Y-Bias and Angularity:©

The Dynamics of Self-Organizing Criticality

From the Zero Point to Infinity

David G. Yurth

Donald Ayres, A.E.

August 2005

Definitions – Self-Organizing Criticality:

Criticality is mathematically defined as the state of highest efficiency in a complex system.[[i]] At the point of criticality, catastrophic events happen in a big way, all at once, and not by gradual degrees. This is as true of rush hour traffic jams as it is of mass extinctions and major weather events. When we understand this aspect of complex systems, we also begin to understand something fundamental about the way Nature works. When it is understood that this set of rules operates at all scales, it then becomes possible to develop a model which explains the observable phenomena which are not accommodated by the Standard Model. It also becomes possible to predict the existence of phenomena not yet discovered, which can be logically presumed to operate according to these rules at larger and smaller scales than previously imagined.

The structure of the cosmos, as observed in L4, is assumed to be universally coherent in terms of SOC rules. These rules provide that as undifferentiated “virtual” information originating in the Physical Vacuum [and emerging via the Zero Point] coalesces with other virtual ensembles to create fundamental pairings [which demonstrate duality, polarity, spin and time domain properties], the process of coalescence adheres to four primary conditions. According to Bak, all four conditions operate simultaneously and ubiquitously at all scales.[[ii]]

The Role of Criticality

Bak’s investigation of SOC system dynamics began as an attempt to model the self-organizing behaviors associated with catastrophic avalanche events. The definitive experiment viewed this set of dynamics as embodied in a randomly organized pile of uniform grains of sand. As Bak and his team constructed each sand pile, they realized that there comes a time when the sand pile can no longer be considered just a stack of single, unrelated grains. As the mound of sand reaches the point of criticality [that point at which the quantum I/* threshold has been breached and the power laws become operative], the sand pile becomes a single, integrated, self-organizing system. As soon as this happens, it is no longer possible to predict the magnitude, location or frequency of any single avalanche event within the system. As the experimental evidence shows, even if we simultaneously know everything there is to know about every single grain of sand comprising the pile, the nature of open, complex and self-organizing SOC systems is such that we cannot improve the consistency, accuracy or reliability of our predictions regarding its behaviors in any locale. In SOC systems as they operate in Nature, there is no linear, 1-to-1 relationship between events occurring in the past and those which are anticipated in the future.

We can predict only what the power laws permit. The importance of this insight cannot be overstated. It means, among other things, that in spite of all the best technologies and instrumentation we will ever devise, we will never, under any circumstances, be able to reliably predict the magnitude, location or timing of any events which occur as part of any complex, open SOC system[[iii]]. This includes earthquakes[[iv]], solar flares, stock market behaviors, mass extinctions, meteor strikes, weather, geologic events or the behaviors of human interactions such as the Internet. If our way of thinking about the world we live is modified to comport with the way the cosmos really works, instead of the way the world is described by the Standard Model, our approach to exploring the mysteries of the cosmos must be altered in ways that are still largely unimaginable.

Complex, Self-organizing SOC Systems

For the purposes of this discussion, a complex, open, self-organizing system is defined as one which demonstrates the characteristics of the condition known as criticality. For purposes of illustration, at the grandest of scales, the Milky Way Galaxy [like all galaxies found in the cosmos] is a complex, open, self-organizing system[[v]].

Figure 2

Hubble/NASA example of Celestial Organization

The fact that this is universally acknowledged to be true presents some intriguing problems which cannot be accommodated by the Standard Model of physics currently in general use.

At a finer scale, the same is true of the solar system. In every sense, it demonstrates all the characteristics, attributes and behaviors associated with self-organizing systems.[[vi]] So does our planet. Taken by itself as a single comprehensive unit, the Earth and its sub-systems all demonstrate the attributes of self-organizing criticality at every scale, from the release of virtual photons produced by energetic interactions to the Earth’s participation as a member of the solar system set[[vii]]. All these systems operate, as Capra[[viii]] has rigorously reported, in an integrated, indivisible aggregation of inextricably inter-related constituents which, in the final analysis, comprise a single overall SOC system.[[ix]]

Simple, Elegant Rules:

According to the experimental data developed by Bak etal, it is evident that open, complex, self-organizing SOC systems simultaneously and universally demonstrate all four of the following attributes:

1. Punctuated Equilibrium: Criticality is defined as the point in SOC system evolution at which an observable event occurs. Between each event or “avalanche” there are relative periods of apparent stasis which are punctuated from time to time by other “avalanches” of various magnitudes. These avalanches can be literal, as in the case of Bak’s sand pile [or the catastrophic rush of a field of snow down a slope], or they can take the form of mass extinctions, the rises and falls of the stock markets, the occurrence of solar flares, earthquakes, tornados, hurricanes or floods, wars, the evolutionary cycles of the Internet, the evolution of languages, etc. The phenomenon of punctuated equilibrium is an intrinsic dynamic comprising the quantum functions which have been observed to operate at all scales in Nature. In this view of SOC behaviors, the geological effects demonstrated by the Grand Canyon, for example, are the product of a series of catastrophic avalanche events rather than the gradual grinding down of geological strata by hydro-dynamic erosion over millions of years. 2. Power Laws: The relationship between the magnitudes, frequencies and locale of individual avalanches can be expressed in terms of a simple exponential equation. There are no singular explanations for large events – the same forces which cause the Dow Jones Industrial Average to rise 5 points on one day also caused the crashes of 1929, 1987 and the Dot.com crash of 1999. Wherever we find that a logarithmic relationship exists between a series of catastrophic events, which can be plotted on a set of X-Y coordinates as straight line with a slope, we can be absolutely certain that the system which produced it is a self-organizing SOC system. The logarithmic relationship which characterizes the power laws governing SOC processes is primary to the formation of matter, energy, Time and all the field forces which operate in the cosmos. All of Nature, at all scales, manifests uniform compliance with this rule. 3. Fractal Geometry: First expressed by Benoit Mandelbrot[[x]] of IBM, fractal geometry is a mathematical construct which illustrates that where a complex, open, self-organizing system exists anywhere in our space-time continuum, it is self-similar at all scales. Fractals are the natural record of the evolution of natural, open, complex, self-organizing systems of all kinds. In this context, Y-Bias/Angularity Theory holds that the “boundedness – unboundedness” attributes manifest by the aggregations of scalar components, occurring at the Zero Point, define the eventual form each event will become at each subsequent scale of organization.

Boundedness, the conceptual construct reflected by the self-similarity which characterizes fractal geometry, occurs as the result of the interaction of scalar components beginning at the primary scale and extending throughout the micro and macrocosm. The formula which describes the fractal properties of SOC interactions is shown as

Z D Z2 + C ([1]), Formula 1

the nature, extent and dynamics of which are a subject of this discussion. By its nature, fractal geometry serves to organize discrete quanta of information into aggregations which are either bounded [as Z] or unbounded [as Z2 + C], in a way which preserves the primary data sets found at the Zero Point throughout each quantum-defined scale of subsequent organization. The fractal formula suggests that SOC dynamics are self-referential, as shown by the function ‘D”, which connotes interaction rather than equivalence. This is the primary function identified by Kafatos/Nadeau which renders ‘background reality-as-it-is’ self-referential at all scales. This function is also the operative dynamic which drives the Implicate Order postulated by Bohm.

When a complex system evolves to a state of self-organizing criticality over any increment of time [Dt], the physical record of its evolutionary history can only be described in terms which are fractal. The shape of a riverine delta, the variegated slopes of a mountain range, the shape of a coral reef, and the corrugated features of the human brain are all records of the evolution of self-organizing systems manifest in fractal form. It is because fractal geometry constitutes the natural expression of the evolution of SOC systems that analysts have been able, for example, to develop applications which efficiently identify non-fractal patterns found in the natural landscape.

4. I/* Noise: In order for any observable event to occur within an SOC system, the interactions between individual components and field effects must exceed quantum-defined scalar “noise” [1/ƒ] thresholds. For an aggregation of components at any scale to become self-organizing, the number of components, their aggregate properties and the Y-Bias/Angularity effects they exert on each other must combine to breach the minimal noise thresholds. By definition, this set of interactive properties and dynamics demands that all such interactions must be accompanied by and combine to create a concomitant set of harmonic resonances, regardless of the scale at which they occur. The nature and importance of harmonic resonance in this regard is addressed later under the sections which discuss the Fibonacci Series and its relationship to Gravitational Forces.

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[1] Z D Z2 + C: This formula contains the term ‘Z’ which means an angle of incidence between two interacting data sets or physical events. The symbol D depicts a realtime feedback loop in which each expression feeds information back to the other at a rate which is equal to the square of the speed of light. This interaction suggests that when until the information fed from the left side of the equation meets or exceeds a minimal quantum limit, shown in Self-organizing criticality as the function 1/ƒ, it remains bound by a nexus considered to be a zero point or ‘seed’ in fractal geometry. When the noise threshold [1/ƒ] is breached, however, the data or resulting physical phenomenon then becomes self-sustaining until the next noise threshold is reached.

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[i] P.Bak, ibid.

[ii] ibid Bak etal

[iii] Bak, P., ibid. pp 160-164. “Only fools, charlatans and liars predict earthquakes.” Richter (father of the Gutenberg-Richter Law and the Richter Scale for measuring earthquake magnitudes).v

[iv] Bak, P., ibid.

[v] Wheeler, J.A., Einstein’s Vision, Springer-Verlag, 1968, page 112. See also A. Dolgov, Yu. Zel’dovdich, M. Sazhin, Cosmology of the Early universe, MGU Publ., Moscow 1988, page 200 (in Russian). See also M. Lavrent’ev et al, On Remote Action of Stars on Resistor, Doklady AN SSSR, 1990, vol 314, no 2, page 352 (in Russian). See also A. Pugach, A. Akimov, “Astronomical Observations by N. Kozyrev’s Methodology: Preliminary Results,” in the press (in Russian).

[vi] Flyvbjerg, H. Sneppen, K. and Bak, P. Mean Field Theory for a Simple Model of Evolution. Physical Review Letters, 71 (1993) 4087. See also, Sheldrake, R., Seven Experiments That Could Change The World: A Do-it Yourself Guide to Revolutionary Science, Riverhead Books, Inc. NY (1995) ISBN: 1-57322-14-0.

[vii] Capra, F., The Turning Point: Science, Society and the Rising Culture. Bantam/ Simon & Schuster, New York (1982).

[viii] F. Capra, Turning Point, ref

[ix] Wilcock, D. Personal Notes: “Consider the Nineveh Constant, discovered by NASA scientist Dr. Maurice Chatelain – where all the planets’ orbits are some form of harmonic division of a master time cycle of roughly 6.5 million years, or 70 multiplied seven times by 60 in seconds. (Vol. 3, Convergence, Divine Cosmos.) The second, as a time quantum, is a basic “beat” frequency of the universe, whose macroscopic structures are the byproduct of harmonic oscillation of the PV, creating stable fields that appear as nested, rotating spheres (i.e. the planetary orbits) with Platonic geometries that are formed by the vibrational nodes on the surface of each sphere – thus explaining many different geometric phenomena I have explored at all levels of scale. Consider Roschin and Godin’s replication of the Searl Effect and the nested magnetic spheres that were detected when it was in operation as one of many examples showing these fields at work. I also have yet-unpublished data showing these nested spheres emerging as zones of redshift variance (correlated with PV density levels by Aspden) in galaxies. It appears that the in-progress interplanetary climate change I am documenting is a byproduct of our entrance into a higher density of PV in the galaxy, causing a moment of “punctuated equilibrium.”

[x] Mandelbrot, B., Fractal Geometry of Nature, WH Freeman & Co., (August 1988) ISBN: 07 16711869.