There is an old story about the original creator of the game of chess, a wily mathematician who submits his invention to the ruler of the country. Asked by the delighted queen what he would require by way of reward, the mathematician requests to be paid in gold. He proposes the queen place one single coin on the first square of the chessboard, two on the second square, four on the next, eight on the next, 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 inventiveness, nonetheless orders her chancellor to total up the number of coins. In disbelief, the chancellor calculates that this simple sequence of 63 doublings has the queen owing the mathematician 18,446,744,073,709,551,615 coins. Arranged neatly on the queen’s chessboard, the stack on the 64th square would reach 300 million kilometres past the orbit of Jupiter.[i]

Variants of this cute thought experiment are sometimes retold in maths classes to give students a taste of how rapidly a system undergoing exponential growth can punch a hole through the ceiling of any given maths problem.

To understand its relevance to 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 century and play the game with iron ore.

It’s the year 1904. Japan is at war with Russia, British troops occupy Tibet, and the Australian Labor Party has just won government for the first time.

Drop 95 million tonnes on the first square of the chessboard – that’s the total tonnage of iron ore mined, shipped and processed by the world economy[ii]. It’s the queen’s first coin.

Jump forward a quarter of a century to 1929: the year of the Wall Street crash and the election in Australia of the Scullin Government. Total iron ore traded: 210 million tonnes. Two coins, give or take.

It takes another 26 years and a world war to drop four coins on the next square. It’s 1955; Robert Menzies is Prime Minister of Australia, the man who will eventually invent the World Wide Web is born, and the world economy is quarrying, shipping and smelting 369 million tonnes of iron ore.

The next doubling comes early: eight coins or 773 million tonnes of ore in 1970, the year of the Apollo 13 spaceflight and two years into the Prime Ministership of John Gorton. This is an important time for Australian players in our exponential game of chess: the colossal iron ore reserves of the timeless Pilbara have been opened up; Dampier and Port Hedland are shipping their first cargoes of rich haematite and planning their own pathways of perpetual doubling.

Sixteen coins in 2006: the booming globalised economy mining and trading nearly 1.5 billion tonnes of iron ore in the year of the hanging of Saddam Hussein.

Smooth out the swings and gyrations of global commodity markets, peer past the dust and dinosaur forms of colossal pieces of earthmoving equipment and ships the size of city blocks. We’re riding a roughly 2.8% annually compounding growth curve, doubling the number of coins on each successive square about once every quarter century.

Modern capitalism is entirely geared, ruthlessly dependent, on maintaining these growth curves in perpetuity. Australian GDP growth has averaged 3.6% for more than a decade and a half. That’s a doubling time of 20 years. China has averaged a blazing 10% GDP growth for three decades, doubling the size of its monetary and material economy every seven years.

When circumstances halt this formidable expansionary march for more than a few months at a time, we call it a recession: confidence shatters, tens of thousands of us get thrown out of work, and all the resources of government and industry focus on getting back on the chessboard to forge ahead with the next doubling.

The big question then, the question that our lives now depend on, is how much longer can we keep doubling up the coins before something gives way?

The only thing we know for sure is that the answer to this question is not ‘forever’.

Land isn’t being created at a rate of 2.8% compounding growth. Neither is water, and neither is iron ore. An economic system that demands exponential expansion on a finite planet, that premises its survival on doubling the throughput every twenty five years, is nothing more than the setup for a brutal high speed collision with reality.

Keep in mind that industrial societies have been playing this doubling game for centuries, that bacteria play it in nutrient-rich petri dishes and metastatic cancer cells play it in us. The endgame is always the same; runaway growth followed by a gruesome population crash and the exhaustion or death of the host medium. In financial markets, we see it in asset bubbles that rise out of the background static on steep curves of hype and self-interest, then burst spectacularly in events known ironically as ‘corrections’.

In 1992, a correction came to the township of Goldsworthy[iii], one hundred arid and beautiful kilometres east of Port Hedland in the northwest of Western Australia.

Goldsworthy was the site of Western Australia’s first major iron ore mine. Today the former settlement of 700 people is a faint grid of empty quadrangles fading back into the spinifex a short distance from the mine void, lost from most maps, existing now only in the memories of the dispersed former workforce and their families. By the time ore depletion was writing the closing chapter on this doomed township, the industry had opened up the largest open cut mine on the face of the planet at Mt Whaleback further south, and iron ore extraction across the Pilbara had more than quadrupled. And so it seemed, as double the coins were laid on the next square of the chessboard, that resource depletion could be sidestepped simply by proving up the next deposit and shipping in a bigger fleet of hardware to match the scale of the new venture.

Freight volumes on our roads. Oil consumption. Greenhouse gas emissions. The catch from the world’s fishing fleets. Stock market indices. Doubling, and doubling again. Go through any number of official government and industry datasets and the fingerprints of compounding annual growth are there.

That’s excellent news of course, since the current strain of economics to which 21st century political activity is heavily addicted only understands growth, and only functions smoothly when everything is measurably larger, faster, heavier and hotter than the year before. The magic aggregator is Gross Domestic Product: GDP, that mesmerising indicator which totals all monetised activity in any given economy and compares it with the year previous. It doesn’t matter if the expenditure was for disaster relief, cancer treatment or road trauma; as long money was involved, it gets counted. In an ironic flourish, this impossible chess game has become known as sustainable growth; the non-negotiable doubling of the coins on the next square, no matter what.

Look closer at the data and something disturbing looms out of the statistical fog like an iceberg. Some of the indicators have peaked, plateaued or commenced terminal decline, and will never, ever grow up that sweet mathematical curve again.

The global fish catch rose with exponential precision until the late 1980s, by which time satellite-guided factory fleets had hammered top-order predators to the edge of extinction. Fish-mining operations have blindly overtaken biological replacement, and so now we’re trawling our way down the marine food chain through a cascade of fishery collapses in the zero-sum pursuit known casually as ‘peak fish’. No further exponential growth there.

Human activity has a so utterly intercepted the planet’s fresh water flows that the New York Times chose ‘peak water’ as one of the ‘words of the year’ for 2010. The UN FAO estimates that 1.8 billion people will be living in regions of absolute water scarcity by 2025.[1] On how many further squares of the chessboard can we double water abstraction and diversion? Answer: none. That growth game is over too.

The big one of course, the base commodity which set all the others in motion for the last fevered century, is oil. A handful of energy planners and advocates have been warning for fifty years that growth in oil supply can only expand so far before fundamental geological reality brings the hammer down on the spreadsheets and models predicting ever-doubling stacks of imaginary coins.

Many of these ‘peakists’ were branded as irrelevant heretics, but there was an awkward silence late in 2010 when the International Energy Agency doubled back on decades of cheerful hallucinations of infinite growth with this startling admission:

“Crude oil output reaches an undulating plateau of around 68-69 million barrels per day (mb/d) by 2020, but never regains its all time peak of 70 mb/d reached in 2006, while production of natural gas liquids (NGLs) and unconventional oil grows strongly…”[v]

We’ve used about half of the planet’s endowment of conventional oil, which is roughly when the peak oil analyst community said it would happen. The magic number was three million barrels of oil sucked into desert refineries and vented into the airsheds over the world’s sprawling megacities every single hour. It may be that that is the most we’ll ever manage, the greasy high water mark on fossil capitalism.

“…unconventional oil grows strongly…” the IEA paper continues reassuringly, without footnoting that ‘unconventional oil’ is code for risky deep sea reservoirs opened up by the melting of the north polar icesheet, and stunningly polluting shale oils and tar sands that cost almost as much energy to refine as they release when burned. A frenzy of hydraulic fracturing of unconventional gas resources is stalling the inevitable for a brief period, although the illusion of the next stack of coins on the board is being maintained at the cost of irreplaceable groundwater resources.

Somehow, the economy is going to have to work out how to grow exponentially while one of its foundation commodities gets kicked out from under it. After the roar of the global financial system resumed in an effort to drown out anything that might have been learned from its near-death experience in 2008, the price you and I pay for petrol is edging back upwards again.

I live in Perth, Western Australia, which in 2010 coordinated the blasting of 390 million tonnes of iron ore free of the ancient fastness of the Pilbara, bound mainly for the blast furnaces of China, Japan and South Korea. We’ve gone through four coin doublings since production ramped up in the late 1960s, and domestic politics here are, as always, mostly fixated on the next doubling. We might do it too, if a small section of the business lobby is successful in dismantling environmental protection legislation built up over a period of decades, and if we can maintain the dispossession of traditional custodians in a paralysing and divisive web of native title laws.

Australian politics has devolved into a beauty contest determining the most adequately qualified administration for managing growth at all costs. Political parties born in the coin-doubling age are committed to delivering the next stack of coins twice as high on the next square, no matter how much it warps the cost of living, irrespective of how many people it prices out of affordable housing, no matter how many species quietly go under, and without regard to the fact that Australia’s greenhouse gas emissions will double over the same time period.

Keep in mind then, the next time you hear state Premiers, or the Prime Minister, or a reputable economic forecasting agency, discussing prospects for economic growth. Listen for the percentage, work out the doubling time, and ask yourself whether you really want to live in Goldsworthy or some other place hurtling toward ghost town obscurity. This is not an economy in the traditional sense of the word, it is the blind asset stripping of an ancient continent, conducted twice as aggressively as it was a generation ago.

Premised on a foundation of fossil fuel incineration which will violently redraw the coastlines if we don’t put the fire out, we were checkmated the moment we bought into the mathematician’s coin doubling scam. It’s time to learn the rules of a different game.

[i]  922,337,203 km if each coin is 1mm thick. True.

[ii] Tip of the hat to Dr Gavin Mudd for raw numbers and straight talking on peak minerals http://users.monash.edu.au/~gmudd/publications.html

[iii] 20°20’24.98″ S  119°31’04.01″ E