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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 xp 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 Et 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 fg and in complex systems there will be many fg relations and multiple levels of dependency so that the very fg relationship itself is constructed by virtue perhaps of some (seemingly unrelated) ab. 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]