Table of Contents

Introduction: The Geometry of Conflict

What is a conflict? At its deepest level, it is a problem of geometry. It is the clash of irreconcilable futures, a point where the desired worlds of two or more minds cannot coexist on the single map of reality.

The following five-part essay develops a formal "Geometry of Conflict" based on the principles of information and complexity. It moves beyond traditional explanations of malice or scarcity to reveal the underlying, abstract structure that governs all human disputes, from a personal argument to a global war.

We will begin by defining the core elements of this geometry: the vast "Possibility Space" of all potential futures, and the simple, incomplete "formal models" that we, as boundedly rational agents, use to navigate it. We will then explore the spectrum of resolution strategies, from the information-creating act of synthesis to the information-destroying act of violence. We will analyze how the intrinsic properties of our belief systems—their simplicity, their rigidity, their fusion with our identity—determine whether a disagreement becomes a negotiation or a catastrophe. Finally, we will examine how our modern, algorithmic media environment acts as a powerful engine for conflict, and we will conclude by outlining a pragmatic "art of peace" for navigating this treacherous but inescapable geometry.

This is a new lens through which to view our oldest problem, an attempt to find the universal logic that underlies the tragic, creative, and endlessly complex human struggle to coexist.

Part 1: The Landscape of Desire

All human conflict, from the subtlest interpersonal slight to the most devastating global war, can be understood as a problem of geometry. It is not fundamentally a problem of malice, though malice may arise from it. It is not a problem of scarcity, though scarcity may catalyze it. At its root, conflict is the result of the structural incompatibility of desired futures within a single, shared reality. The Simplicity-Expressive Power Principle provides the language to describe this geometry, revealing conflict not as an aberration, but as a necessary and fundamental feature of a universe populated by multiple, model-building, goal-seeking minds.

To understand this geometry, we must first define its core elements: the landscape, the agents who inhabit it, and the desires that drive them.

The Possibility Space: A Shared Realit

Imagine the "Possibility Space" as a vast, high-dimensional landscape. Every point in this landscape represents a possible future state of the world. This is the ultimate, high-entropy, computationally irreducible reality that all agents inhabit together. It is the shared game board, the common territory upon which all desires are projected and all actions are played out. The state of this space is governed not by our wishes, but by the complex interplay of physical law, historical contingency, and human action. It is infinitely more complex than any agent can possibly comprehend.

The Agent and the Formal Model

An "agent" is any goal-seeking entity: a person, a corporation, a nation, a political movement, an ideology. Crucially, an agent does not and cannot perceive the full, infinite complexity of the Possibility Space. As a SEPP-bounded entity, each agent navigates this reality using a simplified internal formal model ( $F_{agent}$ ).

This model is a radical act of informational compression. It consists of a set of core axioms about how the world works, what is valuable, and what is possible. For a person, this model is their worldview, their beliefs, and their personality. For a nation, it is its constitution, its national narrative, and its strategic doctrines. For an ideology, it is its core texts and tenets. This model is the agent's map of the infinite territory, and SEPP guarantees that this map is, and always will be, profoundly incomplete.

The Goal State: A Desired Future

Embedded within every agent's formal model is a "goal state". This is the agent's desired future—a specific, preferred, low-entropy region of the vast Possibility Space. For a person, the goal state might be "a happy family and a successful career." For a nation, it might be "security, prosperity, and regional influence." For an ideology, it might be "a classless society" or "a global caliphate."

Geometrically, the goal state is a small, well-defined circle drawn on the infinite map. It is the future that the agent's formal model is designed to navigate towards. The agent's every action is an attempt to move the actual state of the world closer to this desired region of the Possibility Space.

The Geometry of Peace: Compatible Trajectories

With these axioms in place, we can define peace. Peace is not the absence of desire or the absence of action. Peace is a state of geometric compatibility between the goal states of multiple agents.

Imagine two agents, A and B, operating in the same Possibility Space.

Agent A's goal state is to build a quiet, prosperous farm.
Agent B's goal state is to build a bustling, innovative city a hundred miles away.

Geometrically, their desired futures occupy two distinct, non-overlapping regions of the Possibility Space. The actions Agent A takes to achieve its goal (plowing fields, building a barn) do not, in principle, prevent Agent B from achieving its goal (building skyscrapers, laying a street grid). Their trajectories are compatible. They can even become mutually beneficial, or "positive-sum," as the farm can feed the city and the city can provide a market for the farm. Peace is the domain of these non-conflicting, and potentially synergistic, geometries.

The Genesis of Conflict: Mutually Exclusive Geometries

Conflict, then, is born from the moment of geometric incompatibility. It arises when the goal states of two or more agents are perceived to be mutually exclusive. For one agent to realize their desired future, the other must necessarily fail.

This incompatibility can take two forms:

Direct Overlap (Zero-Sum): This is the simplest form of conflict. Two agents project their goal states onto the exact same, finite region of the Possibility Space. Two nations both claim the same piece of resource-rich territory. Two companies both seek to dominate the same limited market niche. Two political parties both seek to hold the same seat of power. Geometrically, their desired circles on the map overlap, and the area of overlap is the subject of the conflict. The game is zero-sum: one's gain is the other's loss.
Axiomatic Incompatibility (Ideological Conflict): This is the deepest and most dangerous form of conflict. It is not just that two agents want the same thing. It is that the fundamental axioms of their internal formal models predict and demand futures that are logically irreconcilable. An ideology whose goal state is "a global atheistic communism" and an ideology whose goal state is "a global theocratic empire" cannot coexist in the same Possibility Space. The very existence of one invalidates the core axioms of the other.

This is not a simple dispute over resources; it is a clash between two competing realities, two different proposed operating systems for the human world. This is the geometry that gives rise to the most intractable and violent struggles in history.

The geometric problem of conflict is thus established. It is the engine of history and the central challenge of civilization. The character of any agent, and any society, is defined not by whether they face this problem—for all do—but by the methods they employ in an attempt to solve it. The nature of this attempt, from reasoned debate to total war, is the subject of our continued exploration.

Part 2: The Spectrum of Resolution

When the desired futures of two agents prove to be geometrically incompatible, a state of conflict exists. The shared reality of the Possibility Space cannot simultaneously accommodate both outcomes. Something must change. The strategies an agent can employ to resolve this tension exist on a spectrum, a spectrum defined by the Simplicity-Expressive Power Principle. The choice of strategy is a choice about how to manage information and complexity. At one end lies the difficult, high-complexity work of model-building; at the other lies the simple, information-destroying act of violence.

High Complexity Resolution: Synthesis and the Expanding Circle

The most informationally complex and generative method for resolving conflict is synthesis. This is the process by which two agents, recognizing the incompatibility of their initial goal states, collaboratively create a new, more complex, and more expressively powerful formal model that can accommodate both of their core needs.

Geometrically, this is the "expanding circle" strategy. Instead of fighting over the small, overlapping region of their initial desires, the agents engage in a creative act of redefining the problem. They work to construct a new, larger goal state—a new circle on the map—that is vast enough to contain the non-conflicting essence of both original desires.

Consider two departments in a company arguing over a limited budget.

Initial State (Conflict): Marketing's model ( $F_M$ ) requires a one-million-dollar budget for a new ad campaign. Engineering's model ( $F_E$ ) requires a one-million-dollar budget to hire new developers. Their goal states directly overlap in the Possibility Space of the company's finite resources.
Simple Resolution (Zero-Sum): One department wins, the other loses. Or they compromise, and both are underfunded and ineffective. This resolution does not create new value.
Synthetic Resolution (Positive-Sum): The leaders of both departments engage in a high-complexity dialogue. They discover that the core axiom of the ad campaign is "increase customer acquisition" and the core axiom of hiring developers is "improve product retention." They realize these are not in conflict. They collaboratively build a new, more complex formal model ( $F_{Synth}$ ): a proposal for a smaller, targeted ad campaign (costing 500k) to acquire customers for a new, specific product feature that the new engineering hires (costing 500k) will build.

This new model, $F_{Synth}$ , has higher complexity than either $F_M$ or $F_E$ alone, but its expressive power is also greater. It has created a new, previously unseen goal state in the Possibility Space that is better for the company as a whole. This is the essence of all successful negotiation, diplomacy, and creative problem-solving. It is a slow, difficult, high-communication, and information-intensive process. It is the signature of a healthy, adaptive system.

Mid-Complexity Resolution: Game and Adjudication

When direct synthesis is not possible, agents can resort to a mid-complexity solution: agreeing to a higher-level, shared formal system of rules ( $F_{Game}$ ) to adjudicate the conflict. This includes everything from a court of law to a sporting event, from a market transaction to a democratic election.

The function of the game is to provide a non-violent algorithm for resolving the incompatibility. Instead of fighting over the territory directly, the agents agree to a set of abstract rules and a defined metric for winning. The winner of the game is then granted the disputed region of the Possibility Space.

This is an informationally richer solution than violence, but a poorer one than synthesis.

It Preserves Information: The losing agent is not physically eliminated from the world. They live to play another day. The overall complexity of the social system is maintained.
It Creates a Binary Outcome: Unlike synthesis, which creates a new, positive-sum outcome, a game typically produces a binary, win/lose result. It does not expand the circle; it simply awards the disputed territory to one party.

Civilization is largely the project of building these complex, robust game structures. The rule of law is the ultimate formal game designed to replace physical violence with an abstract, information-based process of adjudication. A healthy society is one that has a rich, diverse, and trusted set of these formal games for resolving the constant, SEPP-guaranteed emergence of geometric conflicts.

Low Complexity Resolution: Power and Domination

When an agent lacks the capacity for synthesis and refuses to submit to a shared game, it can resort to a lower-complexity strategy: domination. Here, the agent uses a power asymmetry (economic, social, or physical) to unilaterally force the other agent to abandon their goal state.

A large corporation uses its market power to bankrupt a smaller rival.
A colonial power imposes its political and economic model on another society.
A bully intimidates another child into giving up their lunch money.

This is an informationally impoverished strategy. It does not create a new, synthesized goal state, nor does it rely on a shared set of abstract rules. It simply uses brute force to erase the other agent's desire from the map. It ends the conflict not by resolving it, but by suppressing it. This often leads to a brittle and unstable peace, as the suppressed agent's formal model continues to exist, waiting for a shift in the power dynamic to re-assert itself.

The Ultimate Simplicity: Violence as Information Destruction

At the absolute bottom of the spectrum lies the simplest, most primitive, and most informationally destitute strategy for resolving a geometric conflict: violence.

Violence is the attempt to solve the problem of an incompatible formal model by physically destroying the agent that holds it.

Geometrically, if Agent A and Agent B have conflicting goal states, Agent A can choose to resolve the conflict by simply eliminating Agent B from the Possibility Space altogether. If Agent B no longer exists, their desired future ceases to be a factor in the equation.

This is the strategy of ultimate simplicity for one brutal, information-theoretic reason: it is an act of pure information destruction. Synthesis creates new information. Adjudication processes information according to abstract rules. Domination suppresses information. Violence annihilates it. It "solves" the complex problem of competing models by reducing the complexity of the world, by erasing the other modeler.

This is why violence is the constant, primitive temptation in all human affairs. It is the simplest possible "solution" to a complex problem. It requires no creativity, no negotiation, no submission to a higher authority. It is the path of least informational resistance. The entire project of civilization is the struggle to build formal systems complex and powerful enough to make this simple, terrible solution the least attractive option.

Part 3: The Properties of the Warring Models

The existence of a geometric incompatibility between two goal states is the necessary condition for conflict, but it is not sufficient to determine its character. A friendly negotiation and a genocidal war both begin with a geometric conflict. The difference in outcome is determined by the intrinsic properties of the formal models ( $F_{agent}$ ) held by the conflicting agents. The simplicity, rigidity, and identity-centrality of these models act as the control parameters that govern whether a conflict is resolvable through complex, information-rich methods or destined to decay into simple, information-destroying violence.

Model Simplicity and the Absence of Nuance

The first and most critical property is the Kolmogorov complexity of the agent's model. A simple model is one that uses a very small set of axioms to explain the world. While simplicity can be a source of elegance, in the context of conflict, it is a primary driver of escalation.

A Complex Model ( $K(F)$ is high): An agent with a complex, nuanced internal model of the world has a high capacity for conflict resolution. Their model has enough expressive power to understand that the other agent's position might be based on different but still valid axioms. It can see the world in shades of gray. It possesses the necessary intellectual raw material to engage in synthesis—the act of weaving together different perspectives into a new, more powerful understanding. For example, a diplomat with a deep, complex historical and cultural model of another nation is far more likely to find a path to peace than one with a simple caricature.
A Simple Model ( $K(F)$ is low): An agent with a simple, black-and-white model of the world has a very low capacity for resolution. Their model lacks the expressive power to represent the other agent's position as anything other than "wrong" or "evil." The world is divided into a binary of "us" versus "them," "good" versus "evil," "truth" versus "falsehood." This lack of nuance makes synthesis impossible. Any invitation to find common ground is perceived as a corrupting attack on the model's simple, perfect truth. This is the informational structure of the extremist or the fundamentalist. Their simple model is an engine for conflict because its very structure denies the possibility of a valid alternative perspective.

Model Rigidity and the Inability to Learn

The second property is the model's rigidity, its resistance to being updated in the face of new, high-entropy data. This is distinct from simplicity. A simple model can still be flexible. A rigid model is one that has become dogmatic.

A Flexible (Adaptive) Model: This is the model of a scientist or a learner. The agent treats their model as a hypothesis, not as a sacred truth. When confronted with data that contradicts the model (e.g., the other agent's arguments or actions), the agent's primary response is to update the model. This adaptive capacity is the fundamental prerequisite for de-escalation and synthesis. A flexible model allows for the possibility that the geometric conflict arises not from the malevolence of the other, but from a flaw in one's own map of the Possibility Space.
A Rigid (Dogmatic) Model: This is the model of the ideologue. The agent treats their formal model as a perfect, complete, and final description of reality. SEPP proves this is always false, but the agent's psychology denies it. When confronted with contradictory data, a rigid model does not update itself. Instead, it has only two options:
1. Reject the Data: Label the contradictory information as "false," "propaganda," or "heresy."
2. Attack the Source of the Data: If the data cannot be ignored, the agent attacks the messenger.

This is a crucial turning point. The moment an agent chooses to attack reality rather than update their model is the moment the conflict crosses a threshold toward violence. The rigid model cannot tolerate a world that is more complex than its own expressive power. If it cannot update, its only remaining option is to try and simplify the world by force, to make reality conform to its simple, rigid map.

Model Identity-Centrality and the Existential Threat

The third and most explosive property is the degree to which the agent's formal model is fused with their sense of identity.

Model as a Tool (Low Identity-Centrality): An agent can hold a formal model as a useful but disposable tool. A scientist can champion a theory but is prepared to abandon it if the evidence refutes it. A business leader can pursue a strategy but is willing to pivot if market feedback is negative. In this state, a challenge to the model is a useful, information-rich event. It is not a personal attack.
Model as Identity (High Identity-Centrality): This is the most dangerous state for any agent. The agent's sense of self, their social standing, and their core identity become completely entangled with their formal model. "I believe in X" becomes "I am an X-ist." In this state, a challenge to the formal model is no longer a simple disagreement about the map of reality. It is perceived as a direct, personal, and existential attack on the agent's very being.

When a model is fused with identity, the geometric conflict in the Possibility Space becomes a fight for survival. An attack on the model's axioms is an attack on the self. An attempt at synthesis is seen as a demand for self-annihilation. At this point, the simplest and most psychologically attractive strategy becomes violence. If the other agent, by their very existence, represents a living refutation of your identity, then eliminating them feels like an act of self-preservation. This is the geometry of holy wars, genocides, and the most brutal conflicts in human history. They are driven by agents whose sense of self is so completely tied to a simple, rigid model that they are willing to destroy a complex reality rather than update their own internal software.

Part 4: The Informational Ecosystem

The character of a conflict is not determined in a vacuum. It is profoundly shaped by the informational ecosystem in which the agents operate. This ecosystem is the medium through which formal models are shared, tested, and either reinforced or challenged. The structure of this medium—its speed, its reach, its incentive structures—acts as a powerful selective pressure, determining which kinds of models are most likely to survive and spread. A healthy ecosystem fosters the complex, adaptive models that lead to peace. A toxic ecosystem actively cultivates the simple, rigid, and identity-fused models that lead to war.

The Pre-Algorithmic Ecosystem: The High-Friction World

For most of human history, the informational ecosystem was characterized by high friction and low bandwidth. Information traveled slowly, through face-to-face conversation, handwritten letters, or the printing press. This had a profound, and often moderating, effect on the geometry of conflict.

Forced Complexity: In a high-friction world, interacting with a conflicting model often required direct, personal contact. This face-to-face interaction is an inherently high-bandwidth, high-complexity channel. It transmits not just the simple axioms of an argument, but a rich, high-entropy stream of non-verbal cues: tone of voice, body language, emotional expression. This rich data makes it much harder to reduce the other agent to a simple, malevolent caricature. It forces an engagement with their complex humanity, creating a natural pressure toward more nuanced models.
Geographic Containment: The low reach of information meant that incompatible formal models could often coexist in a state of relative peace simply by being geographically separated. Different cultures and ideologies could evolve in their own "valleys" in the Possibility Space without their geometric conflicts becoming immediately acute.
Time for Synthesis: The slow speed of communication provided a natural buffer. There was time for reflection, for complex counter-arguments to be formulated, and for synthetic solutions to emerge through slow, deliberative processes like diplomacy or academic debate.

This is not to romanticize the past, which was filled with brutal violence. But the structure of the informational environment itself often acted as a brake on the most rapid and viral forms of ideological contagion.

The Algorithmic Ecosystem: The Frictionless Battlefield

The modern, digital informational ecosystem has inverted these properties. It is a world of zero friction and infinite bandwidth. Social media, algorithmic feeds, and the 24-hour news cycle have created a new kind of battlefield for formal models, and this battlefield has a powerful, built-in bias. It actively and relentlessly selects for the very model properties that are most likely to lead to intractable conflict.

This ecosystem is a Simplicity Engine. As discussed previously, its business model is based on engagement, and engagement is most efficiently generated by content that is simple, emotional, and identity-affirming.

Selection for Simplicity: The firehose of information on social media creates a cognitive environment where only the simplest, most easily digestible formal models can survive. Nuance and complexity are computationally expensive for the user; they require time and effort to process. A simple, emotionally charged meme or headline ( $K(F)$ is minimal) will always outcompete a complex, nuanced argument for attention.
Selection for Rigidity: Algorithmic feeds create perfect echo chambers. They are designed to show users content that reinforces their existing formal model. By filtering out high-entropy, contradictory data, the algorithm creates an environment where a user's model is never challenged. This systematically cultivates rigidity and dogmatism. The user is protected from the information that would be needed to update their model, making it brittle and fragile.
Selection for Identity-Centrality: The most powerful driver of engagement is identity. The ecosystem therefore selects for content that transforms every issue into a battle between a virtuous in-group and a malevolent out-group. The algorithms learn to feed us models that are not about the world, but about us. A challenge to the model is thus framed as a direct attack on our tribe and our self-worth, maximizing the potential for outrage and escalation.

The result is a devastating feedback loop. The digital ecosystem acts as a global-scale incubator for the most dangerous kinds of formal models. It takes nascent geometric conflicts, strips them of all nuance, places the participants in echo chambers that make them dogmatically certain of their own simple righteousness, and frames the conflict as an existential battle for identity. It is a machine perfectly designed to push agents away from the complex, difficult work of synthesis and down the slippery slope toward the simple, satisfying, and catastrophic logic of violence. It transforms the Possibility Space from a territory to be cooperatively explored into a battlefield for total, zero-sum war.

Part 5: The Art of Peace in a SEPP-Bounded World

The geometry of conflict is an inescapable feature of the human condition. We are SEPP-bounded minds, forever building simple, incomplete formal models of an infinitely complex reality. Our desires, projected from these diverse models, will inevitably clash. The modern informational ecosystem, a powerful simplicity engine, actively accelerates these clashes toward their most volatile and violent conclusions. A final, perfect peace—a state with no geometric incompatibilities—is a mathematical impossibility.

What, then, is the path forward? If we cannot eliminate conflict, how can we hope to manage it? The art of peace is not the search for a final solution, but the cultivation of systems and personal virtues that favor the complex, information-rich end of the resolution spectrum over the simple, information-destroying end. It is the conscious, difficult work of making synthesis and adjudication more attractive than domination and violence. This work takes place on three distinct levels: the personal, the societal, and the technological.

The Personal Discipline: Becoming a Better Modeler

The foundation of a more peaceful world is the individual mind. The art of peace begins with the personal, cognitive discipline of treating one's own beliefs not as a sacred identity, but as a fallible, SEPP-bounded formal model. This requires cultivating three core intellectual virtues:

Complexity: Actively seek out information that increases the complexity and nuance of your internal models. Read the arguments of those with whom you disagree not to refute them, but to find the valid axioms from which they reason. Deliberately build a model of the world that is rich enough to contain contradictions and shades of gray.
Flexibility: Practice the art of the update. Treat moments of cognitive dissonance—moments when reality contradicts your model—not as threats, but as precious, high-entropy signals that your map is wrong. Develop the intellectual humility to say "I was wrong," which is the formal act of abandoning a failed model in favor of a better one.
Decoupling: Most critically, practice the psychological discipline of decoupling your identity from your models. Your beliefs are tools you use, not the person you are. This creates a "firewall" that allows your ideas to be attacked and even destroyed without triggering an existential threat to your sense of self. It allows you to participate in the geometry of conflict as a game of ideas, not a war for survival.

The Societal Imperative: Building Better Games

On the societal level, the art of peace is the art of institutional design. It is the project of building and maintaining complex, trusted, high-level formal systems ( $F_{Game}$ ) whose purpose is to contain and resolve the geometric conflicts that arise between citizens.

The health of a society is a direct measure of the quality and diversity of these "games." These include:

The Rule of Law: A system that ensures conflicts are adjudicated by a shared set of abstract rules, not by the power of the participants.
Democratic Institutions: A system that channels the conflict over political power into a non-violent, rule-bound competition of elections and debate.
Free Markets (well-regulated): A system that channels the conflict over economic resources into a positive-sum game of innovation and exchange.
Scientific and Academic Institutions: A system that channels the conflict over ideas into a rigorous, evidence-based process of peer review and falsification.

The primary threat to a peaceful society is the decay of trust in these containing structures. When citizens no longer believe the "game" is fair, they will abandon it in favor of the simpler, more primitive strategies of domination and violence. The central work of politics is therefore the constant, difficult task of maintaining the integrity and perceived legitimacy of these formal systems of adjudication.

The Technological Challenge: Re-introducing Friction

Finally, we must confront the reality of our toxic informational ecosystem. If the current digital environment is a frictionless simplicity engine that accelerates conflict, then a core task of the 21st century is to re-introduce positive friction and complexity back into our public square.

This is not a call for censorship, but for a radical rethinking of the architecture and incentives of our communication platforms. We must design new systems that, by their very structure, favor the complex models of peace over the simple models of war. This could include:

Algorithmic Design for Synthesis: Building platforms that are not optimized for engagement-at-all-costs, but are explicitly designed to expose users to the "best arguments of the other side," to reward nuance, and to facilitate the discovery of shared, higher-order goals.
Slowing Down Communication: Creating "slow media" environments that, like the high-friction world of the past, provide the necessary time for reflection, deliberation, and the construction of complex, synthetic arguments.
Verifying Identity and Context: Re-introducing the high-bandwidth, high-complexity signals of genuine human interaction into digital spaces, making it harder for simple, disembodied, and malevolent models to proliferate.

Conclusion: The Infinite Game

The geometry of conflict is a permanent feature of our universe. A world without the tension of competing desires would be a world without information, without creativity, and without life. The art of peace is not to wish this geometry away, but to learn to navigate it with wisdom and grace. It is the choice, at every level, to embrace the difficult, complex, and information-rich path of synthesis over the easy, simple, and destructive path of violence.

SEPP proves that our models will never be perfect and our work will never be done. The Possibility Space is infinite, and new geometric conflicts will arise for as long as we exist. The art of peace is therefore not a finite goal to be achieved, but an infinite game to be played. The prize is not "victory," but simply the chance to continue playing—the chance to continue the endless, creative, and uniquely human algorithm of turning the chaos of conflict into the complex and beautiful order of cooperation.