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The Mayan Apocalypse And Gell-Mann's Curve

By John Scales Avery

27 December, 2012

In 2012, the shortest day of the year, December 21, coincided with the end of the Mayan calander, and the media had a pleasant time discussing the end of the world. When the day passed witholut a misshap, everyone heaved a sigh of relief because doomsday predictions had been proved wrong. “Now we are in the clear!”

With this as background, it might be appropriate to consider an observation made by the theoretical physicist Murry Gell-Mann. As he pointed out, a simple mathematical curve which closely approximates the global population of humans over a period of several thousand years is a hyperbola of the form: P=C/(2025-t). The population is equal to a constant divided by the factor (2025-t). Here P is the population and t is the year.

How are we to explain the fact that the population curve is not an exponential? We can turn to Malthus for an answer: According to his model, population does not increase exponentially, except under special circumstances, when the food supply is so ample that the increase of population is entirely unchecked,

Malthus gives us a model of culturally-driven population growth. He tells us that population increase tends to press against the limits of the food supply, and since these limits are culturally determined, population density is also culturally-determined.

Hunter-gatherer societies need large tracts of land for their support; and in such societies, the population density is necessarily low. Pastoral methods of food production can support populations of a higher density. Finally, extremely high densities of population can be supported by modern agriculture. Thus, the hyperbolic curve, P=C/(2025-t), where C is a constant, should be seen as describing the rapidly-accelerating growth of human culture, this being understood to include methods of food production.

If we look at the curve, P=C/(2025-t), it is obvious that human culture has reached a period of crisis. The curve predicts that the world’s population will rise to infinity in the year 2025, which of course is impossible. Somehow the actual trajectory of global population as a function of time must deviate from the hyperbolic curve, and in fact, the trajectory has already begun to fall away from the hyperbola.

Because of the great amount of human suffering which may be involved, and the potentially catastrophic damage to the earth’s environment, the question of how the actual trajectory of human population will come to deviate from the hyperbola is a matter of enormous importance. Will population overshoot the sustainable limit, and crash? Or will it gradually approach a maximum? In the case of the second alternative, will the checks which slow population growth be later marriage and family planning? Or will the grim Malthusian forces, famine, disease and war, act to hold the number of humans within the carrying capacity of their environment?

We can anticipate that as the earth’s human population approaches 10 billion, severe famines will occur in many developing countries. The beginnings of this tragedy can already be seen. It is estimated that roughly 40,000 children now die every day from starvation, or from a combination of disease and malnutrition.

An analysis of the global ratio of population to cropland shows that we have probably already exceeded the sustainable limit of population through our dependence on petroleum: Between 1950 and 1982, the use of cheap synthetic fertilizers increased by a factor of 8. Much of our present agricultural output depends on their use, but their production is expensive in terms of energy. Furthermore, petroleum-derived synthetic fibers have reduced the amount of cropland needed for growing natural fibers, and petroleum-driven tractors have replaced draft animals which required cropland for pasturage.

As population increases, the cropland per person will continue to fall, and we will be forced to make still heavier use of fertilizers to increase output per hectare. Also marginal land will be used in agriculture, with the probable result that much land will be degraded through erosion and salination.

Climate change will reduce agricultural output. The Hubbert peaks for oil and natural gas will occur within one or two decades, and the fossil fuel era will be over by the end of 21st century. Thus there is a danger that just as global population reaches the unprecedented level of 10 billion or more, the agricultural base for supporting it may suddenly collapse. Ecological catastrophe, possibly compounded by war and other disorders, could produce famine and death on a scale unprecedented in history, a disaster of unimaginable proportions, involving billions rather than millions of people.

What would Malthus tell us if he were alive today? Certainly he would say that we have reached a period of human history where it is vital to stabilize the world’s population if catastrophic environmental degradation and famine are to be avoided. He would applaud efforts to reduce suffering by eliminating poverty, widespread disease, and war; but he would point out that, since it is necessary to stop the rapid increase of human numbers, it follows that whenever the positive checks to population growth are removed, it is absolutely necessary to replace them by preventive checks. If he were alive today, Malthus would probably agree that family planning is the most humane of the preventive checks.

In Malthus’ “Essay on the Principle of Population”, population pressure appears as one of the main causes of war. Thus, his Essay contains another important message for our own times: If he were alive today, Malthus would also say that there is a close link between the two most urgent tasks which history has given to the 21st century: stabilization of the global population, and abolition of the institution of war.

John Avery received a B.Sc. in theoretical physics from MIT and an M.Sc. from the University of Chicago. He later studied theoretical chemistry at the University of London, and was awarded a Ph.D. there in 1965. He is now Lektor Emeritus, Associate Professor, at the Department of Chemistry, University of Copenhagen. Fellowships, memberships in societies: Since 1990 he has been the Contact Person in Denmark for Pugwash Conferences on Science and World Affairs. In 1995, this group received the Nobel Peace Prize for their efforts. He was the Member of the Danish Peace Commission of 1998. Technical Advisor, World Health Organization, Regional Office for Europe (1988- 1997). Chairman of the Danish Peace Academy, April 2004. http://www.fredsakademiet.dk/ordbog/aord/a220.htm




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