A lake owner wants to stay at home to tend to the lake’s fish and make certain that the lake itself will not become covered with lily pads, which are said to double their number every few days. Month after month, he patiently waits, yet only tiny patches of lily pads can be discerned, and they don’t seem to be expanding in any noticeable way. With the lily pads covering less than 1 percent of the lake, the owner figures that it’s safe to take a vacation and leaves with his family. When he returns a few weeks later, he’s shocked to discover that the entire lake has become covered with the pads, and his fish have perished. By doubling their number every few days, the last seven doublings were sufficient to extend the pads’ coverage to the entire lake. (Seven doublings extended their reach 128-fold.) This is the nature of exponential growth.
While ‘the water lily and the lake’ appears a strange choice of metaphor since if nothing else it highlights the importance of boundaries to growth, what Kurzweil was trying to communicate was how technology has barely begun to transform our lives.
By contrast, consider the 1972 report to the Club of Rome published under the title “The Limits to Growth.” Much maligned and mostly misrepresented, The Limits to Growth (LTG) was nothing more than a mathematical analysis of linear and exponential growth rates and ultimate constraints. According to the authors, the tyranny of exponential growth rates would eventually lead population and industrial production to explode, setting off a negative feedback in terms of burgeoning pollution and the eventual exhaustion of food and resources. The report never provided specific dates for the depletion of individual materials, although nine our of ten commentaries on the report claim it did (for a post I did on this particular urban legend, see here). Nonetheless, what the report did do was suggest that the idea of inevitable constant human progress was a dangerous myth. Continue reading