A Question of Order
I remember standing in a gallery once, caught between two profoundly different worlds. On one wall hung a Renaissance portrait, a masterpiece of serene, geometric composition. Every line felt deliberate, every proportion exquisitely balanced, as if governed by a compositional prescription. A few rooms away, a vast canvas exploded with the furious energy of a Jackson Pollock drip painting. It was a maelstrom of tangled lines, seemingly random and utterly chaotic. Yet, it too possessed a captivating order, a raw, organic power that felt as fundamental as the ordered grace of the portrait.
This experience crystallized a question that has followed me through a winding career, from the rigid certainties of engineering to the turbulent uncertainties of financial markets: What is "order," and why are we, as humans, so compelled to find and create it, even within a storm?
This contrast between the serene portrait and the furious canvas serves as a perfect metaphor for the central conflict in our understanding of complex systems, especially finance. Traditional finance, much like the Renaissance ideal, is rooted in a classical, mechanistic worldview. It operates on elegant, reassuring axioms, such as the pervasive myth of the efficient market hypothesis. This myth persists not because it is true, but because it satisfies a deep yearning for a simple rationale to make sense of a subjective world. Traditional financial models, with their assumptions of rational actors and predictable, bell-shaped outcomes, are the economic equivalent of the renaissance ideal.
The Pollock painting represents a more difficult, but ultimately more profound, truth. It is the world as it actually is: rough, fragmented, and infinitely complex. For decades, Pollock’s work was debated—was it genius or a random mess? The answer came not from art critics, but from physicists who discovered that his canvases are, in fact, fractals. His process, a chaotic dance of dripping and pouring paint, channeled the principles of complexity, creating a measurable, emergent order. Science, in this case, did not prescribe a false order; it described a true one. This is the mission of this blog: to be the scientist in the gallery of the markets, analyzing the Pollock-like chaos to reveal its hidden, fractal nature.
A Wanderer's Path
My own path to this inquiry has been, like Pollock’s art, one of controlled chaos. I have been a nuclear reactor operator, an engineer, an entrepreneur, a scientist, and a trader. Each role has felt relevant to my current project, and this comfort with interdisciplinary subjects is, I believe, a prerequisite for navigating the subjects we will explore here.
My journey began in a world of procedural order: the U.S. Navy’s nuclear power program. As a reactor operator, I was entrusted with managing a system of immense complexity and consequence, where rules were absolute and failure was never an option. It was a foundational education in science, engineering, the moral weight of responsibility, and a world that allowed for rigid prescriptions to well-understood linear problems.
That orderly worldview collided with a chaotic reality during my graduate studies in engineering. As the principal investigator on a NASA project to develop a microfluidic shear stress sensor, my team and I were tasked with modeling the relationship between turbulent air flows and microscopic fluid dynamics in order to develop a transfer function. We failed. The project was a poignant introduction to the tyranny of the mathematics of chaos. I had encountered a system that resisted our models, a force of nature I could not yet master. It was my first attempt at describing the chaotic nature of a system.
This failure proved to be a pivotal moment. It sparked a deep dive into non-linear mathematics and complexity science. It was in this context that I read Nassim Taleb’s The Black Swan and recognized that financial markets were the ultimate laboratory for studying a chaotic system that "resists control or prediction, while still exhibiting an appearance of structure". I made the decision to pivot, to treat the market as my laboratory and dedicate myself to a decade-long, self-directed research program. This journey was not academic; it was forged in the crucible of failure and a subsequent, relentless search for better methods. It is this combination of perspectival and participatory knowledge—learned by sitting with the problem for years while actively testing theories in the market with my own capital—that I hope to share in these field notes.
The Market as an Ecosystem, Not a Machine
The first and most crucial step in this journey is to abandon a flawed map. For centuries, economic thought was dominated by a mechanistic worldview, envisioning the market as a grand machine of interlocking gears and levers where inputs lead to predictable outputs. This perspective is elegant, reassuring, and profoundly wrong.
The market is not a machine that has been engineered; it is an organism that evolves. It is a Complex Adaptive System (CAS)—a living, dynamic network of millions of interacting agents (traders, institutions, algorithms) who are constantly adapting to each other and to the environment they collectively create. Its behavior is not controlled from the top down; it emerges from the bottom-up "swarm" of countless independent decisions. Phenomena like speculative bubbles and market crashes are not commanded into existence; they are an emergent feature of these interactions.
The natural principles of this ecosystem are not those of the comforting bell curve, which describes a world where extreme events are so rare they can be ignored. The market follows the much wilder rules of power laws, a statistical reality where "fat tails" mean that massive events are an inherent and inevitable feature of the system. This is best explained by the concept of "self-organized criticality." Imagine dropping grains of sand one by one onto a pile. The pile grows steeper until it reaches a critical state, perpetually on the verge of collapse. The next grain of sand could cause a tiny shift or a catastrophic avalanche. The key is that the size of the avalanche is not proportional to the trigger. Financial markets behave like this sandpile. They naturally evolve to a state of fragility where a major crash does not require a large cause; it is an inevitable feature of the system’s structure.
This framework is more than just a better model; it addresses a deep philosophical flaw in how we approach knowledge in finance. The stubborn reliance on bell-curve models is a symptom of a wider epistemological crisis, a preference for theories that are easy to verify or falsify, even if they ignore the messy, "non-Normal," and chaotic nature of reality. To approach understanding of the market, our reason must be inclusive of the non-rational and the chaotic. We must learn to appreciate what the mathematician Benoit Mandelbrot called "the art of roughness".
The Art of the Matter: From Theory to Technology
This decade of focus, this journey from engineering to the heart of market chaos, was not merely a philosophical exercise. It was a systematic effort to translate scientific research into useful and meaningful applications, the core skill of an engineer. The logical culmination of this work is my company,
Adaptive Resonance Technologies (ART) LLC.
The company is not just a business venture; it is the tangible embodiment of the entire philosophy I will lay out. The name itself tells part of the story:
Adaptive: A direct reference to the market as a Complex Adaptive System, a system that is constantly learning and evolving.
Adaptive Resonance: This refers to a neuroscience theory by Stephen Grossberg, which proposes that our brains achieve resonance by constantly adapting their internal models to match external reality. This process is the very essence of learning and prediction. It also subtly echoes the concept of "fractal fluency"—the physiological resonance our brains experience when we process the chaotic but orderly patterns of nature, like those in a Pollock painting.
ART: The acronym itself is a happy coincidence, but it helps represent the idea that navigating complexity is both a science and an art.
ART LLC was born from the realization that if you cannot predict the market, you must find a different way to engage with it. Our work focuses on profiting from the market's inherent chaos by identifying and exploiting structural advantages. We do this through proprietary models that do not attempt to predict the market’s direction, but rather its shape. Our advantage lies in a model that predicts positive skew—the statistical signature of a return profile characterized by many small losses and a few abnormally large gains. By transforming negatively skewed return profiles (like the S&P 500) into positively skewed ones, we can manage risk more effectively and use leverage more intelligently.
Welcome to the Field
This post is an introduction, an invitation to a conversation. "Field Notes on Chaos" is a space for continued exploration at the frontiers of complexity science, finance, and philosophy. It is for those who, like me, find themselves resistant to easy classification and are driven by a deep curiosity about the hidden patterns that govern our world. Our approach will blend rigorous, quantitative analysis with intuitive and even aesthetic exploration, embracing the idea that true understanding requires both the scientist and the artist.
I will leave you with a thought from the great mathematician Michael Atiyah, a quote that has been a guiding light on my own journey. It perfectly captures the spirit of this endeavor:
“In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life”. Michael Atiyah, Mathematician
Welcome to the field. Let’s get to work.
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An Invitation to the Field
To preserve the integrity and focus of our small community, I ask all prospective members to introduce themselves via a short form. If you feel called to this work, I invite you to introduce yourself here in exchange for a 10% discount. Persons working in academia receive a 20% discount here.
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.