torsdag 20 augusti 2009

Malthus is Back Again

Mathematics can be a powerful tool:  In his famous treatise An Essay on the Principle of Population first published in 1798, Thomas Robert Malthus presented a mathematical analysis predicting exponential population growth in time, while food supply would have a much slower linear growth  in time, later referred to as Malthus' Principle of Population.

Malthus thus predicted mathematically an inevitable collapse of human civilization if actions were not taken to limit population growth. 

But the mathematics of Malthus was wrong: populations did not grow exponentially and food supply not linearly: human civilization did not collapse. Not yet at least...

Nevertheless, Malthus is today back again: Based on mathematical climate models the UN International Panel of Climate Change IPCC predicts exponential growth of the global temperature caused by burning of carbonbased fuels, which will lead to a collapse of human civilization on an overheated Earth, if actions are not taken to limit CO2 emission, now. 

Exponential growth is thus feared, but our capitalistic society is driven by dreams of exponential growth at x% per year of
  • GNP 
  • investments 
  • income
  • house prices...
But steady exponential growth is not possible, because it will surpass any limit in finite time: The exponential growth of a financial bubble is eventually followed by a financial crisis until the next bubble can start to grow, exponentially. The overall growth is not exponential because of negative feed-back: The bubble is follwed by a compensating crisis.

Exponential growth represents positive feed-back: The more it grows the more rapidly it grows. A dynamical system with positive feed-back exponential growth is unstable and in order to survive without explosion has to develop a different dynamics somehow curbing the growth by stabilizing negative feed-back. This is the nature of turbulence which is a fundamental aspect of climate. Also compare with the climate feed-back analysis by Richard Lindzen:
  • The earth’s climate (in contrast to the climate in current climate mocdels) is dominated by a strong net negative feed-back. Climate sensitivity is on the order of 0.3°C, and such warming as may arise from increasing greenhouse gases will be indistinguishable from the fluctuations in climate that occur naturally from processes internal to the climate system itself.
The mathematics of exponential growth can be captured analytically and thus is attractive to a mathematical theoretical mind, but it is too simplistic to capture the dynamics of complex systems such as human populations or turbulence. 

Similarly, the IPCC mathematical climate models are most likely too simplistic to capture the dynamics of a the complex system of global climate. Malthus' Principle of Population and the IPCC mathematical models seem to have the same degree of realism. 

In the previous blog I noted that global climate and human population now connect on the agenda of the Optimum Population Trust endorsed by Sir David Attenborough:
  • World population is projected to rise from today's 6.8 billion to 9.15 billion in 2050. The World Population Clock is ticking.  We are rapidly destabilising our climate and destroying the natural world on which we depend for future life.
  • The West should provide money to promote contraception in the Third World and poor countries would be denied 'carbon allowances' unless they control their numbers. 
  • Progress on climate change is being seriously hampered by the widespread refusal to acknowledge the link between total greenhouse emissions and the sheer numbers of emitters. 
  • It is time we abandoned this crazy taboo.
Is this also the agenda of the upcoming UN Copenhagen Climate Council? To limit the number of emitters according to Malthus' Principle of Population? To deny poor people carbon allowances unless they control their numbers. Is Malthus back again?  What do you think?

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