File talk:PPTCountdowntoSingularityLinear.jpg
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see especially: Korotayev A., Malkov A., Khaltourina D. (2006). Introduction to Social Macrodynamics: Compact Macromodels of the World System Growth. Moscow: KomKniga. ISBN 5-484-00414-4, where it is shown that the general trend is hyperbolic rather than exponential.