May 4, 2021


Reality is irreversible

By Scott Ludlam
Cartoon image of man standing on chess board
The systems game and the need for global regime change

Have you heard the one about the original creator of the game of chess, this wily mathematician who submits his invention to the ruler of the country? Asked by the delighted queen what he wants by way of reward, the mathematician requests to be paid in gold. He proposes the queen place a single coin on the first square of the chessboard, two on the second square, four on the next, eight on the one after that, doubling the number of coins on each successive square up to the sixty-fourth.

The queen, perplexed that the mathematician would ask such a meagre reward for his creativity, nonetheless orders her chancellor to total up the coins. In disbelief, the chancellor calculates that this simple sequence of sixty-three doublings has the queen owing the mathematician 18,446,744,073,709,551,615 coins. The coin stack on the sixty-fourth square will reach a little over nine trillion kilometres from earth, nearly a quarter of the way to Alpha Centauri.

Variations on this story are sometimes told in maths classes to give students an idea of how rapidly a system undergoing exponential growth will punch a hole through the ceiling. To understand what it means for us right here and now, imagine the chessboard expanding invisibly to cover our battered old planet, and instead of coins let’s travel back in time a short distance and play the game with metallic ores. Iron ore, bauxite, copper, nickel, every tonne of it. 

Start in the year 1901. The anti-colonial Boxer Rebellion in China reaches its bloody conclusion, the parliament of Australia sits for the first time, and welfare campaigner Emily Hobhouse reports on appalling conditions in British concentration camps in South Africa. Drop about 150 million tonnes on the first square of the chessboard – that’s the total estimated figure of metal ores mined, shipped and smelted by the world economy in that year. Call it the queen’s first coin.

Jump forward a quarter of a century to 1925: the first public demonstration of television transmission is given in London, and Adolf Hitler publishes the first volume of Mein Kampf. Total metal ores mined and traded: 326 million tonnes. Two coins, give or take.

Twenty-seven years and a shattering world war later, we drop four coins on the next square. It’s 1952: the US government successfully tests the world’s first hydrogen bomb, and the Mau Mau launch a guerrilla uprising in Kenya. We’re up to 620 million tonnes.

The next doubling to 1.2 billion tonnes drops in 1967: it’s the Summer of Love in Haight-Ashbury, Suharto takes office as the second president of Indonesia, and the Israeli military occupies the Gaza Strip, the West Bank and the Golan Heights in the Six-Day War.

Sixteen coins in 1995: the year in which the World Trade Organization is established, and Typhoon Angela slams into the Philippines and Vietnam.

Thirty-two coins in 2009, the booming globalised economy now trading more than 4.8 billion tonnes of metal ores in the year the United Nations COP 15 climate negotiations end in failure in Copenhagen.

Smooth out the zigzags of global commodity markets, peer past the dust and dinosaur forms of colossal pieces of mining equipment and bulk freighters the size of city blocks. This is what a mild-sounding 3 per cent annually compounding growth rate will do. An increase of 3 per cent a year will double the number of coins on each successive square about once every quarter-century. Non-metallic mining – that’s all the limestone, sand, gravel and whatever – has grown slightly faster since 1901, doubling every twenty years. Coal, oil and gas are a little slower, doubling about every thirty years. You get the idea.

The simplest explanation for this explosive growth is that it coincides with the rapid and unprecedented expansion in human population – from a little over 1.5 billion people in 1900 to more than 7.8 billion at the time of writing. But simple explanations are sometimes wrong. World population growth hit an inflection point in the late 1960s and began to decline as women’s literacy and access to primary healthcare improved across the Global South, and reductions in child mortality led to smaller family sizes. Nobody suggests our population is set to double again; barring catastrophe, it appears to be headed for a plateau later this century. But there is no indication that the material consumption of the world economy is slowing, by any measure. If anything, the growth curves for key commodities have become even steeper over recent decades.

A better fit for the accelerating growth in material consumption can be found in something non-material: money. If you add up the total monetary value of all the goods and services produced in a country in a year, you arrive at a magic number called the Gross Domestic Product, or GDP.

The world’s combined GDP has been growing at about 3 per cent a year, doubling more than five times since 1901 and almost perfectly tracking the surging growth of the industrial tonnage out on the chessboard. Is this correlation, or causation, or just coincidence? Answering that is harder than it sounds, but for the moment the key thing to notice is that one of money’s main functions is just to multiply itself. And because it only exists as symbolic transactions between people and institutions, it is free to multiply into infinity like the mathematician’s imaginary coins.

The physical flows and fabrics of a living planet are not so free. Between 1901 and 2015, the human infrastructures of mining, farming, factories and quarries processed a staggering 3.4 trillion tonnes of raw materials in total. By the unyielding mathematics of compounding growth, in fourteen decades’ time we’re expected to churn and burn through that amount every single year.

GDP figures accurately track the one-way consumption torrent of the modern economy: from mine to landfill, with a brief pause in the hands of people this kind of economy calls consumers. When particular flows or commodities or workforces buckle or collapse, the doubling shifts somewhere else. To the financial system, the physical flows are almost beside the point; they are simply intermediaries, carrier waves for the duplication of money.

In the glossy annual reports, all the focus is on the input side: tonnages ripped and shipped, board-feet slabbed and chipped, gigalitres pumped and burned, annually compounding metrics of a planet in liquidation.

The architects of this locust economy never sought to design waste retrieval and recycling systems for this growth machine, so it piles up on the edge of town. We’ve brought materials into circulation that have no known disposal path – an ocean of plastics, incomprehensible new chemicals and murderously long-lived radioactive isotopes. The one that is raining scorched leaves onto the chessboard, the one we can’t even see, is the invisible pollution from coal, oil and gas combustion: a careless elbow in the face of the planet’s highly strung thermal regulation systems.

These are the coins of the Anthropocene, and this is what they buy us. Our present political and economic leaders are unswervingly determined to deliver the next stack twice as high on the next square, no matter what. Anybody who suggests that this is an impossibly dangerous way to organise our economy is treated like a freak.

That’s a problem. In the 1990s, US public-policy thinker Joseph P. Overton introduced an idea that would end up carrying his name. He proposed that public debate is characterised by ideas that are considered reasonable and worthy of discussion. These ideas lie safely within the Overton window. Outside this window lie all the ideas considered extreme, ridiculous or outright unthinkable.

The assumption that coin-doubling growth is good and necessary and normal is so mundane, so beyond question, that most days it’s all you can see through the Overton window. There do seem to be some freaks outside, banging on the glass about extinction or something, but because the window has become so firmly fixed in place it’s hard to understand what they are on about.

Joseph Overton suggested that over time, cultural and political tides can move the window, with activists and innovators bringing ideas previously considered extreme into the range of matters that sensible centrists feel comfortable talking about. But today things seem askew: everyone knows something is horribly wrong, but the window refuses to shift.

We were checkmated the moment we bought into the mathematician’s coin-doubling scam. Across much of the industrialised world, the consequences of endlessly doubling down now infuse popular culture like background radiation. Dystopian premonitions hover at the intersections of documentary and science fiction, an annoying cohort of doomers and whole sub-genres of apocalypse porn flirting with the aesthetics of global collapse. A few billionaires are even proposing to go and set up colonies on Mars, but as much as we might wish they’d just fuck off and live under a plastic dome millions of kilometres away, it wouldn’t stop people from being crushed under the next drop of their coins. The window seems to be jammed, stuck somehow, and so rather than continue trying to shift it politely, maybe it’s time we put a brick through it.

Sometime between this coin-doubling and the next, the chess game ends because the board is on fire.

While we’re thinking about that, here’s a different game, one that’s played with only one rule. It works pretty well with about two dozen people; you just need a little bit of space. Here’s how it goes. Everyone stands in a circle, facing inwards, about an arm’s length apart from one another. Each participant has to choose two other people at random – silently, without letting on who they’ve chosen. Ready? Okay – here’s the rule. When the game starts, you have to move so as to stay an equal distance from the two people you’ve chosen. You don’t have to stand directly between them, just try to keep the same distance away from both of them at all times.

That’s it. That’s the rule.


I first came across this game years ago. It was introduced as part of a workshop series on nonviolence and civil disobedience, co-hosted by American author an anti-nuclear campaigner Joanna Macy. In addition to practical techniques for locking down equipment, dealing with police and understanding your legal rights, Joanna Macy stirs in a measure of deep ecology, Buddhist philosophy and something I’d only tangentially read about before, something she calls systems theory. Instead of dropping a bunch of academic papers about chaotic attractors and scale-free networks on us, she starts with this game.

The moment she calls “go”, the circle dissolves. The two people you’re following, now they’re moving too, trying to keep an equal distance from the two people they’ve chosen. In your peripheral vision you’re trying to keep track of where your people are, avoiding collisions with others, aware that everyone is now weaving and careening around each other in a complex, unpredictable and strangely hilarious dance. Give it a few minutes, and unplanned crowd dynamics will arise; the tempo will slow, or everyone will begin to bunch up, until someone makes a move that drags two other people out of the flow and suddenly you’re all in wild motion again.

Just one rule, everyone in the game applying it as best they can in real time.

No supercomputer will ever be able to predict where we’ll all be standing when Joanna calls “stop”. Nobody is in charge of where we end up. We’re all exercising a certain amount of agency, but none of us is completely free of the influence of those we’re bound to. Everything that happens in the game depends on everything else that is happening, and trying to orchestrate or direct a particular end state would seem to be formally impossible. My enduring memory of all the times I’ve played the systems game is of the intangible collective presence that arises: a larger, fleeting something emerging from the moment-to-moment interaction of the crowd’s individual players.

The search for a theory that would explain these dynamics – and the emergence of that something – takes us all the way back to the 19th-century study of thermodynamics, with a handful of scientists and inventors struggling to improve the efficiency of the first generation of steam engines. Through slow trial and experimentation, they were stumbling towards some profound understandings. In his one and only publication, Reflections on the Motive Power of Fire, in 1824 French physicist Sadi Carnot put it like this: “We may therefore state the following general principle: The amount of motive force in nature is unchanging. Properly speaking, it is never created and never destroyed; in reality it [merely] changes form, that is, assumes one or another form of motion, but never vanishes.” This observation ended up being formalised as the first law of thermodynamics, the law of conservation of energy. Energy in the universe is never created or destroyed; it merely changes form.

But changing form carries a cost that you never get back. This second law, flowing from the first, would be of more immediate use to the makers of these machines. Heat dissipates until everything is the same temperature; water flows downhill; friction bleeds energy out of moving machinery and disperses it as waste heat. You’ll never see a cold object spontaneously transferring heat to a warmer object. The whole universe is falling inexorably towards thermal equilibrium – cold and dead and empty and pointless and dead, as though a Morrissey album has founded its own branch of physics.

The second law gave rise to the evocative concept of entropy. This term was coined by German mathematician Rudolf Clausius in 1865 as the measure of disorder in a closed system, which only ever goes up until equilibrium is reached. As energy dissipates, entropy increases, and this is always and forever a one-way ride. It means these bearded imperial nerds will never be able to build a steam engine with anything like 100 per cent efficiency. The moment they light up the coal in the furnace is the moment high-grade chemical energy begins its cascade into low-grade waste-heat, never to return. “Reality is irreversible,” as Russian biophysicist Mikhail Volkenstein put it.

It is in the dissipation that everything interesting happens. Carnot and Clausius and the others may be laying the theoretical foundations for a world lit by coal-fired electricity, but they are writing their treatises by the light of gas mantles and candles. Look closer, at the dance of one of these small, perfect flames. Closer: to see what is happening as the superheated gas boils off the melting wax. The fastest, most efficient way for the candle to dissipate this energy is through a teardrop-shaped flame. Entropy is increasing, heat is flowing from a highly concentrated source to gently warm the surrounding air, and while it lasts, this ephemeral structure will float there, illuminating the room.

Heat a pan of water until it begins to boil, and the water will self-organise into bubbling convection cells – hot water rising, dissipating heated steam into the air, cooling and falling back towards the bottom of the pan. The same overturning convection structures can be observed on the surface of the sun, or in a bowl of hot miso soup. At the scale of the whole planet, slow-moving ocean currents and the largest-scale weather systems are in ceaseless overturn, dissipating equatorial heat towards the poles.

We may all be sliding towards the eventual heat-death of the universe, but the structures and standing waves that form as energy tumbles from high-grade to low have shaped everything we see around us. The study of such “dissipative structures” is one of the tributaries that led, in the mid 20th century, to the development of what is known as general systems theory.

Austrian biologist Ludwig von Bertalanffy went looking for a unifying theory that would describe any complex system with constituent parts; he probably would have enjoyed the swerve and flow of Joanna’s game. In 1946 he wrote: “It seems legitimate to ask for a theory, not of systems of a more or less special kind, but of universal principles applying to systems in general.”

A quick search turns up this definition of system: “A regularly interacting or interdependent group of items forming a unified whole”. Any discipline that seeks to formalise the universal principles of “systems in general” would seem to be hopelessly ambitious in scope. After all, we could be referring to the solar system, or the immune system, or an ecosystem. Or, for that matter, the phone system, the criminal justice system or the global financial system. This is a word that really gets around, and when it shows up it usually means things are getting complex.

Over the decades, this quest for simplicity has ramified into dozens of disciplines and sub-disciplines, elegant propositions and empty dead ends. The cybernetics people, with their feedback loops and ballistics tables. Game theory types, with their bounded rationality and prisoner’s dilemmas. The chaos theory school, wielding strange attractors and infinitely self-similar fractal geometries. More than metaphor, it seemed the stirring of a butterfly’s wings in the Amazon might really trigger a storm in the North Atlantic.

It’s not immediately obvious why Joanna would invoke any of these abstractions at a civil disobedience workshop for a few dozen middle-class kids learning how to shut down logging operations. Or, for that matter, their relevance to people working any dimension of the larger struggle against a coin-doubling economy that has clearly lost its mind. Most of us don’t have the time or the faintest flicker of interest in bringing graph theory or nonlinear dynamics into any part of our waking lives, so, as fascinating as these things might be to some, what is the pitch here, exactly?

By the 1990s, students of what would come to be termed “complex adaptive systems” were turning their minds to questions that had previously been squarely in the domain of political philosophers and revolutionaries. Lines of inquiry that had begun with steam engine efficiency were somehow casting light on patterns of social contention, and the stratification of classes, and outbreaks of industrial action.

Across widely diverse contexts, some researchers clocked the recurrence of a fourfold cycle of innovation and conservation, collapse and renewal, operating at scales from local to global. Named it the “adaptive cycle” and began to see it all over the place: the beginnings of a theory of how natural and social systems undergo regime changes. Ecologists put forward a name for the complex interplay of fast and slow adaptive cycles that sometimes collide with spectacular effect: they called it panarchy. Thermodynamics won’t help us find the people throwing children into the water: that’s a political journey. But ever since I first played the systems game, I’ve wondered whether a theory of collapse and renewal might be valuable when we do finally meet our monsters face to face.


This is an edited extract of Scott Ludlam’s Full Circle, published by Black Inc.

Scott Ludlam

Scott Ludlam is an ICAN ambassador, a former Australian Greens senator for Western Australia and the author of Full Circle.

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