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Expired · 7th July 2009
Ray Grigg
The multi-coloured graph sprawls across two facing pages of the New Scientist magazine (Oct. 18/08). The horizontal axis marks the years from 1750 to 2000, while the vertical axis marks increments of change in 12 crucial categories linking global economic activity with environmental conditions on the planet. All the lines begin to rise steeply after 1950, and by 2000 they have converged in a nearly vertical ascent. Taken together, they are a picture of the present and a prospect for the future – a future that seems to hint at some uncertain but inevitable climax. The following is a more detailed description of the graph's lines.

• Northern hemisphere average surface temperature (orange). It rises from 1750 to 1775 then drops gradually until about 1830, levels out until about 1912, rises again until 1950, drops until 1975, then angles sharply upwards thereafter. This irregular course is probably the result of the warming effect of increasing atmospheric carbon dioxide levels in conflict with the cooling effect of industrial air pollution and volcanos.
• Population (red). It rises gradually from 1750, then ascends sharply after 1950, indicating a doubling since 1950 and a nearly eight-fold increase since 1750.
• Carbon dioxide concentration (dark blue). It follows the population curve but then crosses it on an even steeper trajectory after 1975. Atmospheric concentrations have risen from 280 parts per million to 388, with actual increases during the last decade.
• Gross domestic product (dark red). It marks a slow curve, then is nearly vertical after 1960. All human history was required for the economy to reach its present level; barring any changes, it will double in two decades.
• Loss of tropical rainforest and woodland (dark green). This line follows the gross domestic product curve. About half of the world's tree cover has now been converted to other uses.
• Water use (blue). Not tracked until 1900, it begins by increasing gradually but it has risen to a nearly vertical trend by 1970.
• Paper consumption (yellow). First tracked about 1908, it follows a jagged but nearly vertical ascent after 1950.
• Species extinction (light green). Tracking starts about 1890, showing a sweeping curve that is rising nearly vertically by 2000.
• Motor vehicles (black). From the time they were invented just before 1900, they show little increase until about 1930. After 1945, their trajectory is nearly vertical. Almost one billion vehicles now populate the planet. World traffic fatalities are now about 1.2 million per year, with vehicle accidents injuring 20 to 50 million people annually.
• Fisheries exploited (light blue). Tracking starts in 1950 and shows a steepening curve that is nearly vertical by 1980. Large fish have now been depleted by 90%.
• Foreign investment (brown). Tracking begins about 1952 and shows a zig-zag line rising nearly vertically after 1980.
• Ozone depletion (beige). Tracking begins in 1950 and shows the same dramatic rise.

Considered in their totality, these coloured graph lines form the famous "hockey stick" figure, a relatively long horizontal handle that turns into a sharply rising curve as it reaches the present. Mathematically, these upward-moving lines resemble an asymptote, a condition in which the ever-steepening curve approaches a theoretical vertical. In this situation, any small advance in time on the horizontal axis measures a nearly infinite change on the vertical.

Since numbers seem to be infinite, the asymptote is an interesting mathematical curiosity. In the real world, however, infinity is not an option. Practical limits are soon reached for the number of people we can accommodate on our planet, for the amount of carbon dioxide the atmosphere can hold without poisoning the biosphere, for the forest cover we can remove without radically altering global ecologies. Limited space is available for parking and driving vehicles. Oceans can only provide a finite supply of fish. Species cannot be removed indefinitely from Earth's web of life without eventually shredding the fabric that binds together its biological integrity.

Scientist who examine the "hockey stick" graph are acutely aware of the stark difference between the mathematical possibility of the infinite and the finite limitation of the real. This is why they are getting nervous. When time is plotted against change in an asymptote, just a few moments has an enormous impact on consequence. The nearly vertical trajectory of so many crucial categories in our civilization's graph suggests that a collision with the reality of limits is a "when" rather than an "if".

No one knows when this will happen. But in an asymptote, every moment becomes increasingly important – critical becomes literal. This probably explains the rising level of anxiety in nearly everyone who closely follows the world's unfolding events. The present economic system, built on the assumption of continual growth, does not seem to be sustainable.

Most traditional economists, of course, do not reckon a limit to growth. They see it as a cure to all that ails humanity. And optimists believe the dire concerns illustrated by the "hockey stick" graph can be addressed by the promises of new technologies, recycling, increased efficiencies and human resourcefulness. The future of our civilization seems suspended in the balance between optimistic hopefulness and a catastrophic collision with limits.

In 1848, one of the founders of modern economics, John Stuart Mill, published a landmark book called Principles of Political Economy (Ibid.). He envisioned a time when we would complete our task of "economic growth" and, having satisfied our material needs, could then graduate to a "stationary" economy in which our efforts would be spent on bettering ourselves with "all kinds of mental culture, and moral and social progress... for improving the art of living...". Our present circumstances suggest that we should each take his vision very, very seriously.