Cosmology, Doom, and Gloom: Some Copernican, Anthropic, and Malthusian Musings
If population growth is unchecked, or not sufficiently checked, there are any number of things that could cause a catastrophic collapse and extinction of the human species. These include (but are not limited to) worldwide famine, pandemic disease, global warming, all out nuclear war, and mass extinction of species leading to large scale collapse of ecosystems. Human history would thus consist of three periods, a long period of very low population, followed by a short period of exponential growth, followed by extinction.
Garfinkle, David. "Cosmology, Doom, and Gloom: Some Copernican, Anthropic, and Malthusian Musings" Oakland Journal 16 (2009). 102-118
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