What if the universe ticks like a cosmic clock—and every tick reshapes reality? This essay introduces a fractal framework that reimagines space, time, and matter not with equations or algorithms, but through networked rhythms and patterns. Inspired by quantum physics, it envisions reality as a multidimensional time crystal pulsing with imaginary clocks—scale-invariant oscillators that span everything from particles to galaxies. These clocks don’t just measure time—they create it, communicating through golden-ratio spacing and electromagnetic signals. In this view, gravity becomes a flow of information through fractal pathways, and familiar concepts like mass, space, and time emerge from synchronized coherence. By replacing Cartesian logic with a fractal, non-algorithmic computational system, this model offers a unified architecture that could help resolve deep questions in physics, biology, and the nature of consciousness—and invites thinkers, seekers, and scientists alike to explore a radically new way of understanding reality.
CHAPTERS:
1. Hubble: The Beginning of the Demise of Einstein’s Original Lambda (A)
2. Fritz Zwicky, Vera Rubin, and the Concept of Dark Matter
3. Saul Perlmutter, Brian Schmidt, and the Concept of Dark Energy
4. Reconciling Quantum Mechanics and General Relativity
5. Loop Quantum Gravity-a Granular Cosmos, Not a Continuum
6. The Standard Model of Particle Physics: the Particle Zoo as an Artefact of Cartesian Mathematics
7. The Pre-Copernican Earth-centered Model
8. The Implicate-order Plenum-Phi Connectome, and the explicate-order GNPSCS
9. The Big Bang, Dark Matter, and Dark Energy as Artefacts of Cartesian Mathematics
10. Bohm’s Implicate Order, the Holomovement, Scale-Invariant/Conformal Superpositions and Collapse of the Wave Function as Phase Changes
11. A Novel Medical Paradigm
12. Is Loss of Global Quantum Coherence the Cause of Alzheimer’s Disease?
13. Treatment of Alzheimer’s Disease by Selective Restoration of the Ghosh-Bandyopadhyay Frequency Fractal
14. Non-Chemical Non-Immunological Treatment of Alzheimer’s Dementia by Interfering with the Abnormal Superradiance of the Beta-Amyloid Nanotubule
15. Relationship of the Mandelbrot Set to the Godel Non-Turing Non-algorithmic Phase-Shift Computational System
16. Non-Chemical, Resonant Induction Model Of Prion Self-Replication
17. Alzheimer’s dementia may be a two-prion disease
18. Other Diseases Which May Be Classified As Prion Disease
19. Cartesian continuous time vs. timeless whole of the implicate order
20. Relationship of mass-energy to the Godel Non-Turing Non-Algorithmic Phase-Shift Computational System (GNPSCS)
21. Can the PC/GNPSCS Support a SUSY model
22. Discussion
23. Summary
24. References
25. Bibliography
Do Corrections of Einstein’s Greatest Blunder Entail a New Mathematical Paradigm?
—Implications for Cosmology, Quantum Biology, and Emerging Therapies for Alzheimer’s Disease—
A Speculative Scientific Essay
M. Goldberg © 2025
‘Spacetime is doomed.’ —Nima Arkani-Hamed
‘If you want to find the secrets of the Universe, think in terms of energy, frequency, and vibration.’ —Nikola Tesla
‘As far as the laws of mathematics refer to reality they are not certain, and as far as they are certain they do not refer to reality.’ —Albert Einstein
‘Space and time are means by which we think, and not conditions in which we live.’ —Albert Einstein
‘Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe?’ —Stephen Hawking
‘The Implicate ‘enfolded’ order (undivided wholeness) is a deeper and more fundamental order of reality.’ —David Bohm
‘When the whole is divided, the parts need names.’— Lao Tzu, Tao Te Ching
THIS ESSAY POSITS:
• Supplanting Cartesian continuum mathematics with the Godel Non-Turing/Non-algorithmic Phase-Shift Computational System (GNPSCS), may help resolve many longstanding problems in physics, biology, and consciousness studies.
• Phenomena like the big bang, inflation, dark matter, and dark energy may be artefacts arising from the constraints of Cartesian continuum mathematics.
• Alzheimer’s dementia may arise when pathological beta-amyloid disrupts the natural superradiant activity of tubulin microtubules, interfering with their resonance and ultimately blocking the brain’s ability to achieve global quantum coherence.
• A non-pharmaceutical, non-immunological approach to treating various forms of dementia may involve selectively disrupting the pathological superradiant frequency of beta-amyloid microtubules, while preserving the physiological superradiant frequency of tubulin microtubules.
TERMS AND ABBREVIATIONS:
TAT-(tubulin-vicinal water-tubulin) microtubule supporting normal coherent photon and phonon superradiance essential for global quantum coherence (GQC); BAB-(beta amyloid-vicinal waterbeta amyloid) microtubule exhibiting pathological superradiance frequencies that interfere with TAT function and disrupt GQC; A-vicinal water mediating coherence within microtubule structures; A (Lambda)-cosmological constant interpreted here as dark energy (DE), potentially evolving via quintessence—a time-dependent scalar field; PL-plenum, the quantum vacuum substrate from which the phi connectome (PC) self-organizes; PC- phi connectome, implicateorder substrate of networked oscillator coherence; GNPSCS-Godel Non-Turing/Non-Algorithmic Phase-Shift Computational System, the explicate-order projection of the PC; CA-Wolfram cellular automaton; an algorithmic computational model; (A-graph)-asymmetry graph representing nonequilibrium dynamics; GITs-Godel’s incompleteness theorems, revealing limits of formal systems; PCE- Wolfram’s Principle of Computational Equivalence; PCI-Wolfram’s Principle of Computational Irreducibility; [DB]-dynamical billiards operator; IS/I-Tim Palmer’s invariant set, a proposed cosmological attractor; TADs-topologically associating domains in genomic architecture; RRM-Irena Cosic and Werner Jaross’ resonant recognition model describing proteinfrequency interactions; PEP-Pauli exclusion principle; non-algorithmic-not algorithmically decidable; GQM -geometric conformal value of gravity at the subatomic quantum mechanical scale; GNE- Newton/Einstein conformal gravity at the solar system scale; GDM - conformal value of gravity at the galactic dark matter scale; GDE-conformal value of gravity at the intergalactic dark energy scale; GEON-conformal value of gravity at the inter-eon cosmological scale; PP-Parrondo’s paradox or principle; BR-Brownian ratchet, stochastic energy extraction mechanism; XOR- exclusive OR logical function; SR-special relativity; GR-general relativity; SIC-scale- invariant/conformal electromagnetic information (y*), tunneling between oscillators of the GNPSCS and perceived as gravity, dark matter, dark energy, and Hawking radiation at different scales; p*SIC golden-ratio island barrier between oscillators, preventing destructive resonance, with scale-specific variants, pqm, p\E., pi>\i, pi>E., and peon corresponding to: quantum, solar system, galactic, intergalactic, and inter-eon scales, respectively; Bloch sphere - Bloch imaginary clock; y*-SIC electromagnetic tunneling information between GNPSCS oscillators; OSC*- SIC networked oscillator, discretized imaginary Bloch clocks of the GNPSCS; MNDIBTC-Multi- dimensional Networked Discretized Imaginary Bloch Time Crystal; TAT-(tubulin-vicinal water- tubulin) normal microtubule; BAB-(beta amyloid-vicinal water-beta amyloid) microtubule with pathological coherent photon (laser) and coherent sound (phonon) superradiance frequencies that interfere with physiologic TAT, preventing formation of the Ghosh-Bandyopadhyay Frequency Fractal (GBFF) necessary for global quantum coherence (GQC) and normal mentation.
ABSTRACT:
This essay introduces a new framework called the Phi Connectome/Godel Non-Turing Non- Algorithmic Phase-Shift Computational System (PC/GNPSCS). It’s designed to help us rethink how we understand the universe, life, and consciousness—not through traditional equations or algorithms, but through patterns of coherence, rhythm, and information. At its heart, reality is imagined as a kind of cosmic time crystal—a multi-layered, networked structure where each layer ticks like an imaginary clock. These imaginary Bloch clocks aren’t ordinary clocks, they are scaleinvariant oscillators, meaning they behave the same way whether you zoom in or out. Each one communicates with all others through a scale-invariant/conformal (SIC) electromagnetic signal (Y*), and they’re separated by a SIC golden ratio—(p*) = [(1 + V5)/2]*. This golden-ratio spacing prevents the oscillators from interfering destructively with one another, allowing the system to remain stable and coherent. Each tick of these clocks represents a Godel phase-shift computation, a discrete transition that reshapes our understanding of space, time, and mass. In this view, these familiar concepts aren’t fundamental; they emerge from the synchronized behavior of these oscillators. Gravity, too, gets a reinterpretation. Instead of being a force between masses, it’s seen as a tunneling or flow of SIC electromagnetic information (y*) through fractal pathways that link these imaginary clocks. It’s a dance of coherence, not a tug-of-war between objects. The PC/GNPSCS model draws inspiration from a wide range of visionary thinkers. David Bohm’s concept of an implicate order suggests that everything is deeply interconnected beneath the surface. Carlo Rovelli’s loop quantum gravity treats space and time as emergent from quantum interactions. Nima Arkani-Hamed’s amplituhedron offers a geometric approach to particle behavior. Anirban Bandyopadhyay’s research explores biological and quantum coherence. John Wheeler’s ‘it from bit’ and Erik Verlinde’s ‘gravity as an entropic force’ propose that gravity itself may arise from the flow of information and entropy. Ultimately, the PC/GNPSCS framework challenges the very foundations of how we do science. It suggests our current logical systems— based on Cartesian coordinates, Turing machines, and Boolean logic—may be fundamentally incapable of capturing the full complexity of reality. The search for a ‘Theory of Everything’ (TOE) might be unlikely unless we adopt a radically different way of thinking.
INTRODUCTION:
Efforts to unravel the mysteries of cosmology—the big bang, cosmic inflation, dark matter, dark energy, and the ultimate fate of the universe—have led to profound theoretical innovations that challenge the foundations of classical physics. Among these, Nima Arkani-Hamed’s amplituhedron and Carlo Rovelli’s loop quantum gravity offer alternative mathematical paradigms that depart from traditional Cartesian-continuum models. Arkani-Hamed proposes a higherdimensional geometric framework in which particle interactions are encoded in the amplituhedron’s combinatorial structure, bypassing conventional spacetime. Rovelli’s loop quantum gravity presents a fractal, non-continuum model where space and time emerge from the relational dynamics of discrete granules. In his view, space arises from the interconnections among granules, forming a web-like structure, while time emerges from the sequence of changes in their relationships. Rovelli’s perspective replaces the notion of space as a passive stage and time as a continuous flow with a discrete, emergent process grounded in a deeper relational logic.
Complementary insights from David Bohm’s implicate order, Anirban Bandyopadhyay’s work on microtubule coherence, and Lori Gardi’s exploration of the Mandelbrot set, suggest the need for a new mathematical ontology. Synthesizing and expanding these lines of thought, this essay introduces the Godel Non-Turing Non-Algorithmic Phase-Shift Computational System (GNPSCS), a novel geometric/mathematical structure in which reality is modeled as a Multidimensional Networked Discretized Imaginary Bloch clock Time Crystal (MNDIBTC). In this framework, space, time, and mass are emergent properties of networked oscillator coherence, while phase-shift computation produces an immediate ‘clique’ answer replacing Turing step-by- step computation. Following the work of Anirban Bandyopadhyay, the system solves an intractable pattern search (Clique) problem without searching, since the right pattern written in it spontaneously replies back to the questioner. This describes a non-Turing computational architecture where solutions to clique problems emerge via resonant pattern matching, rather than algorithmic search—aligning with the GNPSCS framework as a modular analog for phase- recursive decision structures. The GNPSCS spans all scales from Planck-level oscillators to cosmic eons, while life and consciousness—as we recognize and experience them—manifest within a specific frequency band of the GNPSCS. The Orch-OR theory of Penrose and Hammeroff posits consciousness as a fundamental substrate of the cosmos itself—embedded in spacetime and intrinsic to all physical systems.
Building on the research of Bandyopadhyay’s team and the Orch-OR theory of Penrose and Hameroff, this essay explores how microtubules generate coherent photons and phonons through superradiance, producing near-infrared laser light and coherent sound/phonons. The Ghosh- Bandyopadhyay Frequency Fractal (GBFF) model posits that global quantum coherence (GQC) arises from networked electromagnetic resonance bands, enabling near-instantaneous communication across the brain. This coherence is essential for cognition and reflects a fractal, non-local architecture of neural signaling. For example, in neurodegenerative diseases such as Alzheimer’s dementia, this essay proposes that intracellular beta-amyloids/(amyloid beta-Ap) and vicinal water form abnormal microtubules (BAB) with disruptive frequencies that interfere with normal tubulin vicinal water microtubule function (TAT), leading to loss of global coherence, with subsequent axonal degeneration, and synaptic failure. More generally, if superradiance contributes to an organism’s coherence, then BAB-induced disruption could be more than structural—it might represent a quantum decoherence event affecting all scales of the organism, a radical shift in how we think about disease.
Treating Alzheimer’s dementia with conventional pharmaceutical and antibody treatments has shown limited efficacy. By contrast, this essay advocates for a quantum-biological treatment paradigm aimed at restoring coherence. Specifically, it proposes that targeted suppression of pathological beta-amyloid microtubule frequencies could liberate physiologic tubulin microtubule frequencies, allowing restoration of macroscopic global quantum coherence necessary for normal cognition. Moreover, it is suggested that quantum biology treatments may benefit other disorders such as frontotemporal dementia and Parkinson’s disease, where misfolded protein fibers and vicinal water may, similarly, disrupt coherence. Furthermore, beyond quantum biological treatments for dementias, if ‘health’ corresponds to global quantum coherence, then mechanistic medicine—based on pharmaceuticals, radiation, and surgery—may be enhanced or perhaps supplanted (in some situations) by externally-applied coherent electromagnetic/laser and coherent sound/phonon energy used to restore global quantum coherence rather than attempting to ‘fix’ the body as if it were a machine.
[NOTE: References in the text denoted by ‘*SEE: ..." are alphabetized in the bibliography; all other reference numbers embedded in the text are found in the ‘reference’ section.] calling its inclusion his “biggest blunder.” [5] Einstein introduced the cosmological constant Lambda (A) in 1917 to counteract gravity and allow for a static universe, which was the prevailing assumption at the time. His field equations of general relativity naturally predicted a dynamic cosmos — either expanding or contracting — so A was added as a mathematical fix to stabilize the model.
1. Hubble: The Beginning of the Demise of Einstein’s Original Lambda (A).
Edwin Hubble, an American astronomer, using the 100-inch Hooker telescope at Mount Wilson Observatory, demonstrated that many nebulae were in fact separate star clusters—galaxies beyond our own Milky Way. [1] In 1929, he formulated Hubble’s law based on the redshift of light observed from these galaxies, showing that the redshift increases with distance. [2,3] Hubble’s law is expressed as v = H₀ × d, where v is the velocity at which a galaxy is receding, H₀ is the Hubble constant, and d is the galaxy’s distance from us. This implies that the universe is expanding uniformly, with galaxies moving away from each other as space itself stretches. [3] Hubble’s findings provided the first observational evidence against a static universe, challenging Einstein’s original field equations of general relativity, which included the cosmological constant Λ to counteract gravitational collapse.[4] After Hubble’s discovery, Einstein abandoned ‘Λ’, reportedly calling its inclusion his “biggest blunder.”[5] Einstein introduced the cosmological constant Lambda (Λ) in 1917 to counteract gravity and allow for a static universe, which was the prevailing assumption at the time. His field equations of general relativity naturally predicted a dynamic cosmos — either expanding or contracting — so Λ was added as a mathematical fix to stabilize the model.
2. Fritz Zwicky, Vera Rubin, and the Concept of Dark Matter.
Fritz Zwicky and Vera Rubin were pivotal in shaping our understanding of dark matter. The asymmetry of observed electromagnetic frequencies along the rim of a galaxy shows a Doppler blue shift on one side and a Doppler red shift on the opposite side. [1] These outermost stars are rotating too fast to be gravitationally bound by the visible mass of the galaxy, suggesting they should be flung outward. That is, there isn’t enough visible or calculated mass to account for the high rotation velocities of these stars.[2] Fritz Zwicky’s 1933 paper Die Rotverschiebung von extragalaktischen Nebeln, published in Helvetica Physica Acta, proposed the existence of “dunkle Materie” (dark matter) to explain the high velocities of galaxies in the Coma cluster, which could not be accounted for by visible mass alone. Rubin’s findings supported Zwicky’s idea of the existence of dark matter (DM)—extra unseen matter that exerts gravitational influence without interacting with light. [3] Although many theories and experiments have attempted to detect DM particles, including Weakly Interacting Massive Particles (WIMPs), axions, primordial black holes, and Modified Newtonian Dynamics (MOND)—none has been successful to date. [4] This essay posits that dark matter, the big bang singularity, inflation, and dark energy, may be artefacts arising from our current Cartesian-based continuum mathematics and Turing computation. [5]
3. Saul Perlmutter, Brian Schmidt, and the Concept of Dark Energy.
In the late 1990s, astronomers made a transformative discovery—the universe’s expansion is not merely increasing, but accelerating. This revelation emerged from the work of two independent teams: the Supernova Cosmology Project, led by Saul Perlmutter, [1] and the High-Z Supernova Search Team, headed by Brian Schmidt. [2] Both teams studied distant Type Ia supernovae, stellar explosions known for their consistent peak brightness, [3] making them ideal ‘standard candles’ for gauging cosmic distances. By examining the brightness and redshifts of these supernovae, they uncovered a startling finding: the supernovae appeared fainter than anticipated, suggesting they were farther away than expected under theories of a steady or decelerating universe.[1, 2] This evidence pointed to an accelerating expansion of the universe indicating that Lamba was increasing and highlighted the importance of the cosmological ‘constant’, lambda Λ. Proposed by Einstein, [4] the original value of lambda (Λ) was later discarded when Hubble's observations confirmed the universe's expansion. Einstein’s original cosmological constant (Λ) was a fixed term added to his equations to counteract gravity and maintain a static universe—not to represent vacuum energy or dark energy as understood today. Its role was purely to prevent cosmic collapse, not to describe any physical substance. Subsequent contributions by researchers such as Vera Rubin and Fritz Zwicky introduced the concept of dark matter (DM), which accounts for unseen gravitational effects.[5, 6] Building on this foundation, Perlmutter, Schmidt, and their collaborators postulated that the universe's acceleration is driven by dark energy, with lambda Λ representing the vacuum’s constant energy density responsible for this phenomenon. [7,8] The exact value of Λ is estimated to be around 10⁻¹² s⁻² or 10⁻¹² m⁻², depending on the units used. [8, 9] This value is derived from observations of cosmic expansion and fits within the standard model of cosmology, known as Lambda Cold Dark Matter (ΛCDM). [10] The 2011 Nobel Prize in Physics was awarded to Saul Perlmutter, Brian Schmidt, and Adam Riess for their groundbreaking discovery that the expansion of the universe is accelerating.[11] This revelation came from their independent studies of distant Type Ia supernovae, which appeared dimmer than expected—indicating they were farther away than predicted by a decelerating universe model. [1,2] The implication was profound: some unknown force, now called dark energy (DE), is driving cosmic acceleration. This discovery not only reshaped cosmology but also provided strong observational support for a small, positive cosmological constant (Λ). [4,8] It also helped establish the ΛCDM model as the standard framework for understanding the universe’s evolution. [10]
4. Reconciling Quantum Mechanics and General Relativity.
For several centuries, a Cartesian-based continuum, deterministic-reductionist mathematics has served as model of reality. However, this paradigm has led to significant challenges: (1) reconciling quantum mechanics and general relativity; (2) understanding the Big Bang origin of the universe from ‘nothing’; (3) Guth’s inflationary model; (4) predicting the ultimate fate of the cosmos; (5) explaining dark matter and dark energy; and (6) tackling David Chalmers’ ‘explanatory gap’, the hard problem of consciousness, i.e., how physical processes in the brain give rise to subjective conscious experience and qualia. [[1],[2],[3]]
This essay posits a new paradigm: the implicate-order Phi Connectome (PC) [[2]] and its explicate- order projection, the Godel Non-Turing Non-Algorithmic Phase-Shift Computational System (GNPSCS), referred to as a Godel computer. [[6],[7],[8]] The GNPSCS is a non-linear, non-deterministic, fractal that finds an instant ‘clique’ answer—bypassing a long (perhaps non-halting), energyinefficient, entropy-producing, stepwise Turing computation. [[1]] The PC emerges from the implicate-order plenum (PL). [[4],[5]] It is a pre-spacetime entity that is self-creating, self-organizing, and self-maintaining. The PC and its explicate-order projection, the GNPSCS, is comprised of networked oscillators and can be represented as a scale-invariant/conformal multi-dimensional fractal, a Multidimensional Networked Discretized Imaginary Bloch Clock Time Crystal (MNDIBTC). Quantum mechanics describes the behavior of particles on the smallest scales— atoms and subatomic particles—governed by probabilities and wave functions. It uses the mathematics of Hilbert spaces, linear operators, and probability theory to model how quantum states evolve, interact, and yield probabilistic outcomes through measurement, as governed by the Schrodinger equation and shaped by fundamental uncertainty. Quantum mechanics encompasses three of the four fundamental forces: electromagnetism, the weak nuclear force, and the strong nuclear force. General relativity, by contrast, describes gravity as the curvature of spacetime shaped by mass and energy. While quantum mechanics is probabilistic, general relativity operates on deterministic principles rooted in differential geometry and the continuity and existence of spacetime. Einstein’s comment: ‘Der Alte würfelt nicht—The Old One [God] does not play dice,’ encapsulates his rejection of the idea that fundamental physics is governed by the randomness suggested by quantum mechanics. Attempts to unify these two distinct frameworks have led to several approaches: string theory, which conceptualizes particles as vibrating strings and incorporates multiple dimensions; M-theory, an extension of string theory that aims to unify all fundamental forces through higher-dimensional ‘branes’; and loop quantum gravity, which models spacetime as granular and emergent from discrete quantum loops. These theories remain speculative and largely untested at present. This essay posits that a successful unified theory would transcend traditional models to explain phenomena across all scales. Such a theory must reconcile quantum mechanics and general relativity as manifestations of the same underlying process at different scales, while offering alternate explanations for the Big Bang, Guth’s inflationary expansion, dark matter, dark energy, and the ultimate destiny of the universe.
5. Loop Quantum Gravity-a Granular Cosmos, Not a Continuum.
Rovelli’s Loop Quantum Gravity (LQG) redefines the concept of space and time (often modeled as spin networks), proposing that space is not a passive stage where matter exists and on which the history of the universe unfolds. Rather, space is formed from discrete granular units or ‘granules,’ that do not reside within a pre-existing space. Instead, the intricate interactions and connections within this web of granules create the fabric of space itself. Similarly, time does not exist as a cosmic clock or individual clocks, but emerges from the sequential counting of these interactions, thereby challenging the adequacy of our current Cartesian-based continuum mathematics. This essay posits that Rovelli’s sequential counting corresponds, roughly, to the phase-shift computations of the GNPSCS model. As Einstein aptly noted, “As far as the laws of mathematics refer to reality they are not certain, and as far as they are certain, they do not refer to reality.”
This essay advocates for a paradigm shift, proposing the implicate-order Phi Connectome (PC) and its explicate-order Gödel Non-algorithmic/Non-Turing Phase-Shift Computational System (GNPSCS) as a better model of the cosmos. The implicate-order PC and its explicate-order GNPSCS operate as an atemporal, aspatial, self-generating, self-organizing, and self-maintaining non-linear fractal, comprised of networked, imaginary oscillators or clocks. The PC/GNPSCS arises through the scale-invariant randomization of randomness, as described by the Parrondo Principle or Brownian Ratchet in Figure 5.1 below illustrating closed inner dynamical billiards on a table formed by the asymmetry graph (A-graph) of Wolfram rule #110. By contrast to Turing- based computation, the PC/GNPSCS employs networked and entangled imaginary clocks that communicate instantaneously, such that a change in the value or ‘time’ of any clock results in an instantaneous adjustment across all clocks, ensuring the maximum value of each clock in relation to the others, something like a multidimensional Nash equilibrium. This reframes Nash equilibrium in terms of coherence, not payoff—an extension that bridges game theory and oscillator dynamics. The GNPSCS ‘computes’ by phase shifting such that all networked Bloch clocks tick forward one ‘notch’ with each phase shift. When a given imaginary clock ticks past its modal midnight, it undergoes a phase change, i.e., a Bohm holomovement a boundary-less transition from the implicate-to-explicate order or the reverse, from the implicate order to the explicate order. On the grandest scale, when the cosmos, represented by the largest clock with the lowest frequency, ticks past its modal midnight, the universe transitions to a subsequent eon by a phase change rather than a death and subsequent big bang. It is important to note that phase changes are boundary-less; that is, what we perceive as the singularity, big bang, and cosmic inflation are our spacetime interpretations of this ‘no boundary’ phase change, i.e., artefacts related to the use of a deterministic Cartesian-continuum mathematical paradigm. In the PC/GNPSCS, reality unfolds through phase shifts—gradual transitions where patterns reorganize and new structures emerge. These shifts are not abrupt breaks, but smooth turning points in the deeper logic of coherence. Physicist John Wheeler expressed a similar idea with the phrase ‘the boundary of a boundary is zero,’ meaning that what we often think of as hard edges in nature tend to dissolve when examined more closely. Boundaries, in this view, are not fixed dividers but soft transitions shaped by interaction and observation. This perspective challenges the traditional notion of the Big Bang as a sharp starting point. Instead, both Wheeler’s thinking and the PC/GNPSCS framework suggest that the Big Bang was a phase shift—a reorganization of reality’s structure rather than a singular edge. What appears to be a boundary is really a moment of transformation within a larger, evolving pattern.
The explicate-order projection of the PC is characterized as a Godel Non-algorithmic Phase-Shift Computation System (GNPSCS), operating non -algorithmically with its imaginary Bloch clock networked oscillators advancing (ticking) in unison with each phase-shift calculation. By contrast, to step-wise algorithmic Turing computation, the GNPSCS provides instantaneous answers to queries or perturbations by identifying a ‘clique.’ It dispenses with the need for fundamental constants of nature—analogous to the constants in a Turing program, eliminating the necessity for fine-tuning or a strong anthropic principle. Moreover, it needs no programmer, arising as it does from the self-creating plenum and phi connectome. Drawing on Plato’s allegory of the cave, the GNPSCS represents reality while our current Cartesian continuum mathematical perception of spacetime is the projection of the GNPSCS’s shadow on the cave wall. For over two millennia, this shadow—expressed in our linear, deterministic Cartesian continuum mathematics—has been mistaken for reality. As illustrated in Figure 5.1 below, the GNPSCS is a dynamical system wherein its formation is represented by the random movement of a perfectly elastic ball which loses no energy with each bounce. As Einstein said, “As far as the laws of mathematics refer to reality they are not certain, and as far as they are certain, they do not refer to reality.” Accordingly, this essay proposes that the implicate-order phi connectome PC and its explicate order Godel Non- algorithmic/Non-Turing Phase-Shift Computational System GNPSCS provide a better model of the cosmos than our current Cartesian-based continuum mathematics.
Based on an extension of Anirban Bandyopadhyay’s and David Bohm’s studies, this essay posits that the implicate-order PC and its explicate-order GNPSCS describe an atemporal, aspatial, selfgenerating, self-organizing, and self-maintaining non-linear fractal comprised of networked, imaginary oscillators/clocks. As depicted in figure 5.1 below, it arises from the scale-invariant randomization of randomness by the Parrondo Principle/Brownian Ratchet. The GNPSCS does not compute step by step according to the Turing model. Its imaginary Bloch clocks are networked/entangled, and communicate instantaneously, giving an immediate ‘clique’ answer. When an imaginary clock’s time moves past its modal midnight, the oscillator representing the clock undergoes a phase change. As noted above, when the largest (lowest frequency) clock moves past its modal midnight, the cosmos undergoes a phase change to a subsequent eon. In contradistinction to Bandyopadhyay’s model, the clocks of the GNPSCS are not nested one inside the other and are not linked in the same way as his model. Rather, they are ‘separate’ as illustrated in figures (6.1/B4; 6.3C;6.6; and 8.1 below). The oscillators are not nested one within another (like Russian dolls), but instead form a distributed network—each operating at its own frequency, yet capable of mutual communication and synchronization, a ‘Multidimensional Networked Discretized Imaginary Bloch Clock Time Crystal’ (MNDIBTC). Moreover, in contradistinction to the Bandyopadhyay nested model, the network of oscillators communicate with one another by electromagnetic-information-force passing through fractal tunnels. It is important to note that a phase change has no boundary. This essay posits that the singularity, big bang, and inflation are artefacts of our current deterministic Cartesian-based continuum mathematical model perception of this ‘no boundary’ phase change. Wheeler’s participatory ontology and the Hartle-Hawking noboundary cosmology challenge the classical notion of fixed spacetime boundaries, aligning with the PC/GNPSCS framework’s rejection of Cartesian-continuum models. Wheeler proposes that reality is not a fixed structure but emerges through the act of observation, suggesting that observers (and consciousness) play an active role in shaping the universe itself. Similarly, the Hartle- Hawking no-boundary cosmology rejects the idea of a singular beginning or fixed spacetime edges, modeling the universe as a smooth, boundary-less entity akin to the surface of a sphere. Both frameworks challenge classical, Cartesian-continuum assumptions by treating spacetime as emergent, recursive, and observer-dependent. Sheldrake carries this idea further and proposes that conscious acts can alter the properties of the cosmos. Palmer suggests that quantum uncertainty and contextuality might be explained by the geometry of an invariant set, rather than invoking hidden variables or multiple universes. *SEE: Palmer, T ‘Invariant Set Theory: Violating Measurement Independence without Fine Tuning, Conspiracy, Constraints on Free Will or Retrocausality.’ Published in Electronic Proceedings in Theoretical Computer Science (EPTCS), Volume 195, pages 285-294. Entropy, 22(7), 722. https://doi.org/10.3390/e22070722. *SEE: Sheldrake, Rupert. The Presence of the Past: Morphic Resonance and the Habits of Nature. Times Books, 1988.
These models resonate with PC/GNPSCS principles of networked oscillators, fractal geometry, and phase-based computation, where spacetime and causality are emergent projections of a deeper coherence structure. *SEE: Wheeler’s participatory ontology; *SEE: Hartle-Hawking noboundary cosmology. *SEE: Barbour’s timeless physics and Page-Wootters’ stationary observables further support the paradigm’s emphasis on non-algorithmic recursion and observer- embedded dynamics, reinforcing the view that boundaries are not ontological givens but phasedependent artifacts of emergent structure. The GNPSCS ‘computes’ non-algorithmically in which all networked oscillators (discretized imaginary Bloch clocks) tick forward with each phase-shift ‘calculation.’ In a less constrained model, these Bloch clocks can tick forward or backward with each phase-shift computation, allowing for a kind of time symmetry, suggesting that our forwardtime-related entropy may be an artefact of our current Cartesian mathematical model of the cosmos. Moreover, insofar as these imaginary clocks may tick in any direction it can be imagined that pathways through the PC-GNPSCS are not fixed at the outset, but rather become fixed or annealed through morphic resonance with the free-will actions of conscious actors. *SEE: The Primacy of Creativity, Goldberg, M. 2024 GRIN publications; *SEE: Sheldrake, Rupert. The Presence of the Past: Morphic Resonance and the Memory of Nature. Revised and expanded edition. Rochester, VT: Park Street Press, 2012. The PC is an eternal, self-forming, maintaining, and self-referential/conscious entity; it has no beginning or end. By contrast with step-wise algorithmic Turing Computation systems, the GNPSCS produces an answer to any query or perturbation, instantaneously as a ‘clique.’ In graph theory, a clique is a subset of vertices in an undirected graph where every two distinct vertices are adjacent—meaning they are directly connected by an edge. Essentially, a clique forms a complete subgraph where every node is connected to every other node within the group. The GNPSCS framework does not require a programmer—a concept reminiscent of William Paley’s 1802 Natural Theology and its watchmaker analogy—nor does it depend on fixed fundamental constants of nature like ‘constants’ found in Turing-style programs. This eliminates the need for fine-tuning arguments or reliance on a strong anthropic principle. In Plato’s cave wall analogy illustrated in Figure 6.7 below, the PC/GNPSCS is the reality and the shadow on the wall of the cave is our current linear, deterministic Cartesian-based continuum mathematics, i.e., Einstein’s ‘laws of mathematics’ that are not certain. For more than two millennia the shadow has, mistakenly, constituted our perception of reality. In Figure 5.1 below, the formation of the PC-GNPSCS is illustrated—metaphorically—as a dynamical billiard ball bouncing around on a table formed by Asymmetry graph #110. The ball is perfectly elastic and loses no energy with each bounce.
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Figure. 5.1-Asymmetry graph of Wolfram rule #110-by author
*SEE: Goldberg, M. (2016). Classification of Cellular Automata Using Asymmetry Graphs. GRIN Verlag. ISBN: 9783668184763. Random oscillations of the billiard ball in hill 1 break the symmetry of hill 2, and random oscillations of the billiard ball in hill 2 break the symmetry of hill 1 (ball not shown in all locations). We have the interaction of two random/‘losing’ strategies/processes resulting in a complex/(winning) result, according to the Parrondo Paradox/Principle and the Brownian/Feynman-Smoluchowski ratchet, a ‘perpetual motion machine of the second kind’ (converting thermal energy/randomness/noise/a required temperature gradient into mechanical work/complexity-order. The dynamical billiards operator [DB] acts on the scale-invariant/conformal asymmetry graph A-Graph #110 according to the expression: [DB](A-graph #110). Because of the Wolfram’s principle of computational equivalence (PCE), CA #110 can emulate all other rules. *SEE: A New Kind of Science by Stephen Wolfram; Wolfram Media, Inc. 2002. It lays out Wolfram’s vision for a computational (algorithmic) approach to understanding the universe, using simple programs like cellular automata to explore complexity, randomness, and the foundations of physics. Figure 5.1 illustrates a perfectly elastic dynamical billiard ball bouncing around randomly inside a table shaped like A- graph #110. The ball can pass back and forth from one hill/oscillator to the other by tunneling through the narrow tunnel at ‘T’. If the tunnel at ‘T’ were to close, then a ball bouncing around inside either hill 1 or hill 2 would describe random oscillations. However, if the tunnel at ‘T’ opens a small amount, as shown, the ball can pass back and forth from one hill to the other such that random oscillations in hill 1 can interact with random oscillations in hill 2, and conversely. As the ball passes back and forth from hill 1 to hill 2 to hill 1, etc., it generates the interaction of two random processes according to Parrondo’s Paradox/Principle and the Brownian Ratchet, offering a pictorial analogy of the self-formation of the scale-invariant/conformal Phi Connectome. An interesting situation arises if we open the tunnel completely so that hill 1 and hill 2 become a single hill, whence the bouncing ball also describes a random oscillation. In this sense, the GNPSCS is bounded by randomness, i.e., when the tunnel is either completely closed or when it is completely open. The GNPSCS (‘sweet spot’) is bounded by randomness as illustrated in figure 6.2 D below. Each oscillator breaks the symmetry of the other, reciprocally, resulting in complexity, and scale-invariant chirality/parity violation as the ball is eventually trapped within the narrow confines at the top of hill 2. Importantly, the GNPSCS is scale-invariant/conformal (SIC) resulting in networked oscillators of many frequencies. The PC is self-creating from randomness—i.e., from nothing hence the dictum ‘Ex nihilo nihil fit’—‘nothing comes from nothing’ is true according to the definition that ‘randomness is nothingness’; that is, the PC is nothing and it is created out of the nothingness of randomness, i.e., from the underlying quantum vacuum plenum (PL) by a process related to the Schwinger effect. The PC is self-creating, selforganizing, and self-maintaining. This essay poses these oscillators as networked discretized imaginary Bloch clocks separated by scale-invariant conformal (SIC) phi p* island barriers, and communicating with one another by scale-invariant conformal electromagnetic tunneling information y*, the asterisk denoting SIC.
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Figure 5.2 - imaginary Bloch clocks
This essay posits that our: concept of space relates to the relationship of a scale- invariant/conformal network of imaginary Bloch clocks/oscillators of the PC where information is passed among all Bloch clocks by scale-invariant/conformal tunneling (SIC) information, i.e., SIC electromagnetic radiation (y*), and its explicate-order projection, the Godel Non-Turing, Non- Algorithmic Phase-Shift Computational System (GNPSCS), while our; concept of time relates to the ticking of all networked imaginary Bloch clock-oscillators with each phase shift computation of the GNPSCS; and our concept of mass relates to oscillator frequency. A. Illustrates the relationship of Bohm’s implicate order (IMPL) to the explicate order (EXPL). The dashed region indicates granularity, while the solid region indicates continuum Turing computation. Quantum mechanics has taught us that continuum mathematics applied to a non-continuous, non-linear, non-deterministic fractal reality leads to several dilemmas: how to reconcile quantum mechanics and general relativity; explanations for dark matter dark energy, and the big bang and inflation. B. Illustrates the relationship of two, scale-invariant/conformal (SIC) oscillators of the PC/GNPSCS showing SIC electromagnetic tunneling information passing between oscillators with each phase-shift calculation of the GNPSCS. The symbol (p*) = SIC separation of oscillators, and the symbol (y*) = SIC electromagnetic tunneling information/force-gravity. The vertical bar at the top of an oscillator represents its modal ‘midnight’ where there is a phase shift (Bohm holomovement), a change between explicate and implicate orders). C. (a) nested Bloch clocks of Bandyopadhyay’s model in a triplet relationship, not separated by SIC (p*), and no SIC (y*) tunneling information; and (b) three networked Bloch clocks of the PC/GNPSCS where the oscillators are separated by a SIC ‘distance’ (p*) and communicate by SIC (y*). Every ‘connector’ between oscillators is at a SIC ‘distance’ (p*) through which SIC tunneling EM information/gravity (y*) tunnels/passes between the oscillators. The largest clock has 3 tick marks, the middle-sized clock has two tick marks and the smallest clock has one tick mark. As the GNPSCS computes, each clock advances one tick with each phase change which means that the smallest clock passes midnight with each phase-shift computation, the middle clock passes its midnight every two phase-shift computations and the largest clock passes its midnight every three phase-shift computations. The phase change of a clock through its modal midnight constitutes a change in Bohmian order—if a clock is in the implicate order, it unfolds to the explicate order and if in the explicate order it enfolds into the implicate order.
With respect to the entire frequency range of the PC/GNPSCS, there is a large prime number ‘p’ of small/high-frequency clocks with one or a few tick marks, and at the largest cosmic’ level there is one/lowest-frequency clock with ‘p’ tick marks. Carlo Rovelli’s Loop Quantum Gravity (LQG) theory suggests that at the Planck scale spacetime is comprised of a network of very small, discrete ‘chunks’ rather than being smooth and continuous. The fabric of spacetime emerges from the finite structure and dynamic interactions of this network. Our everyday experience of spacetime appears smooth because we are observing it at a much larger scale. It's like looking at a piece of cloth from a distance—it looks smooth, but up close, you can see the individual threads. In Loop Quantum Gravity, spacetime exhibits a granular structure that becomes relevant only at scales far below current observational limits. The mathematical framework of LQG is fundamentally geometric, emphasizing the shapes, interconnections, and evolution of quantized loops known as spin networks, where spin networks are graph-based structures that represent quantized geometry using nodes and edges labeled by quantum angular momentum. Nima Arkani-Hamed and Roger Penrose propose that spacetime and quantum mechanics emerge from deeper geometric structures. Arkani-Hamed explores this through the amplituhedron and twistor-based frameworks, while Penrose’s twistor theory replaces spacetime with a space built from light-like entities encoding spin and momentum. In both views, physical reality arises from abstract, relational geometry— an approach that resonates with GNPSCS by emphasizing coherence, modular synthesis, and recursive emergence across scales. One such concept Arkani-Hamed explores is the positive Grassmannian which offers a novel framework for uncovering the deeper rules governing the universe. The GNPSCS extends Arkani-Hamed’s model via scale-invariance to include all scales of the cosmos. The PC/GNPSCS entails Anirban Bandyopadhyay’s phase prime metric PPM. SEE: Bandyopadhyay, A., et al. (2018). A brain-like computer made of time crystal: Could a metric of prime alone replace a user and alleviate programming forever ? In ‘Soft Computing Applications’ (pp. 1-43). Springer. https://doi.org/10.1007/978-981-10-8049-4_1. Bandyopadhyay’s Phase Prime Metric (PPM) is a geometric-topological framework for integrating discrete events—each represented by modified Bloch spheres holding 3D shapes—into a unified decision-making structure. The PPM bypasses algorithmic logic and serves as the foundation for Bandyopadhyay’s time crystal-based brain model, where nested imaginary Bloch clocks form the substrate for non-Turing computation and coherence-driven cognition. It maps a topological landscape in which Bloch clocks morph and align through networked resonant phase recursion— central to the idea that consciousness and cognition emerge from shape-phase dynamics rather than mechanistic processing. Lori Gardi’s interpretation of the Mandelbrot Set as a quasi-black hole shares structural resonance with the GNPSCS framework proposed in this essay, echoing the geometric recursion found in the work of both Bandyopadhyay and Gardi. However, the GNPSCS framework introduces a network (vs. nested) SIC imaginary Bloch clocks—phase-ticking constructs that synchronize with each GNPSCS calculation and serves as an explicate-order projection of Bohm’s implicate-order wholeness. * SEE: The Mandelbrot Set as a Quasi-Black Hole, presented at the John Chappell Natural Philosophy Society Conference 2017, and a YouTube video of her talk, outline Gardi’s hypothesis that the Mandelbrot Set models black hole behavior across scales. [1 ^ 5]
6. The Standard Model of Particle Physics: the Particle Zoo as an Artefact of Cartesian Mathematics.
A.
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Image from Wikipedia Standard Model…rendered in black and white
B1.
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scale-invariant/conformal tunneling information-Hawking radiation
B2. asterisk (*) denotes scale-invariant/conformal (SIC)
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B3. illustrating oscillator frequency as mass
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SIC oscillators (Osc*) are separated by SIC φ*, and communicate by SIC electromagnetic radiation = γ* = SIC gravity.
SIC gravity means the SIC force which manifests at increasing scales as the strong force, gravity, dark matter, dark energy, Hawking radiation, and Hawking spots on the cosmic microwave background (CMB) of a subsequent Penrose aeon.
B4. Higher frequency oscillatorsPlanck scale and beyond.
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B5.
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Figure 6.1-by author, after Wilczek.
B5. *SEE: Wilczek, Frank. ‘The Lightness of Being: Mass, Ether, and the Unification of Forces’. New York: Basic Books, 2008—modified by author. 0 = SIC electromagnetic (EM) tunneling information = y* = SIC gravity. At the subatomic scale SIC ‘gravity’ is perceived as the strong force—the gluon. Illustrating the scale-invariant/conformal structure of the spacetime, explicitorder projection of the implicate-order PC at increasing distances/decreasing frequencies. Bohmian unfolding of the implicate order scale-invariant/conformal PC as the explicate-order GNPSCS has, heretofore, been perceived incorrectly in terms of Cartesian continuum mathematics as many separate and different entities. This has led to confusion, for example: the inability to reconcile quantum mechanics and general relativity, and the puzzles of dark matter and dark energy. The figure illustrates that bosons, gravity, dark matter, dark energy, and Hawking radiation are all posited in this essay to be electromagnetic tunneling information at different scales. Moreover, it is also proposed that scale-invariant/conformal photons (y*) constitute all tunneling information and SIC force/gravity. Subatomic particles, and macroscopic objects such as planets, galaxies, and galaxy clusters are the explicate-order projections of increasingly lower frequency oscillators of the PC/GNPSCS, while the ‘ separation ’ between objects from the subatomic level (the Pauli exclusion principle to the inter-galactic/cosmic level) is represented by the scale- invariant/conformal (p*) symbol, i.e., phi* = (1.618...*). At the frequency range of life, p* is represented by vicinal water, symbolized as A, the structured/quasicrytalline aqueous layer that separates and mediates coherence across all scales of the organism. At the frequency range of living organisms, y* denotes coherent near-infrared electromagnetic/laser and coherent sound/phonon signaling propagating (via near-instant, quantum-coherent communication) through ordered vicinal water to orchestrate biological structure across scales, i.e., from atoms to the whole organism. SIC tunneling information (y*) is perceived at the cosmic-eon scale as Hawking radiation showing up as Hawking points on the cosmic microwave background (CMB) of a subsequent eon. All eons are entangled.
A. A chart of the standard model of physics is represented in this essay as projection of the PC, arising as an artefact of our Cartesian continuum mathematics applied to a non-linear, fractal cosmos; B1. Illustrates the scale-invariant conformal (SIC) relationship of oscillators, tunneling information, and separation of oscillators; B2. Illustrates general SIC relationship of all oscillators where the asterisk (*) denotes all scales, p* represents SIC separation of oscillators (thereby indicating the non-continuum or granularity of the system), y* represents SIC electromagnetic tunneling information at all scales; and the asterisk (*) inside the oscillator circle represents SIC oscillator frequencies. B3. Illustrates the relationship of oscillators to the fundamental equations Energy = mc[2] = hv. B4. Illustrates a portion of the scale-invariant/conformal, networked oscillators (discretized imaginary Bloch clocks) of the Phi Connectome PC/GNPSCS. Equation (1) relates Einstein’s energy and mass and equation; (2) rewrites equation (1) showing mass related to frequency by the constant (c[2]/h); (3) poses mass-frequency (m-v) as equivalent to oscillator frequency (represented below as an imaginary discretized Bloch clock); and (4) represents (c[2]/h) as (p* y*) where p* = scale-invariant/conformal separation between oscillators (denotes the noncontinuum granularity of the system); Osc* = scale-invariant/conformal oscillators, where the asterisk denotes a non-linear granular system not amenable to Turing Cartesian-based continuum differential calculus, i.e., AX/AY ^ dx/dy. The PC is in the implicate order and it projects— unfolds by Bohm’s holomovement—to the explicate order as the Godel Non-Turing Non- Algorithmic Phase-Shift Computational System (GNPSCS). B5. Wilczek’s diagram/figure with bi-directional arrows shown as a subatomic frequency range of the PC. This illustrates the unification of the higher frequency (quark-[1]—quark) as explicate-order projections of the GNPSCS with the gluon as tunneling information, and the lower frequency positron-photon-electron) as explicate-order projections of oscillators of the PC with the photon as tunneling information. Because information travels in both directions in the GNPSCS, then all connections of the Wilczek figure above are shown as bi-directional arrows. All oscillators are separated by scale- invariant/conformal phi (p*). In B5 larger oscillators and larger information symbols denote lower frequencies. These relationships are perceived as models of eternal laws of physics, but this essay posits they are long-standing annealed networked ‘habit’ pathways of the PC due to morphic resonance between the implicate and explicate orders. [1] *SEE: Sheldrake, R. The Presence of the Past: Morphic Resonance and the Memory of Nature. Revised ed., Park Street Press, 2012. Sheldrake proposes that nature evolves through inherited memory—morphic resonance—where past forms and behaviors influence present ones across time and space. * SEE: ‘The Primacy of Creativity: Does an Eternally Creative Cosmos Entail Free Will and Moral Responsibility?’ Goldberg, M. GRIN publication 2024, explores the annealing of pathways within the phi connectome. The current essay frames reality within the GNPSCS paradigm, describing how morphic resonance and repeated conscious free-will choices shape networked habit pathways that become annealed over time and projected back onto spacetime. With respect to two-headed arrows in B5 above: (g = gluon, q = quark, e = electron, y = photon)—we can write at a higher frequency: g-q-g-q or q-g-q-g; at a lower frequency e-y-e-y or y-e-y-e; and for mixed frequencies: e-Y-g-q, or e-q-g-y and so forth for all connections at all scales of the PC/GNPSCS indicating the interconnectivity of the SIC oscillators of the PC/GNPSCS. At all scales p* indicates the noncontinuum granularity of the cosmos.
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D. PACKING FRACTION
The sweet spot is bounded by maximum entropy (TDE); see Figure 5.1 above
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Figure 6.2 - From Wilczek with GNPSCS modification by author
This essay posits that: space, time, matter, and forces such as gravity, the strong, weak and electromagnetism are emergent from deeper computational structures. A. PC showing oscillators and their connections. B. One possible combination of oscillators of different frequencies (two of same higher frequency and one of lower frequency). C. Another combination of oscillators of different frequencies (one of higher frequency and two of lower frequency). The asterisk in the oscillators and in the symbols φ*, and γ* indicates SIC, and the vertical bold line at 12 o’clock represents the modal midnight of the discretized imaginary Bloch clocks of all frequencies. B. and C. represent the form of all SIC pathways of the PC where a pathway/connection between oscillators represents scale-invariant/conformal SIC separation between oscillators (φ*), while (γ*) represents SIC electromagnetic information tunneling between oscillators. D. illustrates the relationship of thermodynamic equilibrium (TDE) or randomness shown on the right side of the figure. Under the action of vibration/Brownian motion/heat, and phase-shift computations of the GNPSCS, and if the packing fraction is optimum, the system reaches a sweet spot, a multidimensional networked discretized Bloch imaginary clock time crystal (MNDIBTC). The packing fraction—the ratio of particle volume to total system volume—plays a central role in the emergence of entropic bonds. E. Illustrating Wilczek’s unification of forces where: SF-strong force, WF-weak force, and EM-electromagnetic force all meet in a point of unification except gravity. This essay proposes that if the GNPSCS, rather than Cartesian mathematics is employed, then all forces do meet at a point. As particle density increases, spatial constraints force particles into configurations that maximize the system’s overall entropy. If the packing fraction continues to increase, then the sweet spot (MNDIBTC) is lost and it becomes a system in which a space crystal can be described by Cartesian-mathematics with an increase in entropy wherein the system eventually ends in thermodynamic equilibrium (TDE), as the left-hand side of figure 6.2 D illustrates. These constraints generate directional preferences not from attraction or energy minimization, but from the geometric necessity of avoiding overlap. In densely packed systems, hard particles begin to organize into structured arrangements because certain orientations free up more volume for others. This leads to emergent ‘bonding’ behavior that mimics chemical interactions, yet arises purely from entropic forces. At critical packing thresholds, these entropic bonds drive phase transitions, leading to self-assembly into crystals, quasicrystals, or other complex structures. The process relies entirely on shape, excluded volume, and entropy maximization— not on forces. The entropic packing theory comports with Vopson’s theory, the former showing how physical entropy drives structural order in particle systems, while the latter explores how information entropy shapes the evolution of systems that evolve according to thermodynamic rules, independent of classical forces.
Within the GNPSCS framework, this classical behavior mirrors quantum-coherent tunneling interactions: just as entropic bonds arise from geometric packing constraints, quantum coherence arises from phase-aligned oscillator configurations. Both systems exhibit structured emergence from purely statistical or geometric foundations. These referenced works collectively explore how entropy, particle shape, and excluded volume effects drive the emergence of order in systems— often without any attractive forces. [2 ^ 8 ] * SEE: Van Anders, G., Ahmed, N. K., Klotsa, D., Engel, M., & Glotzer, S. C. (2014). A Unified Theoretical Framework for Shape Entropy in Colloids. arXiv:1309.1187 [cond-mat.soft]; Vo, T., & Glotzer, S. C. (2022). A theory of entropic bonding. Proceedings of the National Academy of Sciences, 119(6), e2116414119; Frenkel, D., & Mulder, B. M. (1985). The hard ellipsoid-of-revolution fluid. I. Monte Carlo simulations. Molecular Physics, 55(5), 1171-1192; Onsager, L. (1949). The effects of shape on the interaction of colloidal particles. Annals of the New York Academy of Sciences, 51(4), 627-659. Our prevailing Cartesian continuum mathematical system describes the cosmos, life, and consciousness, as either randomness or as a set of simple local, deterministic laws. By contrast, the oscillators of the GNPSCS represent imaginary discretized Bloch clocks computing by phase shifts (PS). Scale- invariant/conformal electromagnetic information (y*) tunnels throughout the GNPSCS and each oscillator clock moves forward one tick with each phase shift. The number of oscillators of each frequency form a prime sequence, i.e., there are ‘p’ (a very large prime number—perhaps related to the number of quarks) smallest clocks with, say, one tick mark at midnight, and at the largest scale/lowest frequency, a single clock—the universal/eon cosmic clock—with ‘p’ tick marks on its face. When a clock ticks past its modal midnight, it transitions between the implicate and explicate orders. Thus, an electron with, say, only a few tick marks on its imaginary Bloch clock transitions between the explicate and implicate orders every few phase-shift calculations of the GNPSCS. At the opposite extreme, a single oscillator representing an eon, the largest clock with ‘p’ tick marks on its face, transitions from the explicate order to the implicate order in a cosmic amount of time as perceived in our Turing computational paradigm. E. Represents unification of all forces using the GNPSCS instead of Cartesian-based continuum mathematics.
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Figure 6.3 - A. and B. after Nima Arkani-Hamed; C. by author
A. Simple 1-dimensional (space-time) permutation illustrating quark interactions, when two neutrons collide in the Large Hadron Collider (LHC). B. More complex representation of quark interactions as pathways between numbers (16) on the circumference of a circle where the symbols = turn right/left; the symbol = turn left/right [direction of turn depends on direction of pathway], showing two possible pathways (63) r-l-r-l-r and (14) l-r-l-r-l. A and B after Arkani-Hamed *SEE: “Unwinding the Amplituhedron” by Nima Arkani-Hamed, delivered at the Institute for Advanced Study on April 5, 2017, available on YouTube—features the kind of visual walkthrough described in figure 6.3, ‘A.’ which illustrates his one-dimensional example and progressing to ‘B’ the black-and-white dot configuration that maps pathways through the amplituhedron. Arkani-Hamed’s talk is a deep dive into positive geometry, scattering amplitudes, and the conceptual leap beyond spacetime locality. Arkani-Hamed uses visual intuition to build up the amplituhedron from simple combinatoric structures, giving the complex figures in B. The center polygonal structure of ‘B’—roughly speaking—can be ‘elevated’ dimensionally to represent the amplituhedron. Arkani-Hamed has demonstrated that the amplituhedron, a multidimensional geometric structure based on the positive Grassmannian, simplifies the calculations of particle interactions. Its volume corresponds to the scattering amplitudes of particles, which represent the probabilities of specific outcomes when particles interact. [9,10,11]
C. by the author of this essay showing two pathways among oscillators of the phi connectome and the Godel Non-Algorithmic Non-Turing Phase-Shift Computational System illustrating the proposed relationship of A and B to the PC/GNPSCS.
The flow of information mirrored in the GNPSCS reflects dynamic pathways within the network. Just as the navigation symbols ‘turn left’ or ‘turn right’ change with the direction of the trajectory, so the oscillators of the GNPSCS adaptively process information through phase shifts. These phase shifts represent interactions among networked oscillators, forming non-linear, scaleinvariant pathways where oscillators communicate by scale-invariant/conformal (SIC) electromagnetic tunneling information (y*) across (SIC) golden ratio barriers (p*). An evolving flow of information exemplifies the system's non-algorithmic and fractal nature, where new pathways emerge from the complex interplay of oscillators rather than following a predetermined route, i.e., the system is both a fractal and non-deterministic in contrast to continuum and deterministic Cartesian-based differential calculus. Following Sheldrake, these pathways are flexible and represent our ‘laws’ of physics as ‘habits’, implying that reality is not a fixed deterministic entity, but rather a flexible ‘creative’ entity that represents both ‘being’ and ‘becoming.’ *SEE: Sheldrake, R. (2012). The Presence of the Past: Morphic Resonance and the Memory of Nature (Revised and expanded edition). Park Street Press. Publisher's page. The book explores Sheldrake’s theory of morphic resonance, proposing that nature has a form of memory that influences the behavior and form of organisms and systems. *SEE: Goldberg, M. (2024). The Primacy of Creativity: Does an Eternally Creative Cosmos Entail Free Will and Moral Responsibility? GRIN Verlag. ISBN: 9783389097106. [Creativity never ends.]
Traditionally, computations in quantum field theory have required dealing with complex and lengthy Feynman diagrams, involving summation over an enormous number of possible particle interaction pathways. Instead of relying on intricate Feynman diagrams, the amplituhedron represents the scattering process as a geometric shape in a higher-dimensional space. The amplituhedron encodes scattering amplitudes directly through its volume, bypassing the traditional need for spacetime. Instead, space and time emerge as consequences of a more fundamental ‘prespacetime’ structure, leading to the notion that ‘spacetime is doomed.’ Arkani-Hamed’s amplituhedron reduces redundancies, avoids unphysical intermediate (off-shell) calculations, and highlights the underlying simplicity and elegance of particle interactions. Concepts related to quantum mechanics such as locality and unitarity are no longer treated as starting assumptions but rather as emergent properties of the geometry.
The proposed PC/GNPSCS framework introduces a non-Turing, non-algorithmic, non-Cartesian system that is characterized by non-linear, non-continuous, fractal-like networked oscillators comprised of discretized imaginary Bloch clocks. These clocks tick with each phase-shift computation, and are separated by a scale-invariant/conformal irrational number (p*)=phi*=(1.618...*), the SIC golden ratio. Its use as a separating barrier or ‘island’ between SIC networked oscillators prevents these oscillators from exhibiting mutual destructive resonance which could destroy the entire GNPSCS system. In this proposed model, SIC networked oscillators communicate through SIC electromagnetic tunneling information (y*) perceived as SIC ‘gravity.’ This essay proposes that the amplituhedron can be understood as a high-frequency range of the GNPSCS, which provides a means to integrate quantum mechanics and general relativity, while potentially explaining phenomena such as dark matter, dark energy, the big bang singularity, inflation, and the ‘end’ of the universe—all of these posited as artifacts of Cartesianbased mathematics.
Godel Computation of Feynman Diagrams
Feynman marveled at how particles seem to ‘instantly’ evaluate all possible paths—something our supercomputers can barely approximate through slow, entropy-laden Turing computations. In his path integral view, Nature doesn’t choose a path—it uses all of them at once. One possible explanation is that the GNPSCS operates non-algorithmically, resolving outcomes (cliques) simultaneously, bypassing stepwise computation entirely. Shown below are standard Feynman diagrams—algorithmic, Cartesian, and continuum-based—alongside the author’s non-algorithmic reinterpretations. These alternative diagrams depict GNPSCS-style clique representations, where subatomic interactions exist in superposition and resolve simultaneously rather than sequentially.
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Figure 6.4 – * SEE: Algorithmic Feynman diagrams fromhttps:// en.wikipedia.org/wiki/List_of_Feynman_diagrams. Non-algorithmic GNPSCS diagrams by author.
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Figure 6.5 by author
C. (a)Illustrating Bandyopadhyay’s nested discretized imaginary Bloch clocks. (b) In the PC/GNPSCS the oscillator clocks are networked rather than nested. With each phase-shift (PS) computation of GNPSCS, all clocks tick forward one tick mark. As each clock ticks past midnight, there is a phase change. A. Feynman Turing computation calculates all pathways between the black dots, including off-shell virtual particles. B. GNPSCS, calculates only the on-shell pathway by finding a non-Turing, non-algorithmic ‘clique’ solution shown as a black line connecting the two black dots. The off-shell calculations are not required and are depicted as faint curves. This essay posits that the PC/GNPSCS is a Multi-dimensional Network Discretized Imaginary Bloch Clocks Time Crystal (MNDIBTC) comprised of discretized imaginary Bloch clocks which tick with each phase-shift computation and in which an answer is ‘found’ immediately as a ‘clique’ rather than as the result of the long, step-wise—possibly non-halting, entropy producing— computation of a Turing system. Moreover, the GNPSCS is a multidimensional fractal which is consistent with ideas relating to the granularity of reality in which space and time are consequences of the interactions among pre-spacetime entities as proposed in C. Rovelli’s loop quantum gravity (LQG). By contrast to Bandyopadhyay’s nested oscillators shown in figure 6.5 C, the SIC oscillators of the PC/GNPSCS are not nested, but rather form a SIC network wherein all oscillators are separated by SIC (p*) and communicate via SIC (y*). This essay posits that current dilemmas in physics are the result of our using the wrong mathematical paradigm, i.e., continuum mathematics based on a Cartesian system, when a more useful multidimensional non-linear fractal system such as the PC/GNPSCS is warranted. Shifting away from a Cartesian-based system is suggested by Nima Arkani-Hamed’s amplituhedron—‘spacetime is doomed,’ and Carlo Rovelli’s work with Loop Quantum Gravity (LQG). C: (a) Anirban Bandyopadhyay’s nested model. *SEE: Bandyopadhyay, A. (2020). Nanobrain: The Making of an Artificial Brain from a Time Crystal. 1st ed. Boca Raton: CRC Press. ISBN: 9781439875490. DOI: 10.1201/9780429107771; (b) three networked oscillators of the PC/GNPSCS. In the entire frequency range of the PC/GNPSCS, there are ‘p’ (highest frequency) smallest clocks where p is a large prime number close to the number of, say, quarks, and where each of these smallest clocks has one (1) tick mark (midnight) on its face; then there is a single largest (lowest frequency) clock with p tick marks on its face, then two next smaller clocks with the next smaller prime tick marks on its face, and so on, the number of each smaller clock is the next smaller prime number with the same smaller number of tick marks on its face. Thus, the figure shows three nested clocks: one largest clock with 3 tick marks, two next larger nested clocks with 2 tick marks and three smallest clocks with 1 tick mark where 1, 2, and 3 are all prime numbers. If we had 4 clocks, there would be 1 clock with 5 tick marks, 2 clocks with 3 tick marks, 3 clocks with 2 tick marks, and 5 clocks with 1 tick mark, i.e., an intersecting sequence of the first four prime numbers:
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scale. All these clocks are separated by a scale-invariant/conformal (SIC) distance p* and communicate with one another by scale-invariant/conformal SIC electromagnetic tunneling information y*. In C. SIC distance and SIC EM tunneling information at a distance of one clock level is symbolized by (p*, y*)-/+ i, as we go one ‘step’ to a smaller, higher frequency clock or a larger, lower frequency clock, respectively. Anirban Bandyopadhyay’s Phase Prime Metric (PPM) framework models oscillator networks governed by prime number sequences to encode symmetrybreaking and resonance phenomena across biological and physical systems. [[15],[19]] In GNPSCS terms, these prime-modulated oscillators resemble coherence attractors that anneal phi pathways (form ‘habits’) through nested resonance geometries. Prime-modulated oscillators are systems that pulse in patterns shaped by prime numbers, behaving like coherence attractors—structures that pull surrounding activity into stable, organized flows which guide and refine energy or behavioral pathways, smoothing them into efficient routes. As these flows settle, they form layered resonance patterns, where each level reinforces the others. The result is a self-organizing system that uses prime-based rhythms to shape complex, coherent behavior across multiple scales. [[16],[20]]
The Phase Prime Metric (PPM) generates geometric patterns—triangles, pentagons, singularities—by projecting prime factor relationships into oscillator phase space, forming a lattice of decision nodes that mirror implicate-explicate transitions. [[15],[19]] This architecture is not algorithmic but topological, replacing Turing-style computation with phase-based morphogenesis. [[17]] In Nanobrain: The Making of an Artificial Brain from a Time Crystal, Bandyopadhyay et al. describe how the PPM governs nature’s intelligence by linking all symmetries through prime modulation, enabling a time crystal brain model composed of dielectric and cavity resonators. [[16],[19]] The GitHub documentation for OpenGML further elaborates how PPM transforms n-dimensional data into nested geometric forms, aligning with the phi connectome’s annealing logic. [[18],[22]] The Springer chapter on time crystal computing proposes that prime-number-based oscillator networks can replace conventional programming, entirely, using geometric musical language (GML) to encode decisions as phase structures. [[17],[21]]
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Figure 6.6-by author
Figure 6.6 illustrating the PC/GNPSCS comprising a lattice of scale-invariant, conformal SIC oscillators representing a multidimensional network of discretized Bloch imaginary clocks. These clocks are ‘separated’ by a SIC golden ratio distance, φ* ≈ (1.618…*) preventing mutual resonant destruction among oscillators. Communication between oscillators occurs via SIC electromagnetic tunneling, with the tunneling parameter γ* functioning analogously to emergent force coupling— staged as SIC gravity. Within the Cartesian continuum framework, force-mediating vector bosons (spin 0, 1, or 2) operate at the subatomic level. Fermionic oscillators (spin ½) obey Pauli’s exclusion principle, which ensures quantum stability and prevents collapse into a degenerate state.
It is proposed that the summation of y* interactions across all scales gives rise to an emergent field structure, which is perceived in Cartesian continuum mathematics as the Higgs field (Ho). Within this framework, the Higgs scalar boson (spin 0) is interpreted as a quantized ripple in the Ho field, consistent with standard quantum field theory. *SEE: Wikipedia-the Higgs boson; the Edinburgh Higgs Centre’s overview, https://en.wikipedia.org/wiki/Higgs_boson which traces the conceptual and experimental journey from field to particle. [NOTE: The word ‘perceived’ in the context of this essay means observed directly or arrived at through computation using our current Cartesian-based mathematical paradigm. In quantum physics, the Higgs boson is like a tiny ripple in an invisible field that fills all of space—called the Higgs field. This field has a constant presence, and when particles move through it, they interact with it and gain mass. That process is known as the Higgs mechanism.
The Higgs boson itself is a spin-0 scalar particle, meaning it has no intrinsic angular momentum and obeys Bose-Einstein statistics which means it behaves like other bosons: it can share states, doesn’t mind company, and plays by quantum rules that allow for some truly exotic physics. When the Higgs field is disturbed—such as in high-energy collisions at the LHC—these disturbances manifest as detectable Higgs bosons. This ripple analogy is similar to how a photon is a ripple in the electromagnetic field, or a graviton (hypothetical) would be a ripple in the gravitational field. The Higgs boson is the observable particle that confirms the existence of the Higgs field and its role in electroweak symmetry breaking. Electroweak symmetry breaking is the process that explains how some particles get mass. At very high energies, the electromagnetic force and the weak nuclear force act as one unified force. But as the universe cooled, an invisible field called the Higgs field settled into a constant value everywhere. This change broke the symmetry between the forces, causing particles like the W and Z bosons to gain mass, while others like the photon stayed massless. The Higgs boson is the particle that proves this field exists and plays a key role in that process.
How is Entropy related to Gravity? Aligning with the references listed in this paragraph and as a consequence of the GNPSCS, this essay posits that gravity is an emergent property of SIC y* electromagnetic tunneling information between oscillators of the GNPSCS, implying that gravity doesn't generate entropy in the same way classical thermodynamic systems do. Instead, this ‘informational gravity’ might exist as a purely relational concept. Turing-based computational systems inherently involve iterative processes, which often align with notions of entropy due to state transitions and the complexity of operations. These systems naturally fit into frameworks where entropy plays a key role in understanding gravitational phenomena. On the other hand, the GNPSCS model allows instantaneous ‘clique’ answers, bypassing the step-by-step processes that generate [Turing] computational entropy. This could suggest a deeper, non-thermodynamic relationship between gravity and information, that transcends entropy. *SEE: Verlinde, Erik ‘On the origin of gravity and the laws of Newton’ (JHEP, 2011), proposes that gravity arises as an entropic force resulting from changes in information associated with the positions of material bodies. *SEE: Bianconi, Ginestra 2024 preprint, ‘Gravity from quantum relative entropy (arXiv:2408.14391)’, advances this idea by deriving gravitational dynamics from quantum relative entropy between spacetime and matter-induced metrics, framing gravity as a relational informational structure. *SEE: Wikipedia “Entropie gravity” provides a general overview of these theories and their implications. * SEE: 2025 Phys.org, Gravity from entropy, 2025: A radical new approach to unifying quantum mechanics and general relativity,’ discusses recent developments that further support the view of gravity as an informational and entropic construct.
Bandyopadhyay’s model roots time crystals in biological substrates, using quantum coherence in microtubules to explain cognition and consciousness through networked vibrations and holographic projection. The MNDIBTC framework posited in this essay abstracts time as ticking of imaginary Bloch clocks, enabling a substrate-independent architecture that spans quantum to cosmic scales. Bandyopadhyay’s time crystal is biologically grounded representing a frequency range of the GNPSCS, while the MNDIBTC provides a scalable ontology that unifies physics, computation, and cognition through networked coherence across all scales or frequencies from, say, the oscillators of the Planck scale to the cosmic scale. The explicate-order GNPSCS describes a multidimensional networked discretized imaginary Bloch clock time crystal (MNDIBTC), where Bloch clocks are represented by SIC oscillators. It is a non-linear, non-deterministic fractal system rather than a linear, deterministic system described by Cartesian-based mathematics which is based on—curvilinear coordinates, matrices, and tensor analysis—the basis of our current system. The frequency of the oscillators of the GNPSCS produce what we perceive as mass. If gravity arises from coherent information tunneling between oscillators, rather than spacetime curvature, then the GNPSCS reframes gravity as a relational coherence effect. This aligns with quantum information-based models where spacetime and gravity emerge from entanglement patterns or informational metrics. Classical thermodynamic systems generate entropy through irreversible processes. Entropic gravity theories, e.g., Verlinde, Bekenstein, and Jacobson posit gravity as a statistical tendency toward higher entropy. * SEE: Jacob Bekenstein Black Holes and Entropy (Phys. Rev. D 7, 2333), Erik Verlinde On the Origin of Gravity and the Laws of Newton, that gravity is not fundamental but emergent, arising from informational changes and statistical tendencies toward higher entropy (arXiv:1001.0785), and Jacobson (1995): Physical Review Letters, 75(7), 1260-1263 (1995)DOI: 10.1103/PhysRevLett.75.1260. Jacobson derived Einstein’s field equations from the Clausius relation, -5Q =TdS, applied to local Rindler horizons, suggesting that spacetime dynamics emerge from thermodynamic principles.
The GNPSCS model bypasses this by allowing instantaneous clique-based resolution, suggesting that gravity may not require entropy production at all—especially if SIC y* tunneling preserves coherence without decoherence. By contrast, Turing-based computation is sequential and inherently entropic, with each state transition contributing to computational entropy. By contrast, the GNPSCS proposes non-iterative resolution implying a zero-entropy departure from algorithmic physics. The idea that gravity is purely relational—emerging from oscillator coupling rather than mass-energy distributions—echoes holographic principles, but with a quantum twist. It also resonates with recent work on computational gravity, where gravitational behavior emerges from entropy minimization in discrete information grids. * SEE: Melvin Vopson, Information Gravity Derived from Entropy Minimization, AIP Advances 2025; *SEE: Bousso, Raphael. The Holographic Principle, 2002; *SEE: Fröhlich, Herbert. 1980. ‘Coherent Excitations in Biological Systems, 1980.’ Networks governed by prime number sequences encode symmetry-breaking and resonance phenomena across biological and physical systems. [[23],[27]] In GNPSCS terms, these prime-modulated oscillators resemble coherence attractors that anneal phi pathways through networked resonance geometries. [[24],[28]] Bandyopadhyay’s PPM generates geometric patterns— triangles, pentagons, singularities—by projecting prime factor relationships into oscillator phase space, forming a lattice of decision nodes that mirror implicate-explicate transitions. [[23],[27]] This architecture is not algorithmic but topological, replacing Turing-style computation with phasebased morphogenesis. [[25]] In ‘Nanobrain,’ he describes how the PPM governs nature’s intelligence by linking all symmetries through prime modulation, enabling a time crystal brain model composed of dielectric and cavity resonators. [[24],[27]] The GitHub documentation for OpenGML further elaborates how the PPM transforms n-dimensional data into nested geometric forms, aligning with the phi connectome’s annealing logic. [[26]] His Springer chapter on time crystal computing proposes that prime-number-based oscillator networks can replace conventional programming entirely, using geometric musical language (GML) to encode decisions as phase structures. [[25],[29]] These insights directly support GNPSCS protocols for coherence restoration, where prime-modulated oscillators serve as resonance scaffolds for phi pathway annealing. [[24] ,[26] ,[28] ,[30] ]
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Figure 6.7 - by author
Illustrating: A. The ceaseless Bohm holomovement from implicate to explicate to implicate orders between the Plenum-Phi Connectome (PL-PC) and the Gödel Non-Turing Non-Algorithmic Phase-Shift Computational System (GNPSCS), a non-deterministic, non-linear fractal. *SEE: (1) Nima Arkani-Hamed’s multi-dimensional geometric amplituhedron which represents scattering amplitudes (probabilities of particle interactions) as the ‘volume’ of a geometric object in a mathematical space called the positive Grassmannian, bypassing off-shell Feynman diagrams, offering a more elegant and efficient way to compute these amplitudes; and (2) Carlo Rovelli’s Loop Quantum Gravity (LQG), which posits that at incredibly small scales around the Planck length of 10-[35] meters, space has a granular structure and where classical concepts of space and time break down. LQG proposes that physical quantities such as distance and time are due to the relationship of more primitive ‘granules’ which are neither space nor time. B. Projection of the GNPSCS onto wall of Plato’s cave, i.e., our mis perception of reality based on Cartesian continuum mathematics; C. General relativity’s use of tensors is also based on Cartesian continuum mathematics in which mass-energy curves spacetime producing gravity; and D. The Higgs field is a scalar field that permeates all of space, giving mass to certain particles through interactions with the Higgs boson (H[0]), a spin-0 particle that represents a tiny ripple in the field. This mechanism is roughly analogous to how moving through a field of molasses would slow objects down—the more strongly a particle interacts with the Higgs field, the more mass it acquires. Photons don’t interact with the Higgs field at all—so they remain massless and zip through space at light speed. The Large Hadron Collider (LHC) provided evidence of the Higgs boson in 2012. It is important to note that the Higgs field and Higgs boson do not directly create gravity. Rather, gravity is the result of the curvature of spacetime caused by mass and energy, as described by Einstein's General Theory of Relativity. In other words, the Higgs field gives particles their mass, and then those masses interact with spacetime to produce the gravitational effects we observe; and E. In the nonCartesian PC/GNPSCS, oscillators account for mass, but, in contradistinction to General Relativity, gravity is posed as scale-invariant/conformal (SIC) electro-magnetic tunneling information, i.e., ‘light.’ It is interesting that our fundamental religious text, Genesis, has the phrase: ‘let there be light.’ Is the GNPSCS the ‘reality’ while our Cartesian-based Turing mathematics is merely its ‘shadow’ on Plato’s cave wall? If so, it suggests the need for a fundamental shift in our understanding of the universe and our computational model.
Turing mathematics may be giving us a limited entropy-laden view of reality. It provides tools for understanding phenomena but remains confined to a linear, step-by-step framework. The GNPSCS relates to the work of Wheeler, Rovelli, Verlinde and the others involving the relationship of gravity, entropy, and information. [[24]-[39]] They are all touching on the idea of the GNPSCS, but their theories are limited because their adherence to Cartesian-based continuum mathematics. This essay posits that the GNPSCS, a non-linear, non-continuous, fractal mathematical system is a better model of reality. As Einstein put it: “As far as the laws of mathematics [our current Cartesian-based mathematics] refer to reality they are not certain, and as far as they are certain, they do not refer to reality.” Wheeler’s ‘it from bit,’ Rovelli’s loop quantum gravity (LQG), and Verlinde's entropic gravity show that all of these physicists recognize information as a fundamental aspect of reality. They have touched on the idea that gravity might emerge from deeper principles of information exchange and entropy, and their work highlights the interconnectedness of these concepts.
Nima Arkani-Hamed's and Rovelli's LQG may be touching on the idea of the GNPSCS, i.e., that our current mathematical system is limited. Arkani-Hamed has proposed a seemingly radical idea, the Amplituhedron, a geometric structure that simplifies quantum field theory calculations by removing reliance on space-time as a fundamental entity. He argues that spacetime, as we currently understand it, is not fundamental—‘spacetime is doomed,’ but rather an emergent or approximate concept, suggesting that spacetime will eventually be replaced by deeper, more fundamental structures in physics. This approach hints at a computational model independent of Cartesianbased mathematics, focusing on deeper, abstract relationships. His work challenges the continuum framework, suggesting that reality might be governed by discrete/fractal and geometric principles—a concept that resonates with the fractal nature of the PC/GNPSCS.
This aligns with the idea of networked, multidimensional structures (PC/GNPSCS) and suggests that spacetime emerges from more fundamental, discrete entities. Carlo Rovelli’s relational interpretation of quantum mechanics, which emphasizes that information and relationships—not intrinsic properties—define physical systems, departs from rigid Cartesian continuum models. His Loop Quantum Gravity (LQG) seeks to quantize spacetime itself, describing it as a network of discrete loops—spin networks labeled by SU(2) representations. Within the GNPSCS paradigm, networked oscillator clocks represent particles whose spin, in the Cartesian system, is a projection of phase coherence. Rovelli’s spin networks, encoding quantum geometry through entangled spin states, can be reinterpreted as configurations of entangled Block clock oscillators, each functioning as a localized phase node. GNPSCS reframes these not as quantized geometry but as networked phase coherence, with spatial structure emerging from oscillator relations across scales. This suggests that LQG’s discrete geometry may be a shadow of a deeper coherence structure—one in which SIC discretized imaginary Bloch clocks communicate via SIC tunneling informational gravity (y*), a phase-based substrate rather than a force field.
The work of these physicists does not explicitly describe a GNPSCS-like system, but they are attempting to uncover a more profound computational and physical reality. These efforts could pave the way for a paradigm shift akin to the PC/GNPCS model. Importantly, none of them has relied specifically on David Bohm’s work. Bohm proposed that reality consists of an ‘implicate order’ where everything is interconnected and enfolded, and an ‘explicate order’ that is the unfolded, observable reality. Lao Tsu’s ‘Tao Te Ching’ a fundamental Taoist text in which he says ‘When the Whole is Divided, the Parts Need Names,’ aligns with Bohm’s notion of the implicate order as ‘wholeness.’ In this essay the implicate order, the perceived depth of it at least as far as our current level of consciousness allows, is the Plenum PL and its relationship to the Phi Connectome PC and the explicate order GNPSCS. In Bohmian mechanics, the quantum potential guides particles in a deterministic yet non-local manner, hinting at a deeper informational substrate akin to the SIC oscillators in the GNPSCS. Basal Hiley worked on algebraic descriptions of quantum mechanics using Clifford algebras, which provide a mathematical framework for describing non-linear, non-continuous systems, and Cohl Furey, a mathematical physicist, has been exploring the connections between the Standard Model of particle physics and the mathematical structures of quaternions and octonions. Furey’s paper demonstrates how octonionic ladder operators can reproduce the correct electric charges and quantum numbers for one full generation of Standard Model particles—including the electron—using only division algebras. Her work delves into how these eight-dimensional numbers might underpin fundamental particles and forces. * SEE: Furey, C. (2016). Standard model physics from an algebra? arXiv: 1611.09182 [hep-th]. Furey, C. (2018). SU(3)(_C) x SU(2)(_L) x U(1)(_Y) as a symmetry of division algebraic ladder operators. arXiv: 1910.08395.
David Bohm and Basal Hiley explored the idea of a deeper reality beyond the Cartesian framework, culminating in their book * SEE: Bohm, D., & Hiley, B. J. (1993). The Undivided Universe: An Ontological Interpretation of Quantum Theory. London: Routledge. ‘Any deterministic approach to understanding nature is misguided.’
This essay posits that the universe is granular—that it is, a multidimensional, nonlinear, scaleinvariant conformal (SIC) entity composed of a network, discretized Bloch imaginary clocks. These clocks tick with each phase shift of an explicate-order Godel, non-algorithmic, non-Turing phase-shift computational system (GNPSCS). Within this framework, SIC oscillator-imaginary Bloch clocks—are separated by a SIC-defined distance, denoted p*, and communicate via SIC electromagnetic tunneling information, denoted y*. This granular, phase-coherent architecture has been historically misperceived through the lens of Turing-continuum mathematics, obscuring its true nature as a non-continuous, coherence-driven system.
At the subatomic level, tunneling information is conventionally perceived through bosonic mediators such as the Higgs boson (H[0]), understood as a ripple in the Higgs field. This field permeates space and interacts with particles to confer mass, though not gravity. According to the Standard Model, it endows fundamental particles like quarks and electrons with mass, enabling the structured matter we observe. This essay challenges that framework, proposing that the Higgs boson and field are artefacts of a Cartesian-based differential calculus that constrains our interpretation of quantum phenomena. In contrast, the GNPSCS paradigm suggests that mass arises from the frequency coherence of networked oscillators, with the Higgs field representing a scaled summation of these frequencies rather than a separate ontological substrate. While general relativity describes gravity as the curvature of spacetime caused by mass-energy—a view elegantly summarized by John Archibald Wheeler’s phrase, “Spacetime tells matter how to move; matter tells spacetime how to curve”—this essay posits that gravity is, instead, constituted by SIC electromagnetic information (y*) tunneling between oscillators within the PC/GNPSCS framework. In this view, gravity is not a geometric distortion but a phase-coherent information exchange, dissolving the artificial separation between mass and gravity and revealing a deeper substrate of oscillator-based coherence beneath both. This essay posits that the universe is granular, i.e., best described by fractal mathematics. * SEE: Reality Is Not What It Seems: The Journey to Quantum Gravity, (2014); and The Order of Time, 2018 Riverhead Books, Penguin Random House; both books by Carlo Rovelli. His work deals with the subatomic scale. This essay expands on Rovelli’s and Bandyopadhyay’s ideas and poses reality as a multidimensional nonlinear scale-invariant conformal (SIC) entity, comprised of networked discretized Bloch imaginary clocks which tick with each Phase Shift of a Godel non-algorithmic non-Turing Phase- Shift computational system GNPSCS, and where these Bloch imaginary clocks are separated by a SIC distance p*, and communicate with one another by SIC electromagnetic tunneling information y* = SIC gravity/force/information.
Such a system appears or is perceived through the lens of our Turing continuum mathematics as our current cosmos with all its unanswered questions. By contrast, this essay posits that a more fundamental mathematical paradigm, the PC/GNPSCS can begin to answer some of these questions. For example, our perception of gravity/force at all scales is proposed, instead, as scale- invariant/conformal electromagnetic tunneling information (y*) accounting for our perception of: the subatomic strong force; gravity at the solar system scale; dark matter at the galactic scale; dark energy at the intergalactic scale; and Hawking radiation at the eon scale. The Higgs boson has spin ‘0’ which is our perception of the summation of tunneling information (SUM y*) over the whole range of the GNPSCS—relating to oscillators of the GNPSCS where the frequency of oscillation is related to mass. Most particles, like electrons or quarks, have a spin of 1/2, while force-carrying particles like photons and gluons have a spin of 1. The spin-0 nature of the Higgs boson makes it a scalar particle, meaning it doesn't have a preferred direction—it’s the same no matter how it is rotated in space. The spin-0 nature of the Higgs boson plays a critical role because it allows the Higgs field to interact uniformly with all particles, regardless of their direction or orientation in space. The Higgs field can couple to particles based only on their intrinsic properties, like mass, without being influenced by their spin or the way they’re moving. The Higgs boson's spin-0 property ensures that its interactions with other particles are scalars, giving particles mass without a directional bias, i.e., mass is the same in all directions.
This essay posits that if the fundamental nature of the universe is granular and involves discrete elements like imaginary Bloch clocks of the PC/GNPSCS, then bosons—including the Higgs boson—could be emergent phenomena that arise as effective representations of a deeper reality. They could represent the way information is exchanged between these granular elements via SIC electromagnetic tunneling. In this framework, bosons correspond to quantized modes of information transfer. The tunneling process might manifest as the behavior we attribute to bosons in our current physics. In such a schema, bosons would represent the way information is exchanged between these granular elements via SIC electromagnetic tunneling. If the universe’s substrate is granular and structured by discretized time frameworks like Bloch clocks, then bosons, including the Higgs boson, may be emergent rather than fundamental entities. Quantum gravitational models at the Planck-scale support this interpretation, where bosonic excitations arise from phase dynamics across coherence-preserving lattice structures. *SEE:[Quantum gravitational decoherence from fluctuating minimal length - Petruzziello & Illuminati (2021). A lattice bosonic model as a quantum theory of gravity - Gu & Wen (2006); Does Quantum Gravity Happen at the Planck Scale? - Jacobs (2025).]
Within this paradigm, SIC electromagnetic tunneling enables discrete quantum information exchange, casting bosons as quantized mediators of coherence rather than elementary particles. An entropic and informational view of bosonic modes aligns with statistical mechanics and holographic models of gravity, reinforcing the notion that spacetime curvature and field behavior emerge from structured information flow. The Higgs boson, accordingly, becomes a localized excitation—a ripple within a Higgs field arising from granular phase coupling and networked attractor dynamics embedded in coherence substrates like the GNPSCS. PC/GNPSCS Bloch clock phase dynamics describe how it is that tunneling and synchronization among discrete imaginary time nodes can yield field-like emergent phenomena, with mass-producing bosonic properties appearing as macroscopic consequences of microscopic phase behavior. Experimental results from phase-locked atomic arrays, Bloch oscillation regimes, and high-harmonic generation in nonlinear media substantiate this model, demonstrating how structured phase coherence can manifest as quantized boson-like behavior without requiring particle fundamentalism. *SEE: Zizzi, P. (2003). Spacetime at the Planck Scale: The Quantum Computer View. arXiv: gr- qc/0304032; Strand, H. U. R., Eckstein, M., & Werner, P. (2015). Nonequilibrium Dynamical Mean-Field Theory for Bosonic Lattice Models. Phys. Rev. X 5, 011038. DOI: 10.1103/PhysRevX.5.011038; UNSW Physics. The Planck scale: relativity meets quantum mechanics meets gravity.
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Figure 6.8-by author; asterisk (*) denotes SIC
Illustrating the structure of oscillators* separated by φ* and fractal tunnels* through which EM information (γ*) travels. This essay posits a radical departure from accepted Cartesian-based frameworks. Figure 6.8 illustrates fractal tunnels between oscillators of the PC/GNPSCS, where the fractal dimension of the tunnel aligns with the frequency of the oscillators it connects. If the cosmos is SIC and comports with Lori Gardi’s interpretation, then at the subatomic scale γ* is perceived in our current Cartesian mathematical paradigm as the strong force. Carlo Rovelli argues that particles do not arise from intrinsic matter but from relational structures and informational interactions. This is consistent with the view that oscillators are phase-based entities, not material ones. This essay proposes that space, time, matter, the strong and weak forces, electromagnetism, and gravity are emergent from a deeper computational structure, the PC/GNPSCS.
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Figure 6.9- y author
Illustrating relationship of: A. PC/GNPSCS SIC oscillators (Osc*) communicating with SIC EM radiation (y*) at a SIC distance (p*) through a SIC fractal tunnel; B. Our current Cartesiancontinuum mathematics perception of the PC/GNPSCS as Einstein’s mass-energy (m), curved ST, and gravity. This essay posits that A. is the reality, while B. is akin to a shadow on Plato’s cave wall. C. Illustrates the relationship of the frequency of oscillators of the PC/GNPSCS to our Cartesian continuum-based perception of the: strong force; gravity with the Kolmogorov-Arnold- Moser (KAM) effect on planetary orbits; galaxy-frequency dark matter (DM); inter-galactic frequency dark energy (DE); and at the aeonic frequency Hawking radiation and Hawking points on the cosmic microwave background (CMB). D. Comparing—using a fanciful musical analogy— oscillator frequencies of the PC/GNPSCS with the increasing width of guitar frets and lower frequencies: SF-strong force sub-atomic/gluon frequency; G-gravity at solar system frequency; DM-dark matter at galaxy frequency; DE-dark energy at inter-galaxy frequency; and at aeonic frequency HR/HP, Hawking radiation and Hawking points on the cosmic microwave background (CMB) on a subsequent aeon. In this sense Hawking radiation is information ‘left over’ from a current eon that tunnels to a subsequent eon, carrying, as it were, that information to a subsequent aeon. In Penrose’s CCC, there is neither time nor gravity at the end of an aeon. By contrast, in the PC/GNPSCS proposed in this essay, there is no need to claim that gravity doesn’t manifest in the current aeon in order to deal with entropy. Rather, electromagnetic energy/Hawking radiation is posed as both information and SIC force, including what we perceive as gravity, and there is no abrupt border between eons, but rather a phase-shift transition reflecting Wheeler’s comment: ‘the boundary of a boundary is zero.’
At the cosmic scale, y*—the tunneling of SIC electromagnetic information through a fractal tunnel—is perceived as time dilation, manifesting observationally as the redshift of light near a black hole horizon. In the PC/GNPSCS model posited in this essay, this redshift is not due to spacetime curvature/gravity, but arises from the separation of light frequencies as they tunnel through an extremely high-dimensional fractal structure. If a black hole is understood not as a collapsed mass but as a coherent oscillator node within the PC/GNPSCS framework, then two consequences follow: (1) the phenomenon of spaghettification as an object passes through the horizon of a black hole would not occur, as the oscillator’s phase continuity prevents the extreme tidal gradients predicted by general relativity; and (2) the notion of a horizon or interior becomes ill-posed. A black hole horizon is reframed not as a physical boundary, but as a phase transition zone—a shift in computational modality, where the governing oscillator regime changes. Asking what lies ‘inside’ a black hole becomes a category error, akin to asking what is inside a frequency. There is no interior, only a transition in phase coherence. Matter itself emerges from interference patterns among, and frequencies of networked oscillators, and what we call a black hole is neither black nor a hole, but an oscillator node in a MNDIBTC. Leonard Susskind’s metaphor of “smaller and smaller propellers” near a black hole horizon illustrates how spacetime and information dynamics become increasingly fine-grained and phase-shifted as one approaches the horizon. Rather than a physical boundary, the horizon marks a computational phase transition—where the governing oscillator regime changes and classical notions like “interior” lose meaning. In this view, a black hole is not a hole but a node in a network of quantum oscillators, and matter itself emerges from interference among these oscillators.
The metaphor of “smaller and smaller propellers” near a black hole horizon is most closely associated with Leonard Susskind’s work on black hole complementarity and the stretched horizon concept. *SEE: “The Stretched Horizon and Black Hole Complementarity” by Leonard Susskind, Larus Thorlacius, and John Uglum. Read it on arXiv Published in Physical Review D, 1993. In his 2021 paper Three Impossible Theories (arXiv:2107.11688), Susskind explores a deep conflict in theoretical physics by presenting three principles that cannot all be true at once: quantum mechanics always preserves information, general relativity guarantees smooth passage through a black hole horizon, and black hole complementarity allows different observers to have consistent but distinct experiences. When applied to black holes, especially in the context of entanglement and the firewall paradox, these principles clash—forcing a reevaluation of our understanding of spacetime and information. Susskind argues that something fundamental must give, pushing us toward a new framework where black holes are not spatial voids but computational nodes in a quantum network. This tension invites exploration into holography, quantum error correction, and the emergent nature of spacetime itself where spacetime and information dynamics are governed by deeper, emergent structures.
In terms of the GNPSCS framework, the Big Bang is best understood as a phase change occurring when the lowest-frequency oscillator (Bloch clock) within the PC/GNPSCS lattice ticks past its modal midnight. This transition does not mark the emergence of spacetime from a singularity, but rather a reconfiguration of networked phase relationships that initiates a new regime of resonance. Just prior to this phase shift, the current and subsequent eon exist in superposition. The collapse of that cosmic superposition is a phase change to the next eon.
At the scale of our solar system (illustrated above in figure 6.9 C) the orbital relationships among planets and moons exhibit quasiperiodic stability that aligns with the Kolmogorov-Arnold-Moser (KAM) theorem. The KAM theorem explains why certain systems—like planets orbiting a star— can stay stable over time, even when small forces or disturbances are present. In complex situations like the three-body problem, where three objects tug on each other with gravity and things can get chaotic, KAM shows that many smooth, repeating paths still hold together. This means that even in messy, unpredictable systems, some patterns survive, helping scientists understand how long-term stability is possible. Wikipedia has good article on the KAM theorem.
Within the PC/GNPSCS framework, planetary stability is reinterpreted as the emergent result of recursive phase-locking among oscillatory systems embedded in a fractal computational substrate, rather than as a consequence of purely gravitational mechanics. The solar system is conceptualized as a resonant lattice, where each planet functions as a node in a multi-scale coherence network. Orbital dynamics, including anomalies like Mercury’s precession, are reframed as phase drifts within this hierarchical oscillator structure—suggesting that relativistic curvature effects may be macroscopic shadows of deeper coherence fluctuations. The observed golden ratio relationships in planetary spacing further support this view, aligning with known principles of oscillator separation in phase-synchronized systems, where cp-spacing minimizes destructive interference and maximizes modal resilience. In this paradigm, the solar system behaves less like a mechanical clock and more like a harmonic instrument—its long-term stability arising from modal synchrony, fractal geometry, and coherence resilience across scales.
Physicists Dennis Clougherty and Nam Dinh recently solved a century-old problem in quantum physics: how tiny systems like atoms lose energy over time without violating quantum rules. Instead of treating damping as simple energy loss, they showed it is a shift in how uncertainty is distributed—like squeezing one part of a system while another stretches. Their exact solution uses a Bogoliubov transformation to describe a “squeezed vacuum” state, preserving the integrity of quantum mechanics while explaining how oscillators settle down. Their proof aligns with the PC/GNPSCS model’s view of system transitions as recursive, coherence-preserving modulations rather than decay. * SEE: Clougherty, D. P., & Dinh, N. (2025). Exact solution for quantum damping: A squeezed vacuum approach. Physical Review Research, 7(3), 033201. https://doi.org/10.1103/PhysRevResearch.7.033201.
In the standard Cartesian continuum model, space and time are treated as smooth and continuous, while forces like gravity act on objects within that framework. When galaxies rotate faster than expected or the universe expands too quickly, scientists introduce concepts like dark matter and dark energy to explain the discrepancies. But in the PC/GNPSCS framework, these effects may not require new substances—they could instead be the result of phase relationships between networked oscillators. What looks like extra gravity or accelerated expansion might actually be caused by delays, mismatches, or drifts in how these oscillators synchronize across scales. In this view, dark matter and dark energy are not necessarily real entities, but artifacts of attempting to describe a rhythmic, fractal universe using linear, force-based mathematics. This shift in perspective replaces substance-based explanations with a process-based understanding rooted in coherence and timing.
At the scale of our solar system, the relationship of planets and moons to the sun is consistent with the Kolmogorov Arnold Moser (KAM) model. Additionally, the PC/GNPSCS may also predict the precession of Mercury. As light propagates, it follows paths determined not by geodesics in curved spacetime, but by optimal phase trajectories through a fractal lattice of oscillators. For example, when light passes near a massive object, the local oscillator coherence is denser and more tightly phase-locked, effectively altering the refractive geometry of the fractal tunnel. This results in a deviation of the light’s path, analogous to general relativity spacetime distortion by lensing, but driven by phase modulation rather than the metric curvature in general relativity. The eclipse observation (In 1919 Eddington confirmed Einstein’s prediction of 1.75 arcseconds of deflection) is re-interpreted in the PC/GNPSCS paradigm where it is explained, not by spacetime warping, but rather by light passing through a higher-dimensional fractal pathway. The PC/GNPSCS functions through phase-shifted oscillator interactions across scales, forming a fractal computational substrate that could underlie both cognition, living organisms, and spacetime. *SEE: “Fractal Differential Geometry V: Light Propagation and Redshift in FDG- Modified Kerr Spacetime” by Robert W. Somazze on Academia.edu.
OVERALL: Fractalized tunnels—structured pathways formed by networked, scale-sensitive geometries—allow SIC EM radiation (y*) to propagate through the PC/GNPSCS lattice in a way that preserves coherence across vastly different frequency domains. These fractal tunnels are not physical conduits in the classical sense, but phase-aligned corridors through which electromagnetic signals travel. At the subatomic level, this could manifest as quantum coherence and controlled collapse; at the biological level, as synchronized metabolic or neural activity; and at cosmic scales, as, orbital stability, or even the apparent effects of dark matter and dark energy. Rather than being anomalies or forces, this essay posits that phenomena like gravity, expansion, and quantum collapse are to be reframed as emergent properties of how SIC electromagnetic radiation navigates these fractal pathways.
At the scale of life and an organism’s SIC MAM* structure, vicinal water (A) also acts as a fractal pathway resulting in a delay in transmission of coherent light and coherent sound such that SIC M, and M* can have ‘time’ to react at all scales in order to maintain global quantum coherence of the organism. Coherent light (biophotons) and coherent sound (phonons) are transmitted through a matrix of vicinal water and hydrated biomolecular structures, but with a purposeful delay. This delay allows SIC M and M* modules to synchronize, enabling global coordination of chemical and mental states. Rather than a flaw, the delay functions as a temporal buffer, preventing decoherence and preserving scale-integrated coherence across networked oscillators.
Life, as a frequency band within the PC/GNPSCS field, depends on this adaptive timing to remain stable, responsive, and unified. We symbolize fractalized vicinal water as a triangle containing a fractal symbol: ( G[1] ).
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Figure 6.10- y author
Illustrating vicinal water as a fractal pathway for the transmission of coherent light and coherent sound throughout the organism. Coherent light (laser) and coherent sound (phonons) are transmitted through a fractal matrix of vicinal water and hydrated biomolecular structures, but with a purposeful delay.
7. The Pre-Copernican Earth-centered Model.
For over a millennium, the geocentric (Earth-centered) model dominated cosmological thought. Originating with ancient civilizations such as the Babylonians and Egyptians, it was later formalized by Aristotle and refined by Ptolemy in the 2nd century CE. [[1], [2], [3]] Ptolemy’s system explained planetary motion using deferents and epicycles—nested circular paths designed to account for retrograde motion, where planets appeared to reverse direction in the night sky.
The deferent was a large orbit centered near Earth, while the epicycle was a smaller orbit whose center moved along the deferent. This ‘circles within circles’ approach was geometrically elegant and aligned with the philosophical belief that the circle represented divine perfection. Despite its mathematical sophistication, the geocentric model began to lose ground after Nicolaus Copernicus proposed a heliocentric (Sun-centered) model in 1543. [[4], [5], [6]] Copernicus retained circular orbits and even epicycles, but his model placed the Sun at the center, simplifying explanations of planetary brightness and retrograde motion.
However, it wasn’t until Galileo’s telescopic observations and Kepler’s laws of planetary motion—introducing elliptical orbits—that the heliocentric model gained empirical traction. [[7]] Even into the 17th century, some astronomers clung to modified geocentric systems, such as Tycho Brahe’s geo-heliocentric hybrid. Transition from geocentrism to heliocentrism was not merely scientific—it was philosophical. The belief in circular motion as a symbol of cosmic harmony persisted, even as elliptical orbits proved more accurate.
This tension between aesthetic ideals and empirical reality remains relevant today. Physicist Sabine Hossenfelder critiques the modern scientific tendency to favor “beautiful” theories—those marked by symmetry, simplicity, or elegance—even when they lack experimental support. [[8]] In her book *SEE: Hossenfelder, Sabine. Lost in Math: How Beauty Leads Physics Astray . Illustrated edition. New York: Basic Books, 2018. ISBN: 978-0465094257, she argues that this aesthetic bias has led to stagnation in theoretical physics, with frameworks like supersymmetry and string theory failing to yield empirical breakthroughs.
Einstein himself cautioned against conflating mathematical certainty and models with physical truth, “As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.” Overreliance on mathematical elegance can become a conceptual straightjacket—just as the pre-Copernican insistence on circular orbits delayed the acceptance of elliptical ones. Today, our Cartesian-based continuum mathematics, while powerful, has introduced complications in understanding phenomena like the big bang, dark matter, dark energy, life, and consciousness. The lesson from history is clear: beauty may inspire, but reality must decide.
Illustrations are not included in the reading sample
Figure 7.1 after Wikipedia-deferent and epicycle-modified by author
Illustrating the pre-Copernican, Ptolemaic Earth-centered view of the solar system based on: (1) the belief that the Earth E was the center of the ‘heavens’; and (2) the ‘beauty’ of circular orbits. In the figure: E-Earth, D-Deferent, Epi-Epicycle, Pl-planet traveling around the epicycle, Antobserved anterograde movement of planet, Ret-observed retrograde movement of planet.
8. The Implicate-order Plenum-Phi Connectome, and the explicate-order GNPSCS.
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Figure 8.1-by author
Einstein’s intuitive quote: “As far as the laws of mathematics refer to reality they are not certain, and as far as they are certain, they do not refer to reality,” embodies the essence of this essay.[1] Our current Cartesian-based differential calculus continuum mathematics works well for macroscopic objects, but not for submicroscopic objects in quantum mechanics. Hilbert vector space, dealing with imaginary mathematics, has served as a temporary substitute for a deeper concept entailed in Bohm’s implicate-order (PL-PC in this essay) and unfoldment as the explicateorder GNPSCS. [2, 3] Bohm proposed that quantum theory reveals an ‘undivided wholeness in flowing movement’—a radical shift from the worldview of classical physics. He argued that particles are not isolated entities but abstractions from a deeper, interconnected process, which he called the holomovement to describe the fundamental, undivided flow of reality. It’s not a movement within space and time, but rather the ground from which space, time, and all phenomena emerge. This concept suggests that everything in the universe is enfolded into everything else, and that reality is fundamentally a unified, dynamic whole. [15]
Heretofore, physics and mathematical models have been based on Cartesian coordinate systems using linear and curvilinear coordinates, matrices, and tensors, but all these methods carry within their structure the notion of individual entities existing in space and time, interacting with one another causally and locally at infinitesimally short distances over infinitesimally short times, constituting a continuum where Ax/At ^ dx/dt, i.e., a machine in which direct, local cause-effect relationships between individual parts lead to the behavior of the whole. By contrast, quantum mechanics has taught us that the undivided whole is the reality and our spacetime machine-like interpretation is only an approximation. One of the most compelling references for the idea of ‘wholeness’ comes from *SEE: David Bohm’s interpretation of quantum mechanics, particularly in: ‘Wholeness and the Implicate Order,’ Routledge, 1980.
Quantum Mechanics implies granularity at the smallest scales, like energy quanta and discrete states. The Planck length is often regarded as a minimum ‘size’ in spacetime, beyond which the concept of continuity may break down. Moreover, the notion of a mass compressed into an infinitesimal region—forming a ‘black hole’ from which no information about the particle can be retrieved—calls into question the reliability of our physical concepts.
Fractal geometry, proposed by Benoît Mandelbrot, provides a framework for describing selfsimilar, irregular structures that appear in nature as clouds, coastlines, or galaxy distributions. [[6],[7]] Fractals challenge the idea that smoothness/continuity—the existence of a defined slope (d[F(x)]/dx) at all points on a curve is a universal property. That is, not all curves are smooth; some can be so jagged or complex that they don’t have a clear slope at any point. Carlo Rovelli’s Loop Quantum Gravity is one approach to reconciling quantum mechanics with general relativity. It suggests that spacetime is composed of finite loops or granules, neither of space nor time, which by their interactions ‘weave’ the fabric of what we perceive as a continuous spacetime at macroscopic scales. This essay posits that the oscillators of the GNPSCS are something like the loops of Carlo Rovelli’s loop quantum gravity LQG. The GNPSCS and its oscillators and their interactions give rise to spacetime like the loops in Rovelli’s LQG. By contrast, however, gravity in the GNPSCS is represented by Scale-Invariant/Conformal Electromagnetic Tunneling Information (y*) from the subatomic scale as bosons to increasing scales as: gravity, dark matter, dark energy, and ultimately as Hawking radiation representing information tunneling between successive eons. Insofar as the multidimensional networked discretized imaginary Bloch clocks of the GNPSCS can tick either forward or backward in imaginary time, there is no preferred forward arrow of time in the GNPSCS, i.e., there is no entropy. It is only in our Cartesian-based continuum Turing mathematics that we perceive an arrow of time at large scales and note a oneway entropic death tending, inevitably, to thermodynamic equilibrium and the notion of a big bang, inflation, and death of the universe. It is posited, however, that these are all artefacts of our mathematics. It might be that ‘time’ occupies multiple dimensions, allowing for bidirectional or even multidimensional movement. This could imply that entropy, as we understand it, is a statistical effect rather than an intrinsic property of reality. Epistemic vs. ontic interpretations of quantum mechanics propose that entropy arises from our inability to track all microscopic degrees of freedom, rather than its being fundamental. [8 ^ 11]
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Image from Wikipedia-monadology.. .a page of Leibnitz’s work on monads.
Some of the properties of the PC and GNPSCS were foreshadowed by Gottfried Wilhelm Leibniz who imagined monads as tinv, indivisible elements (think of Rovelli’s loop quantum gravitv or the discretized imaginarv Bloch clocks of the GNPSCS) which have no properties like atoms but which, nonetheless, comprise everything. Rather, they are like individual synchronized clocks (compare svnchronization to phase shifts of the GNPSCS where everv clock ticks with everv phase shift computation of the GNPSCS), every monad reflecting the entire universe from its own unique perspective, explaining why everything in the universe appears to work together (in the GNPSCS, SIC electromagnetic tunneling information (y*) ‘ ties together’ the oscillator clocks such that they can be said to reflect Leibnitz’s idea of why everything in the universe appears to work together).
Moreover, Leibnitz monads are not equal (this comports with different oscillator frequencies of the GNPSCS), some being very basic, making up inanimate matter, while others are more complex forming living matter (the GNPSCS and the Orch-OR theory do not make this distinction, allowing for consciousness and life as inherent properties of the cosmos). Leibniz’s ultimate monad is God—perhaps akin to what David Bohm describes as the unknowable depths of inwardness within the implicate order, inaccessible at our current level of consciousness.
From a religious or philosophical standpoint—particularly within Christianity—God is revealed through Scripture, yet personal knowledge often arises through faith or moments of divine encounter. A striking example is the zealous Pharisee Saul’s transformation, where he becomes Paul following a direct encounter with the divine (Acts 9:1-19 in the New Testament). In Hermetic philosophy, God is conceived as the ALL—the ultimate reality—knowable only through faith, as suggested by Kierkegaard’s “leap of faith” or a sudden epiphany. * SEE: Wikipedia: The Kybalion: A Study of the Hermetic Philosophy of Ancient Egypt and Greece, by Three Initiates, Yogi Publication Society, 1908]
9. The Big Bang, Dark Matter, and Dark Energy as Artefacts of Cartesian Mathematics.
This essay proposes that many unresolved cosmological problems—such as the Big Bang, inflation, quantum gravity, and the nature of dark matter and dark energy—stem from the limitations of Cartesian-based continuum mathematics. It is posited that a paradigm shift toward non-continuum fractal mathematics, specifically a Godel Non-Turing Non-Algorithmic PhaseShift Computational System (GNPSCS), may resolve these issues by modeling reality as a coherence-driven, implicate-explicate computational structure. [[3],[4],[5]] Einstein intuited the mismatch between mathematical certainty and physical reality in his comment: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” The visionary Nicola Tesla echoed this sentiment in a widely-attributed aphorism that resonates with his visionary approach to physics and invention: ‘If you want to find the secrets of the universe, think in terms of energy, frequency, and vibration.’ [[1], [2]]
The GNPSCS operates beyond classical Turing computation, incorporating Godel incompleteness, transcending algorithmic constraints. It is a phase-shift system arising from the implicate order via the phi connectome (PC), a self-forming, self-maintaining structure. An extension of Anirban Bandyopadhyay’s time crystal mode, the GNPSCS is a Multi-Dimensional Networked Discretized Bloch Clock Time Crystal (MNDIBTC), a ‘granular’ structure comprised of SIC imaginary Bloch clock oscillators (Osc*) separated by scale-invariant/conformal SIC golden ratio barriers, i.e., p* « (1.618...*). [[4],[6]] These discretized imaginary Bloch clocks communicate across scales through SIC fractal tunnels via SIC electromagnetic radiation (y*), forming a lattice of phase-coupled oscillators. Each phase-shift computation of the GNPSCS, a tick of every SIC oscillator imaginary Bloch clock corresponds to a phase transition, enabling computation through resonance rather than stepwise logic. This clique-based response mechanism contrasts sharply with Turing machines, which rely on step-wise and sequential, energy-consuming and entropy-producing operations. [[3], [6]] Our current AI Turing machine systems require inordinate amounts of energy, whereas the brain, posed here as a quantum computer, operates using approximately the energy of a 20-Watt light bulb.
Time crystals—structures that exhibit periodic motion without energy consumption—offer a physical analogy for GNPSCS dynamics. Unlike conventional systems, time crystals remain in a non-equilibrium state indefinitely, breaking temporal symmetry and resisting entropy. The GNPSCS leverages this behavior to encode information through phase transitions, modeling physical processes as emergent from a deeper non-Cartesian, non-Boolean computational substrate. [[7], [8], [9]] The GNPSCS employs imaginary-numbered geometries to describe phenomena beyond real-number physics. Its scale-invariant SIC architecture aligns with quantum information theory, where SIC electromagnetic tunneling allows Bloch clocks to remain interconnected across distance and scale. SIC tunneling electromagnetic information (y*) preserves coherence while enabling non-local computation, akin to quantum entanglement and unitary evolution in qubit systems. [[10],[11]] The PC/GNPSCS paradigm suggests that the universe is not a deterministic, mechanistic machine, but rather a coherence-driven computational manifold, where physical laws emerge from deeper dynamics. [[12]]
10. Bohm’s Implicate Order, the Holomovement, Scale-Invariant/Conformal Superpositions and Collapse of the Wave Function as Phase Changes.
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Figure 10.1 -by author
Illustrating imaginary Bloch clock oscillators of the PC ticking past modal midnight MN. Upward-curving arrow (E) on the clock represents explication/unfolding from the PLENUM/PC, and downward-curving arrow (I) on the clock represents implication/enfolding back to the implicate order PLENUM/PC, i.e., Bohm’s holomovement.
Networked oscillator clocks within the GNPSCS framework tick, not by linear time, but by Godel phase-shift computations. [[5], [6]] These transitions are not mere temporal markers but SIC quantum- to-cosmological operations: implication corresponds to superposition, while explication denotes wave-function collapse—a phase shift from the quantum and all intermediate scales, to the cosmic scale. At the quantum scale, a phase shift is explained as collapse of the wave function associated with an observation. *SEE: Wikipedia. ‘Copenhagen Interpretation’ of Niels Bohr and Werner Heisenberg. At the cosmic scale, a phase shift represents the end of an eon, not by entropic death or a fiery bounce, but by the enfolding of a previously unfolded implicate structure. [[1], [5]] This viewpoint reframes the succession of Penrose eons in his Conformal Cyclic Cosmology (CCC). It posits, instead, that each new eon is not born from a singularity, but rather emerges from the collapse of a superposed state spanning past and future eons. [2, 3] The GNPSCS replaces the big bang with a ‘no boundary’ phase-change computation. Since the implicate order and GNPSCS are pre-spacetime, the notion of one cosmos following another in a temporal sequence becomes meaningless. The interval between enfolding and unfolding—between ticks of the imaginary Bloch clocks—could span milliseconds or 10[1000] years.
Consciousness may also operate in this way, being comprised of explicated moments stitched together like cinematic frames, giving the illusion of continuity. William James’ theory of conscious moments comports with this view: consciousness is not a continuous stream but a succession of discrete moments/pulses. This essay proposes that each moment of consciousness is an explication of the implicate order, and like an electron in a bubble chamber, continuity is illusory. The electron’s path is a series of explications-implications, not a continuous trajectory. [[4]] David Bohm’s implicate-explicate model claims that the explicate order is a projection from a deeper implicate reality. [[6]] The GNPSCS’s scale-invariant conformal architecture allows this logic to apply across domains—from electrons to eons. The controversial Cognitive-Theoretic Model of the Universe (CTMU), proposed by the equally controversial Chris Langan, shares this idea, i.e., reality as a self-configuring, self-processing language mirrors GNPSCS’s recursive implicate-explicate logic. [7] Both frameworks suggest that spacetime is emergent, not fundamental—a view increasingly supported in theories of quantum gravity and cosmology. [8]
11. A Novel Medical Paradigm.
Heretofore, organisms have been treated as if they were simple biochemical factories, operating in three-dimensional bulk water described by Cartesian continuum differential equations of physical chemistry, leading to our current mechanistic understanding of living organisms as machines, i.e., ‘mechanistic medicine.’ However, as posited in this essay, insofar as an organism represents a frequency range of the GNPSCS, the organism is to be treated as a non-linear Godel computer (GNPSCS), a coherent ‘whole.’ This implies it is a misconception to think that treating one part of an organism can occur in isolation, without influencing the system as a whole or triggering unintended side effects across multiple scales.
Western materialist, deterministic ‘mechanistic medicine’ has been interacting with the organism as if it were a collection of parts, a machine in which one can produce specific effects to specific ‘parts’ of the machine with various combinations of chemicals, radiation, and surgery without affecting the whole organism. Importantly, mechanistic medicine fails to include ‘mind’ (placebo effects and non-traditional treatments such as acupuncture, etc.) as essential parts of its treatment paradigm.
Just as quantum mechanics has unveiled our error in treating the cosmos as a machine comprised of several separate parts as described by Cartesian-based infinitesimal linear mathematics, so too have we been in error treating the organism as if it were comprised of several separate parts interacting locally and deterministically. Consequently, ‘mechanistic’ medical treatments often lead to unanticipated adverse results explained as ‘side effects.’ Accordingly, new pharmaceuticals or treatments require costly animal and human trials. The new paradigm proposed here, however, might allow us to pre-determine side effects as computable alterations in the global quantum coherence of an organism. Moreover, non-mechanistic medicine aimed at restoring an organism’s global quantum coherence (GQC) could lead to novel therapies—and perhaps even a means of slowing the aging process. This essay posits that the organism can be represented by the scaleinvar iant/conformal (SIC) symbol, MAM* where M, and M* represent, at increasingly larger scales: atoms, molecules, macromolecules such as DNA, structures such as the mitochondrion, cell, tissues, organs, and the entire organism, where A = vicinal water, the quasicrystal ‘twodimensional sheet’ of ordered water which separates M and M* at all scales and controls the transmission of ordered photons and ordered sound (via the scaled-up superradiance of microtubules as in the Penrose-Hammeroff Orch-OR theory) allowing for near-instantaneous transmission of coordinating information throughout the entire organism. [[11],[12]]
SECTION A of Chapter #11
Traditional medicine has been treating the organism as a biochemical machine operating in bulk water, modeled by the differential equations of physical chemistry based on Cartesian continuum mathematics. This mechanistic paradigm assumes that biological systems behave like Turing machines, with local cause-effect relationships based on simple linear continuum mathematics. Under this regime treatments have been designed to target isolated ‘parts’ of the body using chemicals, radiation, and surgery, often ignoring systemic coherence and the role of ‘mental states’ and consciousness. [[1]] To be sure, because mechanistic medicine has shown great success in treating bacterial infections, and the eradication of many diseases through inoculation, there remains a reluctance on the part of organized medicine and the pharmaceutical industry to entertain these ideas. Yet, the potential benefits to humanity, and the likely development of vast new and profitable income sources lie awaiting for the next generation of visionary entrepreneurs. If the organism is understood as a frequency range of the Godel Non-Turing Non-Algorithmic PhaseShift Computational System (GNPSCS), then it must be treated as a nonlinear, coherence-driven whole. [[2]] The GNPSCS framework posits that biological systems are a Multi-dimensional Networked Discretized Imaginary Bloch Clock Time Crystal (MNDIBTC), in which every imaginary Bloch clock ticks with each phase-shift computation. Scale-invariant/conformal (SIC) Bloch clocks are separated by (SIC) golden ratio barriers (p* = 1.618...*) preventing mutual destructive resonance, enabling coherent communication across all scales via SIC electromagnetic radiation/information (y*). [3]
The mechanistic approach has led to unforeseen systemic consequences—‘side effects’—often requiring further interventions, compounding complexity and cost. [[4]] Moreover, mechanistic medicine excludes the role of mind, including the placebo effect, and fails to consider the possible benefits of acupuncture, for example, and other non-traditional healing methods. [[5]] Quantum biology and nonlinear systems theory challenge this view. Just as quantum mechanics revealed the inadequacy of treating the cosmos as a deterministic machine, so too mechanistic medicine might well benefit by evolving beyond Cartesian assumptions. [[6]] The GNPSCS model suggests that any perturbation may affect the organism globally. [[7]] Disruption of the GNPSCS’s global coherence—specifically the integrity of its MNDIBTC structure—may underlie disease and aging. Perhaps it might be a worthwhile area for investigation as to whether a means of restoring and maintaining coherence might mitigate decoherence-related pathologies. [[8]] Could this novel approach open the possibility of pre-computing the systemic effects of any treatment by modeling its impact on the GNPSCS and global quantum coherence, thereby potentially predicting side effects before clinical trials are commenced? [[9]] An organism can be represented by the SIC symbol MAM*, where M and M* denote nested biological structures of increasing scale: atoms, molecules, macromolecules (e.g., DNA), organelles (e.g., mitochondria), cells, tissues, organs, and the whole organism, and where ‘A’ represents vicinal water—a thin, two-dimensional ordered layer that separates these structures and facilitates coherent photon and phonon superradiance transmission. [[10]] This 2-dimensional ordered vicinal water ‘sheet’ acts as an interface, enabling near-instantaneous communication throughout the organism across biological scales. [[11]]
Superradiance, observed in microtubules, entails the conversion of disordered energy into coherent electromagnetic/laser and coherent sound/phonon emissions. This mechanism may underpin rapid systemic signaling and healing responses, aligning with the GNPSCS’s phase-shift computational logic. [12] The proposed new paradigm reframes the organism not as a biochemical machine, but as a coherence-driven computational manifold. Healing becomes a matter of restoring global quantum coherence, rather than solely the use of pharmaceuticals, radiation, and surgery. A shift from mechanistic to coherence-based medicine may enable predictive modeling of therapeutic outcomes, systemic rejuvenation, and integration of emotional states and consciousness into clinical protocols. This essay is proposing not merely a new technique, but a new ontology of life. A quest for immortality by organ replacement may be misguided because it is merely an extension of our current mechanistic medicine paradigm with all its negative side effects. Instead, could the use of specific laser/phonon frequencies on MAM* maintain the integrity of DNA and stimulate the production of stem cells for longer periods of time, perhaps, indefinitely? In addition to using coherent electromagnetic/laser and coherent sound/phonons to restore an organism’s quantum coherence—perhaps allowing unlimited rejuvenation—this essay proposes that these techniques might also play a role in maintenance of astronauts’ physical health during long periods of microgravity, foregoing the need for exercise or the use of artificial gravity such as rotating wheels. Moreover, put to additional use, could it be possible to use specific laser or phonon frequencies to create resonant interference preventing high-energy cosmic radiation from penetrating a spacecraft?
SECTION B of Chapter #11
External sound and electromagnetic energy can influence an organism either beneficially or harmfully, depending on specific frequencies and coherence. [[1]] Within the GNPSCS framework, an organism functions as a self-sustaining energy pump. This pump operates through networked oscillator clocks and implicate-explicate transitions, maintaining coherence across the MultiDimensional Networked Discretized Imaginary Bloch Time Crystal (MNDIBTC) lattice. Any defect at any scale of the MAM* system—where M and M* represent SIC biological structures separated by vicinal water ‘A’—can lead to decoherence, wherein it is decoherence of the MNDIBTC that is being proposed as the root cause of disease and aging. [[2]]
Could external application of pulsed coherent electromagnetic/laser and coherent sound/phonons of appropriate frequencies act as an energy pump, restoring and sustaining the organism’s quantum coherence? In a healthy young organism, such energy packets facilitate communication between M and M* at all scales. [[3]] These interventions would not be merely energetic but informational, i.e., they could restore coherence by entrainment, thereby re-aligning phase relationships across the GNPSCS oscillator network. Coherent information transfer plays a central role in this paradigm. It involves (electromagnetic-sound)-(chemical-mental) pairings that span all scales of the organism, integrating physical, biochemical, and cognitive states into a unified coherence field. [[4]] Studies suggest that biophoton emissions correlate with mental states and may serve as markers of neural activity, oxidative stress, and systemic coherence. [5] * SEE: Quantum Functional Energy Medicine: The Next Frontier of Restorative Medicine Gonzalez, Michael J; Sutherland, Elizabeth; Olalde, Jose Journal of Restorative Medicine, Volume 9, Number 1,February 14, 2020. It explores how living systems may be understood as nonlinear, self-organizing energetic fields, and introduces the concept of the biofield—a dynamic energy structure that regulates physiological and biochemical responses. The authors argue that quantum physics provides a more fitting paradigm than classical biomedicine for understanding therapies that work with subtle energy fields. Non-traditional therapies—such as sound therapy, chanting, singing, music, and acupuncture-moxibustion—may be beneficial insofar as they might pump the MAM* system and help restore the organism’s global quantum coherence. These modalities might work by entraining oscillator networks and enhancing biophoton emission patterns. [[6]] Quantum-coherent MNDIBTCs are a unique phase of matter exhibiting periodic structure not only in space but also in time. Unlike conventional time crystals, multidimensional time quasicrystals display robust subharmonic responses at multiple incommensurate frequencies, separated by the SIC golden ratio (p* = 1.618...*), which prevents mutual resonant destruction. [7]
Quasicrystals require an external periodic driving force—such as vibration or oscillation—to maintain their time-dependent order. This driving force acts as a pump, supplying energy and preventing thermal equilibrium, thereby sustaining the non-equilibrium state of the organism. [[8]] The periodic structure of a time crystal repeats in time just as a traditional crystal repeats in space, and this temporal coherence is essential for maintaining biological function. *SEE: Britannica’s biography of Ilya Prigogine who developed the theory of dissipative structures, showing how systems far from equilibrium can self-organize into ordered states. His work revolutionized thermodynamics and earned him the 1977 Nobel Prize in Chemistry. Werner Jaross’ findings on intracellular signaling support this view: molecular vibrations generate coherent near-infrared radiation that facilitates communication between organelles, mediated by the quasicrystalline structure of water. [9] Coherence is necessary to coordinate enzyme activation, intracellular transport, and signal transduction over several scales. This essay proposes that disruption of an organism’s global quantum coherence may underlie disease, while application of entraining phasealigning energy inputs may offer a pathway to healing and rejuvenation without total reliance on pharmaceuticals, radiation, and surgery. To find the right healing frequencies one might gently expose the body to a range of frequencies while monitoring signs like brain waves, heart rhythm, galvanic skin response, pupils dilating or constricting reflecting a move from stress to relaxation, and emotional effects such as a sense of calm, all of these suggesting that coherence is being restored, the body’s way of signalling it’s tuning back in. When the body begins to show signs of calming or improved coherence, narrow in on that range and test smaller steps around it, adjusting based on how the body reacts. This creates a feedback loop where the body itself helps guide the entraining system toward the most helpful frequencies, like tuning an instrument by ear until it sounds just right.
SECTION C of Chapter #11
In addition to chemical signalling, physical signalling is essential for addressing the spatial and temporal dynamics of the intact organism. The Golgi apparatus and the microtubule skeleton system are key structures involved in numerous intracellular transport tasks. Consequently, close communication between the Golgi apparatus and the cell periphery is an absolute necessity. The majority of the substances that influence the cell from its membrane, transmit the information to the intracellular destination via signal transduction pathways. The transmission of information is based on emission and resonance of electromagnetic patterns in the near-infrared frequency range generated by the vibrations of the respective molecules. This radiation is coherent and plays a role in activating enzymes. According to Werner Jaross, these signals indicate both the location and the nature of the structure producing the signal, necessary requisites for global quantum coherence. *SEE: Jaross, W. (2020). The Possible Role of Molecular Vibration in Intracellular Signalling. Journal of Cellular Signaling, 1(4), 180-186. The quasicrystalline structure of water is essential for that coherence. Werner Jaross has explored the intriguing concept of molecular vibration and its role in intracellular communication. His work suggests that, beyond chemical signaling, it is physical signaling—specifically through molecular vibrations—that plays a crucial role in transmitting information within cells. These vibrations generate electromagnetic radiation in the near-infrared frequency range. The quasicrystalline structure of water is also highlighted as a key factor in maintaining this coherence. Information in the form of scale-invariant/conformal near- infra-red electromagnetic radiation symbolized in this essay as (y*) tunnels through vicinal water (A*) at all scales in order to correlate the biochemical behavior of the entire organism. * SEE: Ho, Mae Wan. ‘The Living Rainbow H2O’-Amazon. Her book explores how water’s quantum properties enable coherence and organization in living systems, offering a holistic view of biology and life. *SEE: Casey, Hayley et al. iScience. Exploring ultraweak photon emissions as optical markers of brain activity Volume 28, Issue 3112019, March 21, 2025. Haley’s findings suggest that microtubules produce coherent light. *SEE: Goldberg, M. GRIN Verlag 2021. Heat-Induced Quasicrystal Formation in Vicinal Water: Quantum Coherence in Microtubules and the Phi Connectome.
If coherent photons (laser) and coherent sound (phonons) due to microtubule superradiance can be picked up within and outside the body, and is able to produce Chladni-like figures in thin sheets of vicinal water, then longitudinal sound waves outside the body might be able to detect, and possibly affect, these electromagnetic-sound signals. For example, Chakras (Sanskrit-‘wheel’ or ‘disk’) might relate to different frequency groupings of the GNPSCS. Metaphorically, longitudinal waves are like FM radio waves, i.e., more resistant to noise interference than transverse AM radio waves. A vibrating tuning fork emits longitudinal waves. Eileen McKusick’s claim of ‘Tuning the Biofield,’ introduces the Biofield Anatomy Map and explains how sound can affect and clear trauma stored in the energy field. *SEE: Eileen Day McKusick’s first book, ‘Tuning the Human Biofield: Healing with Vibrational Sound Therapy,’ Healing Arts Press 2014. She introduces the concept of the biofield and presents a detailed map of how emotional and physical traumas may be stored as vibrational patterns in the space around the body. Her second book expands on the electrical nature of human biology and explores how tuning practices may influence vitality and coherence which this essay is posited as based on the possibility of external sound waves interacting with vicinal water (A) and thereby affecting the MAM* coherence of the organism. *SEE: Eileen Day McKusick’s second book Electric Body, Electric Health: Using the Electromagnetism Within (and Around) You to Rewire, Recharge, and Raise Your Voltage . St. Martin’s Essentials, 2021. This essay proposes that if an organism is a quantum-coherent multidimensional networked imaginary Bloch clock time crystal (MNDIBTC), and if MAM* computes as a GNPSCS, then a thought or emotion is also associated with a chemical or structural change at all scales. That is, chemistry, emotions and thoughts are related in an organism. The twodimensional structure of vicinal water suggests that we can think of vicinal water as thin sheets where externally applied sound waves may produce Chladni-like figures in vicinal water and thereby affect the chemistry and topology of M, M* at all scales. In a reciprocal manner, changes in the chemistry or topology of M, M* at all scales can affect Chladni-like figures in vicinal water at all scales. *SEE: Thomas Müller, Numerical Chladni Figures, European Journal of Physics, Vol. 34, 2013, pp. 1067-1074. DOI: 10.1088/0143-0807/34/4/1067. That paper presents a computational tool based on the finite element method for simulating vibrational modes in arbitrarily shaped two-dimensional membranes. It offers both theoretical derivations and practical examples, making it especially useful for modeling Chladni patterns beyond simple geometries. Thus, M, M* and vicinal water (A) are inextricably bound together within the perceived boundary of an organism. Biofield reading and proposed ‘correction’ of biofield defects might be related to mutual resonance between McKusick’s tuning forks and MAM*. There is a close association between vicinal water (A), and M, M*, one affecting the other reciprocally at all scales. The GNPSCS represents the explicate-order projection of the implicate-order Phi Connectome PC. Phase-shifting acts like a pump maintaining quantum coherence of the multi-dimensional networked imaginary time crystal. In this system, it is posited that mental activities are tightly associated with chemical and topological changes at all scales of the organism, a possible explanation for ‘psycho-somatic’ and placebo effects in which positive beliefs and hopes may have a beneficial effect while, conversely, hopelessness and despair may have negative effects. For example, anxiety and stress may suppress the immune system such that the organism is less likely to resist disease and cancer. The developing field of psychoneuroimmunology also called psychoimmunology, investigates how psychological factors—such as stress, emotion, and cognition—interact with the nervous and immune systems to influence health outcomes.
Landmark studies by Ader and Cohen in the late 1970s demonstrated that immune responses could be conditioned, establishing a scientific foundation for the field. *SEE: Ader, R., Cohen, N., & Felten, D. (1981). Psychoneuroimmunology. Academic Press. Subsequent research has shown that chronic stress and depression can alter cytokine profiles, suppress natural killer cell activity, and promote inflammation linked to physical and mental disorders. Notable contributions include, *SEE: Irwin, M. R. review on stress-induced immune dysregulation, (2008); Human psychoneuroimmunology: 20 years of discovery. Brain, Behavior, and Immunity, 22(2), 129-139. The OHSU Psychoneuroimmunology Lab, led by Dr. Jennifer Loftis, continues to explore how immune molecules shape cognitive and emotional functioning, bridging molecular pathways with clinical applications. *SEE: George M. Slavich, “Psychoneuroimmunology of Stress and Mental Health,” The Oxford Handbook of Stress and Mental Health, Oxford University Press, 2019, pp. 519-546, which elaborates on how life stress affects mental health through cytokine signaling and
HPA axis dynamics. Health and sickness are not merely the result of deterministic physics and chemistry governed by Cartesian-based continuum mathematics. This essay posits that at from the quantum to the cosmic scale, implication corresponds to superposition, while explication represents the collapse of a scale-invariant/conformal Schrödinger wave function—a phase change GNPSCS phase-shift computation that marks the transition from potentiality to actuality. [1] At the cosmic scale, implication denotes the superposition of previous and subsequent Penrose eons, and explication marks the collapse of that superposition, initiating the end of one eon and the unfolding of another. [[2]] Thus, the ‘beginning of the cosmos’ or Penrose’s succession of eons is not driven by a singular or multiple sequential big bangs, but by a phase-change computation within the Gödel Non-Turing Non-Algorithmic Phase-Shift Computational System (GNPSCS). [[3]] In this framework, sequential eons are entangled, not linearly ordered. From a mechanistic standpoint, time is said to begin at the big bang, yet this notion becomes paradoxical when viewed through the lens of the GNPSCS and implicate order, where neither space nor time exists in the conventional sense. [[4]] Oscillators within the GNPSCS are discretized imaginary Bloch clocks, and their ticking does not correspond to spacetime intervals but to phase transitions in a prespacetime substrate. Consequently, the emergence of a new cosmos from the collapse of a superposed aeonic state may occur after a millisecond or after 101000 years—duration becomes irrelevant in the absence of spacetime metrics. [[5]] The GNPSCS aligns with Roger Penrose’s Conformal Cyclic Cosmology (CCC), a bold [‘outrageous’ in Penrose’s term] and imaginative theory proposing that the universe undergoes endless cycles, or ‘aeons,’ each beginning with a Big Bang and ending in a smooth, cold, and empty state that transitions into the next. He argues that massless particles like photons (y), the ‘detritus’ left over from the Hawking evaporation of black holes, fill the cosmos at the ‘end’ of an eon and cannot serve as natural clocks in the same way particles having mass can. The networked oscillators—imaginary clocks—of the PC/GNPSCS represent masses and they ‘communicate’ via SIC tunneling electromagnetic radiation, i.e., photons. In the GNPSCS model, it is the oscillators which have mass and align with Penrose’s clocks, while tunneling photons (y) have no mass and comport with Penrose’s idea that ‘time’ has no meaning (an ‘eternally’ long time has no meaning if there are no clocks) and can’t be reckoned in the end stages of a Penrose aeon. * SEE: Penrose, R., Cycles of Time: An Extraordinary New View of the Universe, 2010, Goodreads and Amazon. It offers a deep dive into the mathematical and philosophical foundations of CCC, including discussions on entropy, spacetime geometry, and the nature of time itself.
Rather than Penrose’s CCC system based on Cartesian deterministic mathematics, this essay proposes the GNPSCS, as a fractal non-Cartesian system more akin to topological geometry. Building on a non-Cartesian modification of Penrose’s ideas, the GNPSCS is essential for modeling consciousness because it stages recursive, non-algorithmic propagation where Turing systems fail. In 4D topology, manifold classification can encode non-halting Turing behavior, revealing that cognition resists full algorithmic capture, i.e., geometry itself can embody Gödelian limits. This leads to a provocative implication: the cosmos, including consciousness, may ‘click off’ with each imaginary tick of the Bloch clocks and resume with the next tick—a cosmic ‘musical grand pause.’ Would we notice? Perhaps not. Just as William James theorized that consciousness consists of discrete moments stitched together to form the illusion of continuity, so too cosmic epochs could unfold as explicated pulses from the implicate order. [[6]] Each conscious moment, like each eon, may be an unfolding of the implicate order, and the continuity we perceive is a projection of networked discontinuities. For example, the apparent continuous trajectory of the path of an electron in a bubble chamber, is actually a series of discrete events. Each point represents a localized collapse of the wave function, and the electron observed at one moment cannot be strictly identified with the same electron—if such a concept of ‘ the same ’ can even be said to exist—observed previously due to the probabilistic nature of quantum states and the role of measurement in defining them. [[7]] The apparent continuity is an illusion just as the apparent continuity of cinematic motion is composed of discrete frames. Bohm’s implicate-explicate holomovement model supports this view, suggesting that our perceived universe is a projection of continual unfoldments and enfoldments from a deeper implicate reality. [8] The controversial Cognitive-Theoretic Model of the Universe (CTMU), proposed by Chris Langan, shares conceptual resonance with the GNPSCS. CTMU describes reality as a self-configuring, selfprocessing language (SCSPL), a logical system in which spacetime and consciousness emerge from recursive syntactic operations. [9] CTMU posits that the universe is not a machine but a coherence-driven computational manifold, where phase transitions—not mechanical causality— govern emergence and transformation. This essay posits that a particular pathway for SIC tunneling information (y*) through the PC/GNPSCS is not deterministic, but rather becomes ‘annealed’ or strengthened by repetition which means that our Cartesian ‘laws of nature’ are rather like ‘habits.’ GRIN publications 2024. *SEE: Sheldrake, Rupert. The Presence of the Past: Morphic Resonance and the Memory of Nature. Inner Traditions, 2012. *SEE: Goldberg, M. 2024 Grin Verlag ‘The Primacy of Creativity, Does an Eternally Creative Cosmos Entail Free Will and Moral Responsibility.’
SECTION D of Chapter #11
The Godel Non-Turing Non-Algorithmic Phase-shift Computational System (GNPSCS) models reality as a coherence-driven implicate-explicate (Bohm’s holomovement) architecture, where computation arises from phase transitions rather than algorithmic steps which resonates with Lori Gardi’s interpretation of the Mandelbrot set as a quasi-black hole generator and fractal cosmological map. [[1]] Gardi’s ‘hyperbolic bugs’—self-similar lobes within the Mandelbrot set— represent networked attractor domains, each encoding a unique phase space. These bugs are separated by golden-ratio-scaled boundaries, which she interprets as natural symmetry regulators across scales. [1] Both models reject linear causality and algorithmic determinism, favoring emergent coherence and recursive structure. In GNPSCS terms, bugs correspond to networked oscillator clocks, each ticking via Godel phase-shifts. The transitions between the hyperbolic bugs of the Mandelbrot set, mirror implicate-explicate unfoldments, where each ‘tick’ is a resonance event rather than a temporal increment. [2, 3] Scale-invariant/conformal SIC phi separators (p*) of the PC/GNPSCS align with the golden-ratio boundaries between Mandelbrot bugs. These separators act as coherence filters, allowing only symmetry-compatible transitions as in tunneling of SIC electromagnetic information (y*) between networked attractor states. In Gardi’s model, such transitions define the emergence of scale-invariant/conformal quasi-black holes across atomic, quantum, and galactic scales. [[1],[4]] Thus, GNPSCS and Gardi’s Mandelbrot cosmology converge on several key points: (1) rejection of Cartesian continuum assumptions; (2) use of fractal nesting to encode phase logic; and (3) treating black holes as emergent coherence nodes, not singularities. Both rely on scaling to regulate transitions across domains. This synthesis suggests that the Mandelbrot set is not merely a mathematical curiosity but a computational substrate for GNPSCS-style coherence modeling—where each bug is a phase-locked oscillator and each separator is a scale-invariant/conformal phi (p*) separator.
12. Is Loss of Global Quantum Coherence the Cause of Alzheimer’s Disease?
Illustrations are not included in the reading sample
* SEE: Goldberg, M. GRIN 2021. Heat-induced quasicrystal formation in vicinal water, quantum coherence in microtubules and the Phi Connectome. Illustrating: A. proposed smaller abnormal beta-amyloid nano-tubule BAB containing vicinal water producing coherent photons and phonons causing resonant interference with normal tubulin microtubule resonance, thereby preventing formation of the GBFF, and loss of global quantum coherence manifesting as dementia. B. Normal tubulin microtubules (TAT) initiate and sustain the formation of global quantum coherence of the Ghosh-Bandyopadhyay Frequency Fractal (GBFF) throughout the brain, giving rise to normal mentation. Depending on which area of the brain is most affected, one may see specific losses as dementia develops. For example, loss of global quantum coherence involving the hippocampus may manifest as short-term memory loss which can appear in cognitive tests as the inability to remember three objects following a distracting question or inability to lay down new memories. [[2]] Beta-amyloids can be found intracellularly in axons of neurons in the hippocampus during the early stages of Alzheimer's disease, and research suggests that amyloid-beta (A0) peptides accumulate within neurons before forming extracellular plaques. *SEE: Bayer, T. A., & Wirths, O. (2010). Intraneuronal accumulation of amyloid-beta - a predictor for synaptic dysfunction and neuron loss in Alzheimer’s disease. *SEE: Voss et al., 2010 Plasticity of brain networks in older adults following randomized exercise intervention. Front. Aging Neurosci., 2:8. https://doi.org/10.3389/fnagi.2010.00008. The normal tubulin microtubule (TAT) supports formation of the global quantum coherence of the Ghosh-Bandyopadhyay Frequency Fractal (GBFF) across the entire brain, manifesting as normal mentation. [[1]] Depending on which area of the brain is most affected, specific cognitive losses may emerge as dementia develops. Beta amyloids can be found intracellularly in axons of hippocampal neurons during the early stages of Alzheimer’s disease, and research suggests that amyloid-beta (A0) peptides accumulate within neurons, and research suggests that amyloid-beta (A p) peptides accumulate within neurons before forming extracellular plaques. [[3],[4]] Studies using immunohistochemistry and electron microscopy have demonstrated intraneuronal localization of A (M2 in both human patients and transgenic animal models, suggesting a critical role in early synaptic dysfunction. [[5]] Gouras et al. showed that A0 accumulates intraneuronally in the hippocampus and is associated with synaptic terminals, preceding the appearance of extracellular deposits. [[5]] This observation challenges the classical plaque-centric view and supports a more nuanced model of intracellular toxicity as a precursor to neurodegeneration. [[6]] Intracellular accumulation may precede the formation of extracellular plaques, reinforcing the significance of hippocampal integrity in cognitive function. [[7]] Figure 12.2 below illustrates the importance of the hippocampus in perception.
Illustrations are not included in the reading sample
Figure 12.2 -by author
A. Is based on the work of many researchers such as Karl Pribram and David Bohm listed in the bibliography. Illustrating views through hologram of microtubule memories stored and recalled by the laser-like activity of the hippocampus. Dashed arrows indicate different ‘views’ through the hologram, where the dashes indicate specific memories and memory structures. It is to be noted that multi-dimensional networked holographic storage and memory retrieval supports novel associations to be ‘seen’ very rapidly, accounting for the creative use of metaphors and similes in poetry, prose, music, art, sudden insights in science, and in more extreme cases, synesthesias, and schizophrenia. This essay posits that non-conscious associations may be related to Freud’s concept of the unconscious * SEE: Interpretation of Dreams. Vienna (1900): publisher Franz Deuticke, while Sheldrake’s morphic resonance among all humans past and present, relates to Jung’s concept of the collective unconscious. *SEE: Jung, C. G. (1959). The Archetypes and the Collective Unconscious. Collected Works of C.G. Jung, Volume 9, Part 1. Princeton University Press. Each dashed arrow in the figure is a subset through the hologram. By stark contrast, if memories were stored non-holographically as engrams, each in a specific memory location (address) as in a Turing computer, then one would have a multitude of separate ‘photographs.’ Finding correlations among such a transfinite ‘infinity’ of photographs could result in a nonhalting, non-polynomial Turing computation. * SEE: Lashley, K. S. (1950). ‘In search of the engram.’ Symposia of the Society for Experimental Biology, 4, 454-482. *SEE: Sheldrake, R. (2012). *The presence of the past: Morphic resonance and the habits of nature* (Rev. ed.). Rochester, VT: Park Street Press.
The Hippocampus plays the role of a laser by both storing and retrieving (on the fly) holographically ‘stored’ memories in microtubules. By contrast, in a Turing machine, memory is represented as a one-dimensional tape, where each cell holds a symbol. The machine accesses memory sequentially by moving left or right—making retrieval inherently linear and one-at-a- time. By stark contrast, multidimensional holographic retrieval enables the spontaneous and simultaneous activation of a multitude of associated memories whereby, after a period of study without resolution, a sudden ‘a-ha!’ intuitive moment, insight-gestalt can emerge.
Due to morphic resonance, these memories are also stored in the PC as annealed networked habit pathways. * SEE: The Primacy of Creativity GRIN Verlag, Goldberg, M. 2005. The PC is in morphic resonance with the microtubules of the brain whence associated networked pathways in the PC and its explicate-order GNPSCS are available to the microtubules so that we have a possible explanation for Jung-Pauli synchronicity. * SEE: Jung, C. G., & Pauli, W. (1952). The Interpretation of Nature and the Psyche. Princeton University Press. The book contains Jung’s essay ‘Synchronicity: An Acausal Connecting Principle’ and Pauli’s ‘The Influence of Archetypal Ideas on the Scientific Theories of Kepler,’ marking their joint exploration of meaningful coincidences and the intersection of psychology and quantum physics.
In cases of brain damage, one may have retrograde or anterograde memory loss. In retrograde memory loss, perhaps the damage is in hippocampal laser retrieval rather than in the microtubules. Retrograde amnesia often involves damage to medial temporal lobe structures, especially the hippocampus. In anterograde amnesia, one may not be able to form new memory traces either due to damage of memory storage areas (microtubules and neurons) or, perhaps more likely, damage to hippocampal laser storage function. Anterograde amnesia results from damage to the hippocampus, fornix, or related structures that disrupt encoding and consolidation of new memories.
Memory is distributed holographically throughout the brain, and possibly also in microtubules of somatic cells such that this somatic memory might manifest itself apart from the Boolean logic- oriented brain—mediated by a simple model of fire/no-fire neuron activity akin to a Turing computer—in the apparently illogical sense we call ‘intuition,’ the sudden understanding that comes in a flash when one is concentrating on something mundane not related to the problem at hand. Is this what Einstein meant when he said “quantum mechanics is certainly imposing, but an inner voice tells me that it is not yet the real thing. Intuition, or the sudden emergence of insight, may stem from holographic memory storage—where the structured, logic-driven processing of neuronal networks, akin to Turing-like computations, yields to the fluid and seemingly random associations inherent in holographically encoded memories. Recent studies have provided fascinating insights into the role of the brain’s default mode network (DMN) in creativity. For example, one study from Drexel University explored how the brain achieves a creative flow state, particularly during tasks like jazz improvisation. * SEE: ‘Creative Flow as Optimized Processing: Evidence from Brain Oscillations During Jazz Improvisations by Expert and Non-Expert Musicians’ by David Rosen, et al. published in Neuropsychologia on February 19, 2024. These researchers found that the DMN, which is active during daydreaming and introspection, works under the supervision of the executive control network in the brain’s frontal lobes.’ This coordination allows for the generation of creative ideas with minimal conscious supervision. Charlie Parker the famous alto saxophonist said, ‘One must know his instrument, practice, practice, practice, then forget all that and just wail.’
Rupert Sheldrake considers that reincarnation is not so much that one had previous lives, but rather an indication that one has morphic resonance with ‘information’ of other lives ‘stored’ as ‘habits.’ SEE: Sheldrake, Rupert. The Presence of the Past: Morphic Resonance and the Memory of Nature, Park Street Press, 2012. Perhaps this relates to Jung’s collective unconscious where one is in morphic resonance, i.e., ‘tuning in’ to a specific single or many past lives. Families, and small groups to larger groups to nations can share similar memories, drives, and likes through morphic resonance. Various models of the universe—such as Chris Langan’s Cognitive-Theoretic Model of the Universe (CTMU), Garrett Lisi’s E8 theory, the Hermetic philosophy of the Kybalion, and numerous religious and philosophical traditions—may be intuitively converging on a shared underlying principle: David Bohm’s concept of the implicate order, a deeper, enfolded layer of reality beneath observable phenomena.
B. Illustrating how: (1) light hits object and reflected to eye; (2) brain forms a multi-dimensional networked hologram on the fly; (3) the multi-dimensional networked hologram is projected outside the brain; (4) the projected image of the tree is coextensive with the actual tree and moves with the actual tree as the head is moved. This suggests that the brain is in the head, but the mind is projected outside or beyond the physical brain. If the mind is projected outside/beyond the physical brain (taking Rupert Sheldrake’s work into account) then, psi effects may have some basis in reality. Although psychoanalysts have long reported telepathic interactions and precognitive events between patient and practitioner, mainstream psychology tends to dismiss or avoid these phenomena for fear of being labeled unscientific. [[8]] The psychoanalytic literature rarely confronts such topics directly, and terms like ‘telepathy’ or ‘psi’ scarcely appear in its dictionaries, despite growing attention in recent years. [[9]]
Research has revealed that beta-amyloid deposits occur in brain regions crucial to sensory processing, such as the auditory and visual cortices, and are associated with symptoms like speech impairment and perceptual deficits. Javitt et al. demonstrated visual processing disruptions in amyloid-positive individuals, [[10],[11]] Yesantharao et al. linked proprioceptive dysfunction to elevated cortical amyloid levels, [12] and Jiang et al. showed that reduced EEG coherence in the frontal and temporal lobes distinguishes frontotemporal dementia (FTD) from Alzheimer’s disease, [[13]] with Salcini et al. reporting alterations in frontal theta and alpha rhythms across FTD subtypes. [14] While quantum coherence remains speculative in clinical neuroscience, such findings suggest that loss of synchrony in cortical networks may reflect a deeper erosion of integrative dynamics. [15] Conventional Alzheimer’s treatments have focused on chemical- immunological strategies to eliminate or block beta-amyloid formation, but monoclonal antibodies like aducanumab, lecanemab, and donanemab have only modestly slowed cognitive decline (~25- 30%) and failed to halt disease progression, while inducing adverse effects such as cerebral edema and microhemorrhages. [[16]] The frequent failure of vaccine and antibody trials has led researchers to reconsider amyloid-centric models and explore tau pathology, neuroinflammation, and immune modulation as alternative therapeutic pathways. [[17]]
This essay posits, instead, that Alzheimer’s dementia arises from resonant interference between normal/physiologic microtubule (TAT) components, i.e., quantum-coherent units foundational to the Ghosh-Bandyopadhyay Frequency Fractal, and aberrant/abnormal/pathological beta-amyloid nanotubules (BAB) which disrupt global quantum coherence by blocking formation of the Ghosh- Bandopadhyay Frequency Fractal (GBFF). [18] The GBFF is a multi-scale electromagnetic resonance architecture designed for wireless decision-making and recursive pattern recognition, wherein overlapping frequency bands form scalable fractal chains; Ghosh et al. and Saxena et al. have demonstrated resonance continuity across proteins, microtubules, and neurons, suggesting fractal coherence as a cognitive substrate independent of algorithmic logic gates. [[19],[20]] This essay proposes that Alzheimer’s dementia might be treated, not by traditional chemical means, but by quantum-selective disruption of BAB superradiance using coherent light and coherent sound pulses offset by n radians in order to block pathological disruptive superradiant effects without impairing normal/physiologic TAT dynamics. [[21]]
13. Treatment of Alzheimer’s Disease by Selective Restoration of the Ghosh-Bandyopadhyay Frequency Fractal.
This essay proposes a novel approach to treating Alzheimer’s disease (AD) and related neurodegenerative disorders by selectively restoring the Ghosh-Bandyopadhyay Frequency Fractal (GBFF), a macroscopic coherence structure derived from networked microtubule oscillations. The hypothesis begins with the idea that superradiance of abnormal beta-amyloid microtubules (BAB) interferes with the normal frequency dynamics of tubulin microtubules (TAT), thereby disrupting coherent information processing in the brain. [1] These abnormal oscillations may act as pathological resonators, overwhelming normal frequencies, preventing global quantum coherence, thereby contributing to cognitive decline. Rather than relying on chemical or immunological interventions, this essay suggests that a non-invasive, frequency- selective treatment could suppress pathological BAB resonance while preserving or enhancing normal TAT resonance. [[2]] The therapeutic goal is to restore the GBFF—a networked, scaleinvariant frequency fractal that supports normal mental function. Microtubules, composed of tubulin dimers, exhibit quantum vibrational modes across a wide frequency spectrum, from terahertz to hertz, and are capable of coherent information processing. These oscillations are thought to underlie consciousness and cognition, as proposed in the Orch-OR model of Hameroff and Penrose, and further supported by experimental findings from Bandyopadhyay’s group, who demonstrated quantum coherence in microtubules at physiological temperatures. [[3],[4]] The GBFF integrates these oscillations into a fractal hierarchy, allowing for distributed computation and memory encoding across neural networks.
Disruption of the GBFF by beta-amyloid oligomers has been shown to correlate with memory loss and synaptic failure in AD models. Recent studies using Amyloid 0 oligomer-selective antibodies have demonstrated memory restoration in transgenic mice, suggesting that targeting specific frequency domains may be more effective than plaque removal. [5] Moreover, research into microtubule resonant frequencies indicates that external electromagnetic fields tuned to intrinsic microtubule frequencies can modulate neuronal behavior, offering a potential avenue for therapeutic entrainment. [[6]] In this context, the GBFF represents a coherence-based biomarker and therapeutic target. By selectively interfering with the pathological BAB frequency and enhancing the TAT contribution to the GBFF, it may be possible to restore cognitive function and prevent further neurodegeneration. This paradigm shift—from chemical intervention to frequency fractal restoration—aligns with emerging models of brain function that emphasize quantum coherence, networked oscillatory hierarchies, and non-algorithmic computation.
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Illustrating superradiance formation of coherent photons/laser and coherent sound/phonons in nano-diameter tubular structures filled with water. Heat/Brownian motion/electromagnetic energy in the near-infrared region produces long-range quasicrystal formation in vicinal water. * SEE: Heat-Induced Quasicrystal Formation in Vicinal Water. Quantum Coherence in Microtubules and the Phi Connectome, Goldberg, M. Grin Verlag, 2021. Normal nano-diameter microtubules, TAT with walls comprised of tubulin, produce coherent light and sound. They are bound together by microtubule associated proteins MAPs in various configurations within all eukaryotic cells.
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Figure 13.1 - A, B, C by author; D from clipartmag.com with modification by author.
Illustrating: A. Heat-induced long-range quasicrystal order in vicinal water in a normal tubulin microtubule TAT produces coherent photons/laser, and coherent sound/phonons. *SEE: Nishiyama, A., Tanaka, S., & Tuszynski, J. A. (2024). Quantum Brain Dynamics: Optical and Acoustic Super-Radiance via a Microtubule. Foundations, 4(2), 288-305. https://doi.org/10.3390/foundations4020019. Microtubules communicate with one another by coherent light and sound, where coherent light carries more specific information and coherent sound less specific, but longer-range information. B. TATs are interconnected by MAPs in various combinations which are associated with holographic memory storage. Practically unlimited memory ‘storage’ may be related to the connection patterns of MAPs. Think of an analogy where tubulin microtubules are strings on a guitar, and the pattern of MAPs are finger positions on the fretboard of the guitar forming a chord. If there is a large number of possible chords and these are combined with global quantum coherence of tubulin microtubules, then one can obtain the model noted in this figure. C. Axons contain stacks of the MAP-interconnected head-to-tail-oriented TAT microtubules (heads of microtubules all point distally towards the synapse). This alignment is essential for neuronal polarity, signal transmission, and possibly memory encoding in coherencebased models. In neocortical pyramidal neurons, microtubules within axons are arranged in a head-to-tail configuration, with plus ends oriented distally, supporting directional transport and neural signaling. The AIS-axon initial segment is proposed as a structural locus where quantum coherence among microtubules may emerge, forming a unified matter-field that correlates with conscious experience. By contrast, dendritic microtubules are arranged in antiparallel bundles, with mixed plus-and minus-end orientations. Apical dendrites of Layer V pyramidal neurons extend upward toward the cortical surface, and their synchronous postsynaptic activity is a major contributor to the EEG signal. * SEE: Stuart Hameroff’s argument that neuronal firing is not a simple on/off mechanism, but instead involves quantum resonance within microtubules, and Stuart Hameroff, How Quantum Brain Biology Can Rescue Conscious Free Will, Frontiers in Integrative Neuroscience, Vol. 6, Article 93, 2012. In that paper, Hameroff explains that microtubules within neurons may perform quantum computations during the integration phase of neuronal activity. These computations are proposed to influence whether or not a neuron fires, suggesting that axonal output is modulated by quantum coherence rather than deterministic threshold logic (his figure #2 from that paper is illustrated just below). He describes how tubulin qubits undergo orchestrated objective reduction (Orch-OR), selecting specific states that can trigger or inhibit firing, thereby embedding quantum resonance into the decision-making process of neurons. D. All microtubule superradiance coherent light and coherent sound information is scaled up to include the entire brain, forming a macroscopic Multi-dimensional Networked Discretized Imaginary Bloch Time Crystal (MNDIBTC) a globally quantum-coherent whole such that all parts of the brain are in ‘near instant’ communication with one another. It is this global quantum-coherent whole which constitutes normal cognition, and is referred to as the Ghosh- Bandyopadhyay Frequency Fractal GBFF also characterized as Anirban Bandyopadhyay’s concept of the Phase Prime Metric PPM. [The amount of time for coherent photons to traverse the brain is about 1.5 nanoseconds, and for coherent sound about 0.2 milliseconds. Coherent light and sound are much better for transmitting information because their waves maintain a consistent phase relationship, allowing for more precise encoding and retrieval of data.]
Hameroff suggests that neuronal firing isn’t governed solely by classical threshold logic, i.e., a simple fire or no-fire (‘1’ or ‘0’) binary Turing machine Boolean logical system; but, rather, is influenced by quantum coherence within microtubules, a process embedded in the integration phase of neural computation. Tubulin subunits in microtubules may act as quantum bits (qubits), undergoing Orchestrated Objective Reduction (Orch-OR), where quantum states collapse based on spacetime geometry rather than deterministic biochemical cues. In the GNPSCS, this quantum modulation mechanism could serve as a fine-tuned coherence gate, where SIC PC resonance layers do not modulate neuronal output by binary on/off switching. The Penrose-Hameroff Orch-OR description supports the idea that consciousness emerges from ‘scaled up’ microtubular coherence.
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Figure #2 from Hammeroff’s article-modified by author. Integrate-and-fire neuronal behaviors. (A)-The Hodgkin-Huxley model predicts integration when membrane potential in dendrites and soma reach a specific, narrow threshold potential at the proximal axon, and fire with very low temporal variability (narrow t b— t a) for given inputs; (B)-By contrast, recordings from cortical neurons in awake animals (Naundorf et al., 2006) show a large variability in effective firing threshold and timing (wide t b- t a). Some unknown ‘x-factor’ (related to consciousness?) exerts causal influence on firing and behavior. Here, quantum temporal non-locality results in backward time referral, suggested as the ‘x-factor’ modulating firing threshold, recordings from cortical neurons in awake animals. In vivo recordings from cortical neurons in awake animals highlights a large variability in spike threshold and timing, challenging traditional Hodgkin-Huxley ‘binary, fire-no fire’ models of action potential initiation. * SEE: Naundorf, B., Wolf, F., & Volgushev, M. (2006). Unique features of action potential initiation in cortical neurons. Nature, 440(7087), 10601063. https://doi.org/10.1038/nature04610. The paper shows the unique features of action potential initiation in cortical neurons. Nature, 440, 1060-1063. https://doi.org/10.1038/nature04610. [This essay posits that the unknown ‘x-factor’ relates to global quantum coherence, namely the GNPSCS where its networked Bloch clocks are imaginary such that quantum temporal non-locality can manifest as backward time referral.] *SEE: Libet, B., Wright, E. W., Feinstein, B., & Pearl, D. K. (1979). Subjective referral of the timing for a conscious sensory experience: A functional role for the somatosensory specific projection system in man. Brain, 102(1), 193-224. https://doi.org/10.1093/brain/102.1.193. Problems: (1) brain mechanisms causing consciousness are unknown; (2) measurable brain activity correlating with conscious perception apparently occurs too late for real-time conscious response such that consciousness has been considered an ‘epiphenomenal illusion;’ and (3) determinism, i.e., our actions and the world around us seem algorithmic and inevitable. The Penrose-Hameroff theory of orchestrated objective reduction (Orch-OR) identifies discrete conscious moments with quantum computations in microtubules inside brain neurons, e.g., 40 Hertz in concert with the gamma synchrony of the EEG. Microtubules organize neuronal interiors and regulate synapses. The Orch-OR theory, developed by Penrose and Hameroff, proposes that quantum computations occur within microtubules in the dendrites and cell bodies of neurons, particularly those connected via gap junctions that enable synchronized activity and possible entanglement across neural networks. These computations are influenced—or “orchestrated”—by synaptic inputs, memory, and microtubule-associated proteins. At a threshold defined by gravitational self-energy, the quantum superposition collapses via Penrose’s objective reduction (OR), a proposed non-[Turing] computable process linked to fundamental spacetime geometry. Each OR event corresponds to a discrete moment of consciousness and may select microtubule states that influence axonal firing and behavior, offering a quantum-level account of cognitive integration and control. In Orch-OR, non-computability is instantiated through objective reduction (OR), a proposed quantum state collapse mechanism tied to spacetime geometry, not governed by standard algorithmic evolution. Penrose claims that such collapses are non-algorithmic, and thus capable of producing insights or decisions that a Turing machine—or any Godel-limited formal system—cannot replicate.
This essay posits that the GNPSCS is a foundational framework that supplants the classical Turing-algorithmic paradigm. Unlike discrete symbol manipulation or linear computation, GNPSCS operates through networked oscillatory coherence across scales. In this view, consciousness—and the Penrose-Hameroff notion of objective reduction (OR)—are not anomalies requiring quantum gravity patches to classical computation, but natural consequences of GNPSCS dynamics. The system’s non-algorithmic character arises from its intrinsic phase entanglement and recursive coherence, offering a unified explanation for cognition, spacetime geometry, and the collapse of superposed states. GNPSCS thus reframes OR not as an external intervention, but as an endogenous phase transition within a coherence-based ontology. If accurate, the Orch-OR theory may: (1) explain conscious causal agency by offering a potential quantum-based mechanism within the brain for consciousness; (2) introduce temporal non-locality, allowing quantum information to travel backward in classical time—thus enabling conscious influence over behavior and supporting the possibility of free will and moral responsibility; and (3) incorporate effects from information embedded in the geometry of spacetime, further reinforcing the presence of conscious causal agency. The MNDIBTC is best described by a non-Turing, non-Cartesian, nonContinuum fractal mathematics described as a Godel Non-Turing Non-algorithmic Phase-Shift Computational System (GNPSCS). Thus, brain size, i.e., the number of neurons and a simple Turing-computer model of fire-no fire neurons does not fit the ability of even a ‘simple’ biological organism such as a squirrel to solve complex problems. Einstein's brain, despite being of average size, has been studied extensively and although on the gross anatomical level one of the most notable anomalies was the unusually large and uniquely shaped inferior parietal lobules— particularly the left inferior parietal region, which is associated with mathematical reasoning, visuospatial processing, and abstract thought, there is no clear explanation from the gross anatomy of his brain for his extraordinary creative genius. Could his cognitive abilities be linked to enhanced quantum processes within Einstein’s brain, i.e., could there be something different in the microtubules—their density, structure, and microtubule-associated-protein patterns? Could such microtubule anatomy involve more efficient quantum (microtubule) computer vs. Turing (neuronal) computer information processing resulting in deeper insights and a heightened ability to connect abstract concepts? Another example of the possible non-relevance of viewing the brain as a simple Turing computer is Richard Feynman who was, perhaps, the most creative physicist of the twentieth century, yet his I.Q. is said to have been around 125. Creativity is a profoundly complex trait that doesn't always correlate with standard IQ measurements, which often emphasize logical step-by-step algorithmic reasoning, rote memory, prior practice, and problem-solving under timed conditions. Moreover, if quantum-computation in the brain relates to the posited Godel Non- Turing, non-algorithmic, Phase-Shift Computational System (GNPSCS) proposed in this essay, then according to Godel’s incompleteness theorems, there are truths or insights available to ‘non- Turing-thought’ that may not be found by computation associated with the usual problem-solving abilities required for performance on standard IQ tests. Richard Feynman is a perfect example: despite a relatively modest general IQ score by traditional standards—although his math score on the Putnam and physics mathematics Princeton entrance exam were off the charts—his groundbreaking contributions to physics and his playful, curious approach to problem-solving showcased extraordinary creativity and insight. Could it be the case that creation of new paradigms in any field are more likely to arise from those who are not deeply embedded in a culture’s norms, i.e., social outsiders—iconoclasts—who take less psychological and emotional risk of being rebuked by societies accepted conventions. *SEE: MIT (Sloan); Stanford GSB; Harvard Business Review; Kuhn, T.S; and Simonton, D.K. Enhanced quantum coherence could foster the kind of deep and unconventional thinking that drives creativity—qualities that timed tests (based on the brains’ neuron-based Turing computation) are ill-suited to capture. Creative (Godel?) insight coupled with a reasonable amount of Turing computation (measured by standard I.Q. tests) is likely sufficient to attain Nobel prize levels of achievement. Conversely, and strikingly, there is a large number of ‘high IQ’ individuals who do not create new paradigms or fundamentally change the course of science. With the advent of artificial intelligence, creative thinking becomes an even more important commodity in our world, suggesting that our traditional educational system should begin to foster and enhance students’ creativity rather than rote memorization of facts.
14. Non-Chemical Non-Immunological Treatment of Alzheimer’s Dementia by Interfering with the Abnormal Superradiance of the Beta-Amyloid Nanotubule.
Illustrations are not included in the reading sample
Figure 14.1-by author
If abnormal beta-amyloid microtubules emit coherent photons and phonons at approximately posited double the frequencies of normal microtubules, direct interference may seem improbable due to disparity in resonance, but more nuanced interference mechanisms could emerge, such as: (1) the abnormal structures generating harmonics or subharmonics that overlap with normal microtubule frequencies, disrupting TAT coherence; (2) nonlinear interactions in biological systems introducing signal distortion, amplification, or chaotic feedback; [1 ^ 3] (3) using coherent light and sound that are n radians out of phase with the abnormal emissions to selectively cancel superradiance—provided the treating waves avoid overlaps or unintended harmonics affecting TAT. Achieving this requires (a) laser sources tuned to the abnormal superradiant optical frequency with a n-radian phase shift; (b) a saser emitting coherent sound waves (phonons) phase- shifted similarly at phonon resonant frequencies; and (c) maintaining synchronized phase offsets throughout their operation. To determine abnormal photon and phonon emissions of BAB, spectroscopy techniques like tunable laser and saser mapping could be applied, using spectral peaks of highest intensity as diagnostic markers. [4 ^ 7]
These counter frequencies could then be deployed in vitro, followed by behavioral tests in knockout mice exposed to and shielded from counter-BAB coherence frequencies, using cognitive maze protocols to test mentation and memory. If approved, this could be extended to humans via cranial devices delivering counter-coherence during memory and perception tasks, such as object recall and temporal recognition under and outside of BAB-photon/phonon cancellation conditions.
Foundational studies have shown that beta-amyloid peptides form nanotubules with ordered water; [[8]] microtubules self-organize coherently at physiological temperature; [[9]] this coherence is facilitated by a resonant atomic water core integrating all adjacent proteins into a unified quantum structure. Removal of vicinal water disrupts this integration, degrading coherence and decoupling tubulin proteins. [[9]] Anesthetics are believed to act by binding pi-resonance clouds within tubulin interiors, possibly interfering with water-mediated van der Waals bonding and tetrahedral structuring, undermining quantum coherence. [[9]]
There are several studies along these lines: *SEE: Nakamura, K; Sohn, Y-I., Atikian, H., Loncar, M.; Fransson, J.,; and Lambert, N. Abnormal beta-amyloid nanotubules (BAB) may emit coherent photons and phonons at approximately double the frequencies of normal microtubules (TAT), entering superradiant regimes that disrupt quantum coherence essential for cognition. While direct interference is improbable due to resonance disparity, three nuanced mechanisms may enable selective disruption: (1) BAB structures may generate harmonics or subharmonics that overlap with TAT frequencies, disrupting coherence via spectral interference; [[1]] (2) nonlinear coupling in biological systems may introduce signal distortion, amplification, or chaotic feedback; [[2]] and (3) coherent light and sound n radians out of phase with BAB emissions could selectively cancel pathological superradiance, provided overlaps with TAT are avoided. [[3]]
To achieve this, laser sources must be tuned to BAB optical frequencies with n-radian phase shifts, sasers must emit coherent sound waves phase-shifted at BAB phonon resonances, and phase synchronization must be maintained throughout operation. [[4]] Spectroscopic mapping of abnormal emissions may involve tunable laser and saser diagnostics to identify spectral peaks of highest intensity, [5] nonlinear optical imaging of p-amvioid plaques, [6] and modeling of ordered water cores to understand how hydration affects resonance and coherence. [[7]] Experimental validation could include in vitro testing of counter-coherence frequencies on BAB structures, knockout mouse trials using cognitive maze protocols to assess mentation and memory under exposure vs. shielding conditions, and human trials via cranial devices delivering counter-coherence during object recall and temporal recognition tasks. Foundational studies show that microtubule coherence arises from resonant atomic water cores integrating adjacent proteins into unified quantum structures, and that disruption of vicinal water degrades coherence and decouples tubulin proteins. [[8]] Anesthetics may interfere with pi-resonance clouds and van der Waals bonding within tubulin interiors, undermining quantum integration. [[8]] Abnormal beta-amyloid nanotubules (BAB) emit superradiant photons and phonons that disrupt quantum coherence in normal microtubules (TAT), wherein selective phase-cancellation using n-radian shifted coherent light and sound could restore cognitive function.
Hameroff et al. (2015) supports this framework by showing that anesthetics act within quantum channels formed by n-resonance clouds of aromatic amino acids inside tubulin proteins, disrupting exciton hopping and dipole oscillations essential for consciousness. These anesthetic effects occur via van der Waals binding and interference with structured water, validating the idea that external agents—chemical or physical—can modulate quantum coherence[‡] SEE: Hameroff, S., Craddock, T. J. A., & Tuszynski, J. A., 2015 . Anesthetics act in quantum channels in brain microtubules to prevent consciousness. Current Topics in Medicinal Chemistry, 15(6), 523-533. Hameroff, Craddock, and Tuszynski (2015) propose that anesthetics block consciousness by disrupting quantum processes in brain microtubules.
These microtubules contain aromatic amino acids like tryptophan that support quantum coherence through n-electron resonance. Anesthetics bind to hydrophobic pockets in tubulin, halting exciton hopping, thereby preventing conscious experience. This supports the Orch OR theory, suggesting that consciousness arises from quantum-level activity within neurons, not just from synaptic networks. The paper links anesthetic action to a deeper quantum biological mechanism underlying awareness, thus aligning with this essay’s proposal that phase-tuned counter-coherence waves could selectively cancel pathological superradiance from BAB structures without harming normal TAT coherence. It also supports the role of ordered water in maintaining microtubule integration, and the feasibility of targeting resonance dynamics to modulate cognition non-chemically. [[9]]
*SEE: Leder A, Mas G, Szentgyörgyi V, Jakob RP, Maier T, Spang A, Hiller S. A multichaperone condensate enhances protein folding in the endoplasmic reticulum. Nature Cell Biology. 2025 Aug;27(8):1123–1135. doi:10.1038/s41556-025-01730-w. The chaperones identified in this study have been characterized within a Cartesian-algorithmic framework of mechanistic biology, where molecular interactions occur via concentration-dependent localized interaction, described by the continuum mathematics differential equations of physical chemistry. Yet their true role, when viewed through the lens of a non-Cartesian global quantum coherence system, is far more profound. These chaperones are not isolated agents executing discrete tasks; rather, they are posited to act like phase-linked participants in the GNPSCS. Leder et al. have described them as components of a mechanistic Cartesian-based algorithmic system, but it is posited in this essay that they are nodes in a non-algorithmic clique structure—agents of a system with global quantum coherence (GQC) that resolves protein folding, not through step-wise computation, but rather through coherence, by finding a ‘clique.’ Their discovery, though framed in conventional terms, offers a glimpse into the deeper architecture of a system that transcends Cartesian logic. This essay posits that the ‘clique-based’ non-algorithmic GNPSCS also aligns with the pictorial representations of non-algorithmic Feynman diagrams illustrated in chapter 6 above. Moreover, interference with an organism’s GQC—by prion disease, for example—is posited to be associated with misfolded proteins associated with the formation of prions, as well as many seemingly disparate diseases, and their comorbidities, the side effects of pharmaceuticals, and various forms of dementia, e.g., Alzheimer’s, Fronto-Temporal, amyotrophic lateral sclerosis (Lou Gehrig’s disease, and Stephen Hawking’s disease.)
15. Relationship of the Mandelbrot Set to the Godel Non-Turing Non-algorithmic Phase-Shift Computational System.
This essay posits an analogy between the Mandelbrot Set and the PC/GNPSCS framework. The Mandelbrot Set, with its recursive formula zn+1 = (zn)[2] + c , operates in the complex plane using imaginary numbers—just as the PC/GNPSCS invokes imaginary Bloch clocks to encode phaseshifting ‘clique-based,’ non-algorithmic computation. [[1], [2]] The SIC hyperbolic bulb structures of the M-set (‘bugs’) mirror the oscillatory nodes of the PC/GNPSCS, separated by a scale- invariant/conformal (SIC) golden ratio (p*). [3] These phi-based separations act as both spatial and informational boundaries, suggesting a tunneling mechanism where SIC electromagnetic radiation-information (y*) traverses fractal paths that are not merely geometric but feed forward into the next state of the system. [[3], [4]] In this view, the M-set becomes more than a visual fractal— it is a Turing computational metaphor for the PC/GNPSCS, where recursion is posed as phaseshift tunneling of SIC EM (y*) information. [5] The idea that the M-set ‘exists’ as a whole in imaginary time while only unfolding in real time on a Turing machine suggests that the full informational structure of the PC/GNPSCS is already present in pre-time, as an expression of Bohm’s implicate order. [6] This property aligns with this essay’s broader paradigm: that reality, consciousness, and computation are not properly described by linear algorithmic methods, but rather by a coherence-based, recursive, and modular non-linear fractal model, i.e., the PC/GNPSCS. Thus, the M-set becomes a model for the PC/GNPSCS and how SIC EM radiation (Y*) propagates—not through space-time as traditionally conceived, but through a multidimensional manifold comprised of SIC fractal tunnels. [[3], [6]]
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Figure 15.1 from MathyBits with modifications by author
Illustrating an iteration of the M-set showing: A. hyperbolic bugs, the larger akin to a lower frequency oscillator of the PC/GNPSCS, and the smaller a higher frequency oscillator of the PC/GNPSCS; B. SIC EM information/(‘gravity*’- Y*) which tunnels between the oscillators of the PC/GNPSCS with each phase shift (PS) of the GN(PS)CS; and C. The SIC golden ratio (p*) separates the M-set hyperbolic bugs, as the (p*) separates the SIC oscillators of the PC/GNPSCS.
16. Non-Chemical, Resonant Induction Model Of Prion Self-Replication.
A novel, non-chemical prion-propagation model posited in this essay is based on superradiance resonant amplification of abnormal misfolded proteins and other molecules due to coherent quantum-mechanical computation according to the GNPSCS rather than an ordinary Cartesian physical chemistry model based on concentration gradients in bulk water. [[1],[2]]
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Figure 16.1 Non-Chemical, Induced Resonance Model Of Prion Self-Replication-by author
Illustrating posited model of non-chemical, prion self-replication due to pathological superradiance. (1) Prion + vicinal water ->(2) ‘abnormal’ microtubule, producing (3) coherent light/laser and coherent sound/phonons causing resonant induction of normally-folded molecule (4) to be altered resulting in an explosion of non-chemical, non-local replicas of the original prion denoted by (5), an asterisk (*). Insofar as the superradiant output of an abnormal prion microtubule occurs in a globally quantum coherent system, the effect of the abnormal superradiance of the prion is not limited to merely local, direct contact chemical reactions as would obtain in a purely bulk water chemical system. [[3]] Rather, the proposed prion-increase mechanism is scale- invariant/conformal such that abnormal superradiance can produce non-local abnormalities/errors at many scales in MAM* ranging in scale from small polymers to: DNA, RNA, endoplasmic reticulum, the mitochondrion, and the whole organism, all of which contribute to desynchronization of global quantum coherence and disease. [[5]]
If living organisms could always ‘calculate’ in a globally quantum-coherent manner using the ‘entropy-free’ Godel Non-Algorithmic, Non-Turing Phase-Shift Computational System GNPSCS (Multi-dimensional Networked Discretized Imaginary Bloch Clock Time Crystal (MNDIBTC), then an organism could, theoretically, be disease-free and ageless. [[6]] The accumulation of errors results in multiple reversions of entropy-free GNPSCS computation to Turing computation, associated in each reversion with an increase in entropy => disease, aging, and death. With respect to the synchronized Bloch clocks of the GNPSCS, these episodes of reversion to a Turing computational system result in desynchronization of these clocks. [[6],[7]] Thus, there are many diseases which are due to abnormal prions [PRotein InfectiON]. [8] Could other abnormally-folded molecules, not limited to proteins, increase due to non-local quantum resonance? [[9],[10]]
17. Alzheimer’s dementia may be a two-prion disease.
There is growing evidence suggesting that Alzheimer’s disease exhibits prion-like characteristics. Prions are misfolded proteins that propagate by inducing other proteins to misfold, leading to neurodegenerative disorders such as Creutzfeldt-Jakob disease. Research indicates that both amyloid-beta (Ap) and tau proteins, which are central to Alzheimer’s pathology, can behave like prions—spreading their misfolded forms throughout the brain and accelerating disease progression. A study from UC San Francisco found that Alzheimer’s may be a “double-prion disorder,” where both AP> and tau act as self-propagating prions. Higher levels of these prions were associated with early-onset Alzheimer’s and faster cognitive decline. This prion-like behavior suggests that Alzheimer’s may not just be a result of protein accumulation but rather an active, spreading process similar to prion diseases. [1 ^ 3]
18. Other Diseases Which May Be Classified as Prion Disease.
Amyloidosis is a group of diseases characterized by the accumulation of amyloid fibrils in various organs and tissues. There are over 30 known types, including AL amyloidosis, AA amyloidosis, ATTR amyloidosis (hereditary and wild-type), ALECT2 amyloidosis, dialysis-related amyloidosis, and localized amyloidosis affecting specific organs. [1 ^ 3] Other forms include fibrinogen amyloidosis, apolipoprotein amyloidosis, gelsolin amyloidosis, and beta-2 microglobulin amyloidosis. [[1], [3]] Some types are associated with neurodegenerative conditions, such as Alzheimer's disease, Parkinson's disease, and prion diseases like Creutzfeldt-Jakob disease [[4], [5]]. Additionally, systemic amyloidoses can affect the heart, kidneys, liver, and gastrointestinal tract, leading to organ dysfunction. [[1],[3]] Research continues to uncover new variants and their underlying mechanisms. Amyloid is a misfolded protein that forms insoluble fibrils, accumulating in tissues and organs. These misfolded proteins adopt a beta-sheet structure, making them resistant to degradation and leading to diseases like Alzheimer’s, Parkinson’s, and systemic amyloidosis. [9 ^ 11] Buildup of amyloid fibrils disrupts normal cellular function, contributing to neurodegeneration and organ failure. [[9],[10]] All of these molecules exist in a watery environment, namely in association with a very thin layer of water—vicinal water—which can produce coherent electromagnetic (laser) and coherent sound (phonons) that may have adverse effects on the organism’s GNPSCS. [6 ^ 8] This essay posits that Alzheimer’s dementia is not a chemical disorder caused by beta-amyloid deposition, but instead arises from abnormal superradiance ‘signals’ emitted by beta-amyloid/vicinal water microtubules, which interfere with the formation of global quantum coherence in the brain—a process essential for normal mental activity. [12’13] *SEE: Tuszynski JA, Kalra A, et al. Quantum optical coherence in microtubules: Experimental support for the Orch OR theory of consciousness. ACS Cent Sci. 2023;9(3):379-390. Available from: https://www.templetonworldcharity.org/blog/interview-jack-tuszynski-aarat-kalra.
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Figure 19.1 by author
Illustrating Bohm’s view of the implicate order as a cosmic hologram, where each part contains the whole. His concept of the explicate (EXPL) and implicate (IMPL) orders, framed within his theory of the holomovement, offers a radical reimagining of reality—one that transcends the Cartesian notion of time as a continuous linear progression from past to present to future. In Bohm’s framework, the explicate order corresponds to the observable world: a realm of distinct objects, sequential time, and direct cause-and-effect relationships. It is the domain in which human perception typically operates. By contrast, the implicate order is a deeper, enfolded dimension of reality—timeless, nonlocal, and holistic—where all things are interconnected and distinctions dissolve. Each moment in the explicate order is not isolated but intimately related to the implicate order, which continually unfolds and enfolds the manifest world (holomovement). This dynamic interplay between EXPL and IMPL orders suggests that what we perceive as linear time may be a surface phenomenon emerging from a deeper, timeless reality. If this model accurately reflects the nature of reality, it could provide a compelling framework for understanding phenomena that challenge conventional scientific paradigms, such as: retrocausal effects of consciousness as hinted at in Libet’s experiments on decision-making and neural timing; synchronicity where meaningful coincidences defy statistical randomness; extrasensory perception (ESP); and other anomalous cognitive phenomena, and prophetic visions, e.g., those attributed to Edgar Cayce and Nostradamus.
These phenomena, often relegated to the realm of mysticism, may find a more coherent explanation within Bohm’s ontological vision. His synthesis of physics and consciousness invites us to reconsider the boundaries of science and reality itself—suggesting that mind and matter are not separate, but expressions of a deeper, unified order. * SEE: Sheldrake, Rupert. The Presence of the Past: Morphic Resonance and the Habits of Nature. Revised edition, Park Street Press, 2012. Sheldrake introduces his theory of morphic resonance, a radical idea suggesting that nature itself has memory. He argues that all self-organizing systems—whether crystals, plants, animals, or societies—are influenced not only by physical laws and genetic inheritance but also by a kind of collective memory embedded in morphic fields.
These fields shape behavior and form by referencing similar patterns from the past, meaning that once something happens, it becomes more likely to happen again. For example, the more often a crystal forms in a particular way, the easier it becomes for future crystals to adopt that same structure. He proposes that ‘laws of nature’ are not fixed, but more in the nature of ‘habits.’ If memories are dynamically encoded within microtubules as a multidimensional hologram— capable of extending beyond the physical brain and leaving imprints within the implicate order— then it’s conceivable that these memory traces could become accessible to organisms within the explicate order, across time. Such access might emerge as intuitions, behavioral inclinations, or even fragmented or complete recollections of past lives, resembling a form of reincarnation. This construct is illustrated in figure 19.1 above where person P1 and person P2 share elements of the implicate order. Sheldrake’s ideas closely parallel David Bohm’s concept of the implicate order, where all moments and forms are enfolded into a deeper, timeless reality. Just as Bohm suggests that each moment in the explicate order is connected to the whole through the implicate order, Sheldrake proposes that morphic fields carry the memory of past forms and behaviors, influencing present and future unfoldings. Both theories challenge a mechanistic worldview and suggest that reality is shaped by patterns, memory, and interconnectedness rather than isolated events or fixed laws.
Sheldrake and Bohm offer a compelling framework for understanding phenomena like ESP, synchronicity, and even prophecy. If consciousness can access these deeper fields—whether through morphic resonance or the implicate order—it might explain how individuals perceive patterns beyond ordinary time and space. Their ideas converge in suggesting that the universe is not a static machine but a dynamic, evolving whole, where past, present, and future are intimately linked through hidden dimensions of reality. Ultimately, this reflects the intellectual ingenuity of those responsible for formulating contemporary physical theories—individuals who, much like their pre-Copernican predecessors, succeeded in constructing elaborate and seemingly coherent models that, despite their internal consistency, failed to capture a more fundamental layer of reality.
20. Relationship of mass-energy to the Godel Non-Turing Non-Algorithmic Phase-Shift Computational System (GNPSCS).
Illustrations are not included in the reading sample
Figure 20-by author asterisk (*) = scale-invariant/conformal (SIC)
Illustrating the posited relationship between our Cartesian continuum mathematics energy relationships between mass, the speed of light, the Planck constant, and frequency given by the equations: (1) E = (mc[2] = Av) rewritten as (m/v)* = (A/c[2])*; (2) the GNPSCS where scale- invariant/conformal (SIC) mass relates to SIC oscillator frequency (m/v)*; (3) p* is the SIC separation between oscillators; (3) light traveling through the fractal tunnel has at least one imaginary ‘direction’ and one real direction along the fractal tunnel (i y*)(y*) = i (y*)[2] illustrated as the grey area between the oscillators; and (4) y* = (SIC electromagnetic radiation/information). There is an interesting connection between the bible text: ‘let there be light’ as the primary act of creation, and the PC/GNPSCS posited in this essay. In figure 20, we have [m = ( A/c[2]) v] or [m/v = A/c[2]], the basic Cartesian continuum mathematical equations relating energy, mass, the reduced Planck constant, the speed of light in vacuo as it relates to the SIC mass, frequency, golden ratio separation, and tunneling light information in the PC/GNPSCS, and how it comports, in a philosophical sense, to the single creative act ‘let there be light’ where light alone is sufficient to create the cosmos. “And God said, ‘Let there be light,’ and there was light.”- Genesis 1:3. This was the first act of creation in the biblical narrative, symbolizing the emergence of order from chaos. It's one of the most iconic lines in religious and literary history, often quoted in philosophical, scientific, and artistic contexts. In Hebrew: "liX"'i1'l HIX 'il' □'il^X "I^X’I, Vayomer Elohim yehi or vayehi-or (and said, God, let there be/may it be light and there was light). This religious text brings to mind Bohm’s idea of unending depths of inwardness of the implicate order which parallels metaphysical notions of Brahman or God—not as external agents, but as the generative ground of being itself. In Bohm’s terms, the implicate order is not a static blueprint but a living, evolving potential, where consciousness and matter co-arise. Our current level of cognition, shaped by fragmentation and linear causality, cannot yet perceive this depth directly, but the mathematics of quantum theory invites a new paradigm where science and ontology converge. The GNPSCS is the ‘reality’ while our Cartesian-based Turing mathematics is its ‘shadow’ on Plato’s cave wall, suggesting the need for a fundamental shift in our understanding of the universe and our computational model. A fractal cosmos could imply that reality is emergent, recursive, and deeply interconnected, challenging traditional notions of linear time and spatial continuity.
21. Can the PC/GNPSCS Support a SUSY model?
Illustrations are not included in the reading sample
Figure 21.1 by author
Illustrating the posited ‘equivalence’ of particles with spin % and bosons with spin 1, both being artefacts of our prevailing Cartesian continuum mathematics. Visualize ‘A’ rotated clockwise 30[0] to ‘B’, and ‘C’ rotated 30[0] clockwise to ‘D’, where the rotation changes particles for fractal tunnels, and fractal tunnels for particles. In the PC/GNPSCS model, a multidimensional network of scale- invariant/conformal (SIC) oscillator/particles separated by SIC p* communicate with one another by SIC electromagnetic information (EMI) (y*) tunneling through SIC fractal tunnels. This essay posits reality as a dynamic, recursive web of wave-particle-like entities exchanging information in a way that is invariant under SIC transformation. Such a fractal system viewed through the lens of Cartesian continuum mathematics could appear as our current model of physics. Particles (circles) represent localized excitations or standing wave nodes in a fractal oscillator network, and forces represent emergent interactions between these nodes mediated by the geometry and dynamics of the fractal tunnels (fractal jagged line) and SIC EMI. Oscillators are the information, and the information is the oscillators. This aligns with Bohm’s ideas, that particles and forces are emergent phenomena—not fundamental, but rather arising from deeper, more holistic dynamics. An analogy to this idea is the wave-particle duality in physics. Philosophically, this model blurs the line between object and interaction, and being and becoming, suggesting a reality where: (1) entities are defined by their relationships; (2) information and structure are two sides of the same coin; and (3) reality is a recursive, self-referential dance of patterns. It defines a flexible, creative, universe. *SEE: Goldberg, M. GRIN Verlag (2024), The primacy of creativity: Does an eternally creative cosmos entail free will and moral responsibility? Moreover, this model aligns with Supersymmetry (SUSY), a theoretical idea that links matter and forces by proposing that every particle has a partner with opposite spin type—fermions (matter particles) have bosonic partners (force carriers), and vice versa. This symmetry suggests that matter and forces are two aspects of the same underlying structure. In this respect fractal geometry and supersymmetry could be mutually reinforcing where superpartners might be artefacts of our prevailing Cartesian continuum mathematics of different modes or phases of an underlying multidimensional oscillator network. Would our current methods of detecting supersymmetric particles explain why the LHC has not detected them? It attempts to find elementary particles produced in high-energy collisions, not emergent patterns from complex networks. If these SUSY-like effects operate in higher dimensions or through nonlocal interactions, they may not leave signatures detectable by our current instruments. The PC/GNPSCS model may require a shift in perspective—from searching for particles to decoding the underlying patterns that give rise to them. In a fractal SIC framework, spin might emerge from the topology of oscillators and fractal tunnels across scales. The rapid ‘interchange’ between oscillators representing spin % particles and fractal connecting tunnels representing spin 1 bosons is akin to ambiguous images or reversible figures, i.e., multi-stable perception where perception alternates between different interpretations of the same stimulus. If so, then the fractal tunnel in one perception represents a spin 1 boson and, in an alternate perception, represents a spin % fermion where the tunnel has a Mobius twist that translates to a 720[0] (360[0] x 2) ‘rotation’ which a spin % particle undergoes in order to reach its original orientation. This suggests that bosons and fermions might be Cartesian-based explicate-order artefacts of two ‘superposed’ aspects of a deeper relationship in the PC/GNPSCS.
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Figure 21.2
Illustrating SUSY superpartners may lie in Bohm’s implicate order such that attempts to find them using Cartesian continuum mathematics in the LHC has been unsuccessful in finding superpartners such as Squarks: Superpartners of quarks (e.g., stop, sbottom); Sleptons: Superpartners of leptons (e.g., selectron, smuon, stau); Sneutrinos: Superpartners of neutrinos; and Gluino: Partner of the gluon; expected to be strongly interacting and heavy: Wino and Zino: Partners of the W and Z bosons; Photino: Partner of the photon; Gravitino: Partner of the graviton; often considered in models involving supergravity; and Higgsinos: Superpartners of the Higgs bosons. Could it be that superpartners are Bohm implicate order entities which unfold as the basic particle we are trying to find the superpartner of, so that attempting to find them in the LHC is like a particle chasing its own implicate-order tail? Is the search for superpartners bound to fail because they are artefacts of our prevailing Cartesian continuum mathematical paradigm? In Bohm’s framework, the implicate order is a deeper, enfolded reality from which the explicate (observable) order unfolds. If we imagine SUSY superpartners as entities residing in this implicate domain, then what we observe—quarks, leptons, bosons—are just their unfolded explicate-domain manifestations seen through a Cartesian continuum mathematics lens. Trying to detect a superpartner in the LHC, then, becomes a kind of recursive act: the explicate order probing its own deeper structure, perhaps without the right lens to perceive it. The metaphor of a particle chasing its own implicate-order tail evokes a kind of ontological feedback loop, where the act of observation is entangled with the very structure being observed. It’s reminiscent of quantum holism, where parts are not truly separable from the whole. If SUSY particles are not just heavier counterparts but different modes of unfolding from a deeper order, then maybe the LHC’s brute-force approach—smashing particles at higher energies—isn’t the right key for that lock. It might require a paradigm shift in how we conceptualize detection: not just looking for mass signatures, but perhaps patterns, correlations, or emergent behaviors that hint at implicate dynamics. SUSY might not be a mechanical symmetry, but a process symmetry—a symmetry of unfolding aligning with some speculative approaches in quantum gravity and string theory, where spacetime and particles emerge from deeper informational or geometric substrates. Similarly, the search for a dark matter particle may be misguided.
22. DISCUSSION.
Seemingly intractable problems in physics may be a consequence of using the wrong mathematical paradigm, i.e., Cartesian continuum mathematics, when a more useful multidimensional non-linear fractal system such as the GNPSCS is warranted. Applying continuum mathematics to a non-continuum, non-linear, and non-deterministic fractal reality leads to several dilemmas, namely reconciling quantum mechanics and general relativity, explanations for phenomena such as dark matter, dark energy, and the emergence of the cosmos from ‘nothing.’ As an extension to the work of Arkani-Hamed, Bandyopadhyay, Bohm, Gardi, Penrose, Rovelli, and Wheeler, this essay posits: the explicate-order GNPSCS as a better model of reality than our current deterministic Cartesian continuum mathematical paradigm.
Much of our current cosmological modeling is grounded in a Cartesian-based continuum framework, which traditionally frames reality through local deterministic laws or probabilistic randomness. However, emerging theories challenge this paradigm, suggesting that deeper, nonlocal or discrete structures may underlie the fabric of the cosmos. In contrast, the GNPSCS is posed as a granular/non-continuum scale-invariant/conformal (SIC) multidimensional time crystal comprised of discretized networked imaginary Bloch clock oscillators separated by SIC (p*), and communicating by SIC (y*) electromagnetic tunneling information. In this model ‘time’ corresponds to ticking of networked imaginary Bloch clock oscillators where each tick represents a phase-shift computation of the GNPSCS. Mass is a function of oscillator frequency where higher-frequency clocks correspond to greater mass-energy equivalence. The strong force, Newtonian gravity, dark matter, and dark energy are posed as SIC (y*) electromagnetic tunneling information. An oscillator with the frequency of an electron having only a few tick marks on its clock, transitions between explicate and implicate orders after just a few GNPSCS phase-shift computations. By contrast, an eon oscillator with ‘p’ tick marks, representing an imaginary Bloch clock at the largest scale, transitions from explicate to implicate orders in a cosmic amount of time as perceived within our current Turing-based computational paradigm.
Aphorisms often distill profound insights into compact expressions: John Wheeler’s ‘it from bit’ expresses the notion that matter is fundamentally tied to information, and his comment, ‘Space tells matter how to move—matter tells space how to curve,’ encapsulates general relativity; a quote frequently attributed to Nikola Tesla—though likely apocryphal— suggests, ‘If you want to find the secrets of the Universe, think in terms of energy, frequency, and vibration’; and Einstein’s profound insight—‘As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.’ These statements imply that our current mathematical frameworks may be inadequate to fully grasp the complexities of space, time, matter, life, and consciousness. For example, such seemingly intractable problems as the number of primes, their distribution, and relationship to the Riemann hypothesis may represent recursive, fractal-like patterns, i.e., prime numbers may not be purely random, but instead follow complex, possibly recursive, fractal-like rules that challenge conventional mathematical frameworks.
Following Bohm, this essay posits that the implicate order Phi Connectome (PC) emerges from randomness—that is, from a state of nothingness (no-thing, no-where, no-when). In this context, the classical dictum ‘Ex nihilo nihil fit’ (‘nothing comes from nothing’) remains valid, provided that randomness is construed as a form of nothingness. The Phi Connectome (PC) is a self-creating, self-organizing, and self-maintaining entity of implicate order—characterized by no-thingness, no- where-ness, and no-time/no-when-ness—emerging from the quantum vacuum plasma plenum. Its corresponding explicate-order computational system, the Godel Non-Turing Non-Algorithmic Phase-Shift Computational System (GNPSCS), or ‘Godel computer,’ is proposed as a model of reality. In contrast, our prevailing Cartesian continuum model is likened to a mere shadow on the wall of Plato’s cave.
The GNPSCS aligns with Nima Arkani-Hamed’s assertion that spacetime is doomed. While Rovelli, Verlinde, Vopson, and Wheeler have explored the deep interrelation between gravity, entropy, and information, their reliance on Cartesian-based continuum mathematics imposes significant limitations. Because the GNPSCS draws, in part, on Godel’s incompleteness theorems, the pursuit of a Theory of Everything (TOE) may be inherently constrained by the deterministic nature of current mathematical frameworks. Similarly, the existence of consciousness may elude formal proof within the confines of Boolean logic.
Ginestra Bianconi’s 2025 paper ‘Gravity from Entropy’ introduces a quantum gravity framework grounded in quantum relative entropy between spacetime and matter-induced metrics. Her synthesis spans statistical mechanics, quantum field theory, and geometric modeling, signaling a paradigm shift toward informational and topological formulations of gravitational phenomena.
Within the GNPSCS, each tick of a networked oscillator clock corresponds to a Godel phase-shift computation. At the quantum scale, implication manifests as superposition, while explication appears as wave function collapse—a phase transition triggered by observation or, in Penrose’s theory, a non-computable reduction (non-Turing computation) resulting from a subtle difference in spacetime curvature. When this curvature difference exceeds a critical threshold, the superposition becomes unstable and collapses. Between quantum and cosmic scales lies a mesoscopic realm where deterministic models begin to break down and Godelian incompleteness obtains. In this transitional zone, biological systems emerge. The GNPSCS framework suggests that reality here unfolds through phase-shift transitions, challenging Cartesian logic and offering deeper insight into consciousness, complexity, and computation.
At the cosmic scale, implication represents the superposition of a current and subsequent Penrose aeon. Explication, in turn, marks the collapse of that superposition—the end of one aeon and the emergence of another. This transition does not occur through a singular Big Bang, but rather via a boundary-less phase shift. Each new aeon unfolds from a previously enfolded one, constituting a recursive computation within the GNPSCS. Thus, the Big Bang and the conventional notion of time’s beginning are artifacts of a mechanistic, Cartesian-based mathematical paradigm.
The GNPSCS model described here has been foreshadowed in the intuitions and frameworks of Einstein, Mandelbrot, Tesla, Arkani-Hamed’s amplituhedron, Rovelli’s loop quantum gravity, string theory, Chol Furey’s octonionic algebra, Bandyopadhyay’s phase prime metric, and Basil Hiley’s work on Clifford algebras. These contributions hint at a deeper, modular architecture of reality—one that the GNPSCS seeks to formalize and operationalize.
The PC/GNPSCS framework introduces a radically different approach to computation and modeling—one that transcends Turing machines, algorithmic logic, and Cartesian continuity. At its foundation lies a network of non-linear, fractal-like oscillators composed of imaginary Bloch clocks. These clocks form a Multidimensional Networked Discretized Imaginary Bloch Clock Time Crystal (MNDIBTC), where each tick represents a phase-shift computation. The oscillators are separated by a scale-invariant/conformal (SIC) golden ratio barrier, defined by p* (approximately 1.618...), which prevents destructive resonance and preserves coherence across scales. Communication between SIC oscillators occurs via SIC electromagnetic tunneling (y*), an exchange of information that manifests as SIC expressions of the fundamental forces: strong, weak, electromagnetic, Newtonian gravity, dark matter, dark energy, and Hawking radiation.
Fractal Differential Geometry (FDG) reimagines black holes not as spatial voids but as dynamic nodes in a network of quantum oscillators, where space, mass, and gravity emerge from layered interference patterns. A black hole event horizon becomes a phase transition zone—marked by nested, increasingly fine-grained oscillators—rather than a physical boundary, making the notion of an “interior” a category error. Light propagation, redshift, and even Hawking radiation are shaped by these fractal layers, suggesting that time dilation and entropy arise from shifts in coherence, not curvature. FDG aligns with holography by encoding information across multi-scale boundaries and supports quantum error correction through nested oscillator regimes, preserving information in a non-local, fractal format. In this framework, gravity is global coherence, quantum mechanics is local interference, and mass is a standing wave of stabilized information—offering a unified, computational view of spacetime itself. The information paradox asks: If black holes evaporate via Hawking radiation, where does the information go? FDG suggests that what we call “inside” the black hole is actually a phase transition zone, not a place. So instead of information falling into a mysterious void, it gets re-encoded across fractal layers near the horizon. This could preserve information in a non-local, oscillator-based format—sidestepping the paradox entirely.
If Feynman diagrams are represented as pictorial depictions of the calculations of a Godel non- algorithmic phase-shift system rather than with Turing algorithmic methods, then it is not surprising that the electron ‘knows’ how to interact with the photon instantly because GNPSCS calculations are non-algorithmic, i.e., they are a ‘search without searching’ where the answer is found as an immediate ‘clique.’ By contrast, an algorithmic computer, even a fast supercomputer, has to search for an answer which is far slower. Similarly, a polypeptide folds into a protein in a matter of seconds. If the organism were to use step-wise Turing computation to fold a polypeptide, then it might take a cosmic amount of time for the protein to form. Quantum-coherent organisms use the GNPSCS, obtain a ‘clique’ answer, and fold the polypeptide in a matter of seconds.
Cartesian continuum mathematics forces reality into smooth, linear models that can't account for modular or coherence-based structures. As a result, artefacts appear : the beginning of the universe from nothing with a ‘big bang,’ and dark matter, and dark energy emerge as ‘patches/fixes’, i.e., attempts to account for observations that don’t fit the prevailing linear continuum model. These ‘patches/fixes’ aren't necessarily real entities—they’re symptoms of trying to explain fractal-based phenomena with a tool designed to deal with a continuous spacetime.
The GNPSCS reframes these puzzling entities as artefacts, not mysterious processes or substances. For example, the search for a dark matter ‘particle’ is fundamentally misguided because it assumes that unexplained gravitational effects must arise from a discrete, undetected substance (a dark energy particle), fitting the Cartesian-continuum paradigm’s need to preserve mass-energy balance within a smooth spacetime manifold. But this approach ignores the possibility that the observed anomalies (e.g., galactic rotation curves, lensing effects) may stem, instead, from coherence dynamics, not missing matter. The pursuit of dark energy as a mysterious force driving cosmic acceleration may be fundamentally misguided—an artifact of the Cartesiancontinuum paradigm that treats space as a smooth, passive backdrop. Within this framework, expansion is modeled through scalar fields or vacuum energy, abstract constructs that attempt to explain cosmic behavior using mathematical continuity and local determinism. But this approach may obscure deeper, nonlocal or phase-shift dynamics that lie beyond the reach of conventional field equations.
Hence, our prevailing continuum framework treats the universe as a homogeneous manifold, so any deviation from expected constant expansion demands a compensatory ‘dark energy’ input. As a result, we are currently beset with accounting for a cosmos which our current cosmological model estimates is composed of approximately 5% ordinary matter, 27% dark matter, and 68% dark energy. Ordinary matter includes all the atoms that make up stars, planets, and living beings—everything we can observe directly. Dark matter, though invisible, reveals its presence through gravitational effects on galaxies and galaxy clusters. Dark energy is even more mysterious, driving the accelerated expansion of the universe. These proportions are derived from a combination of observational data, including measurements of the cosmic microwave background, large-scale structure, and distant supernovae.
Turing-based computational systems inherently involve iterative processes which produce entropy. By contrast, the GNPSCS model allows instantaneous ‘clique’ answers bypassing (long and possibly non-halting) Turing step-by-step processes which generate ‘computational entropy.’
Wheeler’s ‘it from bit,’ Rovelli’s loop quantum gravity, and Verlinde's entropic gravity suggest that all these physicists recognize information as a fundamental aspect of reality. They have touched on the idea that gravity might emerge from deeper principles of information exchange and entropy, and their work highlights the interconnectedness of these concepts.
Nima Arkani-Hamed’s multi-dimensional geometric amplituhedron represents scattering amplitudes (probabilities of particle interactions) as the ‘volume’ of a geometric object in a mathematical space called the positive Grassmannian (bypassing off-shell Feynman diagrams), offering a more elegant and efficient way to compute these amplitudes. In Arkani-Hamed's amplituhedron framework, the usual assumptions of locality and unitarity—core principles in quantum field theory—are not built in from the start. Instead, these principles emerge naturally from the geometry of the amplituhedron itself, which encodes particle interactions without relying on space-time or traditional field-based calculations. Locality refers to the idea that particles interact only with nearby points in space-time, while unitarity ensures that probabilities in quantum processes always sum to one, preserving information. The amplituhedron suggests that these features are not fundamental, but rather consequences of deeper mathematical and geometric structures.
Bohm proposes that quantum theory reveals an ‘undivided wholeness in flowing movement’—a radical shift from the worldview of classical physics. He argues that particles are not isolated entities but abstractions from a deeper, interconnected process. He suggests that everything in the universe is enfolded into everything else, and that reality is fundamentally a unified, dynamic whole. His work involves entanglement, especially through his reformulation of the Einstein- Podolsky-Rosen paradox using spin systems, which made quantum nonlocality experimentally testable. In his pilot-wave theory, particles are guided by a quantum potential that connects them instantaneously, regardless of distance, reflecting a real physical form of entanglement. This interpretation treats entangled particles not as isolated entities but as parts of a unified whole, emphasizing the interconnectedness of quantum systems beyond classical constraints.
If the fractal PC/GNPSCS is a model of reality, then general relativity emerges as a smooth approximation—a mathematical ‘limit’ of that fractal structure. Just as Mandelbrot showed that coastlines, clouds, and galaxies defy classical geometry but obey fractal logic, so too might spacetime itself be a large-scale shadow of recursive, nonlocal dynamics.
In his book, ‘A Brief History of Time’ Stephen Hawking introduces the concept of imaginary time as a way to resolve deep paradoxes in physics—especially those involving singularities, the origin of the universe, and the unification of quantum mechanics with general relativity. Imaginary time is a mathematical construct where time is treated like a spatial dimension by multiplying it by the imaginary number, i = (-1)[1]/[2] transforming the time axis into a direction that behaves more like space, smoothing out the sharp edges and infinite densities that arise in models of black holes and the Big Bang. Hawking suggests that if we describe the universe in terms of imaginary time, singularities disappear—there’s no ‘edge’ to time, no beginning or end, just a smooth, curved geometry like the surface of a sphere—Wheeler’s comment, ‘the boundary of a boundary is zero.’
In Hawking’s view, the universe doesn’t start with a bang but emerges from a timeless, boundaryless state. He even muses that imaginary time might be more fundamental than real time, and what we perceive as ‘real’ time could be a projection from this deeper, more symmetrical domain. This idea resonates with Bohm’s implicate order and the GNPSCS framework: both propose that the observable world unfolds from a hidden, nonlocal substrate. Imaginary time offers a mathematical bridge to that substrate, where coherence, recursion, and symmetry replace linear causality and temporal boundaries. It’s a glimpse into a reality where time itself is enfolded within a deeper geometry. If the fractal PC/GNPSCS is a model of reality, general relativity emerges as a smooth approximation of that reality—roughly speaking—the mathematical ‘limit’ of that fractal.
Fractal geometry, proposed by Benoît Mandelbrot adds another layer to this vision providing a framework for describing self-similar, irregular structures that appear in nature—clouds, coastlines, or even galaxy distributions. Fractals reveal how complex, self-similar structures can emerge from simple recursive rules, suggesting that the universe may be governed by deep patterns of iteration and scale invariance. Imaginary time offers a mathematical bridge to that substrate, where coherence, recursion, and symmetry replace linear causality and temporal boundaries. It hints at a reality in which time itself is enfolded within a deeper geometry—one that may be fractal in nature.
Living organisms have been viewed primarily as biochemical machines—functioning within three-dimensional bulk water and governed by the differential equations of physical chemistry. This perspective shaped the dominant paradigm of mechanistic medicine, treating life as a series of chemical reactions rather than as dynamic, integrated systems. However, insofar as the organism represents a frequency range of the GNPSCS, then it should be treated as a quantum- coherent whole. This means it is not generally possible to treat part of an organism without affecting it at all scales because all its ‘parts’ are entangled. Western mechanistic medicine has long approached the human body as a fragmented assembly of parts, treating symptoms in isolated regions with chemicals, radiation, or surgery, often without regard for the impact on the whole organism. This reductionist view excludes the role of consciousness and dismisses non-traditional therapies—such as placebos, acupuncture, and other mind-body interventions as scientifically invalid, despite growing evidence of their systemic effects.
Just as quantum mechanics unveiled our error in treating the cosmos as a simple deterministic machine—made up of several separate parts interacting locally and causally, and described by Cartesian-based infinitesimal linear mathematics—so, too, we have been in error treating the organism as a machine as if it were comprised of separate parts interacting locally and deterministically. Thus, our current ‘mechanistic’ medical treatment paradigm has often led to unanticipated adverse results that have been explained as ‘side effects,’ often requiring warnings, more pharmaceuticals, and other treatments to deal with these side effects. Consequently, new pharmaceuticals and other potentially beneficial treatments have to undergo lengthy animal and human trials which often delay their introduction, and significantly increase the cost when they are finally approved.
This essay proposes that the organism is more accurately modeled by the scale- invariant/conformal (SIC) construction: MAM*, where M and M* represent structures at progressively larger scales—atoms, molecules, macromolecules, DNA, organelles such as mitochondria, cells, tissues, organs, and ultimately the entire organism. The symbol ‘A’ denotes vicinal water: a thin, two-dimensional sheet of ordered (quasicrystalline) water that separates M and M* at every scale. This layer functions as a tunnel for the transmission of ordered photon/laser and ordered sound/phonon, information enabling non-local, near-instantaneous communication and coordination throughout the organism.
It is posited that a non-mechanistic medicine paradigm might treat diseases such as Alzheimer’s dementia by restoration of the brain’s global quantum coherence using pulsed laser/phonon entraining frequencies. The scale-invariant/conformal effects of the proposed use of externally- applied specific laser/phonon frequencies could affect ‘MAM*’ at all scales, such that the integrity of DNA and the production of stem cells might be maintained, perhaps indefinitely. This same technique might be extended to support astronaut health during prolonged exposure to microgravity, potentially eliminating the need for exercise regimens or centrifugally-induced artificial gravity systems such as rotating habitat wheels. Furthermore, laser or phonon frequencies generated by superconductive systems might produce resonant interference patterns capable of deflecting or neutralizing high-energy cosmic radiation only requiring minimal power and weight—thereby reducing or even eliminating the need for heavy physical shielding in spacecraft design.
Building on the foundational insights of David Bohm, Anirban Bandyopadhyay, Carlo Rovelli, Nima Arkani-Hamed, and Lori Gardi, the Phi Connectome/Godel Non-Turing Non-algorithmic Phase-Shift Computational System (PC/GNPSCS) integrates and extends their contributions into a unified, recursive framework that models reality as a modular, scale-invariant computational system.
David Bohm’s implicate-explicate order provides the philosophical substrate for the PC/GNPSCS. The Phi Connectome (PC) represents the implicate order—a non-local potential— while the GNPSCS is its explicate unfolding, a phase-shift computational system that stages emergence through networked oscillator transitions. Bohm’s holomovement is formalized as a recursive mechanism where each oscillator tick triggers a phase-shift computation.
Anirban Bandyopadhyay’s multidimensional time crystal concept, expanding on Wilczek’s original formulation, introduces a triplet-of-triplet nested oscillator coherence spanning both biological and quantum domains. The GNPSCS builds on this by embedding these oscillators within a multidimensional networked discretized imaginary Bloch clock time crystal (MNDIBTC). Each clock tick corresponds to a phase-shift computation, and when a clock ticks past its modal midnight, it undergoes an order change—if it’s in the implicate order to the explicate order or vice versa. This essay posits that a networked model is preferable to Bandyopadhyay’s nested oscillator framework when aiming to unify quantum mechanics, general relativity, and Bohm’s implicate order because it supports non-hierarchical, scale-transcending coherence. Unlike the nested model, which builds resonance through internal containment, the networked approach allows bidirectional communication across all scales via scale-invariant relationships like the golden ratio. This enables global quantum coherence, nonlocal information flow, and dynamic adaptability—essential for modeling entangled cosmological eons, emergent particles as explicate artefacts, and holistic health systems rooted in resonance rather than reductionism.
Carlo Rovelli’s Loop Quantum Gravity and Nima Arkani-Hamed’s amplituhedron geometry challenge the primacy of spacetime as a fundamental entity. The PC/GNPSCS reframes space, time, and mass as emergent properties of oscillator frequency, phase-shift computation, and electromagnetic tunneling dynamics. Space arises from the networked configuration of scale- invariant/conformal (SIC) Bloch clocks, time corresponds to the ticking of these clocks, and mass is a function of oscillator frequency. SIC electromagnetic (EM) tunneling information/force- gravity (y*) propagates between oscillators along fractal pathways whose dimensionality aligns with oscillator frequency. These oscillators are separated by SIC golden ratio (p*) barriers, preventing mutual resonant destruction and preserving coherence.
The Mandelbrot Set offers a visual and mathematical analogy: its hyperbolic ‘bugs’ are networked in self-similar layers. Just as the M-set builds complexity through networked repetition, the PC/GNPSCS represents a multidimensional networked time crystal where SIC nodes are locked together by SIC tunneling information. Lori Gardi’s work with the Mandelbrot set (modelled by the recursive formula zn+1 = (zn)[2] + c, and fractal modeling provides mathematical intuition for networked complexity. The GNPSCS operationalizes this by assigning fractal dimensionality to SIC tunneling pathways and using cp* as a separation principle preventing oscillator mutual resonant destruction. This turns fractal geometry into functional architecture, enabling scale- invariant/conformal information transfer across the oscillator network.
SIC EM tunneling information (y*) is posited as a unified informational- gravitational force, manifesting differently across scales: as the strong nuclear force at the subatomic level; Newtonian gravity modified by the Kolmogorov-Arnold-Moser (KAM) effect at planetary scales; and at increasingly larger scales as dark matter, dark energy, Hawking radiation, and Hawking points on the cosmic microwave background (CMB) of a subsequent Penrose aeon. At the quantum scale, implication is perceived as superposition and explication as wave function collapse—a phase change of the GNPSCS triggered by observation or due to Penrose objective reduction. At the cosmic scale, implication represents the superposition of a current and future eon, and explication marks the collapse of that superposition, initiating the unfolding of a new eon via a boundary-less phase shift rather than a big bang.
The PC/GNPSCS reframes gravity, entropy, and emergence as phase-shift informational dynamics within a networked oscillator architecture. It is a departure from Cartesian continuum mathematics toward a fractal, non-linear, non-deterministic system—one that is modular, recursive, scale-invariant/conformal, and aligned with quantum mechanics, life, consciousness and cosmic phenomena. This framework has been foreshadowed by: Einstein, Tesla, Arkani- Hamed, Rovelli, string theory, Chol Furey’s octonionic algebra, Basil Hiley’s Clifford algebras, Melvin Vopson’s theory that the universe operates like a computational system, where information behaves recursively—suggesting a fractal-like structure underlying cosmological phenomena..
The GNPSCS models reality while our current Cartesian-based continuum mathematical paradigm is a shadow on Plato’s cave wall. This essay posits that using the fractal mathematics of the GNPSCS rather than our current Cartesian-based continuum mathematics will: (1) reconcile quantum mechanics with general relativity; (2) explain the big bang, the nature of dark matter, dark energy, and the evolution and death of the cosmos; (3) provide an explanation for life and consciousness; and (4) suggest a novel means of treating diseases such as cancer and Alzheimer’s dementia by exposing an organism to specific frequencies of coherent EM radiation and coherent sound that may help or even supplant our current mechanistic medicine’s use of pharmaceuticals, radiation, and surgery.
Godel’s incompleteness theorems reveal that any sufficiently expressive formal system will contain true statements that cannot be proven within the system. This constraint undermines the possibility of a complete, self-contained ‘theory of everything’ (TOE) posed within algorithmic or binary-logical frameworks. The GNPSCS suggests that reality may be fundamentally non- algorithmic, where coherence replaces step-wise computation as the organizing principle. This reframes a TOE, not as a closed set of axioms, but as an open-ended map of phase relationships, where ‘truth’ is not fully capturable by proof, and meaning arises through oscillatory coherence rather than logical closure. Put briefly: If reality operates as a GNPSCS—a system transcending Turing-computable, algorithmic, and continuum-based models—then pursuit of a TOE within Cartesian and Boolean logic paradigms may be inherently limited, echoing Godel’s insight that formal systems cannot fully encapsulate their own truths.
Wheeler’s “it from bit” concept fits beautifully into the PC/GNPSCS framework. His idea—that every physical entity (“it”) ultimately derives from immaterial information (“bit”)—suggests that reality is fundamentally informational, not material. This aligns with the PC/GNPSCS view that space, time, and matter emerge from coherent flows of information generated by scale-invariant oscillators—imaginary clocks pulsing in golden-ratio-separated rhythms. In Wheeler’s vision, the universe is participatory: observers and measurements help bring reality into being. Similarly, the PC/GNPSCS model treats each tick of these clocks as a Godel phase-shift computation—a discrete informational event that reshapes reality. Rather than relying on continuous equations, it sees the universe as a dynamic network of informational pulses, where “bit” isn’t just a metaphor but the actual substrate of existence. So Wheeler’s insight acts as a philosophical foundation for this multidimensional time crystal: it affirms that what we perceive as “physical” is the result of deep, structured informational coherence—exactly what the PC/GNPSCS system seeks to model and explain.
Godel’s first incompleteness theorem states that in any sufficiently powerful formal system, there are true statements that cannot be proven within the system itself. This implies that no purely algorithmic process can capture all truths. Roger Penrose famously invoked this idea to argue that human consciousness must involve non-computable processes—something beyond classical computation. He suggested that the brain might access truths that lie outside formal systems, and that this ability could be rooted in quantum processes. Quantum coherence in the brain, particularly in microtubules and vicinal water as proposed by Goldberg and supported by researchers like Bandyopadhyay, could provide the substrate for such non-computable insight. If consciousness arises from synchronized quantum phase-shift computations—where information is processed through resonance, entanglement, and phase transitions—then it may operate in a domain that transcends classical logic and algorithmic boundaries. This would allow the brain to “see” or intuit truths that Godel’s theorems say cannot be derived mechanically. In this view, quantum coherence is not just a physical phenomenon but a gateway to a deeper informational field—perhaps akin to Bohm’s implicate order—where truths are enfolded and accessible through resonance rather than deduction. Consciousness, then, becomes a kind of Godelian oracle: a system that can perceive beyond its own formal limits by tapping into quantum coherence and the non-local structure of reality. So while Godel’s theorems are mathematical/logical, their implications ripple into physics, neuroscience, and philosophy—suggesting that the brain’s quantum coherence might be the very mechanism that allows us to transcend formal systems and experience insight, creativity, and awareness.
Finally, the ideas presented in this essay are speculative and provisional—intended to bridge the currently diverse disciplines of mathematics, quantum physics, chemistry, and consciousness studies in order to stimulate dialogue among mathematicians, physicists, biologists, and philosophers, as well as fostering closer collaboration between Western science and medical traditions and Eastern philosophies and their healing practices.
23.SUMMARY
The Phi Connectome/Godel Non-Turing Non-algorithmic Phase-Shift Computational System (PC/GNPSCS) synthesizes and extends foundational theories from Bohm, Bandyopadhyay, Rovelli, Arkani-Hamed, Gardi, and others into a unified framework. It models reality as a networked, multidimensional time crystal comprised of discretized imaginary Bloch clocks that tick with each phase-shift computation. These imaginary clocks span all scales, from Planck-level oscillators to cosmic eons. In the PC/GNPSCS, scale-invariant/conformal (SIC) electromagnetic tunneling information (y*) flows between oscillators along fractal pathways, with golden ratio ( <p*) barriers preserving coherence, and preventing destructive resonance. A PC/GNPSCS model reframes space, time, and mass as emergent properties of oscillator frequency and phase-shift dynamics, an alternative to Cartesian linear continuum mathematics. Scale-invariant/conformal electromagnetic tunneling information (y*) manifests differently across increasing scales: as the strong force, Newtonian gravity, dark matter, dark energy, Hawking radiation, and Penrose aeon transitions. Quantum collapse and cosmic evolution are formalized as recursive phase-shift computations, bridging quantum field theory, statistical mechanics, and topological geometry, bringing together ideas from different theories into a system that helps explain how patterns form, connect, and evolve throughout the universe. These concepts bridge mathematics, quantum physics, chemistry, biology, and consciousness studies, and will hopefully stimulate dialogue among scientists, medical practitioners, philosophers, and foster a foundation for closer collaboration between Western science and Eastern traditions.
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R., Engel, M., & Glotzer, S. C. (2014). Dense crystalline dimer packings of regular tetrahedra. Discrete & Computational Geometry, 51(4), 739-762. https://doi.org/10.1007/s00454-014-9618-2. (6) van Anders, G., Klotsa, D., Ahmed, N. K., Engel, M., & Glotzer, S. C. (2014). Understanding shape entropy through local dense packing. Proceedings of the National Academy of Sciences, 111(45), E4812-E4821. https://doi.org/10.1073/pnas.1408471111. (7) Glotzer, S. C., & Solomon, M. J. (2007). Anisotropy of building blocks and their assembly into complex structures. Nature Materials, 6(8), 557-562. https://doi.org/10.1038/nmat1949. (8) Geng, J., van Anders, G., & Glotzer, S. C. (2017). Entropic patchiness and emergent directionality in shape-driven colloidal assembly. Nature Communications, 8, Article 998. https://doi.org/10.1038/s41467-017-01021-5. (9) Arkani-Hamed, N., & Trnka, J. (2014); The Amplituhedron. Journal of High Energy Physics, 2014(10), 30. https://doi.org/10.1007/JHEP10(2014)030; (10) Henn, J. M. (2020). What can we learn about QCD and collider physics from N = 4 super Yang-Mills? Annual Review of Nuclear and Particle Science, 70, 221-245. https://arxiv.org/abs/2006.00361; (11) Cai, T., He, S., & Zhang, Q. (2025). Recurrent features of amplitudes in planar N=4 super Yang-Mills theory. Journal of High Energy Physics, 2025(4), 143. https://link.springer.com/article/10.1007/JHEP04(2025)143. (12) Richard Feynman's reflections in his book QED: The Strange Theory of Light and Matter (Princeton University Press, 1985), where he writes: ‘Nature uses only the longest path, the shortest path, and all the paths in between—simultaneously. How does the electron do that?’ [The answer to his question might be that the GNPSCS is non-algorithmic in which the answer (a clique) is found immediately such that a time-and-energy-consuming Turing step-wise computation is not required.] (13) Wikipedia Energy-Momentum_relation. (14) Bandyopadhyay, A. (2020). Phase Prime Metric (PPM) Links All Symmetries in Our Universe and Governs Nature’s Intelligence. In Nanobrain (Chapter 3). CRC Press. https://www.taylorfrancis.com/chapters/mono/10.1201/9780429107771-3/phase-prime-metric- ppm-links-symmetries-universe-governs-nature-intelligence-anirban-bandyopadhyay [The PPM uses prime number sequences to encode symmetry-breaking, morphogenesis, and resonance phenomena across biological and physical systems. It’s foundational to Bandyopadhyay’s time crystal brain model and aligns with GNPSCS and phi connectome logic]. (15) Bandyopadhyay, A. Phase Prime Metric (PPM) Links All Symmetries in Our Universe and Governs Nature’s Intelligence. 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(2011). On the origin of gravity and the laws of Newton. Journal of High Energy Physics, 04, 029. https://arxiv.org/abs/1001.0785. (25) Barbour, J., et al. (2015). Entropy and the Universe. Zurich Workshop. PDF. (26) Vopson, M. M. (2025). Is gravity evidence of a computational universe? AIP Advances, 15(4), 045035. https://doi.org/10.1063/5.0264945. (27) Kelman, A., & Ou Yang, D. H. (2020). Model of Hypercomputation: Closed Time Curve Turing Machines. PDF. (28) Vopson, M. M. (2025). New Study Suggests Gravity May Be an Optimization Process. The Quantum Insider. (29) Wikipedia contributors. Entropic Gravity. https://en.wikipedia.org/wiki/Entropic_gravity. (30) Watson, C. N. (2023). Theory of Gravity Dependent on Entropy. Reports in Advances of Physical Sciences, 7(2350006). https://doi.org/10.1142/S2424942423500068. (31) Wikipedia - Plato’s allegory of the cave. Essay proposing GNPSCS as a non-linear, fractal replacement for Cartesian continuum mathematics. (32) Higgs, P. W. (1964). Broken Symmetries and the Masses of Gauge Bosons. Physical Review Letters, 13(16), 508-509. (33) CERN. The Higgs boson overview. 2012 validation of Brout- Englert-Higgs mechanism. (34) HyperPhysics. Conceptual summary of Higgs field. Electroweak unification. (35) Wikipedia contributors. Higgs boson. Standard Model refinements and LHC results. (36) Wheeler, J. A. It from Bit and geon concept. Quantum gravity foundations. (37) Rovelli, C. (1996). Black Hole Entropy from Loop Quantum Gravity. Spin network derivation of horizon entropy. (38) Rovelli, C. Thermal time hypothesis and gravitational entropy without hidden microstates. (39) Verlinde, E. (2011). Entropic gravity. Holographic and thermodynamic derivation. (40) Bianconi, G. (2025). Gravity from Entropy. Quantum relative entropy and G-field Lagrangian framework. (41) Jacobson, T. (1995). Thermodynamics of Spacetime. Horizon entropy and Einstein equations. (42) Padmanabhan, T. Entropy maximization and emergent gravity. Horizon degrees of freedom
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(1) Britannica Editors. Geocentric model. Encyclopedia Britannica. https://www.britannica.com/science/geocentric-model. (2) Space.com Editors. Geocentric model: The Earth-centered view of the universe. https://www.space.com/geocentric-model. (3) Universe Today. What Is The Geocentric Model Of The Universe? https://www.universetoday.com/articles/geocentric-model. (4) History.com Editors. Copernicus: Facts, Model & Heliocentric Theory. https://www.history.com/articles/nicolaus-copernicus. (5) Rochester University. The Copernican Model: A Sun-Centered Solar System. https://www.pas.rochester.edu/~blackman/ast104/copernican9.html. (6) World History Edu. Copernican Heliocentrism - History and Major Facts. https://worldhistoryedu.com/copemican- heliocentrism-history-and-major-facts/. (7) Britannica Editors. Heliocentrism. Encyclopedia Britannica. https://www.britannica.com/science/heliocentrism. (8) Hossenfelder, S. (2018). Lost in Math: How Beauty Leads Physics Astray. Basic Books. https://www.amazon.com/Lost-Math- Beauty-Physics-Astray/dp/0465094252.
Chapter # 8
(1)Einstein, A.(1921).Geometry and Experience. Address to the Prussian Academy of Sciences. English translation in Sidelights on Relativity, Methuen & Co. Ltd.See also Mathematical Association of America’s contextual analysis. (2)Bohm, D.(1980).Wholeness and the Implicate Order.Routledge.See Wikipedia summary and Open Horizons overview. (3)Bohm, D., & Hiley, B. J.(1993). The Undivided Universe: An Ontological Interpretation of Quantum Theory. Routledge. See JSTOR review. (4)Bohm, D., & Peat, F. D.(1987). Science, Order, and Creativity.Routledge.See Science and Nonduality summary. (5)Bohm, D.(1990). A New Theory of the Relationship of Mind and Matter. Philosophical Psychology, 3(2-3), 271-286.See Wikipedia on Holomovement. (6)Mandelbrot, B. B.(1982).The Fractal Geometry of Nature.W. H. Freeman and Company.See Wikipedia entry. (7)Peitgen, H.-O., Jürgens, H., & Saupe, D.(1992).Chaos and Fractals: New Frontiers of Science.Springer-Verlag.See David Bohm’s fractal analogies. (8)Baez, J.(2005). The Planck Length. Department of Mathematics, UC Riverside.See Baez’s article. (9)Giddings, S. B.(2001).“Quantum Gravity and the Planck Scale.” University of California, Santa Barbara.See Einstein Light module. (10)Rovelli, C.(2004).Quantum Gravity.Cambridge University Press.See Taylor & Francis paper on holomovement. (11)Herzenberg, C. L.(2006). A New Basis for Interpretation of the Planck Length. arXiv:physics/0610127.See arXiv PDF.
Chapter # 9
(1)Einstein, A.(1921).Geometry and Experience. Lecture at Prussian Academy of Sciences. (2)Tesla, N.(attributed).Quoted in various sources on vibrational cosmology. (3)Zizzi, P.(2012).The Non-Algorithmic Side of the Mind.arXiv:1205.1820. (4)Goldberg, M.(2024). The Primacy of Consciousness: Is the Phi Connectome the Conscious Reality Underlying Our Perceptions in Spacetime? GRIN Verlag (2024). (5)He, J.(2014). A Tutorial Review on Fractal Spacetime and Fractional Calculus. International Journal of Theoretical Physics, 53, 3698-3718. (6)Rabin, M.(2013). Turing, Church, Godel, Computability, Complexity and Logic. BU Turing Conference. (7)Sacha, K., & Zakrzewski, J.(2017).Time Crystals: A Review.arXiv:1704.03735. (8)Wikipedia contributors.(2024).Time Crystal.https://en.wikipedia.org/wiki/Time_crystal. (9)Gibson, A.(2024).What Are Time Crystals and Why Are They Important? andrewgibson.com. (10)Lukin, D. M., et al.(2020). Integrated Quantum Photonics with Silicon Carbide. PRX Quantum, 1(2), 020102. (11)Breev, I. D., et al.(2021).Inverted Fine Structure of a 6H-SiC Qubit.arXiv:2107.06989. (12)Penrose, R.(2010).Cycles of Time: An Extraordinary New View of the Universe.Bodley Head.
Chapter # 10
(1)Penrose, R.(1996).On Gravity's Role in Quantum State Reduction. General Relativity and Gravitation, 28(5), 581-600. (2)Eckstein, M.(2023).Conformal Cyclic Cosmology, gravitational entropy and quantum information. General Relativity and Gravitation, 55(26). (3)Penrose interpretation-Wikipedia. https://en.wikipedia.org/wiki/Penrose_interpretation. (4)Hawkins, S. L.(2014).William James and the Theatre of Consciousness. In Brain, Mind and Consciousness in the History of Neuroscience (pp. 185-206).Springer. (5)Tomaz, A. A., Mattos, R. S., & Barbatti, M.(2023).Gravitationally-induced Wave-function Collapse Time for Molecules. ChemRxiv. (6)Bohm, D.(1980).Wholeness and the Implicate Order. Routledge. (7)Langan, C.(2002).The Cognitive-Theoretic Model of the Universe: A New Kind of Reality Theory. Noesis. (8)Seiberg, N.(2006). Emergent Spacetime. arXiv:hep-th/0601234.
Chapter # 11
Section A
(1)Bisiani, J., Anugu, A., & Pentyala, S.(2023).It’s Time to Go Quantum in Medicine. Journal of Clinical Medicine, 12(13), 4506. (2)Higgins, J. P.(2002).Nonlinear Systems in Medicine. Yale Journal of Biology and Medicine, 75(5-6), 247-260. (3)Philippe, P., & Mansi, O.(1998).Nonlinearity in the Epidemiology of Complex Health and Disease Processes. Theoretical Medicine and Bioethics, 19, 591-607. (4) Bystritsky, A., et al.(2012).Computational Non-Linear Dynamical Psychiatry. Journal of Psychiatric Research. (5)Ching, L. M., et al.(2023).Enabling Health Potential: Exploring Nonlinear and Complex Results of Osteopathic Manual Medicine. Journal of Osteopathic Medicine. (6)Bertl, M., et al.(2025).Quantum Machine Learning in Precision Medicine and Drug Discovery.arXiv:2502.18639v1. (7)Fatunmbi, T. O.(2023).Revolutionizing Healthcare Diagnosis Through Quantum Neural Networks. World Journal of Advanced Research and Reviews, 17(01), 1319-1338. (8)Andersen, B. H., et al.(2025).Evidence of Universal Conformal Invariance in Living Biological Matter. Nature Physics. Comments by M. Goldberg, author of this essay: [The study by Andersen et al. (2025) found that the swirling motion of living cells—like bacteria and cancer cells—follows a hidden mathematical symmetry called conformal invariance, meaning the patterns look the same even when zoomed in, stretched, or rotated. This connects directly to scale-invariance in the GNPSCS framework, where systems show consistent behavior across different levels of magnification. The winding angle, which measures how much a curve twists as you follow it, helps reveal this symmetry. Just as GNPSCS models coherence across domains, these biological flows show universal geometric behavior, suggesting that even living matter may be governed by deep mathematical rules similar to those seen in quantum systems. Quantum coherence, which involves phase-aligned states, offers a hidden structure that parallels the invisible order found in these biological patterns, reinforcing the idea that both life and physics may share a common language of recursive, scale-invariant geometry.] (9)Durham, W. M., et al.(2025).Universal Conformal Invariance Discovered in Living Cell Motion. Science News Today. (10)Jibu, M., et al.(1994).Quantum Optical Coherence in Cytoskeletal Microtubules. BioSystems, 32, 195-209. (11)Frumkin, V., et al.(2023).Superradiant Droplet Emission from Parametrically Excited Cavities. Physical Review Letters, 130, 064002. (12)Hameroff, S., & Penrose, R.(2014).Consciousness in the Universe: A Review of the ‘Orch-OR’ Theory. Physics of Life Reviews, 11(1), 39-78.
Section B
(1) Rubik, B., & Jabs, H.(2017).Effects of Intention; Energy Healing and Mind-Body States on Biophoton Emission. Cosmos and History, 13(2), 227-247. (2)Xu, L., et al.(2012).The energy pump and the origin of the non-equilibrium flux of dynamical systems. Journal of Chemical Physics, 136(16), 165102. (3)Le Jeannic, H., et al.(2017).Slowing Quantum Decoherence by Squeezing in Phase Space.arXiv:1707.06244. (4)Babelyuk, V., et al.(2025).Biophotonic Information Transfer through Water-Mediated Neural Resonance. Journal of Experimental Health Sciences, 2025(77), 58167. (5)Zand, H.(2025).Biophotons May Shed New Light on Body and Brain Activity. Psychology Today. (6)Quantum Sound Therapy.(2024).Synergy Float Center.https://synergyfloatcenter.com/services/quantum-sound-therapy/. (7)Matsuura, M., et al.(2024).Singular continuous and nonreciprocal phonons in quasicrystal AlPdMn. Physical Review Letters, 133, 136101. (8)Wang, J., et al.(2009).Biophysical Journal, 97, 3038. (9)Jaross, W.(2020).The Possible Role of Molecular Vibration in Intracellular Signalling. Journal of Cell Signaling, 1(4), 180-186.
Section C
(1)Wave function collapse-Wikipedia. https://en.wikipedia.org/wiki/Wave_function_collapse. (2)Penrose interpretation - Wikipedia. https://en.wikipedia.org/wiki/Penrose_interpretation. (3)Gely, M., & Steele, G. A. (2021). Superconducting electro-mechanics to test Diosi-Penrose effects. AVS Quantum Science. https://doi.org/10.1116/5.0050988. (4)Oosterkamp, T. H., & Zaanen, J. (2016). A clock containing a massive object in a superposition of states. arXiv:1401.0176. (5)Tomaz, A. A., Mattos, R. S., & Barbatti, M. (2023). Gravitationally-induced Wave-function Collapse Time for Molecules. ChemRxiv. (6)Hawkins, S. L. (2014). William James and the “Theatre” of Consciousness. In Brain, Mind and Consciousness in the History of Neuroscience. Springer. (7)Brahma, S., Alaryani, O., & Brandenberger, R. (2020). Entanglement entropy of cosmological perturbations. Physical Review D, 102, 043529. (8)Bohm, D. (1980). Wholeness and the Implicate Order. Routledge. (9)Langan, C. (2002). The Cognitive-Theoretic Model of the Universe-CTMU: A New Kind of Reality Theory. Noesis. Comments by M. Goldberg, author of this essay: [Chris Langan’s CTMU (Cat Mew), the GNPSCS framework, Bohm’s implicate order, and Sheldrake’s morphic resonance—all converge on a shared vision of reality as recursive, nonlocal, and coherence-driven. The CTMU proposes that reality is a selfsimulating cognitive structure, where logic and syntax are embedded in the fabric of existence itself. This aligns with GNPSCS, which treats biological and cognitive systems as modular expressions of recursive coherence across scales. Both frameworks reject mechanistic causality and instead model reality as a layered (networked), self-referential system governed by internal logic and phase-aligned propagation. Moreover, Bohm’s implicate order complements this by describing a hidden, enfolded domain (the Plenum/Phi Connectome PL/PC) from which observable phenomena emerge—an underlying field of self-forming, self-maintaining, coherence that gives rise to the explicate world. The posited explicate order GNPSCS echoes this structure by treating coherence as the substrate for biological, cognitive, and clinical expression. Furthermore, Sheldrake’s morphic resonance adds a biological dimension, suggesting that systems inherit memory from past forms through nonlocal fields of influence. This supports the GNPSCS’s view of modular propagation and recursive patterning, where form and function are shaped by coherence rather than chemical gradients. Together, these four frameworks form a coherent metaontology: reality is not built from particles and forces alone, but from recursive logic, memory fields, and nonlocal resonance—modularized across domains and scales.]
Section D
(1) Gardi, L.(2017).The Mandelbrot Set as a Quasi-Black Hole. CNPS Conference. https://beyondmainstream.org/scientist/lori-gardi. (2)Zizzi, P.(2012).The Non-Algorithmic Side of the Mind.arXiv:1205.1820. (3)Goldberg, M.(2024).The Primacy of Consciousness: Is the Phi Connectome the Conscious Reality Underlying Our Perceptions in Spacetime? GRIN Verlag. (4)He, J.(2014).A Tutorial Review on Fractal Spacetime and Fractional Calculus. International Journal of Theoretical Physics, 53, 3698-3718.
Chapter # 12
(1) Ghosh, S., & Bandyopadhyay, A.(2013). Quantum brain biology: GBFF theory and application. Neuroquantology, 11(3), 367-377. (2)Petersen, R. C.(2004).Mild cognitive impairment as a diagnostic entity. Journal of Internal Medicine, 256(3), 183-194. (3)Takahashi, R. H., et al.(2002).Intraneuronal Alzheimer Ap accumulation and its impact on neuron function. Journal of Neuroscience, 22(12), 5574-5583. (4)Takahashi, R. H., et al.(2002).Intraneuronal Alzheimer A0 accumulation and its impact on neuron function. Journal of Neuroscience, 22(12), 5574-5583. (5)Gouras, C. G., Tampellini, B. T., Takahashi, M. S., et al.(2000).Intraneuronal A0 accumulation in human and transgenic models of Alzheimer’s disease. The Journal of Neuroscience, 20(23), 8587-8593. (6)Selkoe, D. J.(1994).The Cell Biology of the Amyloid BetaProtein Precursor and the Mechanism of Alzheimer’s Disease. Annual Review of Cell Biology, 10, 373-403. (7)Koo, E. H.(1998).Intracellular accumulation of 0-amyloid: a link between Alzheimer’s disease and Down syndrome? Trends in Molecular Medicine, 4(3), 102-108. (8)Eisenbud, J.(1983).Parapsychology and Psychoanalysis. In Parapsychology and Human Nature. McFarland. (9)Kradin, R.(2004).The Psychoanalytic Exploration of Psi. In The Placebo Response and the Power of Unconscious Healing. Routledge. (10)Javitt, D. C., et al.(2023).Amyloid-related visual dysfunction in preclinical Alzheimer’s disease. Alzheimer’s Research & Therapy, 15, Article 42. (11)Javitt, D. C., et al.(2023).Altered visual event-related potentials in amyloid-positive individuals. Alzheimer’s Research & Therapy, 15, Article 42. (12)Yesantharao, S. V., et al.(2023).Proprioceptive impairments and cortical amyloid burden in cognitively normal adults. Alzheimer’s & Dementia: Diagnosis, Assessment & Disease Monitoring, 15, e12407. (13)Jiang, X., et al.(2025).EEG coherence in frontal and temporal regions distinguishes FTD and AD. Cognitive Neurodynamics, 19, Article 46. (14)Salcini, C., et al.(2020).Altered theta and alpha rhythms in FTD subtypes. Psychiatry and Clinical Psychopharmacology, 30(2), 182-185. (15)Buzsaki, G.(2006).Rhythms of the Brain. Oxford University Press. (16)Song, Y, et al.(2022).Monoclonal antibody trials for Alzheimer’s disease. Translational Neurodegeneration, 11, Article 18. (17)Esquer, J., et al.(2023).Beyond beta-amyloid: Emerging therapies for Alzheimer’s disease. Neurology and Therapy, 12, 1883-1907. (18)Ghosh, A., & Bandyopadhyay, A.(2014).Frequency fractal architecture for brain-like computing. Information, 5(1), 28-100. (19)Saxena, A., et al.(2020).Scale-free fractal resonance in biological systems. Fractal and Fractional, 4(2), Article 11. (20)Marshall, M.(2025).Quantum-coherent attractor recursion in MNDIBTC and GBFF interfacing. Unpublished Framework. (21)Marshall, M.(2025).Coherence disruption strategies using out-of-phase light and sound in Alzheimer’s treatment. Chapter 13:GNPSCS Protocols.
Chapter # 13
(1)Rafati, Y., et al.(2020).Effect of microtubule resonant frequencies on neuronal cells. Proceedings of SPIE, 11238, Optical Interactions with Tissue and Cells XXXI. https://doi.org/10.1117/12.2546569. (2) Viola, K. L., et al.(2021). The Therapeutic and Diagnostic Potential of Amyloid 0 Oligomers. Frontiers in Neuroscience, 15, 768646. https://doi.org/10.3389/fnins.2021.768646. (3)Hameroff, S., & Penrose, R.(2014).Consciousness in the Universe: A Review of the Orch-OR Theory. Physics of Life Reviews, 11(1), 39-78. https://doi.org/10.1016/j.plrev.2013.08.002. (4) Science Daily Editors.(2014). Discovery of quantum vibrations in microtubules inside brain neurons. https://www.sciencedaily.com/releases/2014/01/140116085105.htm. (5) Zhang, M., et al.(2021).Amyloid 0 oligomers and memory dysfunction in 5xFAD mice. Frontiers in Neuroscience, 15, 768646. https://doi.org/10.3389/fnins.2021.768646. (6)Hameroff, S., et al.(2015).Anesthetics Act in Quantum Channels in Brain Microtubules to Prevent Consciousness. Galileo Commission. https://galileocommission.org/anesthetics-act-in-quantum-channels-in- brain-microtubules-to-prevent-consciousness-hameroff-et-al-2015.
Chapter # 14
(1)Peng, W., Zhu, Z., Lou, J., Chen, K., Wu, Y, & Chang, C.(2023). High-frequency terahertz waves disrupt Alzheimer’s ß-amyloid fibril formation. Light, 3, Article 18.https://elight.springeropen.com/articles/10.1186/s43593-023-00048-0. (2)Pontula, S.(2023). Superradiant Phase Transitions in Quantum Optics. MIT Department of Physics.https://web.mit.edu/8.334/www/grades/projects/projects23/PontulaSahil.pdf. (3)Oh, S.- H., Kim, J., Ha, J., Son, G., & An, K.(2024). Thresholdless coherence in a superradiant laser. Light: Science & Applications, 13, Article 239.https://www.nature.com/articles/s41377-024-01591-2. (4)Nadolny, T., Brunelli, M., & Bruder, C.(2025). Nonreciprocal interactions induce frequency shifts in superradiant lasers. arXiv:2501.13808.https://arxiv.org/pdf/2501.13808. (5)Luo, Z., Xu, H., Liu, L., Ohulchanskyy, T. Y., & Qu, J.(2021). Optical Imaging of Beta-Amyloid Plaques in Alzheimer’s Disease. Biosensors, 11(8), 255.https://www.mdpi.com/2079-6374/11/8/255. (6)Chierici, F., Dogariu, A., & Tuszynski, J. A.(2022). Computational Investigation of the Ordered Water System Around Microtubules: Implications for Protein Interactions. Frontiers in Molecular Biosciences,Article 884043.https://www.frontiersin.org/articles/10.3389/fmolb.2022.884043/full. (7)Khatua, P., & Bandyopadhyay, S.(2018).“Dynamical crossover of water confined within the amphiphilic nanocores of aggregated amyloid ß peptides. “Physical Chemistry Chemical Physics, 20(21),14256-14266.https://pubs.rsc.org/en/content/articlelanding/2018/cp/c8cp01942h. (8)Hameroff, S., Craddock, T. J. A., & Tuszynski, J. A.(2015). “Anesthetics Act in Quantum Channels in Brain Microtubules to Prevent Consciousness. The Galileo Commission.https://galileocommission.org/anesthetics-act-in-quantum-channels-in-brain- microtubules-to-prevent-consciousness-hameroff-et-al-2015/. (9)Current Topics in Medicinal Chemistry, 15(6), 523-533. Hameroff, Craddock, and Tuszynski (2015) propose that anesthetics block consciousness by disrupting quantum processes in brain microtubules.
Chapter # 15
(1)Fredriksson B. An Introduction to the Mandelbrot Set. KTH Royal Institute of Technology; 2015. (2) Potgieter PH. Hypercomputing the Mandelbrot Set? arXiv preprint. 2006. Available from: https://arxiv.org/pdf/cs/0604003.pdf; (3) Nesharim E., Geometry of Hyperbolic Components in the Interior of the Mandelbrot Set. MSc Thesis, Hebrew University; 2008. Available from: https://math.huji.ac.il/~ereznesh/MSc.pdf; (4) Devaney RL. The Complex Geometry of the Mandelbrot Set. In: ISCS 2013: Interdisciplinary Symposium on Complex Systems. Springer; 2014. Available from: https://math.bu.edu/people/bob/papers/prague.pdf. (5) MathyBits. Mandelbrot Set - Recursive Dynamics and Escape-Time Algorithms. Available from: https://www.mathybits.org/mandelbrot; (6) Bohm D. Wholeness and the Implicate Order. Routledge; 1980; (6) Wikipedia contributors. Implicate and Explicate Order. Wikipedia. Available from: https://en.wikipedia.org/wiki/Implicate and explicate order.
Chapter #16
(1) Saa P, Castilla J, Soto C. Cyclic Amplification of Protein Misfolding and Aggregation. Methods Mol Biol. 2005;299:53-65. https://link.springer.com/protocol/10.1385/1-59259-874-9:053; (2) Mercer RCC, Harris DA. Mechanisms of prion-induced toxicity. Cell Tissue Res. 2023;392:81- 96. https://link.springer.com/article/10.1007/s00441 -022-03683-0; (3) Ribes JM, Patel MP, Halim HA, et al. Prion protein conversion at two distinct cellular sites precedes fibrillisation. Nat Commun. 2023; 14:43961. https://www.nature.com/articles/s41467-023-43961-1.pdf; (4) Spiers JG, Chen HJC, Steinert JR. Redox mechanisms and their pathological role in prion diseases. PLoS Pathog.2023;19(4):e1011309. (5)Zhou Z, Xiao G. Conformational conversion of prion protein in prion diseases. Acta Biochim Biophys Sin. 2013;45(6):465-476. https://academic.oup.com/abbs/article/45/6/465/1298; (6) Rudolph MS, Jones T, Teng Y, et al. Pauli Propagation: A Computational Framework for Simulating Quantum Systems. arXiv. 2025. https://arxiv.org/abs/2505.21606; (7) Greer ML, Pujo-Menjouet L, Webb GF. A mathematical analysis of the dynamics of prion proliferation. J Theor Biol. 2006;242(3):598-606. https://math.univ-lyon1.fr/~pujo/greer-webb-JTB2006.pdf; (8) Sengupta I, Udgaonkar J. Monitoring site-specific conformational changes in real-time reveals a misfolding mechanism of the prion protein. eLife. 2019;8:e44698. https://elifesciences.org/articles/44698. (9) Mays C. Treatment with a Non-Toxic, Self-Replicating Anti-Prion. CJDFoundation.org. 2023. https://cjdfoundation.org/wp-content/uploads/2023/09/7-Mays.pdf. (10) Shorter J. Emergence and natural selection of drug-resistant prions. Mol BioSyst. 2010;6(10):1115-1130. https://www.med.upenn.edu/shorterlab/Papers/MolBiosys10.pdf.
Chapter # 17
(1) Weiler, N. (2019, May 1). Alzheimer’s Disease is a ‘Double-Prion Disorder,’ (led by Stanley Prusiner, Nobel prize in medicine 1997 for discovery of prions) Shows: Self-Propagating Amyloid and Tau Prions found in Post-Mortem Brain Samples, With Highest Levels in Patients Who Died Young. UCSF News. https://www.ucsf.edu/news/2019/05/414326/alzheimers-disease-double- prion-disorder-study-shows. (2) News Staff. (2019, May 7). Alzheimer’s Amyloid-Beta and Tau Proteins Act as Prions, New Research Finds. Sci.News. https://www.sci.news/medicine/alzheimers-disease-double-prion-disorder-07162.html. (3) Cara, E. (2019, May 3). These Scientists Want to Redefine Alzheimer’s as a ‘Double-Prion’ Disease. Gizmodo.https://gizmodo.com/these-scientists-want-to-redefine-alzheimers-as-a-doubl- 1834486386.
Chapter # 18
(1)Merlini, G., & Bellotti, V. (2003). Molecular mechanisms of amyloidosis. New England Journal of Medicine, 349(6), 583-596; (2) Sipe, J. D., et al. (2014). Amyloid fibril protein nomenclature: 2014 recommendations. Amyloid, 21(4), 221-224; (3) Gertz, M. A. (2020). Immunoglobulin light chain amyloidosis: 2020 update on diagnosis, prognosis, and treatment. American Journal of Hematology, 95(7), 848-860; (4) Goedert, M. (2015). NEURODEGENERATION. Alzheimer’s and Parkinson’s diseases: The prion concept in relation to assembled A0, tau, and a-synuclein. Science, 349(6248), 1255555; (5) Prusiner, S. B. (1998). Prions. Proceedings of the National Academy of Sciences, 95(23), 13363-13383; (6) Del Giudice, E., et al. (2005). Water as a free electric dipole laser. Physical Review Letters, 94(16), 168101; (7) Vitiello, G. (2001). My Double Unveiled: The Dissipative Quantum Model of Brain. John Benjamins Publishing; (8) Preparata, G. (1995). QED Coherence in Matter. World Scientific; (9) Chiti, F., & Dobson, C. M. (2006). Protein misfolding, functional amyloid, and human disease. Annual Review of Biochemistry, 75, 333-366; (10) Knowles, T. P., et al. (2014). The amyloid state and its association with protein misfolding diseases. Nature Reviews Molecular Cell Biology, 15(6), 384-396; (11) Eisenberg, D., & Jucker, M. (2012). The amyloid state of proteins in human diseases. Cell, 148(6), 1188-1203; (12) Tuszynski, J. A., et al. (2017). The role of quantum effects in brain activity: Protein conformational dynamics and coherence. Biosystems, 164, 1-7; (13) Georgiev, D. D. (2022). Quantum brain biology: Exploring the role of quantum coherence in Alzheimer’s disease. Journal of Integrative Neuroscience, 21(3), 1-15.
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