Singularities

Hal 9000, from the film
2001, a space odyssey

A singularity is a mathematical concept applied to a function of a variable that reaches an infinite value for one or several finite values of its independent variable.

For example, the function y=1/x presents a singularity for x=0, since it is often said that 1 divided by zero is equal to infinity.

Permanent economic growth is unsustainable

2009 World Economic Forum Meeting

Politicians and economists often tell us that job creation requires a GNP growth above 2 or 3%. According to them, the optimum situation and the end of the crisis will be reached when a permanent growth is achieved above these figures, the higher the better. Not many seem to be considering whether such a situation is possible in the long run.

Let us take the simplest case: assume that it were possible to achieve a cumulative annual growth of 3% GNP, indefinitely continued. Would we have achieved utopia, would we be living in the best of worlds?

Maybe, but not for long.

Malthus’s mistake

Thomas Robert Malthus

Since the end of the eighteenth century, apocalyptic warnings as regards the unstoppable increase of the world population have followed one another. In 1798, Thomas Robert Malthus published An essay on the principle of population, as it affects the future improvement of society, with remarks on the speculations of Mr. Godwin, M. Condorcet, and other writers. This essay includes the famous quotation:

Assuming then my postulata as granted, I say, that the power of population is indefinitely greater than the power in the earth to produce subsistence for man.

Population, when unchecked, increases in a geometrical ratio. Subsistence increases only in an arithmetical ratio. A slight acquaintance with numbers will shew the immensity of the first power in comparison of the second.