From: John Conover <john@email.johncon.com>
Subject: Re: Fwd: [64] JAPAN'S FY '96 GDP GROWTH PREDICTED AT 1.3-2.9
Date: Wed, 1 May 1996 04:36:06 -0700
Yea, the Japanese economy is different than the US. If you look at the
fractal dimension of the Japanese GDP, it is almost 4. If you look at
the US it is just over 3. What this means is that there is a long term
"cyclic " phenomena in the Japanese economy, (that is frequently
exploited,) that is very pronounced. In the US it is not. The
Japanese economy has these wild swings every 17 years, or so, and the
GDP will stop, then go into a wild escalation. In the US, it is 5.5
years, (no one knows why,) but it is very mild, and not
exploitable. Germany and the UK are in between.
To look at these things in a serious manner, the statistics over
several decades, or so, are the important issues. In theory, the range
of the economic swings increase with the square root of time, and
since the economic expansion of Germany and Japan have been depressed
for several years, a boom economy can be expected-it seems that these
phenomena have been the case for centuries, but know one knows
why. Fractal dynamics is a "macroeconomic" analytical tool which
provides no causality for the underlying dynamic mechanisms that
create the observable phenomena. All that can be said is that the
causal mechanism is a non-linear dynamical system, with 3, or so,
degrees of freedom in the US, and 4, or so, in Japan-but know one
knows what to label the axis of the degrees of freedom.
With 3, or so, variables in the state equations, forecastability is
possible, (although, maybe, not practical.) With 4 variables, the
initial boundary values in the state equations must be known to 16
digit precision. Unfortunately, the length of the year is only known
to 9 digit precision, (and this is a theoretical limit,) so
forecasting the next year of the US economy is plausible, (but,
perhaps, not practical,) and forecasting the UK's, Germany's, or
Japanese economy is not possible. That is why economist rely on
non-linear dynamic systems analysis, like fractal analysis for
example, to analyze "macroeconomic" issues-these techniques assume no
knowledge of the underlying mechanisms of the economy. Only that they
are stable, which they seem to be over time intervals of many
centuries.
As it turns out, this is not a new technique. Newton exploited it in
the planetary motion stuff (F=MA, F~1/(D^2),) he was commissioned by
the Royal Navy to investigate in the 17'th century. With 2 bodies in
space, the dynamics are predictable. With three, they are not, but
they are forecastable-at least for a short period in the future. The
short period is defined as the "horizon of visibility," and beyond
that, forecastability drops to a 50/50 crap shoot. In point of fact,
the three body problem, (sun, moon, earth,) is not solvable, and we
are not sure that April will be in the spring 4 million years from
now, (4x10^6 years is the horizon of visibility for things with the
relative mass and velocity of the earth, moon, and sun.) Recent
simulations at MIT seem to confirm the issue. Beyond these things,
Heisenberg's uncertainty poses another limit, beyond which, no
predictability or forecastability is possible. I would suppose that
nature has spontaneity is one interpretation. As a practical
limitation of the three body problem, we can not publish navigation
tables that are accurate for more than several years into the future.
The problems were first addressed by Poincare, at the turn of the
century, when he laid the foundations for quantum mechanics. One of
the "classic" analysis was the description of Brownian motion, (which
is used to derive the number of atoms in a liter of gas, as proposed
by A. Einstein.) This technique is what we now call a subset of
fractal analysis, and forms the basis to the theory of the entropic
theory of economics, dam volumetric requirements, weather prediction,
gravel pile safety requirements, wilderness fire propagation and
hazards, ocean wave hazards, and most recently, earthquake
forecasting, etc.
It is a macro-scientific analytical tool that can be used to extend
forecastability where predictability is impossible. Its limitation is
that it can not be used in inductive reasoning to provide causality of
underlying processes. Its main use is where the underlying processes
are so complex that they are undefinable, or unmeasurable, in both a
practical or theoretical sense. In point of fact, the statistics you
are familiar with, (ie., normal curve, bell curve, Gaussian
statistics, standard deviation, root mean square, etc.,) are a subset
of fractal analysis. Fractal analysis is a subset of non-linear
dynamical system theory, (which in the lay press is called the theory
of chaos.)
John
BTW, Statistical theory is often mis-applied in dynamical systems. All
dynamical systems have characteristics that can be represented by
"bell curves," at least over a limited interval of time. However, the
"signature" that the system is exhibiting dynamic system phenomena is
that the "tails" of the bell curve deviate from the "normal" or
Gaussian bell curve by, frequently, fractions of a percent, (which is
called Kurtosis.) "Normal" statistics can provide a forecastability in
these cases limited by the "horizon of visibility." For example, about
three days in weather forecasting, (although we should be, at least in
theory, able to predict a week-but it would require a precise
measurement of barometric pressure and temperature that is not
practable with current technology-about one part in a billion, or so.)
The defining difference between stochastic, (ie., "statistical"
systems,) fractal, and chaotic systems, is that the prediction of a
stochastic system is accurate forever, without exception. In fractal
systems, the accuracy of a prediction deviates from empirical
measurement at a linear rate. And in chaotic systems, the accuracy
deviates at an exponential rate. As examples, pitching pennies is a
stochastic process, stock prices and river flooding are fractal, and
weather is a chaotic process. Obviously, to exhibit "cyclic"
phenomena, a chaotic process is necessary-ie., a fractal dimension
greater than 3.
--
John Conover, john@email.johncon.com, http://www.johncon.com/