Now that we have a solid understanding of the exponential function, we can begin to look at things from a more informed perspective. You may have heard of Moore’s Law, which states that the number of transistors that can be placed on an integrated circuit doubles approximately every two years. This effectively means that computer power doubles every 24 months or so. When Gordon E. Moore, co-founder of Intel Corporation, the world’s largest semiconductor chip manufacturer, described this trend in his famous 1965 paper,1 people were very sceptical. He noticed that the number of components in integrated circuits had doubled every year from the invention of the integrated circuit in 1958 until 1965, and predicted that the trend would continue “for at least ten years.” Many did not believe him. They said it was an inaccurate prediction. We could not expect it to grow any further, due to various technical problems. Those sceptics were wrong. In fact, it has been doubling steadily for more than 50 years, without any sign of stopping. But Moore’s Law is not the whole story. The exponential expansion of technology has been growing remarkably smoothly for a much longer time, and integrated circuits are just a tiny fraction of the whole spectrum of change that pervades technological advancement.
Ray Kurzweil notes2 that Moore’s Law of Integrated Circuits was not the first, but rather the fifth paradigm to provide accelerating price-performance. Computing devices have been consistently multiplying in power (per unit of time), from the mechanical calculating devices used in the 1890 US Census, to Turing’s relay-based Bombe machine that cracked the Nazi enigma code, to the CBS vacuum tube computer that predicted the election of Eisenhower, to the transistor-based machines used in the first space launches, to the integrated-circuit-based personal computer which Kurzweil used to dictate the very essay that described this phenomenon, in 2001.
To get an idea of what exponential growth means, look at the following graph, which represents the difference between a linear trend and an exponential one.
Figure 1.1: The difference between a Linear and an Exponential curve. Courtesy of Ray Kurzweil.
As you can see, the exponential trend starts to really take off where the ‘Knee of the Curve’ begins. Before that, things do not seem to change significantly. It is just like the story of the chess board and the king. In the first few days nothing notable happens, but as soon as the curve kicks in, something dramatic happens and things go out of control. „Robots will steal your job, but that’s OK“ weiterlesen