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Which Square Foot Would You Choose?

Don Fabin's The Dynamics of Change made some interesting claims when it was published in 1967. For example, consider this paragraph from the chapter entitled "She had so many children...."

At the present rate, starting someplace about 1946, the average rate of increase in the world's population is about two per cent. Using the 1962 population as a base, and applying this rate of growth to it, shows that in 650 years--somewhat less than the time backward to the Renaissance--there would be, in our world, one person standing on each square foot of land. At this rate, the perimeter of the coating of human flesh on the globe would, in 6200 years, be expanding at the speed of light--186,000 miles per second." (p. 10)

Task 1: Try to replicate Fabin's mathematical reasoning and verify his astounding extrapolations?

Task 2: Now, using the 2014 world population as a base and the current rate of world population growth (both values are accessible via the Internet), recreate Fabin's reasoning. Are we ahead of...or behind his claims?

Source: D. Fabin's The Dynamics of Change, 1967