July 10, 2010
An exponential rate of change
Here’s a working draft of the second section of Chapter 1 of my book, Finding the Li: Towards a Democracy of Consciousness. I invite constructive comments from readers of my blog.
An exponential rate of change
Let’s start by scoping out the magnitude of what the pfc has accomplished in a relatively short time. For most of us, busily managing the daily challenges of our lives, it seems that things have always been somewhat like this. Sure, technologies change from one generation to the next, and we all know that modern times are more frenetic than they used to be… but isn’t that just what every new generation says? Because we live in the continually swirling events of our own age, it’s difficult sometimes to stand back and see just how different our current age is from every other time in history.
Perhaps the most unique feature about our age is the very rate of change itself. It’s getting faster and faster. At an ever accelerating rate. But how can we quantify something like that? One instructive approach is to look at just one particular changing technology, which happens to lend itself to some fairly good historical quantification: the measurement of time.
Long ago, the Chinese had time wrapped up tighter than anyone else in the world. Their clocks could track time with an error of just a minute or two per day. And they gradually improved on their time-keeping technology, so over a thousand years or so, the error was reduced to about ten seconds a day. That was about the same accuracy of the first pendulum clock in the West, patented in 1657 by the Dutch scientist Christiaan Huygens. But then, something very strange happened. The accuracy of Western clocks kept getting better and better. And the rate of improvement itself kept getting faster and faster. So in less than two centuries the Western clocks were a hundred times more accurate than Huygens’. And less than a century later, a hundred times more accurate still. And in the past century, they’ve become ten thousand times more accurate than that. That’s known as an exponential rate of change, which follows a logarithmic curve, and can be seen in Figure 1.
Figure 1: The exponential rate of increase in the accuracy of time measurement.
In fact, there are many graphs depicting human achievements historically that follow this same exponential curve. Perhaps the most fundamental and striking of them is the graph showing the rise in human population to its current level of nearly seven billion people, as show in Figure 2. The close match between these two curves and their inflection points, where they start going vertical, is no coincidence. It is, in fact, the dramatic increase in technological innovation that has permitted the human population to grow so rapidly.
Figure 2: The exponential rate of increase in human population
If you look closely at Figure 1, you might notice a couple of interesting things. First, see how the Chinese rate of improvement (depicted by the dotted line) was very stable and consistent. It was only the Western rate of technological change that went exponential. And then, take a good look at the right hand side of the graph, representing our current age. In recent times, the line seems almost vertical. But how much longer can it continue on that course? And when you extrapolate this out to all the other areas of technological innovation with similar exponential curves, it’s difficult not to ask, where is this taking us? How did it all get started?
 Chart reprinted from Aveni, A. (2002). Empires of Time: Calendars, Clocks, and Cultures, Boulder, CO: University Press of Colorado. Additionally, see Needham, J. (1969). The Grand Titration: Science and Society in East and West, Toronto: University of Toronto Press, for an earlier version of the same chart.