ADVENTURE THERAPY & ECOPSYCHOLOGY
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must first grapple with another obtuse concept, this time from a mathematical and ecological
perspective: exponential functions.
The Problem With Exponential Growth
As suggested in the preceding section, humans have a hard time thinking about the big
picture. They can also be surprised by how quickly things can change. Time is both difficult to
understand in terms of history, and when looking ahead and trying to estimate how long
something might take (like a dissertation…). In considering how large something might grow if
provided favorable conditions, there are attending consequences that may unfold with each. To
illustrate, a couple of stories - the first involving some grains of wheat and a chess board and the
second involving reindeer living large on an island, offer good illustrations of this concept.
Carl Sagan (1997) in Billions and Billions, offers the story of the Grand Vizier who
invented chess in ancient Persia. As a reward for creating this amazing game, the King offered
him anything his heart desired, however, the Grand Vizier:
…wished only for a modest reward. Gesturing to the eight columns and eight rows of
squares on the board he had invented, he asked that he be given a single grain of wheat
on the first square, twice that on the second square, twice that on the third, and so on,
until each square had its complement of wheat. No, the King remonstrated, this is too
modest a reward for so important an invention…secretly marveling at the humility and
restraint of his counselor, the King consented. When, however the Master of the Royal
Granary began to count out the grains, the King faced an unpleasant surprise. The
number of grains starts out small enough: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024…but
by the time the 64th square is approached, the number of grains becomes colossal,
staggering. In fact, the number is nearly 18.5 quintil-lion. (p. 8, italics original)