How Big Is a Complex Adaptive System?
The question does not make sense. And that is the point.
A companion essay series to Complex Adaptive Markets: How Living Systems Shape Finance
You have seen this, even if you never had a word for it.
A winter dusk, the light going, and above a field or a pier a great dark shape of starlings, thousands of them, folding and pouring across the sky. It thickens and thins, spills into a ribbon, gathers into a sphere, tips and drains into a new shape before the old one has finished. No bird leads it. No bird can see the whole of it. Each one is watching only its nearest neighbours and adjusting, and out of all that small adjustment the great shape comes.
There is no choreographer, and no plan the birds are carrying out. The order is not imposed from above, and it is not stored anywhere. It exists only in the doing, and it lasts only as long as the doing lasts.
Now try to answer a simple question. How big is it?
You could count the birds, if they would hold still, which they will not. You could throw a circle round the densest part. You could measure the widest span at some frozen instant. And none of it would have caught the murmuration, because the murmuration is not the birds. It is what the birds are doing together, and that has no edge you can rule a line along.
Look for the edge and you will not find one. At the heart the birds are packed, the shape solid and dark. Toward the outside they thin, drift, peel away and rejoin, until there is simply sky with a few stragglers in it. Nowhere is there a line where the murmuration stops and the evening begins. There is only a fading, a gradient of togetherness, dense at the centre and thinning to nothing at the rim.
The murmuration does not have a size. It has a state. And the state will not sit still to be measured.
This essay is about a question that feels reasonable and is not. How big is a complex adaptive system? How big is an economy, an ecosystem, a market, a mind? The words line up exactly like the words in how big is this room, and something in us waits for an answer of the same kind: a number, a measurement, a size. But the question slides off, every time, and it is worth understanding why.
The last essay found that there is no basement, that everything solid gives way to process when you look hard enough. This one follows the consequence out to the edges. If a thing is really a process, then it does not have the one property we most take for granted in things. It does not have a size.
Size Is a Property of Objects
Size belongs to objects. It measures the reach of a thing with edges, a thing that starts here and stops there, whose boundary you could walk and whose inside you could pace out. A table has a size. A brick, a field, a planet. They hold still long enough to be measured, and they have an edge to measure to.
A complex adaptive system has neither. Its boundary is not a wall that someone built. It is thrown up by the activity inside it, and it moves as that activity moves. Think of where a forest ends. Not at a line but in a thinning: the trees space out, the soil changes, the rainfall drops below what a tree can live on, and somewhere in that fade you would have to plant a flag and call it the edge, knowing the flag is arbitrary and that by next season the fade will have moved. The forest’s boundary is not a fact about the forest as an object. It is something the forest is doing, and it never stops doing it.
Every complex adaptive system is like this. The boundary of an economy widens when new participants come in and draws close when trade routes shut. The boundary of a conversation moves with each sentence, opening to admit a new subject, tightening when attention narrows, gone the instant everyone falls silent. The edge is emergent. It is a product of the doing, and the doing does not rest.
Sit with the conversation a moment, because it is the clearest case of all. Where does a conversation begin? Not at the first word; its openings were laid down in everything the two of you had said and read and become long before you met. Where does it end? Not at the last word; it goes on working in you both for days. A conversation has no edges in time any more than the murmuration has edges in space. It is bounded only by attention, and attention wanders.
Ask how big a hurricane is and you will get an answer, a width in miles. But notice what you measured. Not a thing. A hurricane is not an object that has weather; it is weather doing something, a turning of air and water and heat, and its edge is wherever the turning fades back into ordinary sky. The figure you were handed was a snapshot of a process mid-turn, already wrong by the time it reached you. We give hurricanes names, as though they were people, and forget that we have named a verb.
So the size is not fixed either, and asking how big it is asks after a property the system does not steadily have. You can answer for an instant. The answer is stale before you finish saying it. The system has already moved, the edge has already shifted, and the number now describes something that no longer exists. Measuring a complex adaptive system is like measuring a cloud. Name its size and the wind has already rewritten it.
Signals and Boundaries
John Holland, one of the founders of the field, spent his life asking what gives a complex adaptive system its identity, if not its size. His answer was signals and boundaries.
Signals are what the agents send one another. The trades, the prices, the alarm calls, the chemical traces, everything that lets one part of the system act on another. Signals are the verbs of the system, the doing passed from hand to hand.
A signal is not a fact sitting in a file. It is information in transit, doing its work only in the passing. A price is a signal: it tells every watcher something, their changed behaviour becomes the next signal, and the system talks to itself without pause. It is that talking, not any stock of stored facts, that holds the thing together.
Boundaries are what shape the flow of those signals. Not walls, in Holland’s picture, but membranes: selective filters that let some signals through and hold others back, that admit this and refuse that. A boundary is defined less by what it holds than by what it keeps out. It is a decision, made and remade, about what belongs to the system and what does not. And it is the pattern of those decisions, not the extent of the system, that gives the system its character.
The cell we drilled into last time had a boundary of exactly this kind. Its wall was not a wall but a gate, forever choosing what to admit and what to turn away, and it was the choosing, not the material of the membrane, that kept the cell a cell. Life is full of boundaries that are really decisions.
This is why two markets of exactly the same size can behave nothing alike. One is deep and various, its signals crossing between many kinds of participant, its boundaries porous and forgiving. The other is the same size on paper but run by a handful of leveraged players moving in step, its signals narrow, its boundaries brittle. Same capitalisation. Same headline number. Entirely different systems. The size told you almost nothing. The signals and the boundaries told you everything.
Complex Adaptive Markets works this architecture out in depth, tracing how the boundaries in a market, between buyer and seller, between liquid and illiquid, between calm and crisis, hold the tension that later releases as movement. The book reads those boundaries as the structure that emergence flows through. Read the other way, which is this series’ way, a boundary is a running act of exclusion, the system deciding again and again what it will not let in. Both are describing the same membrane. It admits by refusing.
The Murmuration Has No Edge
Go back to the birds, because a market is a murmuration too.
A market of trades and glances and second thoughts, dense and coherent at its liquid heart, where a price answers the moment new information lands, and thinning toward its edges, where liquidity runs shallow and a single order can shove everything sideways. The boundary between the market and not-the-market is no line. It is a gradient of how densely people are willing to interact, and it breathes.
Watch what it did in March 2020. In a matter of weeks the willingness thinned and the boundary drew in hard. Assets that had traded freely turned illiquid. Strategies that had lived comfortably in the deep interior found themselves suddenly at the edge, in the shallows, where every move cost too much. Market makers who had quoted without pause pulled back to protect themselves. The murmuration tightened. The periphery went dark. Nothing in the plumbing had changed, the exchanges were open, the data still flowed, but the living system, the actual market of people willing to trade with one another, had shrunk to a fraction of what it had been the week before.
When the fear passed and the willingness returned, the boundary opened again, wider than ever. But it did not return to its old shape. It took a new one, because the interactions that made it were not the same interactions. The system remembered what it had been through. A murmuration that has once been a fist does not forget how.
How Big Is the Universe?
Now turn the question on the largest thing there is.
If the universe is a process, and the first three essays have been arguing that it is, then how big is the universe is a question of exactly the kind we have been taking apart. It asks for the size of a thing with an edge. But the universe has no edge in that sense. Its only boundary is the frontier of its own unfolding, the moving front where new structure is being cut from what could not cohere. And there is nothing on the far side of that front. Not empty space waiting to be filled. Nothing at all, because the space that beyond would need has not been made.
This is the old puzzle of what lies north of the North Pole. The grammar of the question is fine. You can say the words. But there is no north there for the words to reach. Ask what is beyond the edge of the universe and you are standing at the pole, pointing north, at nothing.
We picture the expansion as a balloon swelling into a room, but there is no room. The universe is not growing larger inside some greater space that could hold a larger thing. The space is part of what is unfolding. There is no container and nothing contained, only the unfolding, and to ask its size is to ask the length of something still busy deciding how long to be.
This is the same answer the first essay gave to a neighbouring question. The universe is not infinite because it is unfinished, and it has no size for the very same reason. Infinity and size are both properties of completed objects, and the universe is not a completed object. It is a process that has not stopped, and will not, and so it declines every question that assumes it has.
The universe does not have a size. It has a state. It was one thing a moment ago and will be another in a moment more, and no measurement holds it, because the holding still is exactly what a process will not allow. It is not large. It is not small. It is not finished. It is doing.
State, Not Size
If size is the wrong question, state is the right one.
A complex adaptive system has no size, but at every moment it has a state: a particular set of what is flowing, what is amplifying, what is holding and what is giving way. The state is always specific, always describable, and always passing. It says what the system is doing without pretending the doing has stopped.
You already trust this everywhere but here. Ask a doctor how your heart is and they will not answer with its size. They answer with its state: the rhythm, the pressure, whether it is straining or steady. Size would tell them almost nothing, and the little it told them would mislead, since an enlarged heart is usually a failing one. What they read is what it is doing. We know how to ask the right question of a living thing. We only forget that a market, an economy, a universe, is one.
Traders read states without always naming them so. Bull and bear. Risk-on and risk-off. Trending and mean-reverting. Calm and violent. None of these is a size. Two markets can share a capitalisation to the dollar and sit in opposite states, the one absorbing shocks and shrugging them off, the other amplifying every tremor into a lurch. Same size, same count of participants, different states, and the difference is the whole of what matters. Size is a photograph of a thing. State is a description of a doing, and only the second is any use when the thing is a verb.
This is what a trend follower actually reads. Not how big the market is, which is a fact about an object the market is not, but what it is doing. Is it trending or turning. Is feedback building or fading. Is liquidity deepening or draining. Are the boundaries holding or breaking. These are questions about state, put to a system that has no stable size and needs none to be understood.
The Right Question
The lesson is one line, and it runs through the whole series. The question is never how big. The question is always what is it doing.
Ask how big and you demand that the system hold still, present its edges, submit to the ruler. It will not. It has no edges to present, and it will not hold still, because holding still is the one thing a living system never does. Ask what it is doing and it answers at once, in its signals and its boundaries and its state, in the very activity you were trying to freeze.
Complex Adaptive Markets is built around that second question. It does not measure markets. It reads them, following how signals move between participants, how boundaries channel them, how feedback lifts or damps them, how the system tips into a new state when the pressure crosses a threshold. That is why its framework outlasts the measuring kind. A model that needs the market to stand still fails the moment it moves. A reading that only ever asked what the market was doing has nothing to unlearn when the doing changes. It was watching the verb all along.
None of this is an argument against numbers. Count whatever you like; the counts are facts. It is an argument against mistaking a count for an understanding. The capitalisation is real. It simply does not tell you what the market will do, any more than a man’s weight tells you what he is thinking. The number is true, and beside the point.
What Comes Next
So the question is not how big, but what is it doing. And that turns out to be the doorway to a harder question still.
Because if the system is always doing, always in a state that is already becoming the next, then the person inside it cannot step back and take its measure from without. There is no without. The trader is in the market, the observer is in the system, and every reading they take feeds straight back into the thing they are reading. You cannot survey a territory that is redrawing itself while you walk across it. You can only move with it.
That is navigation, and it is the subject of the next essay: the skill that takes the place of measurement once you have accepted that the thing you are inside has no fixed size, no fixed edge, and no intention of holding still while you decide what to do about it.
Look up again at the starlings. Ask how big they are, and you get a number already false. Ask what they are doing, and the whole sky answers.
The Universe is a Verb is a companion essay series to Complex Adaptive Markets: How Living Systems Shape Finance by Richard Brennan. The ideas explored in these essays are developed in full depth in the book, where the framework moves from cosmic principle to practical application.
Richard Brennan writes on systematic trading, complex adaptive markets, and the philosophical foundations of trend following at atstradingsolutions.com. His books include The Fractals of Finance and Complex Adaptive Markets. The forthcoming Carved by Impossibility completes the trilogy.
Want the theoretical foundation for why trend following works?
The Fractals of Finance: Determinism, Adaptation and the Geometry of Markets
The book explores the full architecture of feedback, fat tails, and fractal structure in financial markets, and what it means for how we trade, invest, and understand risk.
Available now on Amazon in paperback, hardcover, and Kindle.
Want a practical field manual for trading trends and capturing outliers?
The Aussie Turtles Trend Following Guide: A Field Manual for Hunting Outliers adapts the timeless principles of the original Turtle traders into a systematic, rules-based approach for modern markets. Co-authored with Adam Havryliv.
Available now on Amazon in paperback, hardcover, and Kindle.