*"...it 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

**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 **Tim**es*' 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 --

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

**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?**

*human*race.