Dangerous Surprises of Exponential Growth

      In 1968, while I was in graduate school at the University of Oklahoma, the journal Science published "The Tragedy of the Commons" by Garrett Hardin.  Hardin's article describes a situation in which shared resources are overused and exploited -- leading to depletion of resources for the future.  In recent years there has been much criticism of Hardin's essay (and criticism of Hardin) -- but for me it served as a wake-up call to concerns about the environment.  With environmental difficulties growing exponentially -- and with many of us not fully aware of the growing rapidity of exponential growth, I have posed to students this problem:

An 8x8 syllable-square

We may be close to the end before we realize it . . .