The Aimless Stagger and the Purposeful Stride
Two images of movement dominate our thinking about the world. The first is the aimless, memoryless, drunken stagger, where each step is utterly independent of the last. This is the “random walk,” the foundational myth of 20th-century finance, popularized by Burton Malkiel in his seminal work, A Random Walk Down Wall Street. It paints a picture of a market that is fundamentally mindless, a passive recipient of random external news, where prices fluctuate with the capriciousness of a coin toss. The second image is the purposeful, adaptive stride, like that of an organism navigating a complex and often hostile environment. This walk has memory, it has an internal logic, and it has an intrinsic goal. It is a teleological walk.
As has been established in prior explorations on this blog, the world of markets is not the tame, predictable, bell-curved reality of “Mediocristan.” It is “Extremistan,” a realm governed by wild, unpredictable dynamics, where power laws dictate that a tiny fraction of events accounts for the vast majority of the impact.1 It is a world of “fat tails,” where extreme events that should be impossibly rare according to standard models occur with unsettling frequency, and of “self-organized criticality,” where complex systems naturally evolve to a poised state where any small disturbance can trigger an avalanche of unpredictable size. The random walk hypothesis, with its mathematical assumption of Gaussian statistics, has been empirically falsified by the very structure of the world it purports to describe. The observed “cubic law” of returns, a power-law distribution where extreme events are an inherent feature, stands as a stark refutation of the old model. The crucial question is not that the old map is wrong, but what new map can account for the territory as it truly is.
This essay proposes that the market’s movements are not random but are, in the most rigorous sense of the word, teleological. Its dynamics are best understood not as a statistical coin toss but as a target-directed process whose fundamental “purpose” is the perpetuation of its own existence. This analysis will build this concept, the teleological walk, from the first principles of thermodynamics, drawing heavily on the groundbreaking work of Terrence Deacon and Miguel García-Valdecasas in “A thermodynamic basis for teleological causality” on the physical basis of purpose itself.2 It will be shown that the very power-law dynamics that falsify the random walk are, in fact, the inevitable statistical fingerprint of this deeper, teleological nature.
Part I: The Terminal State of a Flawed Idea: Deconstructing the Random Walk
The Random Walk as a "Terminal Process"
To understand the failure of the random walk, one must first understand its nature through a more powerful physical lens. In their work on teleological causality, Deacon and García-Valdecasas introduce a critical distinction between two types of end-directed phenomena. The first is a terminal process, defined as a spontaneous change toward a maximum or minimum state (like equilibrium) that is driven by external conditions and reflects global asymmetries. An object falling to earth, sugar dissolving in tea, or a system reaching maximum entropy are all terminal processes. They are passive, spontaneous, and their end-state is determined extrinsically.
The random walk hypothesis is the quintessential model of a terminal process in finance. It posits that stock price changes are random and independent, driven by the unpredictable arrival of new information from the outside world. The system possesses no internal memory, no intrinsic goal, and no capacity for self-generated action. Its movement is a passive reaction to external stimuli, much like particles in a gas moving toward thermal equilibrium. This model is inextricably linked to the Efficient Market Hypothesis (EMH), which asserts that because all available information is already priced in, no analysis can provide a consistent edge. The market, in this view, is a perfectly efficient, if unpredictable, information-processing machine. As has been argued previously, this is a flawed, mechanistic worldview that treats a living system as if it were a dead one. It models the market as a system tending toward its own heat death, a terminal state of informational equilibrium where no further work (in the form of alpha generation) can be done.
The Empirical Failure: A Tale of Two Distributions
The conceptual elegance of the random walk model is shattered by its collision with empirical reality. A core mathematical implication of a random walk, where successive steps are independent and identically distributed, is that the distribution of price changes over time should converge to a normal or Gaussian distribution—the familiar bell curve. This is a world of “thin tails,” where moderate deviations from the average are common, but large, extreme events are astronomically rare. A "10-sigma" event in a Gaussian world is something one would not expect to see in the entire history of the universe.
However, decades of research by econophysicists, armed with vast datasets and powerful computational tools, have demonstrated this to be unequivocally false. The distribution of market returns is not Gaussian; it is “leptokurtic,” meaning it is more peaked around the mean and has dramatically “fatter” tails. The probability of extreme events does not vanish exponentially as the bell curve predicts. Instead, it decays according to a power law.3 Specifically, the cumulative distribution of large returns has been shown to follow a “cubic law,” where the probability of a return larger than some value x is proportional to x^(-3). This is not a minor statistical discrepancy; it is a fundamental contradiction. The fat tails observed in reality mean that market crashes and manias are not statistical impossibilities or external shocks. They are an intrinsic, predictable feature of the market's native dynamics, a fact the random walk model is structurally incapable of explaining.
The Conceptual Failure: A Category Error
The empirical failure of the random walk is a symptom of a much deeper conceptual error. The model fails not because its mathematics are wrong, but because it applies the correct mathematics to the wrong category of phenomenon. The random walk hypothesis models the market as a simple, passive, physical system, like a collection of gas molecules. In reality, the market is a Complex Adaptive System (CAS)—a living, evolving ecosystem.
As established in prior essays, a CAS is defined by a network of heterogeneous, interacting agents who are constantly adapting their strategies based on feedback from the environment they collectively create. Its most important behaviors—bubbles, crashes, trends—are not dictated from the outside but are emergent properties that arise from the bottom-up interactions of the agents themselves. The random walk model contains none of these essential features. It is a model of a system without purpose, without memory, without feedback, and without internal dynamics. It is a major category error, applying the physics of non-living, terminal systems to a living, adaptive one.
This flawed intellectual foundation has led to its own form of stasis. The random walk hypothesis is not merely a model of a terminal process; the idea itself has reached its own intellectual terminal state. Its trajectory through the history of financial thought mirrors the thermodynamic process it describes. It was a simple, elegant idea that has now been so thoroughly challenged by empirical evidence that it can no longer do productive intellectual work. It persists largely as a pedagogical baseline or a strawman to be knocked down, requiring endless ad-hoc patches like GARCH models to account for the very volatility clusters its core assumptions deny. It has reached a state of intellectual equilibrium where it can no longer generate new, fruitful lines of inquiry. To move forward requires a complete change in foundation, from the physics of dead matter to the physics of purpose.
Part II: A Physics of Purpose: From Thermodynamics to Teleodynamics
To build a new model of market dynamics, one must first establish a rigorous, physical basis for purpose itself, stripping the concept of its mystical or supernatural connotations. The work of Deacon and García-Valdecasas provides precisely this foundation, grounding teleology in the principles of thermodynamics.
The Thermodynamic Toolkit
Their argument begins with the critical distinction between terminal processes and a second, more complex type of phenomenon: the target-directed process. Unlike a terminal process, which is spontaneous and driven by external conditions toward an extrinsic end-state, a target-directed process is non-spontaneous and involves work produced to achieve and maintain an intrinsically defined target state. A living organism maintaining its body temperature, repairing a wound, or seeking food is engaging in target-directed processes. These actions are not spontaneous; they run counter to the spontaneous tendency toward degradation and equilibrium described by the second law of thermodynamics. They require the expenditure of energy to preserve the system's own organization.
This immediately presents a conundrum. The very self-organizing processes that create order and reduce local entropy are, by their nature, dissipative. They are far-from-equilibrium processes that must consume energy gradients to sustain themselves. This means they are intrinsically self-undermining; their very operation tends to deplete the resources that make their existence possible. A fire, a classic self-organizing process, creates intricate structures of flame and heat but does so by consuming its fuel, ultimately leading to its own termination. How, then, can a system use these self-undermining processes to achieve a state of self-preservation?
The Emergence of Teleology through Synergistic Coupling
The paper's central claim is that a target-directed, or teleological, system can emerge naturally from the synergistic coupling of two or more distinct, self-organizing (and individually terminal) processes. The conditions for this emergence are specific:
There must be at least two distinct, far-from-equilibrium, self-organizing processes.
These processes must be reciprocally linked and interdependent.
Crucially, each process must generate the necessary supportive and limiting boundary conditions for the other. They must simultaneously enable each other to persist while also preventing each other from running to their terminal, self-undermining conclusions.
The authors provide a concrete, illustrative model of this principle, which they call an "autogen." This hypothetical molecular system serves as the minimal model for a teleological entity:
Process 1: Reciprocal Catalysis. Imagine a set of molecules that catalyze each other's formation from a pool of substrates. This is a self-organizing, autocatalytic process that rapidly increases the concentration of the catalysts. However, it is a terminal process. It is self-undermining because it will either exhaust its substrate pool or the catalysts will diffuse away from each other, halting the reaction.
Process 2: Capsid Self-Assembly. Imagine a second process where molecules (capsids) spontaneously self-assemble into a closed container, like the formation of a crystal. This is also a self-organizing terminal process. It stops when it runs out of capsid molecules or when the container is complete.
The Teleodynamic Coupling. The emergence of purpose occurs when these two processes become linked. Imagine that the catalytic reaction (Process 1) produces capsid molecules as a byproduct. In this case, Process 1 supports Process 2 by providing its necessary building blocks. In turn, the self-assembly of the capsid (Process 2) creates a container that encapsulates the catalysts. This encapsulation limits Process 1 by preventing the catalysts from diffusing away and by cutting them off from the wider substrate pool before it is fully depleted.
The Emergent Target. The resulting coupled system—the autogen—is a higher-order entity whose behavior is now target-directed. Its "target" is the preservation of this synergistic, co-dependent relationship. If the autogen's shell is damaged, the encapsulated catalysts are re-exposed to substrates, and both processes restart—catalysis creates new capsid parts, which then self-assemble to repair the shell, once again enclosing the catalysts and returning the system to its stable, inert target state. This system exhibits emergent properties like self-repair and even self-reproduction. It acts to preserve its own organizational form and project it into the future. This is the essence of a minimal, naturalized teleology.
This framework allows for a more rigorous, information-theoretic understanding of purpose. The core "goal" of a teleological system like the autogen is not to achieve a specific physical state (e.g., a certain temperature or location), but to preserve a set of constraints—an abstract form of information embodied in the system's organization—against the constant, dissipative pressure of the second law of thermodynamics. The autogen's target is the preservation of the informational relationship between its component processes. The physical matter can be entirely replaced, but the form of the system, the information it represents, persists. This reframes teleology away from mysterious, backward-in-time causation and toward a grounded, scientific concept of information preservation. It is this thermodynamic engine of information preservation that will form the basis of the teleological walk.
Part III: The Teleological Walk: A New Model for Market Dynamics
Applying the autogen template to the financial market allows for the construction of a new model of its fundamental dynamics. The market's teleological engine can be understood as the synergistic coupling of two distinct, self-organizing, and individually self-undermining processes.
The Market's Coupled Processes
Process A: The Arbitrage/Efficiency Process (Constraint Generation). This is the market's well-documented tendency to seek and eliminate inefficiencies. It is a self-organizing process wherein a diverse population of agents, from high-frequency traders to merger arbitrageurs, seek profit by acting to close price gaps, exploit informational advantages, and enforce consistency across assets. This process is analogous to reciprocal catalysis in the autogen model; it is autocatalytic in that the existence of profit opportunities (the substrate) attracts capital and talent (the catalysts), which then seek out more profit opportunities, accelerating the process. This process generates order and constraint in the system.
However, this process is inherently self-undermining. As Friedrich Hayek observed, the price mechanism is a powerful tool for communicating dispersed information.4 Yet, the very act of arbitrage destroys the informational gradient it feeds upon. In a hypothetical, perfectly efficient market, all arbitrage opportunities would be eliminated. This would be the terminal state of this process: a static, "heat death" equilibrium with no potential for alpha, where the game of active management is over. The efficiency process, left to its own devices, would bring about its own demise.Process B: The Narrative/Contagion Process (Substrate Generation). This is the market's equally powerful tendency toward collective belief formation, social contagion, and hype cycles. As explored in the context of the GameStop saga, this is a self-organizing process that creates new, shared structures of belief about value, which are often decoupled from traditional fundamentals. These narratives—whether about a "meme stock," a revolutionary technology, or a new economic paradigm—function as a form of social energy. This process is analogous to capsid self-assembly in the autogen model; it builds large-scale structures (of collective belief) from the interactions of small-scale components (individual agents).
This process is also inherently self-undermining. Narratives, like any form of social energy, eventually burn out. Hype fades, belief wanes, and the population of "infectious" proponents moves to a "recovered" state, as described by epidemiological models like SIR. The terminal state of a narrative is exhaustion and irrelevance.
The Synergistic Coupling: The Engine of the Teleological Walk
The teleological nature of the market emerges from the fact that these two terminal processes are not independent but are reciprocally and synergistically coupled. They each provide the necessary supportive and limiting boundary conditions for the other, creating a higher-order system that avoids the termination of either component.
Narrative Supports Arbitrage: The Narrative Process (B) creates the essential "substrate" for the Arbitrage Process (A). It is the engine of novelty and disequilibrium. By generating hype, speculative bubbles, and dramatic dislocations from historical value, it creates the very price gradients, informational asymmetries, and inefficiencies that the Arbitrage Process feeds on. Without a constant supply of new stories, new manias, and new forms of collective belief, the market would quickly be arbitraged into a state of terminal efficiency. The Narrative Process keeps the game interesting.
Arbitrage Limits Narrative: The Arbitrage Process (A) acts as the crucial limiting boundary condition for the Narrative Process (B). It is the market's reality-testing mechanism. It probes, challenges, and ultimately either validates or destroys narratives. This can take the form of value investors betting against a bubble, or more explicitly, activist short-sellers like Hindenburg Research who hunt for and expose fraudulent or unsustainable narratives. By attacking a flawed story, these predators prevent it from consuming the entire market indefinitely and clear the ground for new narratives to emerge. The Arbitrage Process keeps the game from getting out of hand.
The Emergent Target: Perpetuation of the Game
From this coupling, a higher-order purpose emerges. The "target" of this coupled system is not a specific price level, not a particular valuation metric, and not a state of perfect efficiency. The emergent target of the market is the perpetuation of a dynamic, far-from-equilibrium state where the game itself can continue. The teleological walk describes a system that acts on its own behalf to avoid both the terminal state of perfect efficiency (the death of arbitrage) and the terminal state of total narrative collapse (the death of belief). Its intrinsic, self-generated "purpose" is to keep the game going.
While the synergistic coupling of Narrative and Arbitrage is a primary engine of market dynamics and thus most consequential for investors, it is by no means the only one. The market is a complex ecosystem of many overlapping and interacting feedback loops. Other potent couplings include the relationships between Credit (availability) and Asset Prices, Technology and Capital Investment, and even the internal mechanics of Derivatives Volume and Underlying Asset Volatility. Each of these pairs can form a self-reinforcing or self-limiting dynamic, contributing to the market's complex and often unpredictable behavior.
The key is that these processes do not operate in isolation. Just as an individual can be a father, an employee, and a consumer simultaneously, market participants often embody multiple roles. A trader executing an arbitrage strategy is still susceptible to the pull of a powerful narrative. This multifaceted nature of market actors is precisely what allows these different synergistic couplings to influence one another. The interplay between these myriad processes is what constitutes the market's true emergent character and gives the teleological walk its rich and complex trajectory.
Part IV: The Fingerprint of Purpose: Why Power Laws Are Inevitable
This teleodynamic model does more than provide a new narrative; it makes a specific, testable prediction about the statistical nature of markets. It provides a causal mechanism that explains why the observed power-law dynamics are not just a statistical quirk, but a necessary and inevitable feature of a purposeful system.
The Teleological Walk as a Model of Self-Organized Criticality (SOC)
The concept of Self-Organized Criticality (SOC) has been a recurring theme in these Field Notes, describing systems that naturally evolve to a poised state on the "edge of chaos," where they are maximally sensitive to perturbations. The canonical metaphor is a sandpile, which, as sand is added, builds up to a "critical" angle of repose. From that point on, the system is maintained in this fragile state, where the next grain of sand could trigger an avalanche of any size.5
The teleodynamic model of the market provides the missing "why" for SOC in finance. The market is not in a critical state by accident; it is held there by its own intrinsic purpose. The constant, coupled dance of narrative-creation (a force pushing the system away from equilibrium and making the sandpile steeper) and arbitrage-destruction (a force pulling the system back toward equilibrium, causing small avalanches that prevent total collapse) holds the system perpetually in this critical state. The teleological drive for self-perpetuation is the causal mechanism that explains why the market is a SOC system. It must remain critical to avoid either of its terminal fates.
Price Movements as Avalanches and the Inevitable Power Law
In the SOC framework, price movements are the "avalanches" that redistribute energy (capital) and information (belief) throughout the system. A key finding from the physics of critical phenomena is that in such a system, there is no characteristic scale for these events. The size of the avalanche is not proportional to the size of the trigger; a single grain of sand can cause a massive, system-spanning landslide. This explains the market's profound non-linearity and sensitivity.
This leads to the logical culmination of the entire argument. A fundamental, mathematically proven feature of systems in a state of Self-Organized Criticality is that the statistical distribution of their avalanche sizes follows a power law. Therefore, if the market is a teleological system that self-organizes to a critical state in order to perpetuate itself, then the observed power-law distribution of returns is not an anomaly to be explained away. It is the direct, inevitable, and observable statistical signature of its underlying purpose. The "fat tails" that shatter the random walk model are the very "fingerprints" of the teleological walk. They are the mark of a living, self-preserving system, not a dead, random one.
This dual-process model also provides a powerful framework for reconciling two great, opposing views of market economies. The Hayekian perspective champions the market as a spontaneous, decentralized, information-processing order, a force for efficiency driven by the price mechanism. This maps perfectly onto the Arbitrage/Efficiency Process (A). In opposition, the Polanyian tradition views markets as deeply embedded in social structures, driven by cultural norms, collective beliefs, and political power—not abstract prices.6 This maps perfectly onto the Narrative/Contagion Process (B). The teleological walk model demonstrates that these are not competing explanations but two co-dependent, essential halves of a single, higher-order teleodynamic system. The market is simultaneously a Hayekian information processor and a Polanyian social construct. Its purpose and its complex dynamics emerge from their inseparable, synergistic dance.
The following table provides a summary comparison of the two paradigms.
The Adaptive Market Hypothesis
In 2004, Andrew Lo proposed his Adaptive Market Hypothesis (AMH), a concept further supported by the teleological walk hypothesis presented here.7 While Lo's focus was on creating a framework that reconciled the Efficient Market Hypothesis with behavioral finance, my focus is on unifying this perspective with principles from physics. This synthesis allows for the development of a quantitative framework built upon the teleological walk—a feature not available in the AMH alone. The implications of both the AMH and the teleological walk are far-reaching, and Professor Lo's work was instrumental in paving the way for this synthesis. Readers interested in the evolutionary perspective on market behavior should consult his book, co-authored with Ruixun Zhang, The Adaptive Markets Hypothesis: An Evolutionary Approach to Understanding Financial System Dynamics.
From a Random Stagger to a Living System
The journey from the random walk to the teleological walk is a journey from a model of a dead system to a model of a living one. The random walk hypothesis, a theory of a terminal process tending toward a passive equilibrium, predicts a world of Gaussian statistics that is flatly contradicted by reality. The teleological walk, a theory of a target-directed process acting to preserve its own far-from-equilibrium state, provides a causal mechanism for the market’s self-organization into a critical state. This, in turn, makes the observed power-law statistics not only plausible but inevitable. The very evidence that falsifies the old model becomes the core confirmation of the new one.
This new model reframes the fundamental task of the financial analyst and trader. If the market’s movement is not a random stagger but a purposeful stride, the goal is not to predict the next footstep but to understand the terrain and the nature of the walker. As has been argued in the development of Adaptive Resonance Technologies, the objective shifts from predicting the market’s direction to understanding its shape and engineering an exposure that can profit from its inherent, purposeful chaos. The teleological walk provides the deepest theoretical justification for this approach. It confirms that the market’s chaos is not meaningless noise but the signature of its intrinsic purpose: to keep the game alive.
In the end, this perspective returns us to the central ethos of these Field Notes. It is a search for a deeper, more profound order hidden within the storm. It is an exercise in the art of asking reality the right questions, of moving beyond lazy, terminal ideas toward more fruitful and generative ones. By seeing the market not as a machine to be engineered or a casino to be beaten, but as a living, purposeful system, we transform our own role. We cease to be gamblers placing bets on random outcomes and become, instead, naturalists observing the intricate, emergent, and often beautiful dynamics of a complex ecosystem. We learn to appreciate what the mathematician Benoit Mandelbrot called "the art of roughness," recognizing that the market's wildness is not a flaw, but the very source of its vitality.
Disclaimer: Publication for Informational Purposes Only
The views, thoughts, and opinions expressed in Field Notes on Chaos belong solely to the author and Adaptive Resonance Technologies LLC, and are for educational and informational purposes only. This publication is intended to explore and communicate our investment philosophy, including concepts related to complexity portfolio theory and systematic market inefficiencies.
The content herein is theoretical in nature and does not constitute investment advice, a research report, or a recommendation or solicitation to buy, sell, or hold any particular security, strategy, or investment product. The information is not personalized and is not tailored to the investment needs of any specific person. This publication is designed for a sophisticated audience of finance researchers, professionals, or interested parties.
Adaptive Resonance Technologies LLC is a proprietary trading firm and is not a registered investment adviser. The firm relies on the "publisher's exclusion" from the definition of an investment adviser under Section 202(a)(11) of the Investment Advisers Act of 1940.
All investments involve risk and the potential for loss of principal. The topics discussed are for academic and discussion purposes and should not be used as the basis for any investment decision. Adaptive Resonance Technologies LLC is not liable for any actions taken or decisions made based on the information provided in this publication.
Taleb, N. N. (2008). The Black Swan: The Impact of the Highly Improbable. Penguin Books.
Deacon TW, García-Valdecasas M. 2023 A thermodynamic basis for teleological causality. Phil. Trans. R. Soc. A 381: 20220282. https://doi.org/10.1098/rsta.2022.0282
Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
Hayek, F.A. (1945). The Use of Knowledge in Society. The American Economic Review, 35(4), 519-530.
Jean-Philippe Bouchaud, "The Self-Organized Criticality Paradigm in Economics & Finance," arXiv, arXiv.org, revised Sep 2024. Handle: RePEc:arx:papers:2407.10284.
Polanyi, K. (1957). The great transformation: The political and economic origins of our time. Beacon Press.
Lo, A.W. (2004). The Adaptive Markets Hypothesis: Market Efficiency from an Evolutionary Perspective. The Journal of Portfolio Management, 30, 15-29.