Forbidden symmetry

By Stephen P. King

September, 1992


For the longest time, our knowledge of the inner-workings of the universe has been limited to the narrow window that Galileo, Newton, and other adherents off the Aristotelian and Kantian philosophy have opened for us. With the advent of the theories of relativity and quantum mechanics, many of the long held assumptions as to the true nature of objective reality have come under attack.

Many of the "inviolate" laws of nature have come under scrutiny, revealing a far more intricate and complex web. Only by allowing for a new and wider field of perception and conception are the horizons of knowledge expanded.

In this first of a continuing series of Physica articles, i wish to explore some of the vistas that go beyond the theories of relativity and q. Mechanics, as they are interpreted these days, by using the hologram paradigm. With it the scientific community's continued refusal to examine their basic assumptions as to the metaphysical aspects of reality, as demonstrated by their inability to overcome the shortcomings of their most useful theories, can be surmounted. This is an attempt to force, as it were, nature to show us those phenomena that have allowed us to ask these questions in the first place. I will be exploring the idea that non-local connections, as displayed by various aspects of nature, are manifestations of such "forbidden" phenomena.

Roger penrose, author of the emperor's new mind and a leading physicist, has discovered that sometimes nature slips up and allows us to see the "forbidden;" forbidden by the current understanding of the objective universe. He discovered a tiling symmetry that, interestingly, is based on the constant phi. To quote from an excellent math survey book: the mathematical tourist by Ivars Peterson:

"pairs of rhombohedra [having phi ratios between angles] can... be used to fill a space... where the ratio of the number of rhombohedra is the golden ratio." And further: "a few people did take Penrose's idea seriously, but it took the discovery of tiny metallic crystals composed of aluminum and manganese to alert the scientific world of Penrose's tilings. These crystals had a form as startling and unexpected as five-pointed snowflakes. X-rays and electrons reflected from the crystals showed Penrose's five-fold symmetry --an event, according to the long standing rules of crystalography, that wasn't possible."

These have been named "quasi-crystals" due to their not-quite-crystals nature. They show a level of organization that is only possible if all the atoms that make them up were somehow 'aware' of the orientation and position while the quasicrystals are forming; or as if they were organized by an external non-local morphogenetic field; or as if the atoms were holographically interconnected at some fundamental level. All of these explanations exhibit the various philosophical tacit assumptions used in physics. Yet they all give similar results --so how can we find the true nature of this behavior? By exploring their implications!

This supposedly forbidden phenomena has become a source of consternation for many branches of science and has reintroduced the possibility of non-local connections. Non-local connections have, until now, been considered as heretical as faster than light communication and 'actions at a distance' to the prevalent dogmatic scientific community. It allows us to widen our horizons and to explore the implications to such to the unnatural intellect.

Roger penrose, a neo-Platonist and opponent of the 'identity hypothesis' of artificial intelligence researchers, has been a long time advocate of the idea that non-local connections and 'non-computability' play an important role in both the underlying dynamics of the objective universe and the human brain.

To delineate this, I offer this excerpt from his before mentioned book: "Normally, when nature seeks out a crystalline configuration, she is searching for a configuration of lowest possible energy... I am envisaging a similar thing with quasi-crystal growth, the difference being that this state is much more difficult to find, and the 'best' arrangement can not be discovered simply by adding on atoms one at a time in hope that individual atoms get away with its own energy minimizing problem. Instead, we have a global problem to solve. It

Must be a cooperative effort among a large number of atoms all at once. Such cooperation, I am maintaining, must be achieved quantum mechanically and it is done by many different combined arrangements being 'tried' simultaneously in linear superposition." [a quantum mechanical process] "the selection of an appropriate (though probably not the best) solution must be achieved as the one-graviton (or appropriate alternative) is reached --which would presumably only When the physical conditions are just right." And further: "...the brain is not really like a computer, but it is more like a computer that is constantly changing. These changes can apparently come about by synapses becoming activated or de-activated though the growth or contraction of dendritic splines...this growth or contraction could be governed by something like the process involved in quasi-crystal growth. Thus, not just one of the possible alternative arrangements is tried out, but vast numbers, all superposed in complex linear superposition. ...the successful result of such a calculation would be the 'goal' that takes the place of the simple energy minimizing 'goal' in quasi-crystal growth."

This is part of Penrose's theory relating to the "collapse of the wave function" dilemma in q. Mechanics. I hope to expand on this issue in this and future Physica articles as it is at the root of the metaphysical conundrum of non-local connections and the dual nature of the human mind.

The ideas just presented mark a radical change in paradigm from the Aristotelian and kantian conception of the objective universe (O.U. for short. We are finding new vistas that make the current popular theories (such as the 'Big bang') as absurd and pedantic as the geocentric and flat-earth ideologies of old.

I have found that the still embryonic field of "neural networks" offers a rich framework in which to expand even further these ideas and explore the implications of the hologram paradigm, from a dialectical perspective. Many of the ideas that will be put forward here are speculative and thus we am treading on uncertain and difficult terrain, so I am inviting your comments and critiques on them.

To those readers who may be unfamiliar with neural networks, I offer this (relatively) simple depiction: a group of interconnected yet discrete nodes that work in conjunction to store and process information. Neural nets are an attempt to model the operations of the human brain and autonomic nervous system. They are different from ordinary computing systems in that they operate non-algorithmically to process many data parameters simultaneously in a non-linear fashion. This makes their behavior unpredictable. This would also imply that it is the pattern formed by synergy of the network at any given time that composes its "quasi-algorithm." As the data is processed, the very form of the network is altered irreversibly; thus it heuristically learns new solution parameters by increasing the number and complexity of its inter-connections.

This model serves to exemplify various holographic phenomena in both neural networks and the O.U.:

1) A high degree of inter-connectiveness is necessary to allow for the simultaneous processing of all the pertinent variables and to compare many possible answers against data in memory for validity. Such a quality must be inherent in nature to calculate the huge number of causal interactions possible and find the solution of minimum energy. This is relevant the maintenance of continuity and inertia in the O.U.

2) Neural networks learn new data parameters by means of goal oriented adaptations, this requires a plasticity in the states of the nodes and the connections. This quality is evident in nature as evidenced by the huge capacity for innovation and change in the O.U. it also may imply that causal connections also more flexible than assumed by most.

3) Since the global synergy pattern (at any given instant) is the quasi-Algorithm (for that instant only), all of the 'parts' are operating in a concerted effort in the processing of data, thus demonstrating a holographic non-local connectivity. The O.U. displays this property by the fact that certain processes, such as quasi-crystal growth, operate as if the information as to the state of any single part is enfolded into its global causal structure.

4) The neural network's quasi-algorithms are totally distinct from ordinary syntactical and algorithmic computer programs in that they are as they are not only constantly mutated by their implementation, but also are inseparable from their 'hardware.' This, in turn, acts to create a mutually inclusive relationship between the quasi-algorithm itself and the data being processed. Thus as the data is altered by the processing, the quasi-algorithm is altered irreversibly. This effect may be shown in the O.U. by the fact that time appears to be irreversible at macroscopic levels and quite possibly at microscopic levels as well.

5) The plasticity of neural network states creates a lack of classical deterministic predictability that is implicit in such non-linear systems; it is impossible to predict or retrodict the state of such. This may point to an analogous situation in the O.U. the key distinction between linear and non-linear systems is that the former is a closed system at or close to thermodynamic equilibrium, while the latter is an open system, far from thermodynamic equilibrium; and thus self-perpetuating and self-organizing. The objective existence of such "chaos dynamical" systems are being investigated by Ilya Prigogine and others.

6) The goal of the network, the sought after solution, is reached when the system is brought to a minimum action state, a state of equilibrium, at both local and non-local levels. This would demand an expansion of the concept of a "closed system" upon which classical thermodynamics is based. At any instant the O.U. can be described as such, but not over any extended period of time; it would be open and thus a system far-from-equilibrium. This would validate Hegel's philosophy of the dialectical idea and would demonstrate that the O.U. has a 'becoming' existence rather than a 'being' existence, thus demonstrating its eternal yet dialectical existence.

Assuming that action minimalization (in any form) is the implicit 'goal' of Nature, and that the quantum mechanical non-local inter-connectivity provides a means for global problem solving; it would stand to reason that such a mechanism would provide a means to interface our immaterial self.


This self would be self-realizable by the fact that it has the ability to chose a form of self-expression that is not consistent with principles of locality and could therefore act in ways that are independently willed. The only requirement is that such a Being have a point of reference that is outside of the O.U. So that it could detect the changes it makes.

The laws of consistency and inertia only establish the continuity and boundary conditions of the O.U.; our ability to predict and manipulate it is not limited by our material body's inclusion in it. Even beyond this is our ability to 'see' truth, as in the case of Noesis. Isn't it amazing how nature can be forced to yield her secrets when probed with a sharp enough instrument.

Now to put the pieces together: the objective universe can be modeled as a coherent pattern of causally connected forces and structures created by a continuous process of creation and dissipation of finite and distinct 'monads', each of which is the result of an action minimalization solution of the entire structure --the "collapse of the wave function." Each of these 'monads' defines an event-interval (the measurable state of the particle) via the various characteristic properties of its unique frame of reference without the need of any observer, conscious or not. The 'F.o.R.' of each monad defines the non-local properties as given by the causal relationships with which they are inter-connected with and the event-interval defines the local properties that are locally observable.

The event-interval can be considered as the unique quantal "Minkowskian" interval of each subatomic manifestation of matter and energy that exist causally at any definable point of space-time. It is not possible to separately consider either the local or non-local properties of a quantum monad as having an independent existence; even more, it is not possible to consider either as having a causally impactive actual existence prior to their coming into being, since they are both part of the energy minimalization 'solution' of the entire causally interconnected structure ("CIS"); they can only be considered as probabilities for actual existence at the next monadic manifestation.

Note that I am differentiating between "actual" and "probabilistic" existence, neither is more "real" than the other, they just have different properties; the former are part of the "CIS" while the latter are not --they only act as possible alternative solutions to the action minimalization problem and such are relative to the "CIS." This demonstrates the dialectical antimony between the ideas of being and becoming.

Each F.o.R. and its local complementary event-interval, the measured 'particle', represents a fundamental quantum of 'action' constituting the essential Being that exist at that point in its 'world-line', which in turn constitutes the essential becoming of a particle. All of its past history is enfolded into its present being by means of its quantum mechanical "CIS." The functions of motion and change in state of each monad involve a continuous 'shifting' that can only occur in discrete quanta. This 'shifting' is what constitutes successive temporal displacement --time! (e.g. Relativity's "-ict" in its space-time equations)

The big bang theory of the universe is essentially correct, but only for each individual particle's manifestation in space-time, not for the entire O.U. The entire monad, local particle event-interval and non-local yet finite F.o.R., comes into being ("the big bang"), expands to its maximum state ("inflation") and then collapses back into dissolution (the "big crunch" of a black hole singularity which represents the state of maximum entropy); all in a very short time period --the "Planck time."

This would imply that Einstein's "cosmological constant" is exactly what it is calculated to be; but it is only manifest at the quantum monad level, thus the astronomically observable macroscopic 'flatness' of the O.U. is due to fact that the sum total geometry of all interacting monads is defined by the sum over their relative energies and thus curvatures.

The reason for this discrepancy is to be found in the geometric structure of each monad; locally they have a "non-orientable" positively curved geometry ("Riemannian"), non-locally an "orientable" negatively curved geometry ("hyperbolic"). The two sum up to isomorphism to a geometry of zero curvature.

The infamous "Hubble expansion law" is an effect of the statistical summation of the hyperbolic geometries of all the monads in the O.U. at any given time. While the "quantity of mass needed to cause the big crunch" is defined by the sum of positive curvature geometry in the O.U. at any given time; this may be calculable from the total electromagnetic field density of the O.U., not some ad hoc "dark matter."

To put it more precisely: each monad (the particle event-interval and its unique f.o.r.) Is the defined by the geometrically projected solution 'focused' by a geometrically bounded set (a "non-recursive symplex") of probability wave functions --defined by the monad's causal "world horizon" and the laws of consistency and inertia-- of an infinite holograph-like "manifold" that is defined by all possible probability wave functions (mathematically it has a dimensionality corresponding to the Cantorian "continuum" of fractal complex numbers [for those who have read; it has a "cardinality of À ° ," the set of Real numbers has a "cardinality of a 1"]).

The principles of quantum mechanics and the principles of equivalency of the theories of relativity are a manifestation of the geometric structure of this "Bergson manifold." Since this manifold has a higher action potential than the o.u. due to its dimensional and topological structure, the action minimalization solution of the o.u. is a continuous attempt by it to balance the inflow and outflow of action potential (information) from the Bergson manifold.

To calculate each the various solutions, the interacting sets of wave functions are combined in linear superposition, to 'try out' various configurations until the one-graviton (the minimum space-time curvature) criterion is reached. Such a process non-linearly brings into being the phenomenological Event-interval and its complementary F.o.R. --the entire monad is remanifested in a new state. The infamous wave-particle duality of particles is an effect of this complementarity.

A good visualization tool is that of a matrix of interconnected spherical monads, whose overall pattern of dimensionality and quantitative value is "determined," in accordance with the various geometric constraints given by the physical constants, by the global cooperative effort of each discrete spherical monad and their wave functions (non-recursively bounded symplex components of the Bergson manifold). The variability of objective forms and patterns and the effect known as entropy are the result of the "(thought probably not the best) solution" aspect of the action minimalization computation created by the Heisenberg uncertainty and the Pauli exclusion principles, which act to forbid the exact repetition of the individual "CIS".

This establishes a discontinuous sequence of Leibnitzian monads at each 'Point' in a particle's world-line trajectory that are the result of the discontinuous calculation, actualizing and dissipation of the probabilistic and relativistic "causes" of each discrete monad, in conformance with the laws of conservation and action ("consistency" and "inertia"). The macroscopic patterns that such monads form are then coordinated together in temporal succession the discontinuous and relativistic process of becoming and remanifestation to give the overall phenomenological O.U.

Each monad is an open system within the closed system of the Bergson manifold; and the O.U. is defined by the sum of all monads that are "in the CIS" that one is using as a macroscopic frame of reference for one's observations.

This number is defined by the "baryon number" (aprox. 1088) and is constant; it sets a limit to the number of causal interconnections of the O.U. (which then gives the finite "speed of light" and the finite gravity constant) --thus the O.U. is finite yet unbounded in both "space" and "time," but only relative to the F.o.R. Of any single "CIS" within such; thus no matter where you are and what you are doing, you would perceive a similar view and your measurements of the physical constants are the same.

This theory establishes an uncountable infinity of possible states of being (an uncountable infinite number of wave functions), therefore it is limitless in space, time, qualitative value and innovation. Both the "past" and "future" existence of macroscopic and subatomic structures are probabilistic not an 'a priori' "actual" object as the adherents of the absolute causality of Kantian and Aristotelian philosophy would have us believe (mathematically such is an "NP-completeness" problem of infinite proportions --not solvable at all!). Only the ever changing and irreversible local "present" of the observer is "actual"

And absolute for only that observer, and such only lasts in that state for approximately 10-44ths of a second! Like the quasi-algorithm of a huge neural net-work, interconnected by quantum mechanical and relativistic "causal" links, the patterns of the perceived o.u. are constantly coming into being and remanifesting at subatomic levels (and, quite possibly all levels!).

This, although, does not necessarily imply that such a neural network-like structure is capable of being self-aware; as it could not detect any changes it might produce and it also not capable of "transgressing" its own laws. It could not predict the possible outcomes of its own behavior --the "NP-completeness" problem, thus it would have no ability to chose any alternative that have a higher action potential. This would demand the exclusion of our individual intellects from such an undivided "whole." (cf. Goedel's Incompleteness theorem and the Russell and Banach-Tarsky set paradoxes in relation to this; all of which prove the untenebility of the "logical principle of the excluded middle" for uncountably infinite sets (only) upon which modern logic is based; thus the tacit assumptions of the "identity hypothesis" and the Big bang theory are erroneous --I only wish Roger Penrose would realize this!)

On a personal note, i am being cautious in regard to this hypothesis since it could be incorrectly used to substantiate an orthodox religious outlook. What is manifested as the "classical" O.U. is only an ever changing finite collection of patterns that are being continuously created. We just are physically unable to detect these without elaborate experimental equipment. Just as the moving image on a t.v. screen is but an optical illusion formed by the non-moving pixel's change in color --all coordinated by the weak electromagnetic signal of your favorite channel, or as a projected movie creates the illusion of motion by its rapid frame-to-frame translation, the observed universe is both the side effect and delimiter of an underlying probabilistic and causal process.

The universal "speed limit" of the speed of light is only a boundary condition to differentiate between the geometries of the monad and an effect of the quantization of classical motion, it is not an absolute limit to causal interactions as most assume. It would appear that Plato's "cave" allegory and Zeno's "arrow" paradox are as accurate today as they were two thousand years ago.

The monistic ideologies that are implicit in the absolutist sciences and religions, with their static existential idealism and absolute causality, leave too many unanswered questions as to the genesis and function of the Human Intellect and of the cosmos.

The only workable perspective therefore must allow for the inclusion of an Immaterial aspect of such, a form of dialectical pluralism. It would seem at this point that the necessary dichotomy of the entropic inertial being and negentropic becoming of the O.U. is dissolved by the existence of the Bergson Manifold to define the totality of existence; whereby the mind can define its unique and individual intellects by creating a connection between the Platonistic reality of the Bergson manifold and their objective brains.

In this article we have explored many ideas that may seen foreign and obscure. In fact I am still in the process of mathematically formalizing this theory; but we can discover many new insights if these ideas are given careful thought and by exploring their implications and uses. I have discovered, much to my amazement, that this theory (quantum morphogenetic dynamics) is able to synthesize all of the great current theories that are, even now as I write this,being vigorously examined to find a means to unify them. The dilemma lies in their misinterpretation and the difficulty created by the different philosophical and mathematical principles used and in the different phenomena that they describe --and in the appalling lack of creativity and insight in a majority of scientist as demonstrated by their 'post hoc, ergo propter hoc' reasoning.

The key to this conundrum can be found in the fundamental tacit assumption that the O.U. is an infinitely divisible absolute space-time continuum in which all objects have a continuous existence; this assumption does not stand up to empirical evidence! Such an assumption of absolute causality only acts to perpetuate the nihilistic materialistic and immaterialistic philosophies.

A more accurate assumption would allow for the complementary antimony of both a "one" and a "many." The "one" is the probabilistic universe modeled by the Bergson manifold; and the "many" is the set of all finite monads; the former having a numerically uncountable infinity and the latter a countable infinity --there is a big difference between these two as any person that has studied number theory will attest. This would explain the unique and individual Intellect as the interaction between the material (macroscopic "CIS") brain, continuously created by the discontinuous probabilistic wave function reductions, interfacing by means of its complex neural network structure with the Platonistic "Bergson" manifold itself. This would give the appearance of "ideal forms" as the objects of consciousness by which we define the truth value of our perceptions and conceptions; not as a Kantian 'a priori synthesis'.

The proof of Q.M.D. is already in the experimental evidence of these theories themselves and some new experiments relating to the lack of decay in protons, the lack of experimental evidence of gravity waves and magnetic Monopoles as they are expected (q.m.d. postulates that they are only detectable as aspects of the non-local f.o.r. Of the monad in nature. On the other hand they could be artificially created!), The experimental proof of the Bell Inequality theorem and the observation of black holes and quasars in space.

Q.m.d. also dovetails with the theories of plasma cosmology, Sheldrake's "formative causation" theory and Prigogine's "Dissipative structures" (after a modification of their mathematical and philosophical underpinning).

As in any case of paradigm shift, the intellect initially is repelled by the shock of discovery that the ultimate truth is, ever so much, just beyond reach.



Reyn til runa!





This is only a very small portion of the research material that is involved in this. I hope it provides a good background of this very involved and complex subject without the interested needing a theoretical physics degree.


The Emperor's New Mind by Roger Penrose. Oxford University press. 1989


The Big Bang Never Happened by Eric Lerner. Times books, 1991.


The Nature of Physical Reality by Henry Margenau. Mcgraw-Hill books,1950.


Superstrings and the Search for the Theory of Everything by F. David Peat.

Contemporary books. 1988.


The Principle of Relativity by H. A. Lorentz, A. Einstein, H. Minkowski and

H. Weyl with notes by A. Sommerfeld translated by W. Perrett and G. B. Jeffery.

Dover publications. 1952.


The Mathematical Tourist by Ivars Peterson. Freeman, 1988.


Labyrinths of Reason by William Poundstone. Anchor books, 1988.


Quantum Reality by Nick Herbert. Anchor books Doubleday. 1985


Turbulent Mirror by John Briggs & F. David Peat. Perennial library, Haper & Row.



Order Out of Chaos by Ilya Prigogine & Isabelle Stengers. Bantam books, 1984.


Nerves of Silicon by T. A. Heppenheimer in discover, February 1988, pg. 70-79.


The Silicon Retina by Misha A. Mahowald & Carver Mead. In Scientific American, May 1991, pg. 76-82


Weird Science by David H. Freedman. In Discover, November 1990, pg. 62-68.


The Symplectic revolution by Ian Stewart. In the sciences, May/June 1990, pg.

28- 36.


The Mathematics of Three-Dimensional manifolds by William P. Thurston & Jeffrey R. Weeks in Scientific American, July 1984, pg. 108-20.


Knot Theory and Statistical Mechanics by Vaughan F. R. Jones. In Scientific American, November 1990, pg. 98-103.

Antichaos and Adaptation by Stuart A. Kauffman. In Scientific American, August 1991, pg. 78-84.