideggerian dialogues into something that is formal, symbolic, mathematical.
We have to get away from the notion of a field as something different from the matter that is in it,
or of a field as some sort of thing.
10/22/00
Coherence is not simply a matter of synchronization or resonance. Consider an array R of
oscillators and there will be a variety of measurables like frequency, angular momentum, internal
harmonics, much more depending on the complexity of the individual elements in the array. Call
this set of measurables M. Coherence is does not rise or fall on the basis of the relationship
between any element mi  M with another element mj  M. It could be that within the system
constituted by R there is a dependency that for subarray R(b) to be sustained in its vibrations
subarray R(a) must reach some particular threshold of vibration in order to create a cascade effect
that will release energy to R(b). Alternatively, for some function (R(a))  g(R(a)) there may be
some operators that are conditional upon some states in R(b). Quite abstractly,
f ( R1 , O1 , s1 , s 2 , t1 , t 2 )  g ( Ri , O j , s k , s k 1 , t l , t l 1 )
m.n
where sx denotes a boundary limit of a region of some space of n-dimensions and tx denotes a
boundary limit of some time interval, and Ox denotes a specific operation and Rx denotes a
subarray region of the hypothetical array of abstract oscillators. The execution of f within the
specified bounds leads to (allows) the execution of g within its interval range.
Coherence is to be found in fg and in complex systems there will be many fg relations and
multiple levels of dependency so that the very fg relationship itself is constructed by virtue
perhaps of some (seemingly unrelated) ab. And here we are beginning to navigate, albeit
blindly without the right tools of expression, in the territory of both foundational nonlocality and
what may be termed “quantum ecology.”
The term “fuzzy noncommutative manifold” comes as a suggestion from A. Sitarz, “http://www.cyfkr.edu.pl/~ufsitarz/ncgtecxt.htm
1
We use the word “intelligence” here to cover a host of phenomena and behaviors, including
adaptive learning, cognition, pattern recognition, and reasoning in biological organisms such as
humans but also those processes and models that can in principle at least synthesize such
behavior in non-biological systems. We discuss consciousness and mind in due course but this is
not a book about consciousness, although this appears to be a continuous and unavoidably “hot
topic” with respect to quantum physics. Self-reflexiveness and self-awareness is an important
manifestation that in the theoretical model and mathematics we are evolving does have relevance
on many more levels and scales than that of human beings or similar organisms. What may be
perceived as a simple feedback stabilizing process at the molecular or cellular level can be, in the
context of an organism with hundreds of billions of cells and a complex central nervous system,
something for which an entirely richer language is enabled and appropriate – to those who are
most familiar with such processes by being such organisms themselves. What it all looks like at
other scales, to other observers who are different by virtue of being less complex or more
complex, this is a wildly interesting and exciting source of speculation and investigation, but
perhaps, as many points of departure we are bound to trigger and inspire in this work a subject
for “Volume Four.”
1
2
Perhaps in the end we will name this theory Quantum Relativistic Network Dynamics (QRND) and we
will hope that graciously the forerunners and giants in this work who have invented and used similar
terminology, especially (with all due respect) David Finkelstein, and long before him Gabriel Kron, will
not hold us in too much contempt!
3
[description from Heidegger book on metaphysics]