Kurzweil is famous for plotting curves, and seeing where they intersect.
http://www.kurzweilai.net/articles/art0134.html?printable=1The Law of Accelerating Returns
by Ray Kurzweil
An analysis of the history of technology shows that technological change is exponential, contrary to the common-sense "intuitive linear" view. So we won't experience 100 years of progress in the 21st century -- it will be more like 20,000 years of progress (at today's rate). The "returns," such as chip speed and cost-effectiveness, also increase exponentially. There's even exponential growth in the rate of exponential growth. Within a few decades, machine intelligence will surpass human intelligence, leading to The Singularity -- technological change so rapid and profound it represents a rupture in the fabric of human history. The implications include the merger of biological and nonbiological intelligence, immortal software-based humans, and ultra-high levels of intelligence that expand outward in the universe at the speed of light.
Published on KurzweilAI.net March 7, 2001.
...The Intuitive Linear View versus the Historical Exponential View
Most long range forecasts of technical feasibility in future time periods dramatically underestimate the power of future technology because they are based on what I call the "intuitive linear" view of technological progress rather than the "historical exponential view." To express this another way, it is not the case that we will experience a hundred years of progress in the twenty-first century; rather we will witness on the order of twenty thousand years of progress (at today's rate of progress, that is).
This disparity in outlook comes up frequently in a variety of contexts, for example, the discussion of the ethical issues that Bill Joy raised in his controversial WIRED cover story, Why The Future Doesn't Need Us. Bill and I have been frequently paired in a variety of venues as pessimist and optimist respectively. Although I'm expected to criticize Bill's position, and indeed I do take issue with his prescription of relinquishment, I nonetheless usually end up defending Joy on the key issue of feasibility. Recently a Noble Prize winning panelist dismissed Bill's concerns, exclaiming that, "we're not going to see self-replicating nanoengineered entities for a hundred years." I pointed out that 100 years was indeed a reasonable estimate of the amount of technical progress required to achieve this particular milestone at today's rate of progress. But because we're doubling the rate of progress every decade, we'll see a century of progress--at today's rate--in only 25 calendar years.
When people think of a future period, they intuitively assume that the current rate of progress will continue for future periods. However, careful consideration of the pace of technology shows that the rate of progress is not constant, but it is human nature to adapt to the changing pace, so the intuitive view is that the pace will continue at the current rate. Even for those of us who have been around long enough to experience how the pace increases over time, our unexamined intuition nonetheless provides the impression that progress changes at the rate that we have experienced recently. From the mathematician's perspective, a primary reason for this is that an exponential curve approximates a straight line when viewed for a brief duration. So even though the rate of progress in the very recent past (e.g., this past year) is far greater than it was ten years ago (let alone a hundred or a thousand years ago), our memories are nonetheless dominated by our very recent experience. It is typical, therefore, that even sophisticated commentators, when considering the future, extrapolate the current pace of change over the next 10 years or 100 years to determine their expectations. This is why I call this way of looking at the future the "intuitive linear" view.
But a serious assessment of the history of technology shows that technological change is exponential. In exponential growth, we find that a key measurement such as computational power is multiplied by a constant factor for each unit of time (e.g., doubling every year) rather than just being added to incrementally. Exponential growth is a feature of any evolutionary process, of which technology is a primary example. One can examine the data
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