Toward a Formal Framework for Resonant Magick: A Proto Mathematical Model

Title: Toward a Formal Framework for Resonant Magick: A Proto Mathematical Model

Author: Headmaster Nicholas Kingsley The Grey School of Wizardry

Abstract

The Grey School of Wizardry teaches three core models of magickal operation: the Psychological, the Spiritual, and the Resonance Models. Each provides a disciplined lens for understanding how magickal work may exert effects in the world. Of these, the Resonance Model makes the strongest mechanistic claim. It proposes that magick operates by deliberately constructing resonant conditions that couple into the same quantum probabilistic structure that contemporary physics uses to describe matter, nudging the resolution of superposed possibilities toward particular outcomes.

The present work seeks to develop a proto mathematical framework for this Resonance Model. It does not attempt to deliver a finished physical theory. Rather, it introduces a set of definitions and relations that treat magickal workings as complex resonant systems, physically real in principle, built from correspondences whose combined profiles are taken to influence quantum probabilities. In doing so, the paper offers a family of Equations, symbolic expressions that capture key claims of the Resonance Model in explicit form, suitable for critique, refinement, and possible future testing. Contemporary science supplies the underlying concepts of resonance, superposition, and probabilistic dynamics that this framework attempts to extend.

1. Introduction

Magickal practice has long relied on patterns of correspondence. Practitioners select herbs, stones, colours, symbols, timings, and spatial arrangements in the expectation that particular combinations will incline events toward desired outcomes. Across cultures and centuries, these practices have produced working bodies of lore, yet they have often lacked a clear theoretical foundation.

At The Grey School of Wizardry, the curriculum acknowledges this history while seeking to place magickal theory in a more disciplined frame. The School’s three model structure separates psychological mechanisms, spiritual relations, and resonant effects into distinct but complementary explanatory lenses. The Psychological Model addresses changes in perception, narrative, expectation, and behaviour. The Spiritual Model addresses relational encounters with non physical intelligences. The Resonance Model addresses the structured use of correspondences as a functional system that interacts with the physical world.

The present work focuses entirely on this Resonance Model. It asks a simple question. If we take the model seriously as a proposed mechanism, how might its claims look when written in a symbolic, quasi mathematical form that reflects modern physics rather than vague “energy talk”. The answer is a framework, not a finished theory. The formalization that follows is intentionally unusual, because it attempts to express traditional magickal thinking in terms of resonance and quantum probability. That strangeness has value. It reveals hidden assumptions, clarifies what is actually being claimed, and opens the door to further refinement.

2. Resonance and Superposition as the Mechanism

The choice of resonance as a central concept is deliberate. In classical physics, resonance describes how systems respond selectively to particular frequencies. A wine glass sings when driven near its natural frequency. A bridge amplifies oscillations from wind or traffic. An antenna converts alternating currents into electromagnetic radiation when its geometry resonates with the driving frequency.

In quantum physics, matter is described in terms of states and probability amplitudes. Before interaction or measurement, a system is represented by a superposed range of possibilities. After interaction, one outcome appears and the others are not realised. Quantum theory uses precise mathematical rules to describe how those probabilities evolve and how they update when systems interact.

The Resonance Model takes these observations as its starting point. It proposes that when a practitioner carefully constructs a network of correspondences, they are assembling a complex resonant system whose combined profile is not only symbolically meaningful but physically real in principle. That composite resonance is then taken to interact with its environment at the level of quantum probability, slightly biasing how superposed possibilities resolve. In this view, magickal operation is an intentional attempt to apply resonance and quantum superposition to the world in the way radio engineering applies Maxwell’s equations to electromagnetic waves.

This claim is speculative in the scientific sense, because it goes beyond currently tested applications of quantum theory. It is not intended as metaphor. It hypothesises that specific resonant configurations, constructed through correspondences, might in principle affect matter and the branching structure of future events by changing how probabilities collapse. The following sections translate that assertion into explicit symbolic form.

3. Correspondences as Resonant Elements

We begin by treating a magickal working as a set of discrete elements, or correspondences. Let

• C = {c1, c2, …, cn}
  

represent the set of correspondences used in a given operation.

Each element might be an object, a colour, a word, a gesture, a planetary hour, or any other component that the tradition regards as relevant. Under the Resonance Model, each element is associated with a resonant profile that summarizes its functional character:

• f(ci) → omega_i
  

Here omega_i is a vector in a resonance space that is intended, in the strongest reading of the model, to correspond to a real physical frequency state. Each component can be understood as representing a mode of oscillation in the physical world, such as electromagnetic, acoustic, molecular, or other field based frequencies that characterise the correspondence. Symbolic associations, accumulated cultural meaning, and traditional lore enter the model insofar as they are taken to track, organise, and tune those underlying physical patterns rather than replace them. In support of this idea, it is worth noting that contemporary science already recognizes that physical objects possess distinct vibrational identities. Techniques such as vibrational spectroscopy allow researchers to determine the characteristic oscillatory modes of a substance by measuring how it absorbs or scatters electromagnetic radiation. These spectra function as precise fingerprints, revealing that matter is structured by stable, identifiable patterns of vibration. The Resonance Model does not claim that such spectroscopic signatures are themselves the magickal correspondences used in ritual practice. Rather, spectroscopy demonstrates that the natural world already organizes itself in terms of complex vibrational profiles. It provides a conceptual proof of possibility: if correspondences have underlying physical signatures, even ones not yet measurable by current instruments, they would exist within a world where distinct vibrational identities are a normal and well-documented feature of matter. In this sense, vibrational spectroscopy serves as a scientific analogue that strengthens the plausibility of treating correspondences as resonant elements, even before the School develops tools capable of detecting magickal signatures directly.

In practice, correspondences are not used in isolation. A working combines many such elements. Their contributions are not equal. Some are central to the intention, others are auxiliary or weakly implemented. We capture this by assigning each correspondence a weight wi, representing precision of selection, ritual emphasis, and fidelity of execution. The composite resonance of the working is then

• Omega_total = sum over i = 1 to n of (wi * omega_i)
  

This vector represents the overall resonant pattern that the operation presents to the world. In the Resonance Model these signatures are treated as physical quantities in principle, even though no instrument currently exists that can detect magickal resonance directly. Scientific techniques such as vibrational spectroscopy demonstrate, however, that measuring the vibrational structure of matter is entirely possible in principle. What remains absent is not the idea of measurement itself, but the development of tools capable of identifying the specific resonant signatures posited by the Model. The formalism is therefore used both as a way to talk about structure and as a hypothesis about an underlying frequency state that future work might be able to characterise more directly, whether by adapting existing spectroscopic techniques or by developing entirely new instruments suited to magickal resonance.

4. Coherence and Operational Thresholds

A mere pile of symbols does not constitute a functional working. The elements must reinforce rather than cancel one another. There must be coherence.

To express this, we define a dimensionless coherence factor C_coh:

• C_coh = ||Omega_total|| / (sum over i = 1 to n of ||omega_i||)

  
  

By construction, 0 ≤ C_coh ≤ 1. If all resonant signatures point in compatible directions in the resonance space, the magnitude ||Omega_total|| is comparable to the sum of magnitudes, and C_coh approaches 1. If the correspondences conflict or partially cancel, the composite vector shrinks and C_coh falls.

We can then posit an operational threshold C_min. A working is said to be resonantly coherent when

• C_coh ≥ C_min

  
  

This condition encodes, in compact form, a long standing observation among practitioners. Careful alignment of components matters. Sloppy or contradictory combinations weaken results. The coherence factor provides a handle for thinking about such alignment with more precision.

5. Outcome Space and Probability Bias

If the Resonance Model is to function as a mechanism, it must speak to outcomes. Consider an event that may unfold in several ways:

• F = {F1, F2, …, Fm}

  
  

with baseline probabilities

• p(Fj) for j = 1…m, with sum over j of p(Fj) = 1.

  
  

These probabilities represent how the world would tend to develop in the absence of magickal input, given all other prevailing conditions.

Under the Resonance Model, each possible outcome Fj also has an associated resonant signature kappa_j. This reflects the idea that different futures match different patterns of structure, choice, and environment. A magickal working that seeks a particular outcome Fd is constructed so that its composite resonance aligns with kappa_d.

We then propose a bias relation:

• Delta_p(Fj) = alpha * <Omega_eff, kappa_j>

  
  

where alpha is a small positive coupling constant and Omega_eff is the effective resonance of the working, to be defined more fully below. The inner product < · , · > measures alignment between the working and the outcome. A positive inner product indicates resonance between the structure of the ritual and the structure of the outcome. A negative inner product indicates mild opposition.

The new probabilities after the working are

• p’(Fj) = p(Fj) + Delta_p(Fj),

  
  

followed by a normalization step that restores sum over j of p’(Fj) = 1. In any realistic application of this framework, the product alpha ||Omega_eff|| ||kappa_j|| is assumed to be small compared with 1, so that these adjustments remain subtle rather than overwhelming.

Within the Resonance Model, this is not treated as a loose analogy. The quantities p(Fj), Delta_p(Fj), and p’(Fj) are intended to represent the same kind of probabilistic structure that quantum theory already uses to describe physical systems, extended here by hypothesis to include the influence of ritual resonance. On this view, to say that a working had an effect is to say that for that working, these probability shifts were non negligible for one or more branches of the outcome space.

Several remarks follow. The bias is meant to be small, because magick is not portrayed here as an overpowering force that overrides ordinary causality. It is a modest influence on probabilities. The effect is structured. Outcomes that resonate with the working are favoured. Outcomes that are nearly orthogonal or contrary to its resonance may be slightly suppressed.

The model is directional because the sign of the inner product matters. A practitioner can design a working so that its composite resonance is aligned with the signature of a desired outcome Fd, in which case <Omega_eff, kappa_d> is positive and Delta_p(Fd) is positive. The same practitioner can instead build a working that is deliberately anti aligned with the signature of an undesired outcome Fu, in which case <Omega_eff, kappa_u> is negative and Delta_p(Fu) is negative. The probability removed from Fu is redistributed to the remaining branches when the distribution is renormalised. This expresses, in the symbols, the difference between inviting a future and preventing one.

6. Psychological Stability and the Practitioner

The Grey School’s broader framework insists that models of magick must respect what is known about human cognition. The practitioner is not a neutral, frictionless agent. Attention, concentration, emotional regulation, and narrative framing all affect the quality of the work. The Resonance Model must therefore incorporate a psychological term.

Let mu represent an index of practitioner stability for the specific working, blending such factors as clarity of intention, emotional steadiness, and sustained focus. Let mu_0 be the threshold above which these factors support rather than degrade the operation. We define a smooth stability factor

• S = 1 / (1 + exp( - beta * (mu - mu_0) ))

  
  

where beta controls how sharply stability transitions from ineffective to effective. For low stability, S tends toward zero. For high stability, S approaches one. The logistic shape is not presented as a literal psychological law. It is a convenient way to represent a smooth transition from ineffective to effective ranges of practitioner stability on an abstract scale.

We then scale the composite resonance by this factor:

• Omega_eff = S * Omega_total

  
  

A practitioner in disarray can assemble a theoretically sound set of correspondences yet produce little effective resonance, because their own cognitive and emotional state prevents the system from ringing cleanly. This gives a precise way to describe what many instructors already tell pupils, that the inner state of the practitioner is part of the circuitry.

7. Environmental Coupling

Magickal operations take place in environments that are never neutral. Time of day, spatial location, social context, and physical surroundings all shape how a working interacts with the world. Traditional lore encodes this as planetary hours, auspicious places, consecrated circles, or avoidance of certain locations. In the Resonance Model, environment appears as another multiplicative factor.

Let the environment be described by a collection of conditions E1, E2, …, Em. To each we assign a coupling coefficient gamma_k, which indicates how that condition affects the transmission of resonance into the broader probabilistic landscape. The total environmental coupling factor is

• E = product over k = 1 to m of gamma_k

  
  

Values greater than one represent conditions that amplify or clarify the working’s influence. Values less than one represent conditions that dissipate or interfere. In any practical application, the gamma_k would be rated on a modest scale, for example in a range such as 0.5 to 2, to ensure that the combined factor E remains in a reasonable band.

The final effective resonance is then

• Omega_final = E S Omega_total

  
  

This formulation provides a language for speaking about good timing and proper place in terms that can, in principle, be quantified. It also reveals that psychological and environmental factors interact multiplicatively with the structure of the ritual itself.

8. The Master Relation

By gathering the pieces, we obtain a compact expression for the influence of a working on a target outcome Fd:

• Delta_p(Fd) = alpha E S < sum over i = 1 to n of (wi omega_i), kappa_d >

  
  

This relation, which we might informally term "Kingsley's Equation," encodes the central logic of the Resonance Model in one line. The bias toward the desired outcome depends on several factors:

1. The intrinsic coupling scale of magickal influence, alpha, assumed to be small and positive.

2. The environmental factor, E, representing timing and context.

3. The psychological stability factor, S, representing the practitioner’s inner state.

4. The chosen correspondences, represented by their signatures omega_i.

5. The way those correspondences are emphasized, via the weights wi.

6. The alignment between the working and the desired outcome, via kappa_d.

   
   

In the Resonance Model, this expression is taken as a literal working hypothesis about how ritual resonance would couple into outcome probabilities. The inner product represents the physical interaction between the resonant profile of the working and the resonant character of the outcome at the level of quantum probability. The scale factor alpha encodes how strongly magickal work can, in principle, couple into that structure. To say that a spell worked, in this framework, is to say that for a particular working this term was non negligible for the desired branch of the outcome space.

This formula is presented as a scaffold rather than a final law of nature. It allows instructors and pupils to see how different elements of practice fit together conceptually. It also highlights where empirical exploration might begin and where the speculative leap lies, namely in the assumption that these formally defined resonant structures have a real coupling to outcome probabilities.

9. Methodological Implications

Even in provisional form, a framework like this has several useful consequences for the School’s teaching and research culture.

First, it encourages clarity. When a pupil designs a working, instructors can ask explicitly about the elements represented by each term. Which correspondences are central. How coherent the set appears. What supports or undermines stability. What environmental considerations have been addressed.

Second, it suggests paths for gradual quantification. Although the specific magickal signatures represented by Omega remain beyond the reach of current instruments, contemporary spectroscopy demonstrates that complex vibrational structures can be measured with extraordinary precision. The limitation, therefore, lies not in the possibility of measurement, but in the absence of instruments designed to detect the particular resonant constructs proposed by the Model. These ratings can then be compared to reported outcomes in structured experiments within the community. Poor correlation over time would pressure the School to revise the framework. Strong correlation would encourage refinement and further testing. A further methodological point follows from the discussion of resonance as a physical principle. While current instruments cannot measure the hypothetical magickal signatures omega_i directly, the existence of spectroscopic methods in physics and chemistry demonstrates that vibrational states can in fact be measured with extraordinary precision when appropriate tools exist. This offers a long-term horizon for the School’s research culture. If future scholars were to seek empirical evidence for the Resonance Model, they would not need to invent the concept of vibrational measurement from whole cloth. They would adapt, extend, or reinterpret existing spectroscopic techniques in search of patterns that correlate with ritual structure. Even if such efforts remain far beyond present capability, situating the Model within known scientific instrumentation underscores that resonance is not merely a poetic framing but a possible object of physical detection.

Third, it aligns the School’s language with broader scientific habits of thought without collapsing magickal discourse into a purely psychological or literary register. The model is open to revision. Particular terms may later be redefined, elaborated, or replaced. The utility lies in having a clear starting point that makes the claims visible and discussable.

Fourth, the framework encourages the School to treat scientific findings as foundations and constraints rather than adversaries. Resonant behaviour in physical systems and quantum probabilistic description are already mathematically precise and experimentally supported. Psychological research already demonstrates the importance of attention, expectation, and framing. The Resonance Model takes these established structures as the scaffolding of magickal operation itself. In that sense, contemporary science partly supports the model by providing the very mechanisms it attempts to apply, even though the specific magickal coupling proposed here has not yet been tested in the laboratory.

Finally, it invites interdisciplinary dialogue. Physicists, psychologists, and philosophers who are willing to engage in good faith can see precisely what is being claimed and where the speculative steps occur. That transparency is preferable to loosely defined “energy” language that obscures more than it reveals.

10. Relation to the Other GSW Models

It is important to keep this construction within the larger frame of the School’s three model structure. The Resonance Model is not a universal account of all magickal experience. It is one lens within a broader toolkit.

The Psychological Model continues to explain a wide range of effects in terms of narrative, expectation, and behavioural change, particularly in divination, self work, and interpersonal influence. The Spiritual Model continues to address the relational structure of engagements with non physical intelligences, where covenant, offering, vow, and response form the core of the work.

The Resonance Model, formalized here, offers a way to speak about operations in which the structured arrangement of correspondences is central. A single ritual may be psychologically transformative, spiritually relational, and resonantly structured at once. The models provide analytical clarity rather than rigid compartments. Where the Psychological Model explains results through changes in belief, perception, and behaviour, the Resonance Model claims that a correctly constructed working alters outcome probabilities in the underlying quantum superposition, whether or not any of the people affected are aware that a ritual has taken place. At the same time, it relies on scientifically grounded ideas of resonance and probability for its internal structure, which ties it back to the shared intellectual world that science and wizardry inhabit together.

11. Conclusion

The attempt to write these Equations is not a declaration that magick has been solved. It is, rather, an invitation to take the Resonance Model seriously enough to articulate its assumptions and implications in explicit form.

By treating correspondences as resonant elements, coherence as an operational threshold, probability as the arena of effect, and psychology and environment as integral modifiers, the framework presented here gives pupils and magisters a shared language for discussing the structure of magickal work. It also provides a basis for future refinement. Terms may be sharpened, alternative forms proposed, or entirely new variables introduced as the School’s understanding grows.

What matters for the School is that magick is approached with the same intellectual honesty that one would bring to any other discipline. The Resonance Model, written symbolically and anchored in scientific ideas where possible, opens that door. It sketches a path by which wizardry can engage with questions of mechanism in a way that respects mystery and calls for a more mature and responsible practice.

12. References and Suggested Reading

Griffiths, D. J., & Schroeter, D. F. (2018). Introduction to Quantum Mechanics (3rd ed.). Cambridge University Press.

Feynman, R. P., Leighton, R. B., & Sands, M. (2011). The Feynman Lectures on Physics, Volume III: Quantum Mechanics (New Millennium ed.). Basic Books.

Halliday, D., Resnick, R., & Walker, J. (2021). Fundamentals of Physics, Extended (12th ed.). Wiley.

Eysenck, M. W., & Keane, M. T. (2015). Cognitive Psychology: A Student’s Handbook (7th ed.). Psychology Press.

Radin, D. (1997). The Conscious Universe: The Scientific Truth of Psychic Phenomena. HarperOne. (See also Radin, D. (2018). Real Magic: Ancient Wisdom, Modern Science, and a Guide to the Secret Power of the Universe. Harmony.) Atkins, P., de Paula, J., & Keeler, J. (2018). Physical Chemistry: Quanta, Matter, and Change (3rd ed.). Oxford University Press.

Banwell, C. N., & McCash, E. M. (1994). Fundamentals of Molecular Spectroscopy (4th ed.). McGraw–Hill.