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/

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