In ontdekte ik de octonions en de ANPA.en schreef er een uitgebreide blog over The Simple Geometry of the Big Transformation.
Toen ging ik schrijven over de convergence engine, kwam Doug Matzke weer terug.
Deze blog bevat een uitgebreide update over zijn recente werk met William Tiller.
The Matzke-Tiller Framework: Quantum Information Theory and Consciousness Research
Abstract
The intersection of quantum mechanics and consciousness studies has produced numerous theoretical frameworks attempting to bridge the explanatory gap between objective physical processes and subjective experience. Among these approaches, the collaborative work of quantum computing engineer Douglas Matzke and materials physicist William Tiller represents a particularly ambitious attempt to formalize consciousness within a mathematically rigorous quantum information framework. This article examines their joint theoretical contributions, situates their work within the broader landscape of quantum consciousness research, and evaluates their methodological approach alongside other prominent researchers in the field.
Introduction
The “hard problem” of consciousness—explaining how and why physical processes give rise to subjective experience—remains one of the most significant challenges in contemporary science. While neuroscience has made substantial progress in mapping neural correlates of consciousness, the mechanistic explanation for how neural activity produces qualitative, first-person experience continues to elude researchers. This explanatory gap has prompted several theorists to look beyond classical physics toward quantum mechanics for potential solutions.
The collaboration between Douglas Matzke and William Tiller, culminating in their 2019 work “Deep Reality: Why Source Science May Be the Key to Understanding Human Potential,” represents a sophisticated attempt to ground consciousness in quantum information theory. Their approach combines Matzke’s expertise in quantum computing and hyperdimensional mathematics with Tiller’s experimental work in psychoenergetics and intention-based phenomena.
William Tiller: Psychoenergetics and Experimental Foundations
Background and Credentials
William Albert Tiller (1929-2022) established his scientific reputation as Professor Emeritus of Materials Science and Engineering at Stanford University, where he served for 34 years (1964-1992), including a period as department chairman (1966-1971). His conventional scientific work focused on crystallization processes, resulting in over 250 published papers and several books published by Cambridge University Press. Tiller was a Fellow of the American Academy for the Advancement of Science and received a Guggenheim Fellowship in 1970.
Psychoenergetic Research Program
Following his retirement from Stanford in 1992, Tiller developed what he termed “psychoenergetic science”—the systematic investigation of how human consciousness and intention might influence physical systems. His experimental program centered on Intention Imprinted Electronic Devices (IIEDs), simple electrical circuits that he claimed could be “charged” with specific intentions through meditative practices.
Tiller’s most documented experiments involved pH modification in water solutions. In controlled studies conducted at multiple laboratories, groups of experienced meditators would focus specific intentions (such as increasing or decreasing pH by one unit) into basic electronic devices. These devices were then shipped to remote laboratories where they allegedly influenced the acidity of water solutions over extended periods.
The results, replicated across ten independent studies, showed statistically significant pH changes consistent with the intended modifications. Tiller reported pH shifts of up to 1.5 units in some experiments, with effect sizes far exceeding measurement error margins. These findings formed the empirical foundation for his theoretical model of consciousness-matter interaction.
Theoretical Framework: Dual-Space Physics
Tiller proposed a “dual-space” model of reality consisting of:
- D-Space (Direct Space): Our familiar three-dimensional reality governed by electromagnetic forces and characterized by speeds less than light velocity
- R-Space (Reciprocal Space): A parallel domain existing as the mathematical Fourier transform of D-space, dominated by magnetic monopole forces and characterized by speeds exceeding light velocity
According to this model, consciousness primarily operates in R-space, allowing for non-local effects and explaining phenomena such as telepathy, clairvoyance, and intention-based influence on physical systems. The coupling between these spaces, quantified through thermodynamic free energy calculations, provided Tiller with specific numerical predictions about consciousness-matter interactions.
Douglas Matzke: Quantum Computing and Hyperdimensional Mathematics
Professional Background
Douglas J. Matzke (born 1953) earned his doctorate in quantum computing from the University of Texas in 2002, following a distinguished career at Texas Instruments where he worked on semiconductor design tools and neural computing systems. His doctoral dissertation, “Quantum Computing Using Geometric Algebra,” established his expertise in the mathematical frameworks underlying quantum information theory.
During his 25-year tenure at Texas Instruments, Matzke contributed to fifteen disclosed patents, published over fifty technical papers, and served as chairman of two PhysComp workshops on physics and computation. His work on high-dimensional mathematics and neural networks positioned him uniquely to address the computational aspects of consciousness research.
Theoretical Contributions: Source Science and Quantum Mind
Matzke’s approach to consciousness, which he terms “Source Science,” is grounded in quantum information theory and geometric algebra. His central thesis proposes that consciousness operates as a quantum computing system existing in hyperdimensional space, fundamentally distinct from classical neural computation.
Key elements of Matzke’s framework include:
Hyperdimensional Information Processing
Matzke argues that consciousness utilizes quantum information processing in spaces with hundreds or thousands of dimensions, far exceeding the three-dimensional constraints of physical space. This hyperdimensional architecture enables the non-local, holistic properties characteristic of conscious experience.
Quantum Bit (Qubit) Networks
Drawing from his quantum computing expertise, Matzke proposes that conscious states emerge from networks of quantum bits operating through what he calls “correlithm” processing—a form of quantum neural computation that enables pattern recognition and semantic processing beyond classical computational capabilities.
Information-Energy Duality
Following Wheeler’s “it from bit” hypothesis, Matzke argues for a fundamental information-energy duality in which information becomes the primary constituent of reality, with energy and matter emerging as secondary phenomena. This perspective positions consciousness as an informational system with causal efficacy over physical processes.
The Matzke-Tiller Synthesis: Deep Reality Framework
Collaborative Integration
The collaboration between Matzke and Tiller, documented in their co-authored work “Deep Reality,” represents an attempt to integrate theoretical quantum information science with experimental psychoenergetic findings. Their joint framework proposes that:
- Consciousness operates as a quantum computing system utilizing hyperdimensional information processing capabilities
- Human intentions can be encoded as quantum information and transmitted through non-local quantum correlations
- Physical reality emerges from informational constraints operating in quantum field structures
- The brain serves as an interface between hyperdimensional consciousness and three-dimensional physical reality
Methodological Approach
Their theoretical framework employs several mathematical formalisms:
- Geometric Algebra: Providing a unified mathematical language for quantum mechanics and consciousness studies
- Quantum Field Theory: Describing the fundamental information structures underlying both matter and mind
- Thermodynamic Analysis: Quantifying the energy exchanges involved in consciousness-matter interactions
- Information Theory: Modeling conscious experience as quantum information processing
Comparative Analysis: Positioning Within Consciousness Research
Quantum Consciousness Theories
The Matzke-Tiller framework can be understood within the broader context of quantum approaches to consciousness, which includes several prominent theoretical programs:
Penrose-Hameroff Orchestrated Objective Reduction (Orch-OR)
The most well-known quantum consciousness theory, developed by mathematician Roger Penrose and anesthesiologist Stuart Hameroff, proposes that consciousness arises from quantum computations in microtubules within neurons. Like Matzke-Tiller, Orch-OR emphasizes non-computational aspects of consciousness and proposes quantum information processing as fundamental to awareness.
Key similarities with Matzke-Tiller include:
- Emphasis on quantum coherence in biological systems
- Non-computational approach to consciousness
- Integration of quantum mechanics with neuroscience
Key differences include:
- Orch-OR focuses on specific cellular structures (microtubules) while Matzke-Tiller proposes hyperdimensional processing beyond physical constraints
- Penrose-Hameroff emphasizes objective reduction of quantum states, while Matzke-Tiller emphasizes information-theoretic approaches
Stapp’s Mind-Matter Interaction Model
Physicist Henry Stapp has developed a quantum mechanical model of consciousness based on the orthodox von Neumann interpretation of quantum mechanics. Stapp proposes that conscious observations collapse quantum wave functions, providing a mechanism for mental causation of physical events.
Similarities with Matzke-Tiller:
- Emphasis on consciousness as causally efficacious
- Integration of quantum mechanics with psychology
- Focus on the measurement problem in quantum mechanics
Differences:
- Stapp works within orthodox quantum mechanics while Matzke-Tiller propose extensions involving hyperdimensional spaces
- Stapp emphasizes wave function collapse while Matzke-Tiller focus on information processing
Vitiello-Freeman Quantum Field Theory Approach
Physicists Giuseppe Vitiello and Walter Freeman have applied quantum field theory to neural dynamics, proposing that consciousness emerges from quantum field fluctuations in neural tissue.
Similarities with Matzke-Tiller:
- Use of quantum field theoretical frameworks
- Emphasis on collective quantum phenomena
- Integration with neuroscientific findings
Differences:
- Vitiello-Freeman focuses on neural field dynamics while Matzke-Tiller propose consciousness as existing independently of brain states
- Different mathematical formalisms (standard QFT vs. geometric algebra approaches)
Experimental Methodology Comparisons
The Matzke-Tiller approach differs significantly from other quantum consciousness theories in its emphasis on controlled experimental validation. While most quantum consciousness theories remain largely theoretical, Tiller’s psychoenergetic experiments provide empirical data supporting their framework.
Comparison with Other Experimental Approaches
Princeton Engineering Anomalies Research (PEAR): Robert Jahn and Brenda Dunne conducted extensive studies of human consciousness effects on random number generators. Like Tiller’s work, PEAR experiments showed statistically significant but small-magnitude effects of intention on physical systems.
Global Consciousness Project: Roger Nelson’s network of random event generators has documented correlations between world events and random number generator outputs, suggesting global consciousness effects similar to those proposed by Matzke-Tiller.
Mind-Matter Interaction Studies: Researchers like Dean Radin have documented consciousness effects in double-slit experiments, providing additional empirical support for quantum consciousness theories.
Critical Evaluations and Challenges
Scientific Reception
The Matzke-Tiller framework has received mixed reception within the scientific community. Supporters argue that their mathematical rigor and experimental foundations provide a solid basis for consciousness research, while critics raise several concerns:
Methodological Issues:
- Replication difficulties with psychoenergetic experiments
- Questions about experimental controls and potential artifacts
- Limited peer review of findings in mainstream scientific journals
Theoretical Concerns:
- Lack of specific, testable predictions from the hyperdimensional framework
- Questions about the physical realizability of proposed mechanisms
- Challenges in connecting quantum information theory to subjective experience
Philosophical Problems:
- The “hard problem” of consciousness remains unaddressed
- Questions about the relationship between information processing and qualitative experience
- Challenges in avoiding dualistic implications
Empirical Validation Requirements
For the Matzke-Tiller framework to gain broader scientific acceptance, several empirical requirements must be addressed:
- Independent Replication: Psychoenergetic experiments must be successfully replicated by independent research groups using rigorous protocols
- Mechanistic Understanding: Specific physical mechanisms for consciousness-matter interaction must be identified and tested
- Neural Correlates: The proposed hyperdimensional processing must be connected to observable neural activity
- Predictive Power: The framework must generate specific, testable predictions distinguishable from competing theories
Contemporary Relevance and Future Directions
Technological Applications
The Matzke-Tiller framework has implications for several emerging technologies:
Quantum Computing: Their geometric algebra approach to quantum information processing may contribute to quantum computer design and error correction methods.
Brain-Computer Interfaces: Understanding consciousness as quantum information processing could inform the development of more sophisticated neural interfaces.
Information Medicine: Tiller’s work on intention-based healing suggests applications in personalized medicine and therapeutic interventions.
Research Programs
Several research directions emerge from the Matzke-Tiller framework:
Experimental Validation
- Large-scale replication studies of psychoenergetic effects
- Development of more sensitive detection methods for consciousness-matter interactions
- Investigation of proposed hyperdimensional processing in biological systems
Theoretical Development
- Mathematical formalization of the hyperdimensional consciousness model
- Integration with established neuroscientific findings
- Development of specific, quantitative predictions
Technological Applications
- Design of consciousness-sensitive measurement devices
- Development of intention-based therapeutic interventions
- Creation of quantum information processing systems inspired by consciousness models
Conclusion
The Matzke-Tiller framework represents a significant attempt to bridge quantum information theory and consciousness research through both theoretical development and experimental investigation. Their approach combines sophisticated mathematical formalisms from quantum computing with controlled experimental studies of consciousness-matter interactions.
While their work faces significant challenges in terms of replication, mechanistic understanding, and theoretical precision, it contributes several important elements to consciousness research:
- Mathematical Rigor: The use of geometric algebra and quantum information theory provides a sophisticated mathematical foundation for consciousness studies
- Experimental Grounding: Tiller’s psychoenergetic experiments offer empirical data supporting consciousness-matter interactions
- Interdisciplinary Integration: The framework successfully combines insights from physics, computer science, and consciousness studies
- Technological Relevance: Their work suggests applications in emerging quantum technologies and therapeutic interventions
The ultimate validation of the Matzke-Tiller framework will depend on successful independent replication of their experimental findings and the development of more specific, testable theoretical predictions. Nevertheless, their work represents an important contribution to the ongoing scientific investigation of consciousness and its relationship to physical reality.
As consciousness research continues to evolve, frameworks like Matzke-Tiller’s demonstrate the potential value of combining rigorous mathematical approaches with controlled experimental investigation. Whether their specific proposals prove correct or not, their methodological approach—integrating quantum information theory with empirical consciousness research—provides a valuable model for future investigations in this challenging but crucial area of scientific inquiry.
Bibliography
Primary Sources: Matzke and Tiller
Matzke, D. J. (2002). Quantum Computing Using Geometric Algebra. Doctoral dissertation, University of Texas at Austin.
Matzke, D. J. (1997). “Will Physical Scalability Sabotage Performance Gains?” Computer Magazine, Special Issue on Billion Transistor Processors.
Matzke, D. J., & Tiller, W. A. (2019). Deep Reality: Why Source Science May Be the Key to Understanding Human Potential. Coherent Spaces.
Tiller, W. A. (1997). Science and Human Transformation: Subtle Energies, Intentionality and Consciousness. Pavior Publishers.
Tiller, W. A., Dibble, W. E., & Kohane, M. J. (2001). Conscious Acts of Creation: The Emergence of a New Physics. Pavior Publishers.
Tiller, W. A. (2007). Psychoenergetic Science: A Second Copernican-Scale Revolution. Pavior Publishers.
Dibble, W. E., & Tiller, W. A. (1999). “Electronic device-mediated pH changes in water.” Journal of Scientific Exploration, 13(2), 155-176.
Quantum Consciousness Research
Penrose, R. (1989). The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford University Press.
Penrose, R. (1994). Shadows of the Mind: A Search for the Missing Science of Consciousness. Oxford University Press.
Hameroff, S., & Penrose, R. (1996). “Conscious events as orchestrated space-time selections.” Journal of Consciousness Studies, 3(1), 36-53.
Hameroff, S. (2012). “How quantum effects could account for consciousness.” Philosophical Transactions of the Royal Society A, 370(1980), 4612-4624.
Stapp, H. P. (1993). Mind, Matter and Quantum Mechanics. Springer-Verlag.
Stapp, H. P. (2009). Mindful Universe: Quantum Mechanics and the Participating Observer. Springer.
Stapp, H. P. (2017). Quantum Theory and Free Will: How Mental Intentions Translate into Bodily Actions. Springer.
Vitiello, G. (1995). “Dissipation and memory capacity in the quantum brain model.” International Journal of Modern Physics B, 9(8), 973-989.
Freeman, W. J., & Vitiello, G. (2006). “Nonlinear brain dynamics as macroscopic manifestation of underlying many-body field dynamics.” Physics of Life Reviews, 3(2), 93-118.
Experimental Consciousness Research
Jahn, R. G., & Dunne, B. J. (2005). “The PEAR proposition: Fact or fantasy?” Journal of Scientific Exploration, 19(2), 195-245.
Radin, D. I. (2006). Entangled Minds: Extrasensory Experiences in a Quantum Reality. Paraview Pocket Books.
Radin, D., Michel, L., Johnston, J., & Delorme, A. (2013). “Psychophysical interactions with a double-slit interference pattern.” Physics Essays, 26(4), 553-566.
Nelson, R. D. (2019). Connected: The Emergence of Global Consciousness. ICRL Press.
Schmidt, H. (1993). “Observation of a psychokinetic effect under highly controlled conditions.” Journal of Parapsychology, 57(4), 351-372.
Foundations of Quantum Mechanics
von Neumann, J. (1932). Mathematical Foundations of Quantum Mechanics. Princeton University Press.
Wheeler, J. A. (1989). “Information, physics, quantum: The search for links.” Proceedings of the 3rd International Symposium on Foundations of Quantum Mechanics, Tokyo.
Zurek, W. H. (2003). “Decoherence, einselection, and the quantum origins of the classical.” Reviews of Modern Physics, 75(3), 715-775.
Bell, J. S. (1964). “On the Einstein Podolsky Rosen paradox.” Physics, 1(3), 195-200.
Aspect, A., Dalibard, J., & Roger, G. (1982). “Experimental test of Bell’s inequalities using time-varying analyzers.” Physical Review Letters, 49(25), 1804-1807.
Consciousness Studies and Philosophy of Mind
Chalmers, D. J. (1995). “Facing up to the problem of consciousness.” Journal of Consciousness Studies, 2(3), 200-219.
Chalmers, D. J. (1996). The Conscious Mind: In Search of a Fundamental Theory. Oxford University Press.
Dennett, D. C. (1991). Consciousness Explained. Little, Brown and Company.
Nagel, T. (1974). “What is it like to be a bat?” The Philosophical Review, 83(4), 435-450.
Koch, C. (2004). The Quest for Consciousness: A Neurobiological Approach. Roberts and Company.
Tononi, G. (2008). “Integrated information theory.” Scholarpedia, 3(3), 4164.
Geometric Algebra and Mathematical Physics
Hestenes, D. (1986). New Foundations for Classical Mechanics. Kluwer Academic Publishers.
Doran, C., & Lasenby, A. (2003). Geometric Algebra for Physicists. Cambridge University Press.
Hestenes, D., & Sobczyk, G. (1984). Clifford Algebra to Geometric Calculus. D. Reidel Publishing Company.
Baylis, W. E. (1996). Clifford (Geometric) Algebras: With Applications to Physics, Mathematics, and Engineering. Birkhäuser.
Information Theory and Computation
Shannon, C. E. (1948). “A mathematical theory of communication.” Bell System Technical Journal, 27(3), 379-423.
Landauer, R. (1961). “Irreversibility and heat generation in the computing process.” IBM Journal of Research and Development, 5(3), 183-191.
Bennett, C. H. (1973). “Logical reversibility of computation.” IBM Journal of Research and Development, 17(6), 525-532.
Lloyd, S. (2000). “Ultimate physical limits to computation.” Nature, 406(6799), 1047-1054.
Neuroscience and Brain Function
Kandel, E. R., Schwartz, J. H., & Jessell, T. M. (2000). Principles of Neural Science (4th ed.). McGraw-Hill.
Crick, F., & Koch, C. (1990). “Towards a neurobiological theory of consciousness.” Seminars in the Neurosciences, 2, 263-275.
Dehaene, S. (2014). Consciousness and the Brain: Deciphering How the Brain Codes Our Thoughts. Viking.
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Critical Analyses and Skeptical Perspectives
Tegmark, M. (2000). “Importance of quantum decoherence in brain processes.” Physical Review E, 61(4), 4194-4206.
Grush, R., & Churchland, P. S. (1995). “Gaps in Penrose’s toilings.” Journal of Consciousness Studies, 2(1), 10-29.
Georgiev, D. D. (2020). “Quantum information theoretic approach to the mind-brain problem.” Progress in Biophysics and Molecular Biology, 158, 16-32.
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Conference Proceedings and Collections
Hameroff, S., Kaszniak, A., & Scott, A. (Eds.). (1996). Toward a Science of Consciousness: The First Tucson Discussions and Debates. MIT Press.
Penrose, R., Hameroff, S., Stapp, H., Chopra, D., & Kak, S. (Eds.). (2011). Consciousness and the Universe: Quantum Physics, Evolution, Brain & Mind. Cosmology Science Publishers.
Tuszynski, J. (Ed.). (2006). The Emerging Physics of Consciousness. Springer.
Walleczek, J. (Ed.). (2000). Self-Organized Biological Dynamics and Nonlinear Control. Cambridge University Press.
⟪ Doug Matzke – Formele Theorie ⟫
1. Basale noties
- ℍᴺ: hyperdimensionale informatieruimte (N > 3)
- 𝜺: quantum-information-entity (QIE) ≈ ebit (entangled bit)
- ℂᴳᴬ: Clifford-gebaseerde geometric algebra (GA) over hyperdimensie
- 𝛀: correlithm operator (non-local selector)
- 𝑰: intention operator (externe veldinvloed, vergelijkbaar met projectie)
- Φ: coherentietoestand in de informatieveldruimte
2. Kernaxioma’s
- Informatie is primair fysisch:
∃ 𝜺 ∈ ℍᴺ : 𝜺 = (ℐ, ℱ),
met ℐ: intentionele inhoud, ℱ: formele structuur
⇒ 𝜺 beïnvloedt fysische toestand: 𝜺 ⟶ Δ𝑆 ∈ 𝑃 (physical system) - Hyperdimensionale spinstructuren dragen semantiek:
∃ ℂᴳᴬ-structuur op ℍᴺ zodanig dat:
∀ QIE: 𝜺 = a𝑒₁ + b𝑒₂ + c𝑒₃ + … + n𝑒ₙ,
met 𝑒ᵢ ∈ basis van GA (spinbasis)
⇒ semantiek ↔ rotaties/reflecties in ℂᴳᴬ - Intentie is een projectieve torsie in het veld:
𝑰: ℍᴺ ⟶ ℍᴺ
𝑰(Φ) ≠ Φ ↔ collaps van correlithm superpositie
(vergelijkbaar met selectieve decoherentie, maar intentioneel gedreven) - Correlithm als operator op non-local entanglement:
𝛀(𝜺₁, 𝜺₂, …, 𝜺ₙ) ↦ Φ ∈ ℍᴺ
⇒ correlithms structureren coöperatieve betekenis tussen QIE’s
(Φ is dus emergente semantiek, geen directe mapping) - Beyond-Turing dynamiek:
Computatiestroom is niet lineair-algoritmisch maar torsie-gebaseerd:
⟨𝑰, ℂᴳᴬ, 𝛀⟩ ⟶ Φ(t)
waarbij t ∈ oscillatoire projectie over ℍᴺ
⇒ tijd = secundaire projectie van veldverandering
3. Geometrische structuur (vereenvoudigd)
- ℍᴺ = 𝕊⁷ × 𝕊³ × 𝕊¹ projectiehiërarchie
- Basisruimte = 8D rotaties via octonion-extensie van Clifford
- Transformaties verlopen via:
- intentie (𝑰) = asymmetrische torsieprojectie
- correlithm (𝛀) = entangled netwerkcoherentie
- collapse = veldvernauwing tot Φ ≠ 0
- Resultaat: emergente coherentieconfiguratie Φ als toestand met causale invloed
4. Fysisch modelgedrag (imliciet testbaar)
- Als 𝛀 en 𝑰 gelijktijdig actief zijn, treedt spontane veldreductie op:
ΔΦ > 0 ⟹ verhoogde coherentie + meetbare verandering in systeem P - Dit is operationeel meetbaar via bijv. biofeedback, IHD’s, anomalieën in statistiek
- Veldlagen zijn dynamisch herschrijfbaar: geen fixed circuit maar herschrijfbare coherentietopologie (≠ neuron, ≠ logic gate)
5. Formele rol in ANPA-continuüm
| Component | Matzke’s bijdrage |
|---|---|
| Clifford-structuur | Volgt Rowlands in algebraïsche universaliteit |
| Semantiek | Volgt Kauffman: betekenis = vorm ↔ onderscheid |
| Entanglement als structuur | Eigen bijdrage: correlithm-netwerk |
| Hyperdimensionaliteit | Extensie boven klassieke fysica én AI |
| Intentie als operator | Innovatief: bewustzijn als wiskundig projectief |
6. Formuleerbaar als module
Emergence-compatibele kern: Module:QuantumIntentionalFieldInputs:𝑰,𝜺i,𝛀Space:HNwithCliffordstructureCGAProcess:Forall𝜺i∈HN:Apply𝛀oversuperposed𝜺iApply𝑰asdirectedtorsionCollapsetoΦOutput:coherentfieldconfigurationΦModule: QuantumIntentionalField Inputs: {𝑰, {𝜺ᵢ}, 𝛀} Space: ℍᴺ with Clifford structure ℂᴳᴬ Process: For all 𝜺ᵢ ∈ ℍᴺ: Apply 𝛀 over superposed 𝜺ᵢ Apply 𝑰 as directed torsion Collapse to Φ Output: coherent field configuration Φ Module:QuantumIntentionalFieldInputs:I,𝜺i,𝛀Space:HNwithCliffordstructureCGAProcess:Forall𝜺i∈HN:Apply𝛀oversuperposed𝜺iApplyIasdirectedtorsionCollapsetoΦOutput:coherentfieldconfigurationΦ