IS HISTORY DRIVEN BY A POWER LAW?


This idea which came to me today walking the streets of Barcelona, is surely my most dangerous idea to date. To get an idea of what power laws are all about see How Nature Works by Per Bak here. A power law is said to exist when two phenomena, plotted one against the other using logarithmic scales, produce a straight line. Examples of power laws are the Guttenberg-Richter law for the distribution of earthquakes and their scale, Zipf's law for the distribution of cities and their size, or Gibrat's law in economics.

Power laws have always been something of a problem for social scientists. For social theory to work like we want it to they shouldn't really be there. But it seems that they are.

The basic idea I have in mind at the moment is very simple really. Things are evidently speeding up, in fact they always have been. One of the central motors for the growth of economic value is this: that tomorrow I will be capable of doing more than I am today. In the next minute I will be capable of doing more than I am in this one, and, of course, we can take this down to the smallest time unit you want to imagine. In another language this is called evolution. In fact the process of accumulation of what's called human capital is based on a process which looks something like this.

Let's formulate a more tractable and mundane version of what I'm trying to say. Many writers have beenat pains to point out that there seems to be a principle of societal acceleration at work somewhere. More's law is just one of the most common examples of what this phenomenon might consist in. Everyone nowadays knowns Moores Law, but the fascinating thing is that Moore's law itself itself seems to be operating at ever accelerating speed. In the beginning things doubled every two years, then it was every year, now we're down to every six months. The question is does all this represent a pattern, and if it does, what does this mean? Ray Kurzweil's recent AI presentation seems to be riddled with fascinating exponential functionsTechnology in the 21st Century: an Imminent Intimate Merger, so if you're interested, take a look.