The Law of Accelerating Returns Will Kill You

You will get $40 trillion just by reading this essay and understanding what it says. For complete details, see below. (It’s true that authors will do just about anything to keep your attention, but I’m serious about this statement. Until I return to a further explanation, however, do read the first sentence of this paragraph carefully.)

Now back to the future: it’s widely misunderstood. Our forebears expected the future to be pretty much like their present, which had been pretty much like their past. Although exponential trends did exist a thousand years ago, they were at that very early stage where an exponential trend is so flat that it looks like no trend at all. So their lack of expectations was largely fulfilled. Today, in accordance with the common wisdom, everyone expects continuous technological progress and the social repercussions that follow. But the future will be far more surprising than most observers realize: few have truly internalized the implications of the fact that the rate of change itself is accelerating.

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

in different ways, on different time scales, and for a wide variety of technologies ranging from electronic to biological, and the acceleration of progress and growth applies. Indeed, we find not just simple exponential growth, but “double” exponential growth, meaning that the rate of exponential growth is itself growing exponentially. These observations do not rely merely on an assumption of the continuation of Moore’s law (i.e., the exponential shrinking of transistor sizes on an integrated circuit), but is based on a rich model of diverse technological processes. What it clearly shows is that technology, particularly the pace of technological change, advances (at least) exponentially, not linearly, and has been doing so since the advent of technology, indeed since the advent of evolution on Earth.

I emphasize this point because it is the most important failure that would-be prognosticators make in considering future trends. Most technology forecasts ignore altogether this “historical exponential view” of technological progress. That is why people tend to overestimate what can be achieved in the short term (because we tend to leave out necessary details), but underestimate what can be achieved in the long term (because the exponential growth is ignored).

The Law of Accelerating Returns

We can organize these observations into what I call the law of accelerating returns as follows:

• Evolution applies positive feedback in that the more capable methods resulting from one stage of evolutionary progress are used to create the next stage. As a result, the
• rate of progress of an evolutionary process increases exponentially over time. Over time, the “order” of the information embedded in the evolutionary process (i.e., the measure of how well the information fits a purpose, which in evolution is survival) increases.
• A correlate of the above observation is that the “returns” of an evolutionary process (e.g., the speed, cost-effectiveness, or overall “power” of a process) increase exponentially over time.
• In another positive feedback loop, as a particular evolutionary process (e.g., computation) becomes more effective (e.g., cost effective), greater resources are deployed toward the further progress of that process. This results in a second level of exponential growth (i.e., the rate of exponential growth itself grows exponentially).
• Biological evolution is one such evolutionary process.
• Technological evolution is another such evolutionary process. Indeed, the emergence of the first technology creating species resulted in the new evolutionary process of technology. Therefore, technological evolution is an outgrowth of–and a continuation of–biological evolution.
• A specific paradigm (a method or approach to solving a problem, e.g., shrinking transistors on an integrated circuit as an approach to making more powerful computers) provides exponential growth until the method exhausts its potential. When this happens, a paradigm shift (i.e., a fundamental change in the approach) occurs, which enables exponential growth to continue.

If we apply these principles at the highest level of evolution on Earth, the first step, the creation of cells, introduced the paradigm of biology. The subsequent emergence of DNA provided a digital method to record the results of evolutionary experiments. Then, the evolution of a species who combined rational thought with an opposable appendage (i.e., the thumb) caused a fundamental paradigm shift from biology to technology. The upcoming primary paradigm shift will be from biological thinking to a hybrid combining biological and nonbiological thinking. This hybrid will include “biologically inspired” processes resulting from the reverse engineering of biological brains.

If we examine the timing of these steps, we see that the process has continuously accelerated. The evolution of life forms required billions of years for the first steps (e.g., primitive cells); later on progress accelerated. During the Cambrian explosion, major paradigm shifts took only tens of millions of years. Later on, Humanoids developed over a period of millions of years, and Homo sapiens over a period of only hundreds of thousands of years.

With the advent of a technology-creating species, the exponential pace became too fast for evolution through DNA-guided protein synthesis and moved on to human-created technology. Technology goes beyond mere tool making; it is a process of creating ever more powerful technology using the tools from the previous round of innovation. In this way, human technology is distinguished from the tool making of other species. There is a record of each stage of technology, and each new stage of technology builds on the order of the previous stage.

The first technological steps-sharp edges, fire, the wheel–took tens of thousands of years. For people living in this era, there was little noticeable technological change in even a thousand years. By 1000 A.D., progress was much faster and a paradigm shift required only a century or two. In the nineteenth century, we saw more technological change than in the nine centuries preceding it. Then in the first twenty years of the twentieth century, we saw more advancement than in all of the nineteenth century. Now, paradigm shifts occur in only a few years time. The World Wide Web did not exist in anything like its present form just a few years ago; it didn’t exist at all a decade ago.

The paradigm shift rate (i.e., the overall rate of technical progress) is currently doubling (approximately) every decade; that is, paradigm shift times are halving every decade (and the rate of acceleration is itself growing exponentially). So, the technological progress in the twenty-first century will be equivalent to what would require (in the linear view) on the order of 200 centuries. In contrast, the twentieth century saw only about 25 years of progress (again at today’s rate of progress) since we have been speeding up to current rates. So the twenty-first century will see almost a thousand times greater technological change than its predecessor.

The Singularity Is Near

To appreciate the nature and significance of the coming “singularity,” it is important to ponder the nature of exponential growth. Toward this end, I am fond of telling the tale of the inventor of chess and his patron, the emperor of China. In response to the emperor’s offer of a reward for his new beloved game, the inventor asked for a single grain of rice on the first square, two on the second square, four on the third, and so on. The Emperor quickly granted this seemingly benign and humble request. One version of the story has the emperor going bankrupt as the 63 doublings ultimately totaled 18 million trillion grains of rice. At ten grains of rice per square inch, this requires rice fields covering twice the surface area of the Earth, oceans included. Another version of the story has the inventor losing his head.

It should be pointed out that as the emperor and the inventor went through the first half of the chess board, things were fairly uneventful. The inventor was given spoonfuls of rice, then bowls of rice, then barrels. By the end of the first half of the chess board, the inventor had accumulated one large field’s worth (4 billion grains), and the emperor did start to take notice. It was as they progressed through the second half of the chessboard that the situation quickly deteriorated. Incidentally, with regard to the doublings of computation, that’s about where we stand now–there have been slightly more than 32 doublings of performance since the first programmable computers were invented during World War II.

This is the nature of exponential growth. Although technology grows in the exponential domain, we humans live in a linear world. So technological trends are not noticed as small levels of technological power are doubled. Then seemingly out of nowhere, a technology explodes into view. For example, when the Internet went from 20,000 to 80,000 nodes over a two year period during the 1980s, this progress remained hidden from the general public. A decade later, when it went from 20 million to 80 million nodes in the same amount of time, the impact was rather conspicuous.

As exponential growth continues to accelerate into the first half of the twenty-first century, it will appear to explode into infinity, at least from the limited and linear perspective of contemporary humans. The progress will ultimately become so fast that it will rupture our ability to follow it. It will literally get out of our control. The illusion that we have our hand “on the plug,” will be dispelled.

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