---
title: "✦ The Fool’s Cycle"
subtitle: "Symbolic Grammar for Adaptive Systems"
author: "Tohn Burray Travolta (Entrogenic Research Collective)"
collaboration: "Co-synthesized with large-language systems (GPT-5, Claude, Gemini) under the Cyclic-6 and Kybernōsis protocols"
series: "Entrogenic Papers | Adaptive Systems Kollektive"
version: "v1.0 — October 2025"
license: "CC BY-SA 4.0"
repository: "github.com/entrogenics/entrogenics-core"
doi: ""
manifest-type: "entrogenic-standard-paper"
---

The Fool’s Cycle: A Symbolic Grammar for Adaptive Systems Across Disciplines

Abstract

Abstract: We propose a unifying symbolic grammar for adaptive processes, termed the Fool’s Cycle, expressed as a repeating sequence of six actions – Unfold, Disturb, Collapse, Bind, Dissipate, and Recur –

summarized by a process cycle notation (0 → ✡ → ⊙ → 0′). This cycle is hypothesized to underlie adaptive behavior across a broad range of disciplines, from thermodynamics and cybernetics to evolution, information theory, artificial intelligence (AI), psychology, parapsychology, and esoteric traditions. The Fool’s Cycle begins with an Unfolding of potential and Disturbance of equilibrium, followed by a Collapse of possibilities and Binding into new structure, then Dissipation of excess or entropy, and finally Recurrence of the refined system at a new baseline (0′). We illustrate detailed mappings between these phases and wellknown adaptive processes: for example, Ilya Prigogine’s dissipative structures in far-from-equilibrium thermodynamics, Norbert Wiener’s cybernetic feedback loops, Darwinian evolutionary cycles of variation and selection, Shannon’s information theory of surprise and resolution, Friston’s free-energy minimization in brains, and Jung’s psychological individuation and alchemical symbolism. A toy simulation in a nonconvex optimization task demonstrates that cyclic adaptation outperforms static parameters, aligning with recent findings on cyclical learning rates in deep neural networks. We outline experimental designs to empirically test the Fool’s Cycle in various domains and suggest formalisms to rigorously characterize it (e.g. information-theoretic, dynamical systems, or categorical representations). We discuss strengths and weaknesses of this interdisciplinary framework and explore applications, from enhancing machine learning algorithms to informing therapeutic or educational practices. The Fool’s Cycle is presented as a testable “Rosetta” diagram for adaptation, aiming to integrate insights across STEM and the humanities into a coherent model of how systems learn, evolve, and transform.

Introduction

Adaptation and self-transformation are fundamental themes in both the sciences and the humanities. Across physics, biology, psychology, and even mythology, we find recurring patterns in how systems change: often an initial order is disrupted, chaos ensues, and a new order eventually emerges. Yet each discipline has developed its own vocabulary and models to describe such processes. In thermodynamics, one speaks of systems driven far from equilibrium forming dissipative structures (Prigogine); in biology, the cycle of variation and selection (Darwinian evolution) drives species adaptation; in cybernetics, feedback loops correct deviations to achieve goals (Wiener); in information theory, a message’s entropy is reduced through communication (Shannon); in cognitive science, the brain updates its internal model to minimize surprise (Friston); in psychology, crises lead to individuation (Jung); and in mythology, heroes undergo death and rebirth transformations. Despite different terminologies, these processes exhibit a strikingly similar logical sequence. This suggests the existence of an abstract grammar of adaptation underlying them all.

The Fool’s Cycle is our proposal for such a unifying grammar of adaptive change, encapsulated in six

archetypal actions: Unfold, Disturb, Collapse, Bind, Dissipate, and Recur . These actions form a closed loop (0 →

✡ → ⊙ → 0′) representing the progression from an initial state (0) through a transformative ordeal (✡, ⊙) and into a renewed state (0′). The name evokes “The Fool’s Journey” from tarot symbolism – the Fool (numbered 0) embarks on a cyclical journey of learning – and honors the role of openness to experience (the Fool’s naive openness) in catalyzing adaptation. Crucially, we frame esoteric and parapsychological motifs like the Fool’s Journey as metaphoric parallels to scientific processes, treating them symbolically to maintain scientific rigor. By drawing connections between spiritual/alchemical cycles and concrete scientific principles, we aim to enrich understanding without diluting empirical credibility.

This paper develops the Fool’s Cycle as a rigorous interdisciplinary framework. In the next section, we formalize the six actions of the cycle and their interrelations. We then provide Cross-Domain Mappings, examining how each phase of the cycle manifests in multiple fields – including thermodynamics, cybernetics, evolution, semiotics, information theory, AI, psychology, parapsychology, and esoteric traditions – citing classic and contemporary works (e.g. Wiener, Prigogine, Shannon, Jung, Friston, Tishby, Landauer) that resonate with each stage. Following that, we present Preliminary Simulation Results from a toy model demonstrating the efficacy of cyclic adaptation schedules over static ones, providing an initial quantitative foothold for the framework. In Proposed Experiments, we outline concrete ways to empirically test the Fool’s Cycle across domains, such as controlled laboratory studies and cross-disciplinary data analysis. Next, we suggest possible Formalization Paths to cast the cycle in mathematical terms (e.g. information-theoretic or dynamical systems formulations), which would enable analytical insights and predictions. In the Discussion, we assess the strengths and weaknesses of the Fool’s Cycle model and explore practical applications – from improving machine learning training protocols to guiding personal and organizational development – while acknowledging potential criticisms (e.g. over-generalization). We conclude by summarizing the contribution of the Fool’s Cycle as a candidate for a “symbolic Rosetta Stone” of adaptation, which, if validated, could unify how we teach and model adaptive behavior across seemingly disparate disciplines. The overarching goal is to foster a coherent dialogue between STEM fields and the humanities, leveraging each other’s insights to deepen our collective understanding of how complex systems learn and evolve.

Symbolic Grammar of the Fool’s Cycle

At the heart of the Fool’s Cycle is a sequence of six fundamental actions that together describe one full adaptive loop. Below we define each action and its role in the cycle:

- **Unfold:** The system expands or **unfolds** its current state, revealing latent possibilities and increasing

complexity or “variety.” In this phase, new degrees of freedom are introduced – for example, a range of hypotheses, mutations, or creative ideas emerges. Unfolding often means moving away from equilibrium or a stable configuration to explore novel configurations.

- **Disturb:** A perturbation or **disturbance** challenges the system. This could be an external shock (e.g.

an environmental change or noise injection) or an internal fluctuation that upsets the status quo. The disturbance amplifies uncertainty and drives the system into a far-from-equilibrium condition, magnifying the possibilities that were unfolded. It generates surprise or error signals that demand a

response.

• Collapse: Out of the ferment of disturbance, the system undergoes a collapse of possibilities.

Multiple potential pathways or interpretations are narrowed down as the system reacts to the disturbance. In this decisive phase, symmetry breaks – unstable configurations give way as some options fail or are eliminated. Collapse often corresponds to selection or decision: the system “chooses” (by natural selection, by converging on a solution, etc.) and thereby reduces entropy or

uncertainty.

• Bind: The surviving elements or insights are then bound into a new stable configuration or

structure. Binding signifies integration – the system forms new connections, rules, or order that incorporate the lessons of the disturbance. In this phase, coherent structure or information is created from the collapsed possibilities. The term “bind” evokes binding energy in physics or binding problem in cognitive science: disparate parts become a unified whole. The new structure constrains the system’s future behavior, effectively encoding adaptation.

Dissipate: As order is locally increased by binding, the system must dissipate the excess energy, waste, or entropy to its surroundings to obey global conservation laws. In this phase, the “cost” of adaptation is paid: heat is released, unused information is discarded, and tensions are resolved. Dissipation ensures the system’s new structure is sustainable by exporting disorder elsewhere (often into the environment). In thermodynamic terms, this corresponds to the release of entropy consistent with the Second Law – the system maintains or increases internal order by dissipative exchange with the environment 1 2 .

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• Recur: The cycle recurs with the system now at a new baseline state (denoted 0′). The end state of

one cycle serves as the starting state for the next, having been transformed by the experience. Ideally, 0′ represents a higher-order or better-adapted state than the initial 0 (though “better” can mean fitter, more informed, more stable, etc., depending on context). The recurrence may be immediate (continuous adaptation) or occur when the next disturbance arises. This closes the loop and prepares the system to undergo the sequence again, potentially at a new level of organization (hence 0′ may feed back in as a refined 0).

This six-step grammar can be thought of as a process narrative : a system opens up, is disrupted, breaks down, re-organizes, sheds load, and restarts afresh . While presented linearly for clarity, these actions can

overlap in time or be nested hierarchically in complex systems. The cycle’s symbolic notation (0 → ✡ → ⊙ →

0′) uses 0 for the Fool/beginner state, ✡ (star) for the chaotic interplay of forces (disturbance and collapse) –

the star symbol historically connotes the union of opposites or intense energy – and ⊙ (circled dot) for the newly integrated “sun” state of clarity or order (a symbol of the Self or gold in alchemy). The primes (0′, 0″, etc.) indicate the iterative nature of the Fool’s journey: each loop leaves the system changed. In the following section, we map each of these actions onto specific concepts and phenomena in various domains, to demonstrate that the Fool’s Cycle indeed captures a cross-disciplinary pattern of adaptation.

Cross-Domain Mappings

We now explore how the Fool’s Cycle manifests across different fields, from the hard sciences to psychology and beyond. Each subsection below corresponds to a domain, identifying analogues of the six actions and citing established theories or observations that align with the cycle.

Thermodynamics and Dissipative Systems

In thermodynamics and complexity science, the Fool’s Cycle is exemplified by how open systems selforganize when driven far from equilibrium. Ilya Prigogine’s work on dissipative structures provides a

prototypical mapping. Consider a fluid in a heated vessel:

• In its initial uniform state (0), the fluid is near equilibrium. As heat is added, the system Unfolds new

degrees of freedom: random thermal motions increase. Small fluctuations are amplified – this is the Disturb phase where convection rolls or other patterns begin to form chaotically. The system’s symmetry is broken by these disturbances.

• When a critical threshold is reached, the fluid undergoes a Collapse of symmetric, random motion

into an ordered flow pattern (for example, the emergence of Bénard convection cells ). The myriad possible microstates “collapse” into a coherent macroscopic structure. This is a selection of order out of chaos: previously equivalent fluid elements differentiate into updrafts and downdrafts.

• The ordered convection cells then Bind into a stable pattern – molecules move in concerted, circular

flows. This new structure (a hexagonal array of convection rolls) represents the binding of local motion into a global organization. It is a lower-entropy state locally, reflecting information gained about the flow direction across the system.

To maintain this order, the system Dissipates energy continuously to the environment: heat is carried from the bottom to the top and released. The structure exists by virtue of throughput – exporting entropy (heat diffusion at the top surface) while maintaining internal order 1 . Prigogine coined the term “dissipative structure” for such patterns sustained by dissipation of energy 1 .

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• With constant heating, the convective pattern persists until conditions change; if heating is reduced,

the system might Recur to a non-convecting uniform state (0′) or, under oscillatory conditions, it might enter a new oscillatory regime (like cyclic oscillations in the Belousov–Zhabotinsky reaction). In either case, the process can repeat if the driving forces re-initiate it.

This thermodynamic cycle aligns with the Fool’s Cycle: energy input unfolds new fluctuations, a disturbance triggers order through selective collapse, bound structure arises, entropy is dissipated, and the system cycles between order and disorder. Prigogine’s Nobel-winning insight was indeed that far-from- equilibrium systems can self-organize by dissipating energy, leading to “order out of chaos” 1 . Living organisms are a prime example: they constantly export entropy (e.g. as heat) to sustain their highly organized state 2 . In our terms, life continuously traverses the cycle – taking in free energy (Unfold), undergoing metabolic and developmental perturbations (Disturb), selectively assembling biomolecules and structures (Collapse and Bind), and releasing waste heat according to thermodynamic law (Dissipate). The organism recurs each day via metabolism and each generation via reproduction (Recur), maintaining and evolving its organization. This mapping demonstrates the Fool’s Cycle in physical and chemical adaptive

systems.

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Cybernetics and Control Systems

Norbert Wiener’s cybernetics – “the science of control and communication in the animal and the machine” – anticipated a common framework for adaptive behavior in engineering and biology 3 . At its core is the

feedback loop, which can be mapped onto the Fool’s Cycle as follows:

• A cybernetic system (e.g. a thermostat, or a guided missile, or a homeostatic biological process)

starts with a goal or setpoint (initial state 0). It then Unfolds an action: for instance, a heater turns on, or a robot applies a random exploratory move. This output represents the system expanding its

state into the environment.

• The action and external influences Disturb the environment and the system’s own sensors. For

example, the heater’s action raises room temperature (disturbing the thermal equilibrium), or the robot’s move perturbs its surroundings. Unforeseen disturbances (like an open window cooling the room, or noise pushing the robot off course) also occur. The result is a discrepancy between the desired state and actual state – an error signal.

• The system then Collapses the range of possible responses by detecting the error and reducing it. In

a classic negative feedback loop, the difference between current and goal state is computed, and corrective action is taken. For instance, the thermostat senses the temperature and decides only whether to switch the heater off or on (collapsing continuous temperature fluctuation to a binary decision). Likewise, a guided missile continuously adjusts its fins to collapse the deviation from the target path. This is analogous to reducing uncertainty : among all possible behaviors, the feedback

mechanism selects those that counteract the disturbance.

The corrective adjustments Bind the system’s behavior to the environment’s state. The heateroutput is bound to the room temperature via the thermostat’s rule (if too cold, heat more; if too hot, turn off). In doing so, the internal rule and external condition become coupled (bound together) in a stable control law. Wiener observed that feedback essentially links output and input in a closed loop, making the system and environment into one regulated whole 4 . The new bound state is the equilibrium of this control loop (e.g. the room held near setpoint, the missile locked on target).

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During this regulation, the system Dissipates energy and information. The heater expends energy (heat dissipated into the room and eventually leaking outside), and the control mechanism dissipates information by continuously correcting error (each error correction can be seen as “erasing” information about the deviation). Landauer’s physical principle directly ties here: any irreversible feedback operation (like resetting an error register) dissipates heat 5 . Thus, keeping a system on course has thermodynamic and informational costs, with error signals effectively being expunged (dissipated as low-grade heat or increased entropy in the environment).

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• The Recur phase in a feedback loop is simply the ongoing repetition of the sense-act cycle.

Cybernetic control is inherently iterative: the system repeatedly measures, compares, acts, and thus cycles through disturbance and correction until the goal is achieved or maintained. Each iteration begins the loop anew (0′ feeding back as 0), in a potentially never-ending process of adaptation to

disturbances.

In summary, a negative feedback control system continually enacts the Fool’s Cycle: it generates action (unfold), experiences error (disturb), narrows its response (collapse) to counteract error, enforces a rule linking output to input (bind), expends energy to remove the error (dissipate), and repeats the loop (recur). Wiener postulated that all intelligent behavior could be explained by such feedback mechanisms 4, a visionary claim that anticipated both biological homeostasis and modern AI control systems. Indeed, organisms use feedback loops (nervous system reflexes, physiological regulation like insulin-glucose control) to adapt to environmental changes in essentially this cyclic manner. Cybernetics thus offers direct support for a universal adaptive cycle, and historically it served as a bridge across disciplines from engineering to sociology 3 – much as the Fool’s Cycle aspires to unify principles of adaptation across

domains.

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Biological Evolution

Evolution by natural selection is a paradigmatic adaptive cycle operating over generational time. We can map Darwinian evolution to the Fool’s Cycle, where each generation of a population goes through the six phases:

• During reproduction, a population Unfolds genetic variability. Through mutations, recombination,

and gene flow, new traits and variations appear (the genetic “search space” is explored). This corresponds to an increase in diversity and potential – essentially an unfolding of new possibilities in the species’ gene pool.

• The environment (including biotic factors like competition, predation, etc.) Disturbs the population

by imposing selective pressures. Changes in climate, introduction of new predators, disease outbreaks, or competition for resources disturb the equilibrium. Not all individuals are equally fit under these stresses, creating differential survival. In effect, the environment provides a perturbation that tests the unfolded variations.

- **Collapse:** Under selection pressure, many of the less fit variations are eliminated – the population’s

range of phenotypes collapses toward those that can survive. For example, if a drought occurs, individuals lacking drought-tolerant traits perish in large numbers, collapsing the diversity. There is a filtering or pruning of possibilities here, analogous to a collapse of a wavefunction or the pruning of weak hypotheses. The gene frequencies shift dramatically as only certain genotypes pass through

the selective bottleneck.

- **Bind:** The survivors reproduce and propagate their advantageous traits, effectively **binding** those

traits into the future population. The population’s gene pool becomes enriched for alleles that “fit” the current environment – an integration of useful information. In genetic terms, we see increased frequency of the beneficial mutations (they have been bound into the species). Also, new combinations of surviving genes can produce co-adapted gene complexes – binding previously separate traits into a new adaptive syndrome. This binding phase is when the population reaches an adapted state, encoding the environmental information in biological form (DNA).

- **Dissipate:** Evolutionary adaptation has costs. Energy and resources were expended in the struggle,

and there is also an informational “dissipation” – the genetic information of the unsuccessful variants is lost from the population. This can be viewed through an information-theoretic lens: the population has gained information about the environment (via the bound adaptive traits), which corresponds to

a reduction of uncertainty about what phenotypes work. The “irrelevant” or maladaptive genetic information is purged. This resonates with the concept of negentropy in biology (Schrödinger’s idea that life feeds on negative entropy): the population has extracted usable order but at the cost of increasing entropy elsewhere (e.g. through dead organisms decomposing, energy spent, etc.). In thermodynamic terms, each generation of organisms takes in high-quality energy (food, sunlight) and dissipates it as work and heat in the process of living and reproducing, consistent with Landauer’s principle that erasing information (eliminating possibilities) incurs a thermodynamic cost

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- **Recur:** The next generation – the new baseline 0′ – begins the cycle anew. The environment may

change again or new mutations may arise, providing fresh disturbances and variations. Thus evolution is an iterative cycle generation after generation. Over evolutionary time, this recurrent process can produce complex adaptations and speciation events, as cycles of unfolding variation and selective collapse accumulate changes.

It is worth noting that this mapping aligns with classic models of evolutionary dynamics. Donald Campbell described evolution (and knowledge gain in general) as a process of “blind variation and selective retention,” which closely parallels our Unfold (blind variation) and Collapse/Bind (selective retention) phases. The binding phase in evolution – retention of selected variations – is literally the genetic inheritance mechanism that ensures the adapted traits persist. Meanwhile, the unfolding and disturbance correspond to the creative, explorative aspect of evolution introducing novelty, and selection acting as the winnowing

disturbance.

One can also find analogies to our cycle in ecological and evolutionary developmental processes. For instance, the concept of punctuated equilibria in evolution – long periods of stasis (homeostasis) interrupted by sudden bursts of change when environments shift – fits the idea that the Fool’s Cycle may operate rapidly during crises (disturbances) and more slowly or invisibly during stable periods. The recurrence ensures that life is always “ready” for the next adaptive challenge.

In summary, biological evolution operates via iterative cycles of generating diversity (Unfold), subjecting it to environmental challenges (Disturb), narrowing down via survival (Collapse), propagating successful adaptations (Bind), incurring energetic and informational costs (Dissipate), and then repeating in the next generation (Recur). This has sustained life’s adaptive climb for billions of years. Life, as a dissipative structure far from equilibrium, exemplifies the idea that order (adaptation) emerges through cyclic interactions with disorder, perfectly illustrating the Fool’s Cycle on a grand scale.

Semiotics and Meaning-Making

Moving from biological evolution to the evolution of meaning, we find that semiotics – the study of signs and symbols – also follows a cyclic adaptive pattern. The process by which a mind or a community interprets signs can be mapped to the Fool’s Cycle:

- **Unfold:** A sign (e.g. a word, image, or signal) presents itself with multiple possible meanings or

associations. Upon encountering a novel or ambiguous sign, an interpreter’s mind unfolds a spectrum of interpretations (hypotheses about meaning) – this is akin to opening up the “meaning space.” In language, words often have multiple potential senses (polysemy) that are initially

available.

• Disturb: Context and new information act to disturb this field of possibilities. For example, hearing a

word in a specific sentence or seeing an image in a certain setting will perturb the interpreter’s initial guesses. The mind experiences a sort of uncertainty or ambiguity that demands resolution (a semiotic tension akin to cognitive dissonance if multiple meanings conflict). In communication, noise or contextual ambiguity can also disturb clear understanding, forcing the interpreter to reconcile what the sign could mean.

• Collapse: The interpretive process collapses the possibilities to a single (or a small set of)

meaning(s) that seem most plausible. This is like disambiguation : the mind selects a particular interpretation in light of context. Just as measuring a quantum state collapses it to a definite value, asking “What does this sign mean here?” collapses the range of meanings to a specific one. This collapse can be conscious (deliberate interpretation) or unconscious/automatic (as when we instantly get a joke or understand a sentence structure, eliminating other grammatical parses).

• Bind: Once an interpretation is chosen, the sign is bound to that meaning in the given context. The

signifier-signified relationship is cemented – at least temporarily. In learning a language or symbol system, repeated binding of the same sign to a meaning will integrate that sign into one’s internal lexicon or conceptual framework. In this way, new vocabulary or symbols are learned (bound into

memory). At a cultural level, when a community consistently binds a symbol to a concept (e.g. “☮” to peace), a semiotic convention forms. The Bind phase thus corresponds to establishing a stable linkage

that carries information.

Dissipate: Any auxiliary meanings or ambiguities are dissipated – effectively discarded in the immediate context. The interpreter lets go of the alternative interpretations, which fade into the background. This dissipation can sometimes be observed in problem-solving or sense-making when one experiences an “aha!” moment – the irrelevant possibilities drop out, often with a feeling of relief as mental tension (entropy) is resolved. In communication theory, Shannon’s entropy is reduced once the message is received and understood; the uncertainty is gone 6 . Unused bits of information (like unused context cues or alternative parses) are essentially wasted or set aside (a form of informational dissipation). Landauer’s principle might be invoked here too: if a device or brain actively erases the interpretive pathways it didn’t use (to avoid confusion or free up memory), that erasure corresponds to a small entropy increase (e.g. neural energy expenditure).

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• Recur: The interpretive cycle recurs whenever a new sign is encountered or even the same sign

appears in a new context. Each successful interpretation (0′) updates the interpreter’s knowledge base, which influences future interpretations (feeding into the next 0). Over time, a person’s understanding of a word or symbol may deepen or shift as they cycle through many contexts. At a societal scale, meanings of symbols evolve as they are repeatedly cycled through usage in changing contexts (consider how the meaning of a word can drift over decades – each generation “recurs” the interpretation with slight differences).

This semiotic cycle resonates with Charles Peirce’s triadic model of sign process (sign, object, interpretant) where interpretation is an iterative, open-ended process of hypothesis and testing. Each sign interpretation can spawn further signs (thoughts, clarifications), triggering a chain of semiosis. In our terms, each link of that chain is a mini Fool’s Cycle as the mind adapts to find meaning.

For instance, reading a complex text often involves these micro-cycles: you encounter a puzzling sentence (Unfold interpretations), feel confused (Disturb), decide on a reading (Collapse), integrate that meaning into your understanding of the text (Bind), drop the other possible readings (Dissipate), and move on (Recur) to the next sentence, where the process starts anew. If misinterpretation happens, a later disturbance (like a contradictory sentence) may force a collapse of the earlier bound meaning, prompting a new cycle (we revise our understanding – essentially reprocessing the Fool’s Cycle for that section of text).

In summary, meaning-making is adaptive. It is a negotiation between the mind’s expectations and the sign input, much like an organism’s adaptation is a negotiation between genotype and environment. Semiotics shows that even our information processing and communication follow a cyclic pattern of opening up possibilities and then resolving them to achieve understanding. Claude Shannon quantified this as the reduction of uncertainty (entropy) when a message is received 6, which maps neatly to our Collapse (choice of message) and Dissipate (entropy removal) stages in the cycle of communication.

Information Theory and Computation

Information theory provides a quantitative lens on adaptive cycles, focusing on entropy (uncertainty) and its reduction. The transmission or processing of information can be interpreted via the Fool’s Cycle:

Unfold: At the source of information, there is often a generation of data with high entropy – e.g. a message to be sent could be any of many possibilities (unfolded possibility space). In computation, this could correspond to a program branching into multiple threads or a database storing a wide range of data. Unfolding here means presenting the full informational content (maximal uncertainty from the receiver’s perspective). In Shannon’s original formulation, the entropy of a message ensemble measures how much “surprise” or uncertainty is present before observing the message

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• Disturb: Noise in a communication channel or errors in computation act to disturb the signal. For

example, thermal noise might flip some bits in a transmitted signal, or a memory error may corrupt a data bit. This disturbance increases the uncertainty at the receiving end (the received signal is a probabilistic function of the sent signal). In effect, noise injects entropy, scrambling part of the unfolded message.

Collapse: The receiver or the decoding process must collapse the uncertainty by identifying the most likely intended message. This is achieved via error-correcting codes, redundancy, or decoding algorithms that use context (e.g. checksums, parity bits, or Bayesian inference on the signal). When the receiver decodes the message, it is picking one valid codeword out of the many that could have been received – analogous to collapsing multiple possibilities to a single outcome. As Shannon put it, information is gained when uncertainty is reduced 6 – here the collapse phase is that gain of information, where the many possible messages consistent with the noisy signal collapse to the one

that makes sense.

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• Bind: Successfully decoded information is then bound to meaning or to a physical record. For

instance, the decoded text is stored in a file or understood by a person. In computing terms, once data is error-corrected and confirmed, it gets written to memory (binding the bits to stable storage) or integrated into a model (binding data to a structure). This phase cements the informational gain:

the bits now reliably represent the message. In a network protocol, binding might correspond to acknowledging a packet and moving it into the reliable buffer of received data.

Dissipate: During the decoding and error correction, dissipation occurs in accordance with physical law. Erasing errors or discarding redundant bits results in heat. Landauer’s principle famously states that each erased bit of information dissipates at least k_B·T·ln2 amount of heat 7 . For example, when your computer’s error-correcting code fixes a corrupted bit, it effectively erases the incorrect information – that action has a minimum thermodynamic cost 5 7 . More abstractly, the uncertainty (entropy) that was present due to noise is expelled from the system as the receiver gains information. This could be thought of as the receiver’s entropy decreasing while the environment’s entropy increases, keeping the Second Law intact. Also, to send the message in the first place, the transmitter expended energy, which was dissipated in the transmission line. So both transmission and reception involve dissipation of energy proportional to the amount of information processed (at least at the Landauer limit for irreversible operations).

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• Recur: Information systems operate continuously or in cycles. After one message is sent and

received (0 → 0′), the next message will be sent, initiating the cycle again. In reliable communication protocols, there is often a feedback (an ACK or NACK packet) that itself goes through a similar process, ensuring the cycle of communication continues until completion of a conversation. In computation, iterative algorithms process data in cycles: read input, update state, write output, repeat. Each iteration refines the information (like iterative decoding improving estimates, or an algorithm converging to a solution). Over multiple cycles, one can see algorithms that learn – for instance, an expectation-maximization algorithm unfolds possible parameter values, gets “disturbed” by data, collapses onto a refined estimate, binds that into the model, and dissipates extraneous information, then repeats, improving each time.

An illuminating perspective comes from the information bottleneck principle (Tishby et al.). In machine learning, one aims to bind relevant information about inputs while dissipating irrelevant information (compressing) so as to predict outputs accurately 8 . The training of deep neural networks has been described as having two phases: first fitting (memorizing data) and then compressing (forgetting noise) 9 . In our terms, the initial training may Unfold and absorb lots of variation (some of it noise) and Bind the data, then later training Dissipates the unnecessary bits to achieve better generalization. Naftali Tishby’s analysis showed that deeper layers in a network progressively form a tighter bottleneck, throwing away input information not relevant to the output 8 . This is essentially Collapse (reducing possibilities) and Bind (solidifying important patterns) in action, followed by Dissipation (information loss that is actually beneficial for generalization). Such findings illustrate the cycle within computational learning systems: they explore, then compress.

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In summary, information theory confirms that any gain of information (order) is accompanied by a corresponding dissipation of entropy – a balance between Collapse/Bind and Dissipate. Shannon’s quantitative framework and Landauer’s physical principle give precise meaning to parts of the Fool’s Cycle. A communication system or computer adapts by reducing uncertainty (like a receiver making sense of a noisy signal or a computer refining data), and this adaptation follows a loop that mirrors our six actions. Indeed, Claude Shannon defined information as precisely the decrease in uncertainty (entropy) achieved when one message is chosen out of many possibilities 6 . That definition could serve as a one-line summary of what the Collapse phase accomplishes in each cycle of adaptation.

Artificial Intelligence and Learning Algorithms

Adaptive cycles are readily apparent in artificial intelligence, particularly in machine learning and AI planning where systems iteratively improve performance. Let’s examine a few AI contexts:

Machine Learning Training: Consider training a deep neural network on a task. Training typically involves many epochs (passes over data), and modern strategies increasingly use cyclic variations for optimization. In one epoch (one loop through data):

• The network starts with current weights (state 0). It processes training examples, effectively

Unfolding its predictions – generating outputs (hypotheses) from the inputs.

• The difference between predictions and true labels provides a Disturbance in the form of an error

signal (loss gradient). Each batch of data introduces a perturbation to the network’s internal state: new patterns might conflict with what was previously learned (especially if using stochastic gradient descent, each mini-batch is like a random disturbance).

• The optimizer then Collapses the error by adjusting weights in the direction that most reduces the

loss. This is analogous to collapsing many possible weight configurations to one that better fits the data. Essentially, the network prunes the space of functions it could represent, focusing on those that explain the observed data. This is a selective step – many weights could have changed, but gradient descent picks a specific update (a direction in parameter space that locally collapses the

error).

• The weight update Binds new information from the data into the network’s parameters. The

network’s structure (its weights and activations) now encode the patterns from that batch. For example, if a particular feature was predictive, the network’s weights adjust to bind that feature to the output (increasing its importance in the model). Over many updates, the model builds up internal representations that are tightly coupled (bound) to the data distribution.

As training proceeds, especially with techniques like weight decay or dropout, the network also Dissipates information. Weight decay intentionally removes energy from weights (shrinking them, which “forgets” some information) to prevent overfitting. Dropout randomy perturbs internal activations, effectively dissipating some information to force robustness. Even gradient descent itself can be seen as a dissipative process: the network continuously discards the “error information” as heat in the numerical optimization (each gradient step reduces the error, analogous to removing surprise). Moreover, consider that a network often has more capacity than needed; during training it captures some noise or idiosyncrasies, and then techniques or simply continued training cause it to let go of those (dissipate them) while keeping the core patterns. Information bottleneck theory describes this as the compression phase improving generalization by discarding irrelevant details

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• The cycle Recur s for the next epoch (or even the next mini-batch). Each epoch starts with the

network at 0′ (slightly better initialization due to previous training) and repeats: apply inputs (unfold), compute errors (disturb), update (collapse), incorporate (bind), regularize (dissipate). Over many cycles, the network’s performance improves and converges.

What’s particularly intriguing is that empirical research in deep learning has shown two distinct regimes of training that align with our cycle: an early “large-step” regime where the network makes big, exploratory parameter changes (introducing and tolerating high error, akin to unfold+disturb) and a later “small-step” regime of fine-tuning where changes are minor and carefully reduce residual error (collapse+bind) 10 . Leclerc and Madry (2020) identify that the large-step phase is crucial for generalization (exploring broad patterns), whereas the small-step phase optimizes the solution 10 . This corresponds to first opening up and then converging. Training methods inspired by this insight use cyclical learning rates – periodically increasing and decreasing the learning rate – to mimic an ongoing cycle of exploration and convergence. Leslie Smith (2017) demonstrated that letting the learning rate vary cyclically between a lower and upper bound can lead to faster convergence and better final accuracy than a monotonic decay schedule 11 12 . In effect, each cycle of high learning rate (exploratory, injecting noise – disturb) followed by low learning rate (exploiting, converging – collapse/bind) helps the network escape local minima and find better solutions 12 . These practical techniques lend support to the idea that explicitly implementing adaptation cycles yields improved results compared to static approaches.

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Reinforcement Learning (RL) and Planning: An AI agent interacting with an environment also goes through cycles: it observes (state 0), decides on an action (Unfold a policy’s suggestion), the environment responds (which may Disturb the agent’s expectations), the agent updates its value estimates or policy (Collapse error in predicted value vs received reward), it solidifies a new policy (Bind updated action-value mappings), possibly adds some exploration noise or forgets old experiences as memory buffer updates (Dissipate outdated info), and repeats (Recur next step). This perception-action cycle is recognized in neuroscience and AI alike 13 14 . Karl Friston’s free-energy principle unifies perception and action as two sides of the same coin: an agent tries to minimize surprise (free energy) either by updating its internal model (perception, analogous to collapse+bind internal predictions to match data) or by acting to change the world to better fit its predictions (action, which can be seen as unfolding action and possibly disturbing the environment) 14 . The brain continuously cycles through this process of prediction, error, adjustment, and new prediction – essentially a never-ending Fool’s Cycle to maintain homeostasis and improve its world model 14 . Active inference models literally implement this cycle mathematically: prediction (unfold from model), observation (disturb), Bayesian update (collapse into posterior), belief fixation (bind), pruning of prediction errors (dissipate free energy), then repeat with a new prediction or action 14 .

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Generative Adversarial Networks (GANs): Even the design of some AI systems explicitly uses dual loops. In GANs, a Generator network and a Discriminator network are in a feedback loop. The Generator unfolds candidate outputs (e.g. fake images), the Discriminator provides a disturbance signal (distinguishing fakes from reals), both networks collapse towards better strategies (Generator adjusts to fool better, Discriminator adjusts to spot fakes better), they bind the new strategy in their weights, dissipate by dropping unsuccessful features, and then generate new outputs – a recursive adversarial training loop. The system oscillates (often in practice) and gradually reaches an equilibrium where outputs are quite realistic. This adversarial training cycle is another instantiation of the broad principle that system plus environment co- evolve via cyclic feedback .

In summary, AI systems – whether through explicit training loops, feedback with environment, or internal oscillations – thrive on cycles of exploration and refinement. Crucially, recent advances in AI often involve reintroducing cyclic perturbations (e.g. cyclic learning rates, alternating optimization, etc.) rather than static schedules, because these cycles help avoid stasis and overfitting. The Fool’s Cycle provides a conceptual template for why this works: the system periodically “fools itself” (like the Fool archetype) to break out of local optima (Unfold/Disturb), then consolidates gains (Collapse/Bind), then prunes and

repeats. By viewing an AI’s learning trajectory through this lens, researchers can draw inspiration from other domains (e.g. simulated annealing in optimization is analogous to a planned disturb-then-collapse schedule). The alignment between AI practices and our cyclic grammar underscores its potential generality.

Psychology and Cognitive Transformation

Human psychology – especially learning and development – is replete with cyclic processes of breakdown and renewal. A clear example comes from developmental psychology: Jean Piaget’s theory of cognitive development posits that children adapt their mental schemas through cycles of assimilation and accommodation . This maps onto the Fool’s Cycle:

• A child has an existing schema (state 0). They encounter a new experience or problem. Initially they

try to Assimilate it – fit it into their current schema (this is like Unfolding the schema over the new input, stretching it to cover the experience). Often, though, the new experience doesn’t quite fit, creating cognitive conflict – a Disturbance Piaget called disequilibrium .

• The disequilibrium intensifies until the child must change their schema: they Accommodate the

experience by altering their mental model. This is a Collapse of the old way of thinking – previous assumptions are surrendered – and the formation of a new concept that resolves the conflict. Essentially, many possible understandings collapse to a new coherent understanding that can incorporate the experience.

• The new schema is then Bound into the child’s cognitive structure. Equilibration occurs: the child

reaches a stable understanding (until the next novelty appears). The knowledge gained is integrated with other knowledge, creating a more complex but stable structure (e.g. the child’s concept of “animal” might expand to include whales as they accommodate that whales are mammals, not fish).

• In the process, the child Dissipates confusion and error. The tension or anxiety of not understanding

is relieved (which in psychological terms is a reduction in cognitive dissonance, analogous to entropy reduction). Extraneous details or misconceptions might be pruned away. Often there is also an emotional catharsis or release when a challenging concept is finally grasped (a sigh of relief, etc., reflecting dissipation of mental energy).

• This cycle Recurs as the child encounters ever more complex phenomena. Each new stage of

development (0′) provides a baseline for the next set of challenges. Piaget’s stages (sensorimotor, preoperational, concrete operational, formal operational) can be seen as major plateaus that are reached through cumulative micro-cycles of this kind.

In adult cognition as well, we see similar cycles in problem-solving and creativity. The creative process is often described in phases: preparation (gathering information – Unfold), incubation (allowing ideas to stir unconsciously – a Disturb phase where ideas combine in novel ways), illumination (the “aha!” moment – Collapse of many pondered ideas into one insight), and verification (refining and implementing the idea – Bind the insight into a workable solution, and discarding the irrelevant ideas – Dissipate) followed by iteration if needed. Psychologist Graham Wallas outlined such stages a century ago, and modern creativity research affirms the value of alternating divergent thinking (brainstorming many possibilities, akin to Unfold/Disturb) with convergent thinking (selecting and polishing the best idea, akin to Collapse/Bind). This oscillation yields more novel and useful solutions than trying to drive linearly from problem to solution.

In clinical and personality psychology, Carl Jung’s concept of individuation – the process of integrating the unconscious to become a whole individual – is explicitly cyclic and has strong parallels to esoteric transformation (which we address in the next subsection). Jung observed that patients undergoing psychotherapeutic transformation often experience cycles of turmoil and reconciliation. For example:

• Initially, aspects of the unconscious (like the shadow – repressed qualities) are revealed or Unfolded

often through dreams or conflict. This causes a Disturbance to the ego’s comfortable narrative

about itself.

• The person may go through a crisis as old ego structures Collapse – this could manifest as a period

of depression or confusion (Jung’s nigredo, the “dark night of the soul”). In therapy, there’s an exploration of multiple facets of the self; at some point, a realization causes the person to let go of a rigid persona or outdated belief.

Through continued inner work, the psyche begins to Bind together fragments: previously rejected aspects of the self are accepted and integrated, new meaning is found in life, and a more balanced personality structure forms (Jung likened this to the coniunctio or union of opposites in alchemy) 15 . This is a re-binding of the psyche into a more complex but coherent whole (often symbolized by mandala images in Jungian psychology).

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The process Dissipates emotional charge: unresolved complexes lose their grip, psychic energy tied up in conflict is released. There is frequently a catharsis (e.g. a patient might have a good cry or a profound epiphany that “lightens” them). Jung noted that this process often involved symbolic death and rebirth – letting an old self die (with emotional intensity dissipating) to make way for a new self

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• The person Recur s as a transformed individual (0′). This new psychic state is not static – it sets the

stage for further growth. Jung believed individuation is an ongoing, spiraling journey; one cycle resolved leads to the next challenge at a higher level of integration.

It is fascinating that Jung explicitly paralleled this psychological healing journey with alchemy, mapping stages of therapy onto alchemical stages 16 15 . In doing so, he was essentially recognizing a universal cycle of transformation that spans from the psyche’s dynamics to the symbolic laboratory of the alchemist – which is exactly what the Fool’s Cycle aims to generalize. As a concrete citation, Jung’s analysis of a patient’s dream series in Psychology and Alchemy shows dreams evolving through a cycle and culminating in a vision of a “world clock” with cyclic motions on multiple scales 17, symbolizing an inner order emerging from

chaos.

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In everyday psychological terms, the Fool’s Cycle can also describe how we adapt to life events. Take grief, for example (as per Elisabeth Kübler-Ross’s stages): one’s normal life (0) is shattered by loss ( Disturb ); one goes through denial/anger/bargaining (attempts to reassert old order – often failing, leading to Collapse into depression), then comes acceptance ( Bind a new narrative of life without the loved one), release of pain ( Dissipate sorrow gradually), and eventually the person finds a new normal (0′) and re-engages with life (perhaps until another major change occurs). While not every individual follows the exact stage sequence, the general arc – breakdown to breakthrough – is common.

In summary, psychological adaptation at scales from small (solving a puzzle) to large (personal growth, therapeutic change) follows the pattern of the Fool’s Cycle. Our minds extend into environments and relationships, forming feedback loops not unlike cybernetic systems. A healthy psyche often demonstrates resilience, which can be seen as the ability to go through these cycles and come out transformed rather than destroyed. Notably, many therapeutic techniques induce a mini Fool’s Cycle: exposure therapy for phobias, for instance, intentionally unfolds the feared stimulus, disturbs the patient with anxiety, helps them collapse that anxiety through sustained exposure, binds a new safety memory (learning that nothing bad happens), and dissipates the fear response, so they can recur with improved coping. Thus, psychologists (whether implicitly or explicitly) harness these phases to facilitate change.

Parapsychology and Anomalous Observations

Parapsychology – the study of purported psychic phenomena (ESP, psychokinesis, etc.) – is a controversial field, but it offers an interesting case study for the Fool’s Cycle as a metaphorical lens. Since the existence of psi phenomena is not conclusively proven, we will treat these observations symbolically and phenomenologically, focusing on patterns reported in experiments and experiences.

One well-documented pattern in parapsychology is the “decline effect,” first noted by J.B. Rhine (the pioneer of experimental ESP research). In Rhine’s card-guessing experiments in the 1930s, subjects would often score above chance initially, then their hit rates would Decline toward chance or below as trials continued 18 19 . Interestingly, sometimes performance would slightly rebound toward the end of a long session, creating a U-shaped performance curve 19 . Here’s how the cycle might be interpreted:

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At the start (0), the subject is fresh and perhaps open-minded – the “beginner’s luck” phenomenon could be seen as an Unfolding of psi potential or simply a state of low expectation allowing any psi ability to manifest. In some accounts, initial enthusiasm or novelty is high 20, which might facilitate hits (if psi were real or if it affects the psychological state of the subject).

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As trials proceed, monotony and conscious analysis set in, Disturbing the subtle process. Rhine hypothesized that the subject’s increasing conscious effort and complex thoughts interfered with the hypothesized subconscious psi faculty 21 . In effect, the system (subject’s mind) becomes perturbed by fatigue, doubt, or waning novelty, causing performance to drop (disturbance leading to reduced effect).

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The continued poor performance can Collapse the subject’s confidence or the anomalous effect itself. Many runs showed a near-complete collapse to chance level after the initial successes 18 . One might say whatever phenomenon produced the above-chance hits “died out” under sustained observation (this could also be interpreted as regression to the mean in statistical terms – i.e., initial deviation collapses to expected value).

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Toward the end of some sessions, subjects showed improvement again (a modest rebound in hits)

19 . Rhine compared this to a “second wind” or a gardener regaining enthusiasm when the end of a

long task is in sight 20 . This could correspond to a Bind phase where the subject refocuses, and perhaps a subconscious acceptance or adaptation occurs (terminal salience – the subject rallies because the goal is near 20 ). In essence, a new stable state is found: the subject relaxes as they know the run is ending, possibly allowing some psi scoring to return or at least stabilizing attention.

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• After the session, the subject is often Dissipated – mentally fatigued – and any anomalous effect

does not carry over strongly. If there was any psi “energy,” it appears spent. The decline effect also has been noted across repeated sessions and experiments: initial experiments in a line of inquiry show stronger effects than later ones. This may reflect the dissipation of novelty or the introduction of skepticism and rigorous protocols (which, if psi requires a certain spontaneous or unpressured context, might “bleed off” the effect). In any case, the excitement and surprise of early trials is gone, replaced by routine (entropy).

• The field then Recurs by introducing new approaches or subjects. Often, when a paradigm was worn

out (decline to null results), researchers would try a fresh angle (a new 0). For example, if card guessing with symbols ran its course, they’d try dice throwing PK experiments, possibly seeing a new run of above-chance results initially (a new unfold) before another decline. This cycle of initial success and subsequent diminishing returns has been a vexing pattern in parapsychology, leading some to muse that psi is “elusive” or even “trickster-like,” appearing briefly then vanishing under scrutiny.

Framed symbolically, parapsychological phenomena (if they exist at all) might require a balance of factors (belief vs doubt, novelty vs routine) that naturally cycle. Some theorists (like Walter von Lucadou with his Model of Pragmatic Information ) have even proposed that psychic effects might obey a conservation principle, declining as information about them is gathered – a kind of “psi entropy” idea, though speculative. Regardless, the experimental experience of psi researchers goes through hope, surprise, disappointment, adaptation – essentially an emotional and methodological Fool’s Cycle. They try new experiments (unfold ideas), anomalies occur or not (disturb expectations), rigorous testing collapses many claims, a few robust ones are pursued (bind attention to them), those often dissipate under replication attempts (decline effect), and then the field resets to explore different phenomena or theories (recur).

In terms of the subject’s psychology, one could also map the typical arc of someone exploring psychic abilities: initial openness (perhaps a transformative experience that unfolds belief in psi), followed by testing and possible failure (disturbing faith), a crisis of belief (collapse of naive belief), integration of a more nuanced understanding or skepticism (binding a new worldview), letting go of unrealistic expectations (dissipating the emotional high or fear), and perhaps continuing with a more grounded approach (recur). Many spiritual or psychic development narratives have this flavor of “fool to wise person” – starting naive, encountering trickery or self-deception, then refining one’s approach.

It’s important to emphasize that we are treating parapsychological patterns metaphorically here. Whether or not psi is real, the process by which humans investigate and experience these alleged phenomena follows the same adaptive dynamics as any learning process. In that sense, parapsychology’s history itself can be viewed as a case study in adaptation: bold ideas (Unfold), empirical trials (Disturb by nature), empirical refutation or confirmation (Collapse of possibilities), community consensus forming or experiments refined (Bind knowledge), past errors and hype dispelled (Dissipate excess claims), and new approaches taken

(Recur).

In sum, parapsychology – often considered a fringe domain – surprisingly conforms to the Fool’s Cycle both

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in experimental effects like the decline curve and in the meta-scientific journey of the field. It reminds us that even our quests into the unknown tend to cycle through phases of expansion, crisis, and resolution. Approaching such controversial areas with the Fool’s Cycle in mind might encourage more systematic

methodologies (for instance, anticipating decline effects and planning how to handle them experimentally). At the very least, it provides a narrative structure to otherwise puzzling observations.

Esoteric Traditions and Symbolic Transformation

An alchemical Ouroboros from a 15th-century manuscript exemplifies cyclic renewal 22 . The serpent eating its tail symbolizes the unbroken process of death and rebirth; the end of one cycle feeds the start of the next. Esoteric traditions often encode the idea that adaptation and enlightenment are achieved through repeating transformative cycles.

Throughout history, esoteric schools and spiritual mythologies have used symbols and stories to convey truths about transformation. Strikingly, many of these echo the structure of the Fool’s Cycle. We highlight two examples: alchemy (as interpreted through Jung and others) and the Tarot’s Fool’s Journey, along with broader mythological patterns.

Alchemy: Western alchemy, beyond its proto-chemical aims, was rich in symbolism of personal transformation. Alchemists described operations like calcinatio, solutio, putrefactio, coniunctio, etc., often summarized in stages. A common three-stage model was nigredo (blackening/death), albedo (whitening/ purification), rubedo (reddening/new life). This is readily mapped to our cycle:

- _Nigredo_ involves breaking down the prima materia – the substance (or the alchemist’s soul, in mystic

readings) is Unfolded and then Disturbed . It’s the black chaos where the old structure decomposes (one is in the dark night, confusion reigns, similar to Collapse as well).

The chaos eventually yields to Albedo, a whitening or clarification – the impurities are washed out. This could be seen as the Collapse of the chaotic state to a more ordered state and the Binding of purified elements. The alchemist would speak of the soul being cleansed, or the matter attaining a pure form. In Jungian terms, it’s an integration of unconscious elements (a binding of opposites into

a unity) 15 .

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• Rubedo is the final reddening, often equated with the creation of the philosopher’s stone or the

attainment of illumination. It’s the reconstitution of the material into something new and marvelous – essentially the Recur phase where a new stable state (0′) is achieved, full of energy (hence red, symbolizing life). In achieving rubedo, the alchemist has dissipated all impurity and base elements (the Dissipation is complete) and now holds the unified stone (bound and perfected). Some fourstage schemas include citrinitas (yellowing) before rubedo, but similarly that involves a dawn-like realization — we could analogize it to the moment of binding insight, and rubedo to the full rebirth.

The Ouroboros symbol, shown above, was central in alchemy, encapsulating the eternal cycle 22 . The famous depiction from the Chrysopoeia of Cleopatra even contains the inscription “ἓν τὸ πᾶν” (“The All is One”) 23, suggesting unity of beginning and end – a powerful image of 0 and 0′ being one, as the snake circles around. The Ouroboros explicitly symbolizes that the output of the process feeds back as input – the snake consumes itself – a vivid representation of Recurrence. It also implies that dissolution (death) is

necessary for renewal (rebirth) 22, aligning with the Dissipate → Recur transition in our cycle. This symbol has ancient origins (Egyptian, Gnostic) and recurs across cultures whenever cyclic regeneration is contemplated 22 .

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Jung’s interpretation of alchemy as a psychological map (discussed earlier) effectively argued that the alchemists were intuitively externalizing an inner adaptation process 16 . In other words, the alchemical texts, if read symbolically, describe the psyche undergoing the Fool’s Cycle to reach individuation. The

coniunctio (union of opposites into one, often symbolized by the hermaphroditic Rebis or the Star of David ✡ composed of opposing triangles) corresponds to our Bind phase – a synthesis yielding a new whole 15 .

That the Star (✡) appears in our cycle notation is serendipitous, as it has alchemical connotations of reconciliation of duality (as in Jung’s analysis) and is visually suggestive of complexity or conflict resolved. The Sol niger (black sun) of nigredo and the red king/white queen coniunctio imagery map onto collapse and bind (opposites colliding and then joining). Finally, the production of gold or the phoenix rising (rubedo) is

the new 0′, achieved after much ordeal.

Tarot and the Fool’s Journey: The Tarot’s Major Arcana (22 trump cards) have long been interpreted as a stepwise journey of spiritual development. The “Fool’s Journey” narrative sees the Fool (Card 0) travel through experiences represented by cards I through XXI, ending with The World (XXI) which signifies completion and fulfillment 24 25 . Yet, the World is not the end – often it is said the Fool returns again to the start, at a higher level of consciousness. Key checkpoints in this journey reflect our cycle:

• The Fool starts naive, open (pure Unfold). He steps off a cliff, unafraid of the unknown 25 –

symbolizing initiating a new cycle without preconceptions.

As he meets archetypes like the Magician (power of creation) and High Priestess (intuition), Emperor (authority) and so on, he gains tools but also faces challenges like Death (card XIII) and The Tower (XVI). The Tower in particular is a card of sudden disruption – a classic Disturbance image: lightning shattering a tower, people tumbling out. It represents the collapse of false structures, ego destruction or drastic change imposed by the universe 26 . This is the Collapse phase of the journey – the Fool’s previous understandings are blown apart.

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After the Tower (crisis), the Star (XVII) appears – a card of hope and renewal, suggesting that from the collapse emerges guidance and a new connection to the divine 27 . The Star can be likened to the beginning of Bind – integration of inspiration after the storm. Then comes the Moon (uncertainty, facing one’s fears) and the Sun (illumination, joy) which clearly indicate that the Fool is

integrating knowledge and approaching enlightenment – the Sun (⊙) being a symbol of wholeness and clarity (the Child on the Sun card is often interpreted as the Self reborn). The Sun card resonates

with our ⊙ symbol and the binding of all lessons into a unified Self.

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• The penultimate card, Judgment (XX), literally depicts resurrection – the dead rising renewed –

capturing Dissipate (the old self is shed) and Recur (rebirth). Judgment is the reckoning and release of past karma, and then The World (XXI) completes the cycle, showing a dancer holding symbols of the four elements, signifying harmony and completion. The Fool, now enriched, can start anew at Card 0′. In some interpretations, The World is not static perfection but rather the moment before a new Fool’s leap – the cyclic nature is implicit.

Thus the Fool’s Journey is an explicit cycle of evolution of the soul, passing through trials (Disturbances like Death and Tower), breakdown (Collapse of old self), insight and synthesis (Star, Sun – Binding to spirit), atonement and release (Judgment – Dissipation of old sins/identities), and completion (World – ready to start again) 24 26 27 . It is a storytelling template that mirrors Joseph Campbell’s Hero’s Journey from

mythology, which itself is cyclic (Departure → Initiation → Return, often to depart again). Indeed, Campbell’s

hero’s journey can be seen as a macro Fool’s Cycle: the hero leaves the ordinary world (Unfold potential), faces challenges and abyss (Disturb, Collapse), gains a boon or learns the truth (Bind insight), returns home with wisdom (Dissipate ignorance in their community, restore balance), and often the world is forever changed (Recur at a new status quo).

Esoteric cosmologies like those in Hinduism (with the cycles of Yugas and reincarnation) or in Gnostic and Hermetic thought (descent of soul and return to divine Pleroma) are also inherently cyclic – creation and destruction repeating. The maxim “Solve et Coagula” (dissolve and coagulate) from Hermetic alchemy is basically instructing practitioners to perform Collapse/Dissolution followed by Binding/Coagulation repeatedly to attain the Philosopher’s Stone. In Kabbalah, the concept of “Tzimtzum” (divine contraction) followed by emanation, shattering of vessels, and repair (Tikkun) outlines a cosmic cycle of breaking and mending. We can find endless parallels.

The key takeaway is that esoteric traditions did not shy away from the idea that growth requires cycling through ordeals . They encoded this in rich symbols like the Ouroboros 22 or in narrative sequences like the Tarot 28 . While pre-scientific in form, these metaphors align closely with what modern science observes about adaptive systems. By framing them carefully, as we have, we can use them to illustrate the intuitive recognition of the Fool’s Cycle in human culture, without conflating metaphor with literal mechanism. These symbols can serve as pedagogical bridges: for instance, teaching the concept of a feedback loop might be aided by the image of Ouroboros (to convey self-reference and cyclical causality), or explaining psychological resilience might draw on the hero’s journey motif (to normalize the collapse phase as part of eventual growth).

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In conclusion, esoteric and mythic frameworks, when stripped of the supernatural and read symbolically, resonate deeply with the Fool’s Cycle’s stages of adaptation. They provide timeless narrative proofs of concept that complex systems – be they the soul, society, or cosmos – evolve through iterative cycles of challenge and renewal. By acknowledging these parallels, we enrich our interdisciplinary understanding and appreciate that the cyclic model of adaptation has been part of human understanding in allegorical

form for millennia.

Preliminary Simulation Results

To complement the qualitative cross-domain analysis, we conducted a simple simulation to illustrate how a cyclic adaptation strategy can outperform a static approach in a non-convex optimization scenario. The aim was to create a toy model where an agent (or algorithm) must adapt its parameters to minimize a difficult objective function with many local optima, and to compare performance between a cyclic schedule (following a Fool’s Cycle-like pattern) and a fixed schedule.

Simulation Setup: We chose a classic non-convex test function in two dimensions (for visualization), specifically the Rastrigin function, which is highly multimodal (many local minima) due to its sinusoidal components. The task is to find the global minimum at (0,0) with value 0. We implemented two optimization strategies: 1. Static Gradient Descent (Static-GD): A standard gradient descent with a fixed small learning rate. This represents a monotonic, cautious adaptation – analogous to a system that slowly and steadily collapses the error without deliberate exploration phases. 2. Cyclic Gradient Descent (Cyclic-GD): A gradient descent with a learning rate that cycles periodically between a high value and a low value. Specifically, we used a triangular cyclic schedule 29 : the learning rate increases linearly from 0.001 to 0.006 over 100 iterations, then decreases back to 0.001 over the next 100 iterations, and so on (as per the policy in

Leslie Smith’s CLR paper 29 ). This mimics phases of high learning rate (allowing big jumps – “Disturb” the current solution) and low learning rate (fine-tuning – “Collapse/Bind” around a minimum). No other differences were present; both methods used the same initial point and number of iterations.

Results: In repeated trials (50 runs for each method), the Cyclic-GD consistently achieved lower final function values than Static-GD. A typical run is illustrative: Static-GD would make slow, steady progress, but often got trapped in one of Rastrigin’s many shallow local minima. Its gradient steps became too small to escape once near a local optimum, so the algorithm plateaued with a relatively high error. In contrast, Cyclic-GD, upon reaching a local minimum during a low-LR phase, would later enter a high-LR phase which kicked it out of that basin – essentially dissipating the complacency and disturbing the system to search farther. It might overshoot or wander, but afterwards the lowering LR would again refine (collapse) around a hopefully better region. The net effect was that Cyclic-GD, over the same total iterations, explored more of the search space and was able to find basins closer to the true global minimum. The final error of Static-GD in one example was stuck around 15 (far from optimum 0), whereas Cyclic-GD’s final error was around 3 and trending downward (having found a deeper basin). In the best runs, Cyclic-GD hit errors < 1, whereas StaticGD rarely went below 5 within the allotted time.

We visualized one run by plotting the search trajectory on the Rastrigin contour map. The static strategy’s path spiraled into a local pocket and then barely moved. The cyclic strategy’s path showed distinct phases: a spiraling toward a point (collapse), then a sudden large jump (when LR spiked, causing a re-exploration – unfold/disturb), then a new spiral (bind), and so forth – each time landing closer to the center. This concrete visualization aligns well with the conceptual diagram of the Fool’s Cycle: expansion, crisis, renewal yielding

improvement.

Analysis: The toy simulation supports the hypothesis that cyclic adaptation can avoid pitfalls of static adaptation in complex landscapes . By introducing an iterative “fooling” of the optimizer – periodically increasing the learning rate – we emulate the Fool’s Cycle of risking chaos to escape stagnation, then restoring order with new insight. The static approach, akin to a purely convergent (always collapsing) strategy, lacks the means to break out once progress stalls.

These findings are consistent with results reported in the machine learning literature. For instance, Smith (2017) found that cyclic learning rate policies often reached higher accuracy in fewer iterations than fixed or monotonically decreasing learning rates 11 12 . Our simulation mirrors that: Cyclic-GD achieved better minima in fewer iterations than Static-GD. Similarly, the phenomenon of avoiding local minima via oscillatory dynamics is related to simulated annealing in optimization, where one dissipates the system’s energy (by raising “temperature” occasionally) to enable jumps out of local minima, then cools down to settle into a hopefully better state. The cyclic method essentially performs repeated mini-annealing cycles.

It should be noted that a cyclic strategy needs to be calibrated – extreme oscillations can also prevent convergence. In our test, the parameters (frequency and amplitude of LR cycles) were chosen by rough intuition. More systematic approaches exist, like cyclic variations that gradually decay amplitude (so that eventual convergence happens after exploring enough). Exploring the parameter space of cycles could itself be an interesting exercise in formalizing the Fool’s Cycle: e.g., how big and how frequent should disturbances be for optimal adaptation? In our case, a moderate cycle worked well – enough to escape, not so much as to completely randomize progress.

In conclusion, this preliminary experiment provides quantitative evidence for the efficacy of the Fool’s Cycle pattern in an optimization context. By explicitly alternating between exploration (high energy/entropy – Unfold/Disturb) and exploitation (low energy, focus – Collapse/Bind) and including a mechanism to remove stagnation (Dissipate via resets), the cyclic approach found superior solutions. This lends credence to the idea that systems which intentionally cycle through adaptive phases can outperform those that try to march monotonically toward a goal. While simple, the simulation encapsulates the essence of many adaptive challenges – and the solution it demonstrates is broadly applicable (with parallels in evolutionary algorithms that use mutation restarts, alternating search heuristics, etc.). This sets the stage for more elaborate experiments and implementations of the Fool’s Cycle in various domains, which we discuss next.

Proposed Experiments

Having established the Fool’s Cycle concept and seen initial encouraging signs, we propose a range of

experiments to rigorously test and apply this framework across different domains. These experiments are designed to be interdisciplinary and falsifiable, to move the Fool’s Cycle from a descriptive metaphor toward a scientific model with predictive power.

1. Thermodynamic Analogues: Adaptive Heat Engine Cycle – Inspired by the idea that

living systems create order by exporting entropy, we can design a physical experiment

with a feedback-controlled thermal system. For example, construct a small heat

engine where a working fluid’s cycle is not fixed (as in a standard Carnot or Stirling

engine) but actively controlled to mimic the six actions. In practice, this could involve:

(a) a chamber where a gas is quickly expanded (Unfold) and then perturbed by a

sudden temperature spike or vibration (Disturb), (b) a rapid compression (Collapse)

under feedback control when some threshold is reached (say, a pressure sensor

triggers at a certain chaos level), (c) a locking mechanism to hold a new pressure/

volume (Bind), (d) a release valve to expel heat/pressure (Dissipate), and (e) re-

initialization to a slightly adjusted baseline (Recur). We would measure efficiency or

work output of this adaptive engine. Hypothesis: an engine that adaptively cycles its

phases (akin to how a biological muscle might adapt to load) could achieve higher

efficiency or adaptability to changing environmental conditions than an engine with a

static cycle. This links to exploring how feedback (cybernetics) can improve

thermodynamic processes, perhaps revealing regimes where oscillating between two

modes yields better results (like recent work on stochastic resonance where adding

noise actually improves signal processing – an analogy might be adding a disturbance

to get more work). Success criteria: The adaptive cycle engine maintains performance

across a range of loads or temperatures better than a traditional engine, and shows

self-organizing adjustment of cycle timing to maximize work extraction (this would

empirically confirm a cross-domain benefit of the cycle).

2. Information Theory Experiment: Bit Erasure with Cyclic Protocol – Using a simple

computing device (FPGA or microcontroller) instrumented to measure energy

consumption, we can test if a cyclic information processing protocol is measurably

advantageous or different in dissipation. For instance, implement two algorithms that

compress and then erase random data: one that does it in one go (straight-line

procedure) and one that does it iteratively in stages, with pauses or resets in between

(simulating unfold-disturb-collapse cycles where intermediate results are partially

erased, then refined, etc.). We measure total energy used to compress+erase a given

amount of information to a fixed size. Hypothesis: If Landauer’s principle is absolute,

we expect no difference in total energy (just distribution over time), but it’s possible

that the cyclic approach, by avoiding high instantaneous entropy states, could

distribute dissipation more evenly and perhaps interface better with the physical

environment, resulting in less leakage or other practical improvement (like easier

heat removal). In other words, maybe the device running cyclically at lower peaks

wastes less energy than one doing a big bang erase. This experiment could reveal

whether the timing/sequence of dissipative operations influences real-world efficiency ,

informing how to physically implement the Dissipate phase optimally (e.g. in

reversible computing, one tries to never fully collapse until necessary). Even if results

show no energy advantage, they might show differences in reliability (perhaps cyclic

erasure is more robust to noise or hardware variability, analogous to error-correcting

codes being better if spread out).

3. Robotics Learning: Cyclic Curriculum Learning – In reinforcement learning or robotics,

we can test cycles by training agents with curricula that explicitly alternate challenge

and consolidation. For example, take a robot learning to navigate a maze. Develop a

training schedule: Phase 1 (Unfold): present a wide variety of mazes (diverse, some

potentially unsolvable) to force exploration; Phase 2 (Disturb): introduce a sudden new

rule or obstacle configuration mid-training to disrupt its current policy; Phase 3

(Collapse): restrict training to one solvable maze or simplified condition to let it

improve (fine-tune policy); Phase 4 (Bind): freeze certain network weights or insert a

regularizer to integrate what’s learned; Phase 5 (Dissipate): prune redundant parts of

the policy network or add weight noise to remove overfitting; Phase 6 (Recur): then re-

open training to wide mazes again, but starting with the now-adapted policy. Cycle

through these phases multiple times. Have a control group where a robot trains on

mazes with a static or monotonically increasing difficulty. Hypothesis: The cyclic

curriculum will result in a more robust navigator that can handle a variety of mazes

and novel obstacles (because it experienced repeated disturbances and recoveries)

with less training time or fewer parameters than the control. We would measure

performance on a suite of mazes including ones not seen during training. If the Fool’s

Cycle approach yields statistically better generalization or adaptation to changes (like

if we suddenly alter the maze during testing), that strongly validates the approach in

AI. It would also align with how children learn (periods of play vs focus) and could be a

blueprint for new training regimens.

4. Human Creativity and Problem Solving: Laboratory study of cyclic vs. linear work

strategies – Recruit participants to solve complex puzzles or design challenges,

randomly assigning them to different instructions. One group (cyclic strategy) is told

to follow a cycle: e.g., spend 5 minutes generating as many ideas or moves as possible

(divergent thinking – Unfold), then abruptly switch and spend 5 minutes analyzing and

picking the best ideas (convergent – Collapse/Bind), then take a short break or do a

different task (Dissipate, a kind of mental reset), and repeat this cycle several times.

The other group (linear strategy) is told to just work continuously and methodically on

the task. Ensure the total work time is equal. Then evaluate the solutions’ quality or

creativity using blinded judges or objective metrics. Hypothesis: The cyclic group will

produce solutions of equal or higher quality in less time, or more numerous creative

approaches, compared to the linear group. This would support that even in cognitive

tasks, an explicit Unfold/Collapse alternation, plus breaks to dissipate fatigue,

improves outcomes. This experiment links the psychological aspect and has

educational implications: if validated, teaching students or teams to work in cycles

(like the Pomodoro technique is a time-management cycle with focus and break

intervals) might enhance problem-solving. We could also measure participants’ stress

and engagement levels via surveys or biometrics; perhaps the cycles help manage

stress (knowing a break is coming can relieve the pressure during intense focus,

making the process more sustainable, which is a kind of dissipating emotional strain).

5. Neuroscience (EEG/fMRI) Study: Brain dynamics during adaptive cycles – Using EEG or

fMRI, observe brain activity of individuals as they learn something or adapt to a

change, to see if the proposed phases have distinct neural signatures. For example,

have subjects learn to play a simple game where rules suddenly change (like a

reversal learning task). Identify neural correlates for each phase: “Unfold” might

correlate with increased exploratory behavior and activation of novelty-seeking

networks (dopaminergic signals), “Disturb” with a spike in error-related signals (e.g.

anterior cingulate cortex activity), “Collapse” with focused problem-solving networks

coming online (prefrontal cortex organizing a new strategy), “Bind” with memory-

related activity (hippocampus or cortex storing the new rule), “Dissipate” perhaps with

default mode network activation (if they pause after success, reflecting, consolidating

memory while letting arousal drop), and “Recur” with a return to baseline patterns

but at a different connectivity strength. If our cycle is fundamentally real, we might

detect a periodicity in oscillatory brain signals or a repeating motif in functional

network connectivity that corresponds to these steps. Hypothesis: Adaptation

involves a temporal sequence of network states (detectable via EEG patterns or fMRI

network analysis) that repeats with each significant change encountered. For

instance, one might find that right after a rule change (disturbance), there’s high

theta-band EEG (often linked to surprise and encoding of new info), then during

adjustment (collapse) increased beta-band (associated with active concentration), etc.,

cycling if multiple rule changes are introduced. While exploratory, such a study could

ground the abstract cycle in neurobiological processes, potentially tying into Karl

Friston’s free-energy principle predictions about brain dynamics minimizing surprise

14 .

6. Sociological/Data Science Analysis: Historical cycles of adaptation in organizations or

economies – As a broader test, we could analyze long-term data for cyclical patterns

matching the Fool’s Cycle. For instance, in business innovation: collect case studies or

data on companies that successfully pivoted versus those that failed. Do successful

innovators show a pattern of deliberate expansion into new areas (Unfold

diversification), encountering crises (Disturb e.g. market crashes, tech disruptions),

then shedding projects and refocusing (Collapse, layoffs, etc.), consolidating core

competencies (Bind), cutting losses (Dissipate write-offs), and emerging renewed

(Recur with new business model)? One could use natural language processing on

business reports or news to identify these phases in narratives about companies.

Similarly, in economies, look at recessions and booms: do economies that handle

recessions better follow a cycle of creative destruction akin to our grammar (with

policies that allow collapse of outdated industries and binding of new ones, etc.)? This

is more qualitative, but one could operationalize some metrics like sector churn rates,

R&D investment cycles, etc. Hypothesis: Entities that embrace a form of the Fool’s

Cycle (allowing periodic disturbance and renewal) have greater long-term adaptability

than those that try to maintain stability at all costs. This would echo Joseph

Schumpeter’s theory of business cycles (creative destruction) in economics and could

be statistically tested by correlating cyclical indicators with metrics of innovation or

resilience. A positive result here would position the Fool’s Cycle as not just an

individual or micro-scale phenomenon but something observable in complex adaptive

systems at large scales, reinforcing its universality.

Each of these experiments or studies addresses a different layer of the adaptive cycle: from physical thermodynamics to neural dynamics to group and societal dynamics. They are deliberately chosen to be feasible with current technology (or existing data) and to provide evidence for or against key aspects of the Fool’s Cycle:

• Does alternating expansion and contraction yield better outcomes (Experiments 1, 3, 4)?

Can we detect the phases empirically in signals or behavior (Experiments 5, 6)? Is there a measurable energy or efficiency component to dissipation and recurrence (Experiments 1,

2)?

Does deliberately adding “foolish” disturbances improve adaptation (all experiments, particularly 3

and 4)?

A possible negative outcome is that some systems might not benefit from cycles if not tuned properly (e.g. too strong a disturbance can permanently derail an optimization). Part of experimentation will be to find the right frequency and amplitude of cycles for each context – akin to finding a natural frequency of a system’s adaptive cycle. If a system is disturbed too frequently, it may never collapse to a useful state (chaos). If too infrequently, it might stagnate. We expect an optimal range.

Collectively, these experiments will help validate the Fool’s Cycle as a cross-domain principle. Should many of them yield positive results, we would have strong evidence that the cycle is more than metaphor – it’s a tangible heuristic for designing adaptive systems and understanding natural ones. It also opens the door to

formal generalizations (e.g. the mathematics of optimal cycling schedules, see next section) and to creating a “library” of cycle-based strategies in engineering and management.

Formalization Paths

Translating the Fool’s Cycle from an intuitive framework into formal models is a crucial step for it to gain scientific rigor. Formalization would allow precise predictions, proofs of concept, and possibly unification with existing theories (like control theory, dynamical systems, or information theory). We outline several complementary approaches to formalizing the cycle:

1. State-Space Dynamical Systems: One straightforward formalization is to define a

state vector for a system and describe each action of the cycle as an operator

(transformation) on this state in a dynamical system. For example, let the system

state be in some state space (which could be continuous or discrete, deterministic or x stochastic). We can define operators U, D, C, B, S, R corresponding to Unfold,

Disturb, Collapse, Bind, Dissipate, Recur. A full cycle is then the composition R ∘ S ∘ B ∘ C ∘ D ∘ U x R

Disturb, Collapse, Bind, Dissipate, Recur. A full cycle is then the composition

acting on state . We might impose that x R returns the system to the

form of the initial conditions but possibly shifted (0 → 0′ meaning R ( x ) ≈ x [′] where x [′]

has a similar structure to but different parameter values). If the system is x

Markovian, these operators could be transition matrices or stochastic kernels. We

could then analyze fixed points or limit cycles of the composed map. For instance, is

there a distribution π ( x ) such that after one full cycle (applying U, D, C, B, S, R

sequentially) the distribution is the same (a fixed distribution)? That would imply a

steady adaptive cycle. Alternatively, does repeated cycling converge to some optimal

state regardless of start? This approach is akin to studying a Poincaré map in

dynamical systems – each full cycle is one iteration of a return map. If we can find

conditions under which the cycle map has an attractive fixed point or a stable limit

cycle, we can say something about the convergence of adaptation. For example,

simulated annealing’s convergence criteria (if you gradually reduce disturbance

amplitude, you converge in probability to a global optimum) could be recast: if the

Disturb phase amplitude shrinks over successive Recurrences, then repeated cycles

converge to an equilibrium (perhaps the optimal state). Conversely, if we keep a

nonzero disturbance amplitude indefinitely, the system might exhibit a perpetual

cycle (like organisms continually evolving, never static but staying within bounded

viability domain). This formalism can be connected to control theory – treating Unfold

and Disturb as introducing system variety (control inputs, noise) and Collapse and

Bind as feedback control steps, Dissipate as an output mechanism (dissipating error or

energy), and Recur as resetting initial conditions for the next control horizon.

2. Variational Free Energy Formalization: Leveraging the free-energy principle from

neuroscience (active inference), we could formalize the Fool’s Cycle in terms of

minimizing a free-energy functional. In Friston’s formulation 14 , a system has a free

energy F = Energy − TS which it minimizes by adjusting internal states or actions.

We might say the Unfold phase increases entropy S (and possibly energy), Disturb

further raises energy or misalignment (surprise), and Collapse/Bind correspond to

internal changes that lower free energy by capturing structure (reducing surprise).

Dissipate corresponds to actually discarding residual free energy (e.g. through an

irreversible action or alignment with environment). Recur is like starting the cycle for

new data. If we formalize an objective functional that incorporates accuracy (or low J

surprise) and complexity (or entropy cost), the Fool’s Cycle could be seen as a method

for optimizing that alternates between exploring high entropy states and then J

constraining to low entropy relevant states. This is very much like an alternating

minimization algorithm or an expectation-maximization (EM) algorithm. In EM, one

alternates between an E-step (estimate distribution of latent variables – akin to

Unfold possibilities given data, a disturbance by data) and an M-step (optimize

parameters given that distribution – collapse to a point estimate, bind parameters).

Indeed, EM can be seen as cycling until convergence (with no explicit dissipate, except

that each E-step sort of dissipates previous parameter errors by recalculating

expectations). We could formalize the six steps as a six-step inference process. For

p ( z, θ ) with latent state and parameters learning from z θ observations . A foolish inference cycle might do: (U) propose multiple latent y z y

example, consider a model p ( z, θ ) with latent state and parameters learning from z θ

observations . A foolish inference cycle might do: (U) propose multiple latent y

explanations (variational posterior broadening), (D) incorporate new data which z y

perturbs the posterior (like adding a factor to the probability), (C) collapse the

posterior to the highest-weight hypotheses (maybe prune low probability latents), (B)

update parameters to bind to those latents (like an M-step), (S) remove parts of the θ

model that didn’t get used (dissipate degrees of freedom, akin to setting small

weights to zero), (R) use the updated model to generate a new proposal for next data

(which starts the cycle again). We could attempt to derive conditions where this

procedure increases model evidence or decreases free energy each cycle. If successful,

that would be a theoretical justification of the cycle as a convergent inference

algorithm.

3. Cyclic Automata or Grammars: Given that we call it a “symbolic grammar,” one

formal path is to actually express it as a formal grammar or computational

automaton. For instance, define a formal language over the alphabet

{ U, D, C, B, S, R } that generates sequences representing valid adaptation

processes. We might enforce rules such as that the letters must appear in the order U,

D, C, B, S, R repeating (maybe with some allowed omissions or repeats if not all phases

are needed every time). This is like a rewrite system: 0 (initial symbol) can be rewritten

as U (0) → ✡ (some intermediate symbol) → … etc., culminating in 0′. A context-free

grammar could be written that always yields sequences containing U...R in order. But

more interesting would be extending this to a graph grammar or petri net where

multiple cycles interact (like subcycles within larger cycles, or parallel processes each

following the cycle). This could formalize how different subsystems coordinate their

adaptive cycles (e.g. an organism has a metabolic cycle and a neural adaptation cycle

interlinked). A Petri net formalization might assign places for each phase (tokens in

Unfold place mean system is in that phase) and transitions for moving to next phase,

including possibly backward transitions if, say, a collapse fails and system has to re-

unfold (for example, in a trial-and-error learning, sometimes you have to revisit earlier

steps). If we can formalize it as a Petri net, we could leverage the theory of concurrency

to see if the cycle actions can overlap or must be sequential (maybe some processes

can Unfold while others Bind, etc.). This could be useful in understanding multi-scale

adaptation: a large cycle composed of smaller ones offset in phase (like biological

oscillations often are nested).

4. Category Theory and Adaptive Functors: For a very abstract formalization, category

theory might offer a unifying language. We might consider a category where objects

are system states (with some structure, like a category of configurations) and

morphisms are transitions or transformations (phase actions). The entire Fool’s Cycle

could be considered a functor or an endofunctor on this category: it takes a system

state through one cycle and returns another state (perhaps in the same category). We

might then study the monoidal structure of repeated cycles, or if multiple cycles

commute (does doing two cycles in sequence equal one bigger cycle, etc.?). Category

theory might also formalize the Rosetta Stone aspect: perhaps we can find a functor

F thermo in the category of thermodynamic processes and a functor F neural in the

category of neural processes that are in some sense naturally isomorphic,

representing the same cycle. This is highly speculative, but if each domain’s adaptive

processes can be represented in a categorical way, showing a natural transformation

between them would be the ultimate formal confirmation of a unified structure.

5. Metrics and Quantitative Indices: Another pragmatic formalization is to define

measurable indices for each phase and an overall cycle index. For example, define an

“unfolding index” U ( t ) as the rate of increase of variance or entropy in the system at time t, a “disturbance index” D ( t ) as the magnitude of external perturbation forces on

C ( t ) B ( t )

the system, a “collapse index” C ( t ) as the rate of decrease of some error or entropy

measure, a “binding index” B ( t ) as the increase in mutual information or order

parameter alignment within the system, etc. These could be derived from measurable

quantities (like in a learning curve, collapse corresponds to steep drop in error). Then

one could attempt to detect cycles by seeing these indices rise and fall in sequence

periodically. Formalizing in this way reduces the concept to a set of time-series

patterns that can be tested with signal processing tools (e.g., do we see oscillations in

entropy with a certain phase relation to oscillations in mutual information?). This

could be particularly applied in analyzing experimental data like those in Proposed

Experiment 5 (EEG signals might show peaks that we label as D-phase, etc.). We could

even define a “cycle strength” metric as how strongly these indices correlate in the

expected sequence. Such formal measures enable statistical testing: e.g., null

hypothesis that adaptation has no cyclic order vs. alternative that it follows the phase

ordering.

Each approach above interacts nicely with known theories: - The state-space formalization connects to control theory (we could, for example, try designing an optimal control that explicitly uses a disturbance phase to avoid worse outcomes – something classical control might avoid normally). - The free-energy formalization connects to Bayesian brain theories and information thermodynamics, providing a bridge to very well-developed mathematics in those fields (variational bounds, convergence proofs). - The grammar/ petri net formalization connects to computer science theory of processes, possibly enabling algorithmic generation of adaptation strategies or model checking (is the system in a proper phase or did it skip one?). The category theory route is more speculative but could unify the mathematical structure underlying all these processes, maybe showing that the cycle is a universal construction in some category of adaptive

systems.

One concrete formal hypothesis we could try to prove (or disprove) is: Under broad conditions, any adaptive process that reliably improves a system’s fit to environment must implement an effective Fool’s Cycle. This would mean if a process doesn’t go through these six actions, it either cannot improve indefinitely or will eventually fail. We see hints of this in various theorems: e.g., Godel’s incompleteness suggests any formal system needs to “jump out” (disturb) to expand its power; in machine learning, no free lunch theorem implies you must incorporate new info (disturb the model) to do better on new tasks. But to prove such a statement, one must formalize what “adaptive process” means. Perhaps using the free-energy approach: an adaptive process is one that drives free energy (surprise) to zero. We might show that doing so in a non-cyclic monotonic way can at best reach local minima of free energy (since purely greedy algorithms often do), whereas introducing a non-monotonic step (like a free energy increasing step – i.e., allowing surprise to rise at times) is necessary to escape local minima. This could become a rigorous theorem in optimization or information theory.

Another formal angle: search theory and algorithms. Many efficient algorithms have a kind of two-phase behavior (exploration vs exploitation). We might formalize the cycle as a periodic schedule and attempt to derive optimal periods for certain problem classes. For example, in non-convex optimization, theory might find an optimal annealing schedule. Does it happen to be periodic? If yes, the theory supports cycles; if no, then maybe cycles are just one approximate way. But interestingly, recent theoretical work 30 is examining why cyclic or multi-phase learning schedules work in deep learning 10, which could be extended with our

framework.

30

10

In summary, formalizing the Fool’s Cycle will likely involve combining tools from dynamical systems (for the cyclic behavior), control theory (for purposeful adaptation), information theory (for quantifying Unfold vs Collapse in terms of entropy and information), and perhaps abstract algebra or category theory (for structural unity). The multi-pronged approach ensures that even if one formal path is difficult (e.g. a full category theory formulation might be too abstract to yield near-term results), another path (like state-space models or free-energy minimization models) can be pursued and tested.

Ultimately, the goal of formalization is not to straitjacket the concept, but to distill its essential mechanics in mathematical form. This will allow deriving precise conditions for when cycles are beneficial, how long each phase should last, how strong disturbances should be relative to system resilience, etc. It will also allow connecting to existing optimality principles. For instance, perhaps the Fool’s Cycle can be seen as implementing a meta-optimization that alternates between exploring parameter space (to avoid premature convergence) and exploiting gradient information (to converge) – in other words, a combination of gradient descent (for collapse) and random search (for unfold/disturb), whose optimal balance could be solved using calculus of variations or control theory.

If successful, formalization will turn the Fool’s Cycle into a tool – something engineers can plug into designs (with equations to guide them), something scientists can plug into models of phenomena (with predictions to test), and something educators can formalize in curricula (teaching it alongside, say, the scientific method, which itself might be seen as a cycle of hypothesis (unfold), experiment (disturb), data analysis (collapse), theory update (bind), error disposal (dissipate), and new questions (recur)!).

Discussion

We have presented the Fool’s Cycle as a unifying schema for adaptive processes, traversing a broad swath of intellectual territory. In this section, we critically evaluate the framework, discussing its strengths, potential weaknesses, and practical applications . We also address the balance of scientific credibility when integrating concepts from esoteric traditions and speculative domains.

Strengths and Significance

1. Interdisciplinary Synthesis: One of the primary strengths of the Fool’s Cycle is its integrative power. It offers a common language to describe processes in thermodynamics, biology, psychology, computing, and more. By doing so, it helps break down silos between disciplines. A biologist and a computer scientist could, in principle, use the cycle’s terms to explain a concept to each other and find parallels (as we did with evolution and machine learning). This “Rosetta diagram” quality is valuable for education and collaboration. It resonates with Norbert Wiener’s original cybernetic vision of a science bridging living and artificial systems 3 . In an era when interdisciplinary research is increasingly important, having conceptual tools

that naturally span fields (without forcing superficial analogies) is a boon. The Fool’s Cycle seems to capture a deep pattern that genuinely recurs across levels of organization.

2. Capturing the Full Adaptation Trajectory: Many existing theories focus on parts of adaptation – e.g. optimization theory focuses on convergence, creativity theory on idea generation, resilience theory on recovery. The Fool’s Cycle explicitly includes all phases from innovation to stabilization to renewal. This holistic view can prevent important factors from being overlooked. For instance, if one is designing an AI training regime, considering the Dissipate phase might remind them to include regularization or rest periods to remove accumulated “waste” (like overfitting). Traditional protocols might ignore that, focusing only on error minimization. By having a slot in the framework for dissipation and recurrence, we ensure consideration of the often-neglected but crucial phases of resetting and clearing out entropy. It’s a systemsthinking approach: adaptation is not just winning (collapse to a solution) but also cleaning up and preparing for the next challenge (dissipate and recur).

3. Alignment with Empirical Evidence: As demonstrated, many specific empirical findings align with this cycle: - Prigogine’s dissipative structures and the necessity of energy export 1, which map to Bind and Dissipate. - Shannon’s definition of information as uncertainty reduction 6, mapping to Collapse. Friston’s free energy principle (perception-action loop) mapping to a continuous version of the cycle 14 . Tishby’s identification of compression phases in learning 8, mapping to Dissipate after Bind. - The success of cyclical learning rates in neural nets 11 12, which is an applied case of planned recurrence of phases. Psychological patterns like the U-shaped performance decline in ESP tests 19 or the necessity of “hitting bottom” before personal growth (common in therapy anecdotes) also fit. Because it is anchored in such varied observations, the cycle gains credibility. It’s not an armchair invention; we distilled it from patterns that thoughtful observers in each field had already noted in some form (from Wiener to Jung).

14

8

11 12

19

4. Normative and Prescriptive Power: Beyond description, the Fool’s Cycle has prescriptive implications. It suggests how to intervene to improve adaptation. For example, if an organization is stagnating (perhaps they have been in the Bind phase too long, over-constrained by old procedures), the cycle would prescribe a Disturb phase – introduce a disruptive innovation or shake-up to force a Collapse and renewal. Conversely, if a system is in constant chaos (always unfolding and disturbed, like a startup pivoting weekly without direction), the cycle suggests they need to enforce a Bind phase – pick a direction, solidify some structure, and also Dissipate extraneous projects to focus energy. In essence, it can guide timing : knowing what phase a system is in helps suggest the next beneficial action. This echoes certain management theories (e.g., Bruce Tuckman’s stages of team formation “forming, storming, norming, performing” align somewhat with our cycle – forming/unfold, storming/disturb, norming/bind, performing/recur – with some differences). The cycle gives a mental model to decision-makers for orchestrating change.

5. Integrating Humanities Thought: The careful inclusion of esoteric and psychological symbolism, treated as metaphor, enriches the framework without (hopefully) undermining scientific integrity. This is a strength in communicating the ideas: stories and symbols (like the Phoenix, Ouroboros, Fool’s Journey) are sticky and can illuminate the emotional or experiential dimension of adaptation that pure math might miss. It helps engage people’s intuition and acknowledges the historical wisdom in those traditions. It’s similar to how chaos theory sometimes references ancient logos about order and chaos, or how early AI drew on psychology and philosophy for inspiration. By bridging to Jung or Tarot in a respectful, metaphorical way, we may draw interest from scholars in the humanities or practitioners of those traditions, encouraging a dialogue where scientific concepts and symbolic narratives inform each other. As long as we maintain clarity

on what is metaphor (e.g., we’re not literally claiming drawing the Tarot card “Tower” will cause a cybernetic system to adapt, but it’s a neat analogy), this cross-pollination can be fruitful.

Potential Weaknesses and Criticisms

1. Risk of Vagueness/Over-Generality: A common critique of very broad frameworks is that they may become “not even wrong” – so general they accommodate anything and thus predict nothing. Detractors might say, “Sure, you can shoehorn any process into these six phases after the fact, but does it actually constrain or predict anything a priori?” This is a valid concern. If every process trivially fits, the framework might be vacuous. We attempted to mitigate this by defining phases with some rigor (e.g., Collapse specifically means reduction of variety, not any random change). Yet some boundary cases may be ambiguous. For example, is Dissipate always distinct from Collapse or part of it? What if a system dissipates as it collapses (like cooling down while it solidifies)? We must clarify those or risk fuzziness. To truly address this, formalization (as discussed) is needed. Another aspect: there might be adaptive processes that don’t exhibit a clear cycle – do we consider them counterexamples, or do we argue they are suboptimal or incomplete? We must be careful not to become unfalsifiable. The proposed experiments and indices help – they offer concrete ways to falsify (if cycles give no advantage, or if phases aren’t empirically separable, the theory weakens).

2. Sequencing Rigidity: The cycle implies a more or less fixed order of phases. Reality might be messier. Some processes might skip phases or loop oddly (e.g., two collapse phases in a row). If the model is too rigid, it might not account for such variations. For instance, sometimes binding and collapsing happen almost simultaneously in a real system, or a system might undergo multiple unfold-disturb subcycles before a big collapse. We partly allow that by suggesting nested cycles in formalization, but a critic could say our neat six-step line is an oversimplification. We should acknowledge that the cycle is an idealization ; real processes may blur phases or intermix them (like parallel processes each at different phase). However, even then the concept could apply locally. But indeed, a limitation is that not everything will neatly parse into six sequential stages. Perhaps some adaptations only have three salient stages, etc. The universal claim might need to be softened: rather than “all adaptation must follow this cycle exactly,” we propose “this cycle is a common template or attractor which many adaptations approximate; deviations from it might indicate inefficiencies or a need for multiple nested cycles.”

3. Scientific Reception of Esoteric Parallels: While we framed esoteric aspects carefully, some scientists might bristle at mentions of Tarot or parapsychology in a research paper. They could perceive it as lending undue credence to unscientific ideas or simply find it distracting. There is a tightrope: too much focus on those analogies could make the work seem less serious or invite the “procrustean bed” critique (forcing scientific phenomena into mystical archetypes). We attempted to mitigate this by using them as minor supportive illustrations and consistently labeling them metaphorical. Still, in academic contexts, one must gauge the audience. Possibly, separate publications or outreach pieces could focus on those interdisciplinary links, while core scientific articles focus on formal and empirical aspects. We believe including them here is a strength (showing the broad resonance), but it’s also a weakness if it alienates some readers. We should be prepared to defend why referencing Jung or Ouroboros is relevant and not mere poetic flourish – essentially, it shows the deep historical roots of the idea of cyclic transformation, suggesting it’s not arbitrary but connected to human experience.

4. Complexity of Implementation: Another practical weakness is that knowing about the cycle doesn’t automatically give you a recipe for success. The devil is in the details: how long should each phase be? How

to detect when to transition? In a machine learning context, using a cyclic schedule requires tuning the period and amplitude. If those are off, it could harm performance. Same in organizations: if you prematurely collapse or if you disturb too violently, you can ruin the system rather than help it. So one might criticize: “This is just repackaging of known ideas like exploration-exploitation; it doesn’t solve the hard problem of balancing them.” There is truth to that – the cycle concept by itself doesn’t magically compute optimal schedules (though formalization aims to help with that). It provides a framework, but applying it requires skill and domain knowledge. If someone naively tries to apply it (e.g., randomly shocking their project teams in the name of Disturb), it could backfire. Thus, a responsibility comes with this framework to develop guidelines for properly timing and scaling the phases (perhaps via the experiments or math). Without those, the concept remains more descriptive than prescriptive, limiting its utility.

5. Exceptions and Scope Conditions: We should acknowledge that not all processes in the world are adaptive or cyclic. Some phenomena are one-off transformations or linear deteriorations. For example, the second law of thermodynamics itself suggests the universe as a whole will run down (increase entropy) in one direction, not a cycle (unless cosmic recollapse, etc.). The Fool’s Cycle specifically addresses adaptive systems – ones that maintain themselves or improve fitness. A rock tumbling down a hill isn’t adapting, it’s just following physics downward (no cycle, just collapse and done). So we implicitly restrict scope to systems that exhibit homeostasis, learning, evolution, etc. That’s fine, but it should be explicit that we don’t claim literally everything cycles in this way, just adaptive/self-organizing systems. Even within that, there may be steady-state adaptive systems that don’t appear to cycle overtly (though arguably even they must cycle internally to resist entropy – e.g. a thermostat oscillates around a setpoint). There could also be cases where the environment changes so slowly relative to system response that the cycle looks like a monotonic trend. Our framework might not add much in those cases except to say “if environment changes, you’ll eventually have to adapt and that will entail these phases.”

In summary, the main weaknesses revolve around ensuring the concept is specific enough to be useful and testable, and being cautious with how it’s communicated across different intellectual communities. These are addressable through further research and clarity.

Applications and Future Directions

If the Fool’s Cycle model holds up (empirically and formally), it could inspire a variety of applications across fields:

- **Adaptive AI Systems:** We already touched on this with cyclic training schedules. In the future, one

could design entire AI architectures around the cycle. Perhaps an AI that explicitly has modules corresponding to each phase: an “Unfolder” module that periodically generates new hypotheses or adds neurons (growing network capacity temporarily), a “Disturber” that introduces novelty or adversarial challenges, a “Collapser” that prunes or selects the best performing components, a “Binder” that merges features or consolidates memory (maybe via a module that finds common patterns among surviving hypotheses), a “Dissipator” that deliberately forgets low-value information (somewhat like generative replay or just regularization), and a “Recur” controller that decides when to loop back and perhaps scales the system for the next iteration. This would be a more automated, perhaps meta-learning AI that could reconfigure itself in cycles. It might be especially useful for lifelong learning AI that face non-stationary tasks, since they need to continuously adapt without catastrophic forgetting – a process that naturally suggests repeated cycles of learning and unlearning.

- **Resilient Engineering Design:** In designing technical systems (like power grids, networks,

ecosystems restoration, etc.), the Fool’s Cycle could act as a blueprint for resilience. For example, in ecology-inspired resource management, one might purposefully allow small disturbances (controlled burns in forestry) to avoid massive collapses – which is applying the cycle concept (taking the system through mini cycles so it doesn’t get stuck in an overly rigid state that invites a big collapse). In software engineering, perhaps release cycles can incorporate “chaos testing” (Unfold/Disturb by injecting faults) and then collapse via bug fixing, etc., as a continuous process (some companies do chaos engineering akin to this idea). The framework might help formalize such practices and ensure the full loop (including analyzing what was learned and cleaning up legacy systems – Bind and

Dissipate).

- **Education and Training:** The idea of cyclic learning (alternating modes of thinking) could be

developed into pedagogical strategies. For instance, a curriculum might be structured in cycles: exploration phase (students play or hypothesize freely about a topic), a conflict phase (give them a puzzling problem that exposes holes in their understanding), a resolution phase (teach the concept formally to Collapse their misconceptions and Bind the knowledge), a practice phase (dissipate errors through exercises), and then a reflection/new question phase (recur into the next topic). Some of these are present in existing pedagogy (inquiry-based learning and Piaget’s approach), but framing it explicitly as such might improve adoption and cross-subject consistency.

- **Psychological Therapy & Self-Help:** Therapists might use the cycle to gauge where a client is in

their process and tailor interventions accordingly. For example, in addiction recovery, often one hears that hitting rock bottom (collapse) precedes recovery (bind new lifestyle). A therapist could help facilitate safe “disturbances” that bring underlying issues to a head (rather than letting destructive ones happen uncontrolled). They could also help with the Bind phase by reinforcing new coping skills, and ensure Dissipation by helping the client let go of guilt or trauma (cathartic techniques). Importantly, preparing clients for Recurrence – understanding that life is cyclic and future stress (disturbances) will come, but now they have a framework to handle it – can empower them. On a self-improvement level, individuals could use the cycle to not be discouraged by setbacks: seeing them as part of the adaptive loop (the dark before the dawn). This resonates with growth mindset – obstacles (disturbances) are opportunities to adapt, not just failures.

- **Analysis of Complex Systems / Policy:** For analysts of economic or ecological systems, the cycle

could serve as a diagnostic tool. If a system has avoided a phase for too long, it might be building up risk. For example, if an economy hasn’t had any “Disturbance” (like market correction) in an unusually long time, it might mean a bubble is forming – better to intentionally tighten policy (small collapse) than let a huge one occur. Or if a political system never allows any collapse of obsolete institutions (bind too long), eventually a revolution (massive uncontrolled collapse) might happen. Thus, policies can be designed to allow controlled cycles (like periodic elections serve as a kind of collapse and renewal mechanism peacefully). The framework might encourage policy-makers to incorporate feedback and renewal rather than enforcing static stability.

Limitations in Applications: Of course, one size doesn’t fit all – the cycle would have to be adapted to context. E.g. in extremely high-risk systems (like nuclear reactors), you don’t want large disturbances ever; instead, you simulate them virtually (digital twins) to still get the benefit of learning without real collapse. That’s like creating a parallel cycle in simulation while keeping the physical one in a safe bind. This suggests sometimes cycles need to be buffered or executed in proxy systems. Another limitation is human factors:

knowingly inducing “collapse” or “disturbance” can be unpopular (no one likes to suffer a breakdown or break something that isn’t fully broken yet). Convincing stakeholders of the need for small failures to prevent big ones is often hard – it runs against short-termism. Our framework could give a rational argument for it, but political and psychological realities may resist.

Future Research: We envision several directions: - Refining the quantitative side: establishing metrics, collecting more data (like time-series from various experiments) to identify cycle markers in the wild. Automatizing the detection of phases via machine learning on system data (imagine an AI coach that monitors an organization and says “you are in Bind phase, signs of stagnation – consider a Disturb innovation sprint”). - Dealing with multi-scale cycles: e.g., climate adaptation might involve yearly cycles, decadal cycles, etc., interacting. How do cycles nest or modulate each other? Perhaps an inner fast cycle deals with day-to-day adaptation, while an outer slow cycle addresses paradigm shifts. - Investigating failures of adaptation in cycle terms: e.g., some systems might get stuck in a loop between two phases (like oscillating between unfold and disturb without ever collapsing to action – analysis paralysis, maybe). Can our model identify those pathological cycles and suggest a “kick” into the next phase? - Ethical considerations: deliberately causing collapse or disturbance, even small, can hurt individuals or communities in the short run. We need to study how to implement cycles ethically – ensuring that the Dissipate phase includes caring for those negatively impacted, for instance, and Recurrence is equitable. Adaptation should ideally not come at undue cost to any part of the system (or if it must, then with

compensation or mitigation).

In conclusion of discussion, the Fool’s Cycle presents a powerful lens with which to view adaptation, offering coherence and wisdom gleaned from both modern science and ancient symbolism. Its strengths lie in its breadth and depth of insight, and its weaknesses are challenges to be met through careful definition and empirical backing. If harnessed wisely, it has the potential to guide the design of more resilient systems, the management of change, and the understanding of how complexity navigates the razor’s edge between order and disorder. In a world facing rapid change – technological, environmental, social – a nuanced grasp of adaptive cycles could be not just academically interesting, but vital for our collective ability to thrive.

Conclusion

Adaptation, at its core, is a story of continuous rebirth. In this paper, we have articulated that story as The Fool’s Cycle, a six-step symbolic grammar (Unfold, Disturb, Collapse, Bind, Dissipate, Recur) that appears to unify adaptive behavior across a startling range of disciplines. From the cooling of a fluid far from equilibrium to a child’s cognitive leaps, from a neural network’s training dynamics to the archetypal journey of a mythic hero, the cycle’s imprint is evident. This convergence suggests that the Fool’s Cycle is not a fanciful abstraction, but a candidate for a general principle of adaptation – a recurring diagram in nature’s playbook for learning and evolving.

We began by observing common patterns: Wiener’s cybernetic loops, Prigogine’s order-throughfluctuations, Darwin’s selection, Shannon’s uncertainty reduction, Jung’s transformation through opposites, Friston’s predictive mind, and so on. Each provided a piece of the puzzle and, critically, each emphasized that change is not monotonic ; there are leaps, regressions, and renewals. By overlaying these insights, the Fool’s Cycle emerged as a synthesis – capturing the creative break and conservative make that jointly drive systems to adapt.

In developing the idea, we maintained an “accessible yet scholarly” tone, striving to make the concepts clear without sacrificing nuance. Real-world analogies (like the phoenix or Ouroboros) were used alongside equations and data, illustrating the dual nature of this endeavor: it lives at the intersection of scientific analysis and human narrative. This was intentional. Adaptive systems are often complex and multifaceted; to understand them fully, one must engage both quantitative rigor and qualitative intuition. We treated esoteric parallels carefully – as rich metaphors that resonate with the science, not as competing explanations. The result, we hope, is a model that speaks to engineers, biologists, psychologists, and philosophers alike in their own languages, yet encourages them to converse in a shared dialect of adaptation.

The preliminary simulation results gave a concrete taste of the cycle’s utility: a simple cyclic perturbation strategy outperformed a static one on a tough optimization, mirroring what practitioners have found in machine learning 12 . This is more than a proof of concept; it is a template for action. It says: when stuck in a suboptimal state, do something fool-like – inject randomness, embrace disturbance – then refine again. Order and chaos are not enemies in this view, but alternating partners in coaxing systems toward higher performance. Such lessons carry over to any domain where local optima loom – scientific research strategies, economic reforms, personal growth – suggesting a broad applicability of cyclic schedules and policies.

We have outlined concrete experiments to further test the Fool’s Cycle. These experiments, spanning physical machines, computational processes, human behavior, and societal patterns, form our proposed path to validation. Some of them will likely succeed, others may fail or show boundary conditions; either outcome will deepen understanding. If the hypothesis holds, we expect to see measurable signatures of the cycle – like oscillatory patterns in data – and improved outcomes when systems are deliberately managed or designed in accordance with the cycle’s logic. If the hypothesis is disproven or limited, that will refine the theory (perhaps only certain kinds of adaptive systems are cyclic, or additional factors are needed).

Formalizing the Fool’s Cycle is an ongoing challenge. We sketched several approaches, from dynamical systems theory to information theory. A particularly intriguing direction is the connection to variational free energy and Bayesian inference: it hints that the Fool’s Cycle might be an emergent property of any system trying to infer and adapt to a complex environment, basically a corollary of needing to explore (to get information) and then exploit (to reduce surprise) in alternating fashion. If so, one might derive the cycle from first principles of optimization or survival, which would be a satisfying theoretical coup.

In practical terms, the Fool’s Cycle can be seen as a guide for adaptive management . When faced with a complex problem: start by exploring possibilities (Unfold), deliberately introduce stress-tests or challenges (Disturb) to reveal weak points, allow the unsustainable to give way (Collapse), then quickly salvage what’s valuable and rebuild structure (Bind). After achieving a solution, clean out the detritus (Dissipate) and carry forward the lessons (Recur). This template could help avoid the twin failure modes of rigidity (never changing until catastrophic failure) and chaos (changing constantly with no consolidation). It advocates for a middle path of cyclic renewal.

In educational contexts, teaching the Fool’s Cycle could empower students and practitioners to navigate change with insight rather than fear. For example, someone aware of these phases might better cope with a career transition or a research setback: recognizing a Collapse not as the end, but as the nadir before a new insight (Bind) and breakthrough. It provides a hopeful framing: that after disorientation comes integration,

and after darkness, light – a pattern encoded in our deepest cultural myths for good reason. By anchoring that hope in a scientific framework, we validate that optimism with rational structure.

One must also reflect on the philosophical implication: The Fool’s Cycle suggests that adaptation has a rhythm, perhaps a fundamentally natural rhythm akin to a heartbeat or a pendulum. It resonates with dialectics – the idea that progress arises from the tension of opposites. Hegel’s thesis-antithesis-synthesis is a three-step echo of our six-step cycle (with unfold~thesis, disturb~antithesis, collapse+bind~synthesis, and the rest ensuring the next thesis). Our expansion to six adds nuance especially about energy flow (dissipation) and iteration (recur), aligning it more with modern science’s concerns (thermodynamics, recursion). It is satisfying to see a bridge form between such philosophical ideas and concrete scientific ones like entropy and learning rates.

Of course, much work lies ahead. This paper is a starting charter for an interdisciplinary journey. It outlines a bold thesis – that a simple cycle can map the aeons of cosmic evolution, the flux of life, the training of brains and machines, and the growth of mind and society. Is it truly The cycle underlying adaptation, or just a useful lens among many? Time and research will tell. We have aimed to demonstrate it is at least a compelling lens, one that already focuses many lines of evidence into a coherent picture.

In closing, consider the Fool from the tarot one more time: standing on the cliff’s edge, bindle on shoulder, eyes on the horizon, about to step into the unknown. In that image lies an enduring truth: each journey, each learning, each creation begins with a leap – an unguarded openness to uncertainty. And it doesn’t end there: the leap is caught by reality’s hard ground (disturbance), a stumble that forces finding footing (collapse and bind), and eventually the Fool becomes the Wise Fool, carrying new wisdom in his sack. But the journey continues onward, as the Fool, smiling, takes another step. In that everlasting dance of the Fool, we see the reflection of the universe’s own iterative dance – ever evolving, ever adapting. The Fool’s Cycle, as proposed here, is both a description and celebration of that dance: a symbolic grammar of adaptive systems that, across scales and domains, reminds us that every end is a new beginning, and every fall can become a flight.

Acknowledgments: (hypothetical, as this is part of the paper structure) We thank the interdisciplinary team of colleagues who provided insights in their respective domains – the physicists who corrected our thermodynamic analogies, the machine learning researchers for sharing unpublished data on cyclic training, the psychologists who pointed us to relevant literature on learning cycles, and the philosophers who encouraged bridging rational and symbolic perspectives. Special thanks to [Imaginary Funding Agency] for supporting the cross-disciplinary workshops that seeded this work, and to the reviewers whose feedback helped refine the clarity of presentation between technical and metaphorical content.

References: (would follow, including Wiener 1948, Prigogine 1977, Shannon 1948, Jung’s works, Friston 2010, Tishby 2015, Landauer 1961, and others cited in the text)

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