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Copyright (c) 2025 Woo Ker Yang (Patrick Woo) patrickwoo.1976@gmail.com
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This document aims to present compelling research showing how the Random Move and Hold pattern, observed across various domains, is correlated with deeper and prevalent mechanical dynamics in nature. These underlying dynamics result in the observed move and hold behaviour.
The title of this document, “The Unifying Theory,” may seem ambitious. Its intention, however, is not to propose a new law of physics, but to offer a new lens for observation. This theory is built by reasoning from established scientific principles and observable phenomena to reveal a pattern so pervasive it has become invisible.
This document explores this dynamic from two perspectives:
The Objective Pattern: We will connect the “Random Move and Hold” behavior to authoritative scientific concepts like Self-Organized Criticality and Punctuated Equilibrium, arguing that the “hold-then-break” dynamic is a fundamental signature of change in complex systems.
The Subjective Blind Spot: We will also investigate why our minds often fail to recognise this non-linear reality, and how our cognitive tendency to linearize the world makes us vulnerable to surprise.
Ultimately, this document seeks to demonstrate that the “Random Move and Hold” pattern is not a mere stylistic effect, but a legible signature of a fundamental process. FPS-R, in turn, is the grammar designed to articulate it.
At its heart, FPS-R is not just a tool for creating motion; it is a model for a pattern of change that can be observed across countless natural and artificial systems. The dynamic is a familiar one, and it is described in many scientific fields through concepts like “tipping points”, “critical mass,” “phase transitions”, and “self-organised criticality”.
This dynamic consistently unfolds in two phases:
This “hold-then-break” dynamic is the signature of complex systems. If these processes were linear, they would be predictable. Calamities could be easily sidestepped, and “Acts of God” would be simple entries on a calendar. Instead, the non-linear, threshold-based nature makes these events surprising, dangerous, and difficult to model.
While we will use “hold-then-break” as the default term to describe this mechanic, it is not meant to be a rigid or a special technical term. We may use more proper forms like “hold-then-action” or “hold-then-shift” where they better describe the specific situation.
This leads to a profound insight: the non-linear, “hold-then-break” dynamic is not an exception to the rule; it is the rule itself. It is the default mode of progress, growth, and locomotion in the universe.
This flips the burden of proof. The question is no longer whether the ‘random-move-and-hold’ pattern exists, but rather, ‘Why would any natural system not exhibit this kind of phrasing?’ Perfect linearity is what requires explanation.
Humans are good at high level abstraction and extracting meaning from noise. It will overload and overwhelm our minds to jump at every shadow and moving leaf. Parsing complexity is taxing on our cognition.
This simplifying and linearising is our way of survival and self-preservation. We prioritise, figuring out what is important and urgent (immediately threatening to our existence), and what is “probably just noise”. Our brains employ various cognitive strategies to simplify and categorise information.
Incidentally, machine learning exhibits a parallel to this behaviour.
In machine learning, this process can be likened to dimensionality reduction, where we filter out unnecessary details to focus on the most relevant features.
For example, when observing a long, curvy branch, our brains might abstract it into a simpler representation—a straight stick. This abstraction allows us to quickly understand the branch’s general direction and purpose without getting bogged down by its intricate details.
This process of linearisation and the process of dimension reduction is like linear regression in machine learning and data science. Linear regression simplifies data with complex shapes into a basic form that can fit into a linear model. It captures the essential trend while ignoring noise and outliers. The trained model can then be used to make predictions based on new data, like how we use our simplified mental models to navigate and make decisions in the real world.
We linearise because the nuances and tiny crooked details hold no useful significance for the tasks we commonly use those things for, hence we discard them, pushing them to the back of our minds.
In real-world situations, we aim to model reality as closely as possible. By observing outcomes, we can study and understand the underlying principles. With distilled knowledge and insights, we can make predictions, anticipate pitfalls, and avoid them.
When studying complex systems, we often dismiss certain details as insignificant. However, these small details can contribute to the outcomes in a big way. Because our perception of reality is shaped by simplification and linearisation, we may mistake simplicity for reality itself. This makes it difficult to determine which complexities truly affect the outcome. Therefore, we study and analyse complex systems to better understand which factors are significant.
In this respect, FPS-R is not just a tool for simulating organic behaviour. It is a grammar for modelling the default texture of reality. It provides a language for the crooked branch, not the straight rod, treating structured, non-linear phrasing as the fundamental starting point, not a complex effect to be added on top of an artificially simple system.
To make the “Illusion of Linearity” and the recursive nature of non-linear progress more tangible, consider this simple analogy:
Imagine a boy who sets out to complete three jigsaw puzzles (A, B, and C) over two weeks. The next day, he is free to choose to continue working on the same puzzle, or one of the other two puzzles, according to his inspiration and preference that day. Hence, the order of the puzzles that the boy works on may be A, C, B, B, C, C, A. He will keep working day after day until all puzzles are complete.
Let us assume that he makes the same progress each day on the puzzle of his choice.
If we chart the total progress of “all puzzles,” we might see a perfectly smooth, linear graph steadily trending towards 100% completion.
This high-level graph is the Illusion of Linearity. It is the project manager’s Gantt chart, the executive summary. It is a useful abstraction, but it is not the reality of the work. The “hold-then-break” dynamic, which is the true signature of the work, is hidden by this perspective.
To find reality, we must change our “camera” and zoom in.
If we change our focus to the progress of just Puzzle B, the picture changes instantly.
This second scenario is a far more accurate model for real-world projects. The boy’s “whim” represents shifting priorities, a new request from a manager, or a sudden, urgent bug that pulls focus from the planned task. The “hold-then-break” dynamic is the actual experience of the puzzle itself.
The analogy gains even more significance as we zoom in on a single day during the “move” phase of working on Puzzle B. At the beginning of the day, the puzzle is 4% complete; by the end of the 8-hour day, it reaches 8% completion. If we could view a time-lapse video of the puzzle board over the course of these 8 hours, would we see the pieces filling in at a linear rate, such as 20 pieces per hour?
Consider the boy. Let us assume he is highly skilled at solving puzzles, consistently and effectively placing each piece. Even under these ideal conditions, there will still be pauses in his progress.
Each piece he picks up requires a slightly different amount of pause time as he contemplates the shapes and references the picture on the box. He has “floating islands and clusters” of pieces that can fit together independently but are not yet connected to the final puzzle. After making several moves, he may spend time rearranging these clusters, breaking them apart and rejoining them. Between placing pieces, he scratches at an insect bite from the night before, shifts his weight, absently flexes his fingers, scratches his head in thought, taps his fingers against the pieces, reverses his last move, and perhaps takes a bathroom break. At midday, his mother calls him for lunch.
In essence, the timing of placement from piece to piece is likely to vary significantly.
This leads to a deeper insight: the non-linearity we observe is not purely fractal; it reflects a pattern of self-similarity at different scales. It is recursive (the generative process that builds the pattern).
Complete_Project is defined by a series of Complete_Session calls.Complete_Session is defined by a series of Place_Piece calls.Place_Piece is itself the fundamental unit of the “hold-then-break” dynamic: a HOLD (find piece, study shape, reason) followed by a BREAK (connect the piece).This means the “hold-then-break” dynamic is the generative rule that builds progress from the “nano” level up.
Crucially, the “holds” are not a failure of progress. They are essential, productive parts of the recursive process. The pause to think, the time to sort, the cognitive “incubation”—these are all necessary HOLD states that enable the BREAK of connection. Linearity, which only measures “pieces placed,” would misinterpret these critical “hold” states as “zero progress.”
Now, we extrapolate this model to a real organisation.
If this one boy working on one simple project is already a “complex multi-parameter system”—defined by shifting priorities (Level 1) and a recursive, fractal “hold-then-break” process (Level 2)—what happens when we scale this to a team?
The complexity explodes. The non-linear “move-and-hold” phenomenon is not just likely; it becomes the inevitable, emergent norm of the entire system.
This analogy demonstrates that “linear progress” is a fiction—a simplified model we impose on reality. The “hold-then-break” dynamic is the fundamental, recursive signature of how work, thought, and all human activity truly unfolds.
The “hold-then-break” dynamic is not limited to abstract puzzles or human organisations; it is the fundamental signature of life itself. A living organism is the ultimate “complex multi-parameter system,” and its development provides a powerful, tangible precedent for the recursive non-linearity at the heart of this theory.
This is best understood through the core biological principle of Resource Allocation. Every organism, from a single cell to a human, operates on a finite “energy budget.” This budget must be dynamically allocated between two competing, fundamental mandates:
The “Illusion of Linearity” would have us believe that growth is a smooth, continuous upward curve. The reality, as observed in developmental biology, is a non-linear “hold-then-break” pattern driven by this trade-off.
On a macro timeline, human growth is not linear. A child does not grow a steady 0.1mm per day. Instead, studies on saltatory growth (growth in bursts) have shown that growth is a “hold-then-break” process. A child may experience long periods of “hold” (stasis) lasting days or weeks, followed by a sudden “jump” (a growth spurt) where measurable change occurs in a 24-hour period.
The smooth growth charts we see in pediatrician’s offices are an abstraction—a “linear regression” of noisy, non-linear data. They represent the “Illusion of Linearity” from the Puzzler analogy, hiding the true, recursive, and phrased reality of the “work” being done.
when the body is sick or injured, it “holds” its growth. This is not a passive pause; it is an active resource diversion.
This is the biological equivalent of the Puzzler switching from Puzzle B to Puzzle A. The organism’s central command system, facing a new, urgent priority (an infection, an injury), diverts the finite energy budget away from the “growth” project and towards the “repair” project (e.g., mounting an immune response, healing tissue).
The fetus provides a perfect example of a nested non-linear system, mirroring the fractal nature of the theory. The fetus’s “hold-then-break” growth pattern is a system entirely dependent on and nested within another complex system: the mother.
The mother’s body is also juggling its own “growth vs. maintenance” trade-offs (her health, her nutrition, her stress levels, her own physiological loads). A “hold” in the mother’s system (e.g., a period of high stress or poor nutrition) directly impacts the resources available to the fetus, which may then trigger a corresponding “hold” in its own developmental “jumps.”
This demonstrates how “hold-then-break” dynamics propagate recursively across interconnected systems. Biology does not operate on simple, linear cause-and-effect. It operates as a complex, recursive “organisation” of “puzzlers,” all juggling priorities. The non-linear, “hold-then-break” rhythm is the emergent, inevitable, and observable signature of life itself.
It can feel paradoxical, almost redundant, to have to point out that nature moves in rhythms of bursts and holds. This is because the pattern is so pervasive that it has become invisible. We mistake familiarity for triviality. This is the “Triviality Trap”: the more ubiquitous a pattern, the harder it is to see as a distinct, formal principle.
Our brains are wired to accept the non-linear as natural:
We can observe the “random-move-and-hold” pattern in plain sight, as it appears in the mechanistic rhythms of systems at every scale:
| Domain | Burst-Hold Pattern Example |
|——————-|—————————-|
| Biology | Neuronal firing (action potential → refractory)
Metamorphosis (dormant latency (cocoon) → transformation) |
| Ecology | Predator-prey dynamics (boom → collapse → recovery) |
| Geology | Earthquakes (stress build-up → sudden release)
Landslides (fault expansion → sudden release) |
| Elemental Systems| Lightning (charge accumulation → electrical discharge)
Bushfire (heat + fuel accumulation → ignition → spread) |
| Astronomy | Star formation (gas accumulation → ignition) |
| Learning Curve| Skill acquisition (practice → internalisation → burst of fluency) |
| Emotions | Meltdown (emotional stress build-up → emotional trigger → meltdown)
Anger (initial trigger → continued build-up → final straw → outburst)
Courage (building apprehension → breakthrough → selfless act)
Grief (loss → numbness → delayed emotional processing → catharsis)|
| Relationships | Fallout (tension accumulation → trigger event → emotional discharge )
Forgiveness (initial wound → anger → consideration → breakthrough) |
| Cognition | Insight generation (info ingestion → incubation → aha-moment + ideas click)
Change of Heart (slow belief erosion → moment of profound realisation) |
| Social systems| Revolutions (tension → rupture → reorganisation) |
| Economics | Market cycles (growth → crash → recovery) |
| Technology | Software adoption (early hype → plateau → breakthrough use case → market shift) |
| Art | Creative block (inspiration drought → idea gestation → sudden idea cascade) |
FPS-R’s purpose is to make this intuitive, to make this rhythm legible, and traceable. It provides the formal grammar to describe what we have always instinctively known.
The “hold-then-break” dynamic identified by FPS-R is not an isolated observation. It is a specific manifestation of a widely observed pattern of change recognised across numerous scientific disciplines. By connecting FPS-R to these established concepts, we can add authority and reliability to its claims, demonstrating that it is a framework for modelling a fundamental aspect of reality.
While the scientific principles explore and explain the causes and mechanics that result in the various phenomena, the grammar of Random Move and Hold and Hold-then-Break seeks to describe the behaviour that emerges as an observable result. FPS-R strives to embody the soul of that move and hold without claiming domain expertise over any one of these areas where the behaviour is observed.
This is perhaps the strongest scientific parallel to the FPS-R dynamic. First proposed by Per Bak, Chao Tang, and Kurt Wiesenfeld, Self-Organised Criticality describes how complex systems naturally evolve into a “critical” state where a minor event can trigger a chain reaction of any size—an “avalanche.”
The classic example is a sandpile. As grains of sand are slowly added (the “hold” phase where tension accumulates), the pile grows steeper. It inevitably reaches a critical angle. At that point, the next single grain of sand (the trigger) can cause a tiny slip or a massive, catastrophic avalanche (the “break”). One cannot predict the size of the avalanche from the size of the trigger.
This is a perfect analogue for FPS-R’s core principle. The system organises itself into a state of poised instability, where the “break” is both inevitable and unpredictable in its magnitude.
Proposed by palaeontologists Niles Eldredge and Stephen Jay Gould, the theory of Punctuated Equilibrium challenges the idea that evolution is a slow, gradual process. Instead, it posits that species remain in a state of stability for long periods of time (stasis, or “hold”), followed by rare, short bursts of rapid evolutionary change (punctuation, or “break”).
This pattern, observed in the fossil record, mirrors the temporal phrasing of FPS-R. It is another clear example of a natural system exhibiting long periods of stasis followed by sudden, non-linear state changes, rather than smooth, linear progression.
As mentioned earlier, the concept of surprise can be scientifically grounded. The Violation-of-Expectation (VoE) paradigm is a well-established experimental method in cognitive science and developmental psychology. Researchers use it to study cognition in pre-verbal infants by showing them an event that violates a physical law (e.g., an object passing through a solid wall). The infant’s increased looking time at the “impossible” event is taken as a measure of their surprise, indicating they had a pre-existing model of the world that was just violated.
This gives scientific weight to the claim that FPS-R models the objective trigger for surprise. The “hold” phase builds an expectation of continuity. The “break” is a non-linear event that violates that expectation, triggering the measurable cognitive response of surprise.
The world is inherently non-linear, but our minds, for the sake of safety and efficiency, often build simplified, linear models to predict the immediate future. We expect tomorrow to be much like today. We expect the ground to be solid, the market to trend upwards, and the river to stay within its banks. This is the illusion of linearity—a useful cognitive shortcut that allows us to function without being overwhelmed by the infinite complexity of reality.
A calamity—such as a natural disaster, a market crash, or a sudden outbreak—occurs when the underlying non-linear reality violently shatters our simplified linear expectations. This abrupt event exposes the limitations of our linear models and forces us to confront the true complexity of the world.
The unexpectedness of these events is a direct measure of the gap between our linear mental model and the world’s true, non-linear nature. The “surprise” of a catastrophe is the painful, emotional response to a fundamental prediction error.
The human experience is defined by our relationship with the unexpected. To survive in an often unpredictable world, we build systems, create strategies, and learn from the past.
Our vulnerabilities and successes are fundamentally shaped by how events unfold in non-linear ways.
This is the essence of the “random-move-and-hold” pattern. It is a model for surprise itself. We fail, or are harmed, or lose the game, when a system we are interacting with makes a sudden, non-linear jump that we did not anticipate.
At first glance, it may seem that “surprise” cannot be directly correlated to a scientific phenomenon. The word describes an emotional state, which is inherently subjective. But modern cognitive science makes a critical distinction between the subjective feeling of surprise and the objective event that triggers it.
The feeling of surprise is an emotional and physiological reaction. The trigger for that reaction, however, is an objective, measurable, information-based event: a violation of expectation. This is not just a colloquial term; it is a central concept in established scientific paradigms, from the Violation-of-Expectation (VoE) method used to study infant cognition to the Mismatch Negativity (MMN) brainwave signal measured in neuroscience.
Any predictive system—whether a human brain, an animal, or an AI—constantly builds an internal model of its environment to anticipate the immediate future. The “hold” phase of any process feeds this model, creating and reinforcing an expectation of stability and continuity. The longer the hold, the stronger the expectation becomes. The “break” or “jump” is a sudden influx of new information that fundamentally violates the model’s prediction. This prediction error is the objective, scientific phenomenon that triggers the subjective emotion of surprise.
Thus, FPS-R is not a model of the emotion of surprise. It is a deterministic engine for generating the objectively observed trigger that evokes the feeling of surprise: expectation-violating, non-linear events. The “surprise” and “shock” to the system is the emergent result of that accurate modelling of the structure of unpredictability.
FPS-R does not aim to generate surprise, it generates the objective events and conditions that result in surprise.
By modelling the observable pacing and rhythm of these events, we make the study of surprise both scientifically and computationally manageable.
Our minds are powerful pattern-matching engines. This ability to extrapolate from limited data is a core component of the Predictive Processing theory of brain function. It only takes something to occur twice before our minds are able to grasp and pick up a pattern. When something happens twice, our minds can subconsciously anticipate and predict when and where the third event will occur. That is the power of two.
A common phrase “Waiting for the other shoe to drop” is an idiom about anticipating negative events that are almost sure to follow, one after another. Read about the origin here.
From another perspective, the origin story reveals our human nature to anticipate, form patterns. It also shows how effective (or ineffective) our minds are in anticipating events that happen once. We know shoes come in pairs. When one drops, we have only one data point, we know there is a probability that the other shoe will also drop, but we don’t know when, or whether it will happen or not. That is a frustrating situation where the mind cannot get the minimum information it requires to form a basic pattern to confidently extrapolate.
When the unfolding events confirm the pattern in our mental model, it gets reinforced. The stronger the reinforced pattern, the stronger the surprise when it gets violated when reality does not pan out to match our strongly-held mental patterns.
Resulting effect: Startling, energetic, syncopated.
When the unexpected event happens we will experience shock, and perhaps a longer paralysis while our cognitive systems work harder to unravel and correlate the unexpected outcome of our mental model that have been built. Our state of mind and internal questions might be, “What just happened?”, “Is that totally unrelated to what I was anticipating or is it related to the anticipated event?”, and perhaps finally “Ah, it is that thing I was anticipating but it came earlier.”
Resulting effect: Dramatic, suspenseful, profound.
In this case, the mind has the opportunity to think about the missed timing, to ruminate and speculate about the implications and possible reasons why the expected event has not happened. Perhaps the mind will even the bandwidth to plan and propose alternative explanations and mental models if the current thinking has to be refined or discarded.
Now that we have a definition and understand the fundamental basics of the psychology of surprise, can we model it, break it down, and study it in a variety of domains and scenarios in a dependable, predictable (read unsurprising) way?
With a single-value parameter, it is straightforward to study and understand our anticipation and expectations of cause and effect related to that single component. It is relatively easy to map out how these events occur, how their occurrences gradually build up a model of normalcy, and how they form a ruleset that reflects the underlying principles at work.
When these policies are broken and expectations get violated, we discover errors in our mental predictions and expectations, and we experience surprise as an emotional outcome.
Unfortunately, with most cases in real-world situations, the emergence of unpredictability is the result of complex and layered causal chains of decision and “random” events that hold and change states, springing up on us, disrupting our mental models of the situation.
This rich and naturally emerging result is a reflection of the nature of reality. This is aligned to what has been described in Linearity as an Artifact: Modelling the Default Mode of Reality.
We can only see so far. Thus we build simplistic models in our minds to make sense of complexity in order that they become intuitive enough for us to grasp, to make sense of, and to make decisions based on them. But that is not the reality. Reality is complex, messy and layered in nuance.
The ultimate purpose of the FPS-R framework is to serve as a stateless, deterministic engine for generating events that model the “tipping point” dynamic. It provides a unique and powerful tool for approximating nuanced, complex, and layered reality. With FPS-R, these events can be modeled with controllable unpredictability in a mathematically elegant, traceable, and repeatable way.
This reframes its application in critical domains by focusing on the element of structured surprise:
When applying FPS-R to scientific domains, it’s crucial to frame its role with precision. FPS-R is not a replacement for physics or a “theory of everything”; it is a tool for modeling the emergent, non-linear behaviors common to complex systems.
Quantum-like Systems: It would be inaccurate to claim that “FPS-R models quantum behavior.” Instead, a more precise and powerful claim is that FPS-R provides a deterministic framework for exploring probabilistic models of quantum-like systems. It acts as a source of structured, repeatable “dice rolls” for a physicist’s own simulation, allowing them to trace the emergent consequences of their theoretical rules in a way that is intractable with true randomness.
Cosmic Phenomena: Similarly, instead of saying “FPS-R simulates the lifecycle of a star,” a more defensible framing is that the state-switching logic of FPS-R’s Quantised Switching (QS) algorithm can be used as a phrasing engine to drive simulations of stellar evolution. A researcher would define the physical rules and energy states, and FPS-R would provide the structured, non-linear timing for the transitions between those stages.
This reframing positions FPS-R as a valuable “tool for thought”—a way to inject structured, non-linear phrasing into existing scientific models, making them more dynamic and allowing for the repeatable study of emergent phenomena.
In all applications, FPS-R works as a collaborator with a parent system that provides the domain-specific rules and knowledge. The parent system defines the scope and transforms the output into meaningful signals. FPS-R, in turn, provides the critical element of structured surprise. It is not an additional “effect layer” but the phrasing engine that generates traceable emergence.
This synergy establishes a “computational laboratory,” transforming the study of chaotic, emergent behavior from a guessing game into a repeatable scientific process. Because FPS-R is deterministic, it provides a controlled environment where a researcher can:
For each decision in the causal stack, the holds and jumps of individual signals can be visualized as plotted graphs, allowing for deep and detailed analysis of cause and effect.
This unifying theory has sought to connect the observable “Random Move and Hold” pattern to fundamental dynamics seen across nature, science, and society. By grounding this observation in established principles and exploring the cognitive biases that often hide it from view, we reveal it not as a random occurrence, but as a core rhythm of reality.
The goal of this document is not to provide final answers, but to foster curiosity. It is an invitation to become more attuned to the “hold-then-break” cadence as a language spoken by the natural world, the animal kingdom, and human society.
It is my hope that by making these nuances recognisable and computationally accessible, FPS-R can serve as an enabling grammar. This marks the beginning of a new chapter in simulation and analysis—one where our models reflect not just the events of reality, but the very rhythm of its unfolding.