TCS Daily

Nonlinear Thinking

By Arnold Kling - October 23, 2003 12:00 AM

" takes a long time to recognize a change in a long-term trend"

--Alan Blinder


This year, I attended the Pop!tech conference, an annual event that looks at technology and culture. The conference exemplifies what I would call nonlinear thinking.


The term "nonlinear" has been misused and abused by pundits, to the point where it has degenerated into a fuzzy, feel-good (or feel-cool) expression. I want to use it here in a more well-defined sense.


Points, Lines, and Curves


Try this brain teaser: suppose that we have a petri dish with some bacteria. The amount of bacteria doubles every minute. After exactly one hour, the petri dish is full of bacteria. When was the petri dish half full?


The answers generally fall into three different groups. The first group consists of people who say, "Don't you need to know how many bacteria you started with?" I call this group the point people. They are not comfortable with abstract mathematics, so they see the world in terms of points. They think that what makes this problem difficult is that you have not provided them with a precise starting point.


The second group consists of people who say, "I'm not sure, but I guess it was maybe around half an hour or maybe a little later." I call this group the linear people, because they try to use a linear approximation to solve the problem. If the petri dish is full after an hour, then if it had been almost empty to begin with and the bacteria were growing linearly, it was half full after half an hour. Often, linear approximations work well, but in this case it is completely wrong.


The third group of people actually gets the answer. As a hint, ask yourself this: if the petri dish is half full after 30 minutes, and the bacteria population doubles every minute, how long will it take until the petri dish is full? If that does not help you know the answer to the original question, then ask yourself: if the petri dish is half full after 25 minutes, and the bacteria population doubles every minute, when is it full? Keep trying this for different times until you see the right answer to the original question.


The people who get the right answer are the curve people, the nonlinear thinkers. They are able to comprehend the nonlinear, exponential relationship between bacteria and time, which on a graph would show an increasing curve.


Environmentalists as Point People


My sense is that environmental radicals tend to be point people. This makes their long-term forecasts particularly suspect. For long-term forecasting, nonlinear thinking is best. Linear approximations may work well for forecasts one or two years ahead. Point-based thinking is rarely accurate for more than a few months in today's dynamic economy.


For example, an environmentalist might take the ratio of oil consumption to world GDP as a point and the forecast for world GDP in 50 years as another point. The environmentalist might then conclude that we will not have enough oil in fifty years.


The economist Robert Solow showed what was wrong with this type of thinking thirty years ago. At that time, the "Club of Rome" had what they claimed was a complex, nonlinear model which forecast environmental catastrophe. However, because their analysis took no account of prices, technical substitution, or technological change, it was no better than a point-based tool for forecasting. One of the speakers at this year's Pop!tech, Geoffrey Ballard, pointed out that every prediction made by the Club of Rome has been false.


Economists as Linear People


Most economists are good at math, so my guess is that they would have handled the brain teaser quickly and correctly. Moreover, economists know that many of the processes that are important in our field, such as compound interest and economic growth, are nonlinear. But the economics curriculum in graduate school is focused on training students to make linear approximations. Studying economics at a leading graduate school involves loading techniques for linear approximations into your analytical tool kit. Naturally, these are the techniques that you use when you do professional research.


Economists also shy away from nonlinear forecasting because it is risky. As The New York Times' Katie Hafner reminds us, George Gilder's nonlinear forecasts for bandwidth demand were off target. In fact, a lot of the telecom bubble can be described as a forecast for Internet growth of 10x per year when in fact it was closer to 3x per year. If you build capacity for three years ahead using the 10x model, you will multiply capacity by 1000x, when the 3x reality means that demand only increases by 27x. That is a lot of excess capacity.


However, the odd thing about nonlinear forecasts is that they can be wildly wrong in the quantity dimension without being far off in the time dimension. Even at 3x growth, demand will catch up to capacity within a few years. One can argue that the telecom industry's mistake was not so much the amount of capacity that they built as the high-leverage way in which it was financed. High leverage only works if you can predict the quantity demanded accurately at a given point in time. High leverage is a good idea in a relatively linear world, but not a good idea in a nonlinear world.


Alan Blinder's lament about the difficulty of picking up long term trends is a result of over-reliance on linear thinking. The trend that he was talking about was a pickup in the rate of economic growth. This pickup was best anticipated by a nonlinear thinker coming from outside the economics profession -- Ray Kurzweil.


In The Age of Spiritual Machines, Kurzweil focused on the implications of Moore's Law. One way to think about his thesis is to imagine that we add up the total intelligence on earth by summing up the amount provided by human beings and the amount provided by computers. Today, the proportion supplied by computers might be much less than 1 percent. Yet Kurzweil would be confident that the proportion supplied by computers will be 99 percent by the end of the century. That is because the capability of a typical computer is doubling about every two years, while the capability of the typical human grows more slowly.


Kurzweil might project that a computer will have the same mental capacity as a human in the year 2030. If the computer only has 1/8 the capacity of a human at that date, you might think that he is spectacularly wrong. However, if computer intelligence doubles every two years, then the computer will catch up six years later -- and once it catches up, it will zoom past.


The implications of the increase in computing power for economic growth are large. However, economists have been slow to catch on. One of the first economists willing to adjust economic forecasts for Moore's Law was Brad DeLong. I tried to sketch out the thinking of DeLong and other economists in my essay on rational exuberance.


Nonlinear Lifespans


The speakers at Pop!tech tried to identify important issues on which to focus over the next decade or more. Given the rapid pace of technological change, this requires nonlinear thinking.


As it turned out, many of the speakers were pleading for the audience to pay attention to a particular idea, because it required monetary investment or regulatory relief to succeed. Examples included, global public health, therapeutic cloning, ocean exploration, wireless broadband, hydrogen fuel cells, and livable urban architecture.


One of the more interesting proposals was for a "war on aging." Rather than try to eradicate diseases one by one, Aubrey de Grey believes that we can look at cell damage as occurring in a limited number of ways. Once there is a way to prevent or undo each of these modes of damage (he claims that there are only seven), we can extend a healthy life indefinitely -- a veritable fountain of youth. He believes that this might be feasible in twenty or thirty years.


Longevity has been increasing fairly rapidly for the past hundred years, from about 45 years at the beginning of the 20th century to close to 77 years at the beginning of the 21st. However, if we reach the point where longevity increases at a rate greater than one year per year, then from that point on people will live forever.


For example, suppose that when you reach the age of 80 the "war on aging" has progressed to the point where longevity is 100. At that point, scientists have another twenty years to come up with new ways to extend life. This might take you to the age of 130, which gives scientists another thirty years... and you live forever.


It seems reasonable to assume that, as with all new technologies, the best anti-aging techniques will go through a period during which they are unproven and expensive. What this means is that there could be a relatively short window -- five to ten years -- such that people who die before the start of that window just miss out on immortality, people who naturally live just after the end of the window will all be immortal, and the fate of people who would naturally die during the window will depend on luck. During this "window," longevity will go from, say, 85, to infinity. That is nonlinear!


Inconsistent Predictions


Some of the nonlinear predictions made at Pop!tech 2003 were mutually inconsistent. For example, geologist Peter Ward sketched a number of catastrophic scenarios for planet earth, many of which were only likely to occur after hundreds or thousands of years. He said that we need to start worrying about these contingencies.


When I asked Christine Peterson about Ward's concerns, she scoffed, "In a thousand years, we won't need the earth." Her area of focus is nanotechnology, which she believes will produce remarkable results in the middle of the century. Where this leads is that over the next few hundred years we will develop the technology to engineer our environment and to travel in space.


One question that produces inconsistent predictions is that of energy supply and demand. Ballard sees a future in which hydrogen replaces gasoline as a means for storing and transporting energy. Since hydrogen is not a primary energy source, he believes that another source of power must be developed. He speculates that we will have to return to nuclear power as the solution.


I wonder whether some other approach to the energy issue will come to fruition more quickly. Nanotechnology and computers might facilitate conservation and continued innovation in the internal combustion engine. Biotechnology might be used to engineer plants that can efficiently convert solar energy to human use. In a nonlinear world, a technological substitute for fossil fuels that is only a concept today could still be far away in ten years and yet be an established solution in twenty.


What Great Race?


Hearing the nonlinear thinking of Pop!tech helps to soften my concern about the future of Social Security. When economists make predictions about Social Security or Medicare, we use linear approximations. Those approximations do not take into account nanotechnology or a successful war on aging or other scenarios that were spun out at Pop!tech. What I call The Great Race seems to pale by comparison. Instead, what is uncertain is the continuity of the human race.

TCS Daily Archives