Tuesday, August 02, 2005

Malthusian Mathematics

From Collapse by Jared Diamond ("Malthus in Africa," page 312):

"That's because (Malthus reasoned) population growth proceeds exponentially, while food production increases only arithmetically. For instance, if a population's doubling time is 35 years, then a population of 100 people in the year 2000, if it continues to grow with that same doubling time, will have doubled in the year 2035 to 200 people, who will in turn double to 400 people in 2070, who will double to 800 people in the year 2105, and so on. But improvements in food production add rather than multiply; this breakthrough increases wheat yields by 25%, that breakthrough increases yields by an additional 20%, etc."

Of course a 20% or 25% increase is multiplicative, not additive. Apart from lightly mocking Diamond's choice of phrase, I never really bought into the "food production is additive" bit. It seems like an unsupported assumption. I have to admit I've never actually read Malthus.


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