The Game That Builds Its Own Board
If the universe emerges from rules, infinity is a category error.
A companion essay series to Complex Adaptive Markets: How Living Systems Shape Finance
Imagine sitting down to play a game that has no board.
No squares. No edges. No territory laid out in advance. There is only a rule. You make a move, and the rule answers. Not by adding a square to some growing grid, but by striking out almost every square that could have come next, until one is left standing. You move again. It strikes out again. Move by move a shape appears beneath your hands, and you would swear the board is growing. It is not. The board is what survives the striking out. It is the residue of everything the rule refused.
Hold on to that image. Everything that follows leans on it.
Because a question arrives, when you first meet it, with the quiet force of something that has been waiting a long time to be asked.
Why is the universe not infinite?
Most people reach for cosmology. The Big Bang, the observable horizon, the expansion of space. Thirteen point eight billion years, ninety-three billion light-years across. None of it is wrong, and none of it touches the deeper issue, which is not about measurement at all. It is about category. The question assumes the universe is the kind of thing that could be infinite: an object, a container, something whose dimensions might in principle extend without limit. That assumption sits so deep that most people never notice they have made it. But the assumption is where the real question lives.
Perhaps the universe is not an object at all. Perhaps it is a process, and a process cannot arrive at infinity, because infinity is the first thing a process rules out. Like the board, the universe is not the sum of what has been added. It is what is left when everything that could not follow has been struck away.
This is the first essay in a series called The Universe is a Verb. Across six episodes we follow that one idea into physics, language, biology, cosmology, and the markets we trade. The claim underneath all of it runs against the grain of how we usually picture creation. We imagine structure piling up, a universe assembling itself, more today than yesterday. The truth runs the other way. Structure is not built. It is carved. The series is a companion to Complex Adaptive Markets: How Living Systems Shape Finance, which takes up the same questions in the life of markets.
We start with infinity because it is the cleanest test. If the universe emerges from rules, the answer to the question is not simply no. The answer is that the question rests on a mistake, and the mistake, once corrected, shows how the universe actually works. Not by accumulation. By subtraction.
The Board Is Not Added To. It Is Carved.
Go back to the game, and look more closely at what the rule is doing.
We say the rule places a tile, and we picture something appearing where nothing was. That is the wrong picture. The rule conjures nothing. It takes the whole field of tiles that could come next, every arrangement the current state might permit, and it forbids almost all of them. What we call the next tile is simply the one arrangement it did not forbid. Nothing is added to the board. Possibilities are removed from it, and the tile is what is left. The board emerges the way a statue emerges beneath the chisel: by loss.
Now ask how big the board is.
At any moment it is finite. It holds exactly as much as the removals have left standing. It does not matter how long the game has run, or whether it will ever stop. At every point in its history the board is finite and unfinished. It is not infinite, because a completed whole was never on offer. Infinity is everything at once, with nothing left to rule out, and a process that works by ruling out can never reach it. The one thing subtraction cannot leave behind is a finished totality.
This is not a technicality. It is the whole argument. The universe is not infinite for the same reason a sculpture is never the whole block of marble. What stands at the end is always less than what was possible, and what was possible was never a thing you could hold. It was only the field from which the actual was cut.
The Computational Universe
Stephen Wolfram spent decades watching what simple rules do when they iterate. His early work explored cellular automata, grids of cells that update by local rules, step after step. What he found startled him. Extraordinary complexity pours out of trivially simple rules. Structure, organisation, apparent randomness, all from the same source. The output looks rich and unpredictable. The process underneath is plain and finite at every step.
It is tempting to say the rules generate the complexity, as though richness were being manufactured and stacked onto the grid. Look again at what a rule is. A rule is a constraint. For any given neighbourhood of cells it permits exactly one successor and forbids all the rest. The complexity we marvel at is not what the rule builds. It is what the rule fails to forbid. Order is the shape left behind once every incoherent continuation has been struck off. The automaton does not paint the pattern onto the grid. It clears away everything the pattern is not.
Suppose Wolfram has read the architecture correctly. Then the universe at any moment holds exactly as much structure as the removals have left standing. No more, no less. The process may run forever. The structure may deepen without bound. But it never becomes infinite, because infinity would require the ruling out to be finished, and a process that runs forever never finishes. It stays unbounded and incomplete. That is not a defect. It is what it means to be shaped by loss rather than gain. Loss has no last stroke.
It From Bit
John Archibald Wheeler was among the most original physicists of the last century. He named the black hole. He worked alongside Bohr and Einstein. And late in his life he reached a proposition stranger than anything he had met before.
Wheeler proposed that the physical world arises from information. It from bit, he called it. Every particle, field and force takes its existence from binary choices, yes or no, this or that, here or not here. The tangible its of the world resolve out of answered questions.
Notice the shape of a bit. A yes and a no. And a no is a removal. To answer a question is not to add a fact to a heap. It is to discard every answer but one. Each settled bit narrows the field of what can still be true. The it that remains is not what was assembled. It is what was left when the discarding was done. Reality does not accumulate its answers. It sheds them, and to shed is to subtract.
This runs straight into the oldest puzzle in quantum mechanics, where measurement is no passive reading. Before measurement a system holds a spread of possibilities. The measurement does not add the outcome. It removes the alternatives. The single fact that survives was not made out of nothing, and it was not lying there in advance. It was narrowed into being. Each interaction takes away what can no longer stand, and the world is exactly as determinate as the questions already settled.
So the universe is not a thing that happened once and has coasted ever since. It is happening now, in every measurement, every exchange of energy, every gravitational tug. Each is another question closed, another possibility struck out, another part of the board cut to its final shape beneath our feet.
Not infinite. Unfinished. And never merely added to.
The Mathematics of the Unfinished
A tradition inside mathematics has been pressing this point for more than a century.
The constructivists, led by L.E.J. Brouwer and later formalised by Arend Heyting, refuse the completed infinity. Classical mathematics treats infinity as an actual, finished totality: the set of all natural numbers, whole and complete; the real line, entire in both directions. The constructivists will not have it. A mathematical object exists only so far as it has been constructed by a finite process.
The refusal is not a matter of taste. A completed infinity cannot be constructed, and what cannot be constructed cannot cohere as an actual object. It is ruled out for the same reason the universe rules it out: it is a whole with nothing left to determine, and determining is the work that never ends. What survives the constructivist’s scrutiny is the sequence that is always finite and always open to extension. The natural numbers are not an infinite collection sitting complete. They are a process that can be carried further without limit and is never done. Unbounded, because there is no final step. Not infinite, because there is no finished whole.
Brouwer was thinking about the foundations of mathematics, not the cosmos. But the insight travels wherever a process leaves structure in its wake. The universe does not need to be infinite to be limitless. It only needs to be unfinished, and unfinished is what a process of loss always is.
Unbounded Is Not Infinite
This is the pivot the whole argument turns on, and it is worth slowing down to feel its weight.
We use infinite and unbounded as if they meant the same thing. In ordinary talk they often do. For a process that works by removal, the difference is everything.
A river that never reaches the sea is unbounded. It does not stop, it meets no wall. Yet at any moment its length is finite: it has run exactly as far as its water has carried it. That it will keep running does not make its present length infinite. It makes that length temporary, a snapshot of something still underway. And notice how the river makes its valley. Not by laying earth down but by taking earth away. The valley is not what the river added. It is what the river removed.
The universe follows the same logic. If space-time comes from a rule applied step by step, then at any moment it holds exactly as much space-time as the removals have left standing. The process may never stop or meet a boundary. The residue is finite all the same. Unbounded and deepening, yes. Infinite, no.
Infinity could only enter if the universe were handed over whole, pre-made, set on the table before the game began. The moment you grant that it emerges, that it is cut from what could not hold, infinity turns incoherent. A process that runs forever is not infinite. It is perpetual. The two are not the same, and the difference is the point. A perpetual process leaves a residue that is always finite, always shifting, never whole, always becoming something other than it was. Not a limitation. The signature of a living universe.
The Category Error
Ask why the universe is not infinite and you are asking the wrong kind of question. Not because the answer is unknown, but because the question smuggles in a category that does not fit.
Infinite is a property of objects. It describes a completed totality, a thing with no edge, a container with no wall. The universe, if it emerges from rules, is not an object. Its structure is a residue, not a totality. Asking whether it is infinite is like asking whether a symphony is heavy, or the colour blue is fast. The grammar holds. The meaning falls apart.
And there is a sharper edge beneath the category error. Infinity is not merely the wrong description of the universe. It is precisely what a process of removal can never leave behind. Every step discards possibilities and leaves a finite residue. No run of removals ever arrives at everything, all at once, complete. Infinity is not just the wrong answer. It is the one outcome the process forbids.
So the right question is not how big the universe is. It is what the universe is doing. Is it expanding? Is it still cutting new structure from what can no longer cohere? Is it still in the act of becoming? These questions respect the verb in the cosmos. They do not freeze a process into an object and then reach for a ruler.
This is not wordplay. Ask the wrong question and you build the wrong tools. Treat a process as an object and you design for measurement when you should be designing for navigation. Assume the territory holds still and you draw a map and expect it to last, when a territory still being cut will always outrun its map. The map was true a moment ago. It is already out of date.
That failure runs through every system that shares the universe’s character. The markets we trade among them.
The Bridge to Markets
No one was handed a finished price series on the first day of trading. There is no ledger somewhere holding every price that will ever print, waiting to be revealed. But it is just as wrong to say the market builds its price series tick by tick, each price a brick on a rising wall. The market does not add prices. It eliminates them.
Watch a single moment of trading. A field of possible prices hangs over the book, every level a buyer might pay and a seller might take. The trade does not manufacture a number and set it down. It rules levels out. It strikes off every price that will not clear, every valuation the two sides refuse to sustain, until one is left standing, the one that survives the disagreement. Price is the verdict. And a verdict subtracts. It throws out every claim the evidence will not carry and keeps the one that holds.
A trend forms the same way. We talk as if a trend were built, momentum stacking up, structure rising. A trend is what is left once the market has cleared away the alternatives. The positions that fought the move are stopped out, margin-called, abandoned. Traders whose view could not cohere with the flow are removed from it, one by one, until what remains is a crowd leaning the same way. The trend is not the sum of what was added. It is what failed to be removed. Everything it is not has already gone.
This is no metaphor. It is one logic at two scales. If the universe is a game that cuts its own board, a market is a game that cuts its own price series. The series is not waiting in advance and it is not piling up behind. It is taken from the field of the possible, moment by moment, by an endless act of removal. Both are unbounded. Both are unfinished. Neither is infinite. Neither is built.
The consequence for trading is direct. If the next price is neither revealed nor manufactured but cut, then the future is not hidden and it is not open. It is unsettled. The removals that will produce it have not yet happened. No model, however clever, can outrun a process of removal that has not run, because the residue does not exist until the ruling out is done. Prediction, in the strong sense, is not merely difficult. It is incoherent.
The right response to such a system is not prediction but navigation: reading what has been cut so far, answering the shape as it emerges, adapting as more of the field falls away. Trend followers do this by instinct, whatever words they use for it. They do not ask where the market is going. They ask what it is doing. They read the shape that has survived and set themselves inside it. Their discipline is not forecasting. It is attention to a process that shows its structure by clearing everything else away.
Watch a trend appear. It does not arrive whole, like an object set on a table. It emerges. A move begins. The positions against it start to fail. Feedback engages and the failure spreads. A crowd of competing views is thinned, the incoherent bets cut away, until one direction is all that stands. Noise becomes signal, not because signal was added, but because the noise was carried off. The market is computing its own shape in real time, by subtraction.
This is why models tuned to historical distributions fail at the worst moments. They treat the price series as a finished object, a fixed data set to extrapolate from. The series is not finished, and it was never a deposit of stored facts. It is a residue still being cut. The next stroke has not fallen. Extrapolation assumes the board already exists. It does not.
The Foundation Beneath the Framework
The argument is clean because it asks you to commit to almost nothing. Not the specific rules, not a solution to quantum gravity, not a choice between Wolfram’s hypergraphs and Wheeler’s participatory universe. You need one premise: the universe proceeds by elimination, not accumulation. The rest follows.
If it works that way, then at any point only finitely many possibilities have been ruled out, and finitely many removals leave a finite residue. Always. It does not matter how long it runs or whether it stops. At every moment the result is finite, unfinished, and cut from something larger.
That is the destination Wolfram, Wheeler and the constructivists reach by three different roads, from computation, physics and mathematics. The universe is not infinite. It is unfinished. A game cutting its own board, with no last stroke to make.
Complex Adaptive Markets works the same ground in practical depth. It traces how markets generate structure through interaction, how feedback amplifies and dampens it, how memory persists in price, and how adaptive systems produce the trends, outliers and regime shifts that define the financial landscape. The book reads those dynamics as emergence. This series reads the same dynamics from the other side, as what is left once everything incoherent has been cleared away. Both are looking at one set of events. If markets are cut from the field of the possible rather than piled up within it, then the tools for navigating them must respect that, and the book is where those tools are built.
What Comes Next
The universe is not infinite. It is unfinished. And it is not built. It is carved.
That is the first step. If the universe is a process, the language we use for it matters, because our noun-heavy grammar freezes a moving world into still objects and then asks us to measure them. The next essay takes up that trap through the physicist David Bohm, who argued that the structure of our language hides the structure of reality, and who tried to answer it with a language built on verbs. He called it the rheomode. In it the universe is not a thing but an activity, and the moment you see it that way, the question of infinity dissolves.
The board is still being cut beneath our feet. Not built. Carved.
And so are we.
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.
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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.