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Golden Error Phase Wave

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PSIence fictionirregular science[1]

Physical arrangement of electric conductors as a parallel array or straight wires that pass electrical current all in the same direction will create a mutual attraction among the conductors, by way of the magnetic pinch they co-create.


When a helical conductor is connected as a toroidal helix, the coil loops passing through the inside of the torus hole all conduct in the same direction through the hole. This creates a magnetic pinch.


Proper parametric selection of a toroidal form's major and minor diameters will optimize the geometry for the pinch effect by the conductors passing through the hole, becoming a resonant trap for harmonic overtones in the resonance.


The golden error phase-wave will always exist in toroidal resonance while space-timing is yet flat.


Caveat —The bifilar-connection scheme across a diameter of a torus has a pinch-effect of fractional component depending on which degree of torus knot is tested. Torus knots of various degrees have various ratios of loops through the hole passing current in both directions through the hole due to the bifilar connection scheme.

Solid geometry postulate

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Figure 1: Linear translation on a 2-torus (animation by Corrado Falcolini) URL: http://www.scholarpedia.org/article/Kolmogorov-Arnold-Moser_theory

As an electrodynamical system[2], a torus knot of integer loop and twist angular harmonics can only approximate a Golden Ratio harmony, being the golden ratio is irrational. That is, integer harmonics cannot create an irrational ratio, and a phase-angle error must ensue or become a lossy dissipation against system power.


In a more figurative sense, there will be a dissonant thrumb in the system when the optimum Q is found. The dissonant thrumb is the Golden Error Phase Wave.


A ready generator of Golden Ratio approximations is the Fibonacci Sequence.


The poloidal/toroidal ratio of dual, orthogonal angular harmonics of the torus, or the loop/twist ratio, provide a special circumstance.


The multiphase-coils are specifically selected as torus knots to afford influence to each the other along the general surface topology of the torus. While non-entangled helical torus winding will create a surface-directed-influence between coil loops, that direction will point around the torus ring. The torus knot is different. The torus knot winding travels extra trips around a torus to eventually rejoin with its beginning, provided the trips to twists are an integer ratio. The extra trips around the torus of a torus knot (poloidal loops) provide a inter-loop direction that is angled away from the torus ring. multi-phase sets of torus knots then afford toroidal rotation along the surface of the toroid (through the hole) of the influence between phased loops.


The context of the golden error phase wave (GEPW)is only pertinent when the multi-phased torus knots comprise a set of torus knots upon the same torus surface. Therefore, the GEPW operates in principle within an annular ring form, assumed by the inter-phase coil-loop dynamics, defined by the surface between the torus knot loops.


Further clarifying the context, as an entangled helix, a set of torus knot of three phased-coils provides minor-diameter rotation of flux patterns. This rotation moves like the smoke rolling in a smoke ring.


The simple summation series, the Fibonacci sequence afford insight to build an Electroforms with toroidal-poloidal ratios of 2/1, 3/2, 5/3, 8/5, 13/8, 21/13, etc. Any two neighboring numbers in the Fibonacci sequence have a ratio approximating the golden mean. Larger Fibonacci number pairs yield more accurate results.

The importance of the Golden Ratio (1.618…)

The Fibonacci squares forming a golden spiral.

Without the mathematical balance of an equiangular spiral, the orthogonal force of electromagnetism may fractalize, and not self-compress on a common center. It is not known yet how important the approximation may be in a toroidal system.


Scalar engineering

A Golden error in the Euclidean integer-ratio angular-harmonic toroid will engender a dissonant, transient waveform that propagates through the toroid ring as harmonic amplitude variations from loop to loop, rotating through the loops as the difference of Phi (the golden ratio) and the ratio of the integer angular harmonics of the toroidal dynamic.


The golden error phase-wave (GEPW) may be the engineering handle to spin-tune the scalar vortex of a toroidal knot, and be a literal error-feedback signal on a feedback-loop-phase-lock on frequency tracking the golden dwell. The GEPW will disappear for a tuned Gravity Wave Antenna.

Engineering Affordance

It is not the typical electromagnetic resonance at play. Rather, it is a nuclear magnetic resonance brought to focus upon a point center, encircled by the neutral ring of the torus center. Optical electrostatic topologies emerge as the nuclear resonance coheres with the evanescent molecular fields of the matter wave of the ring. Physical scale is mandated, per atomic specie of the ring and helices, by the Znidarsic Velocity. Lensing of causality toward the center, a temporal aberration of space-timing, simulates inertia under the programmatical control of the pulse-density-envelope creating such harmonics upon the GWA

DonEMitchell 09:08, 9 June 2012 (MDT)

With a proper, symmetric pinch assisting a hyperbolic warp in event-timing-rates, a hyperbolic waveform as an impulse can absorb without dissonance or reflection. Non reflected impulse energy is converted to a bosonic gradient strain, a Vector boson forming point-centered hyperbolic space-timing. The strain on space-timing, the gradient on the rate of event fulfillment, is caused by the co-accelleration of twin electromagnetic vortices for a brief moment during the sharp rising edge of electromagnetic potential.

GEPW cult-speak

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There is no magic without an incantation over the Phrase-sensitive vessel. A word dimples time to capture energy as potential, so long as the resonant EM system energy hosting the knot in time remains to overcome losses of a macro-system.



  1. yet, experimenter/Builder Gilds are encouraged.
  2. See Dynamical Systems: Scholarpedia.org (http://www.scholarpedia.org/article/Dynamical_systems)