PREDICTIONS – 10 Years Later - Santa Fe Institute

2. NEEDLES IN A HAYSTACK
Intel’s microprocessors as they appeared over time. The ratio MIPS/$
shows them to be following an S-shaped curve. The learning process is
still young because the data occupy only the early exponential-like part
of the curve. Consequently estimates of the final ceiling carry large uncertainties
(of up to 100% or more). Our a priori knowledge of a level
for this ceiling is so poor, however, that even very uncertain estimates
are useful.
It is interesting, for example, to know that we have a long way to go.
This may sound like a trivial conclusion, but thanks to the way it was
obtained, it says more than simply “man will always be making progress.”
It says that a certain amount of computer evolution is guaranteed
to us by the fundamental technologies available today. Breakthroughs
will certainly come along. Nothing as dramatic as the discovery of the
transistor, however, will be warranted in order to reach three to four
times today’s levels of performance/price. Expectedly, the appearance
of an earth-shaking breakthrough, a discovery of importance unprecedented
during computer history, might define a much higher ceiling to
be reached through a follow-up curve.
There are more concrete benefits from fitting an S-curve to these
data points. The mathematical description of this curve, the logistic
function, relates price and performance with time in a quantitative way.
Specifying two of these variables dictates a value for the third one. The
most obvious place to use such a result is in pricing a new product. Its
performance (MIPS) has been measured and is not easy to change. For a
chosen introduction date, the function determines the MIPS/$ ratio
which yields a price value. With such guidelines to decision making,
one can aspire to keep doing the same thing—be successful!—and be
less subject to errors resulting from today’s stressful environment.
But in addition to price setting, the results of such a study provide a
means for deciding on corrective actions following delays on product
delivery. Product announcements precede delivery by a variable amount
of time. Like cash sitting at home, products coming to market late are
worth less. How much should a price be dropped following a nonscheduled
delay? Alternatively, how much should the performance be
improved if we insist upon keeping the same price?
With the logistic-growth function determined, mathematical manipulations
(partial time derivatives) can provide answers to the above
questions. For the first case, we find that the price adjustment following
51