From: John Conover <john@email.johncon.com>
Subject: Re: A year ago today, the NASDAQ was at an all time high
Date: 14 Mar 2001 01:24:52 -0000
Its funny you should mention that-I got the e-mail as I was writing
about the complexity characteristics of the logistic equation. Peters
has one of the best presentations of the Ljapunov exponent I've
seen. (Both of his books are excellent and practical for the equity
investor, BTW.)
If one tries to determine a and b in the logistic equation, the error
of prediction, although quite small to start with, grows
exponentially. The constant in the exponential error growth is the
Ljapunov exponent.
Its an important concept these days. The idea that things like
recessions could be averted through manipulation of monetary policy,
(an idea in vogue in the 70's,) and then fiscal policy, (the vogue
idea in economics in the 80's,) has largely been abandoned.
The idea now, (its the way the FED does things-and the FED is the
largest consumer of mathematical programming software in the world
today,) is to continually measure the parameters-almost real time,
(like a and b in the logistic equation-but they have hundreds or
thousands of such parameters,) and then tweek things dynamically, very
quickly to avoid the predictive implications of Ljapunov exponent, and
exercise some control over the economy.
Its a new field in complexity theory called "adaptive control," and it
is in its infancy, (the people at the FED published a paper on it a
few years ago-in the list of authors was one Alan Greenspan; it is
most used to mitigate inflation, which is the most evil demon that a
finance minister can face.)
Adaptive control is domain of the Santa Fe Institute, (among others,)
and Stephanie Forrest, (formerly of SFI, now at the University of New
Mexico,) is one of the foremost researchers. (She did the genetic
algorithm programming as an graduate student for Robert Axelrod's
famous iterated prisoner's dilemma experiments in political science,
too-which changed the paradigm of the profession, and gave substantial
evidence that John Nash's game-theoretic solutions were correct; of
interest, note how the computer abstraction played a part in
mathematical proof!.)
John
BTW, note the paradigm of the FED when using adaptive control
techniques. They tend to use NLDS and stochastic methodologies
interchangeably-which, and when, depends on practical issues.
Jeff Haferman writes:
> BTW,
> You may be interested to know that Edgar Peters has a new
> book out:
> "Complexity, Risk, and Financial Markets", by Edgar Peters,
> John Wiley and Sons, 2001, ISBN 0-471-39981-7, (paperback).
> This differs from Peters earlier books ("Chaos and Order
> in the Capital Markets..." and "Fractal Market Anaylsis")
> in that there aren't really any equations in the entire book
> (there may be one or two fairly simple equations). Another
> book by Peters (1999 "Patterns in the Dark") drew some
> criticism on the reviews at Amazon that it was "dumbed down"
> to "reach a broader audience". I haven't read "Patterns
> in the Dark", but I have read "Complexity, Risk, and
> Financial Markets" and it is a good, thought-provoking read.
> The other nice thing is that it is relatively cheap ($16 or so).
> I like mathematically rigorous writing, but this was a book
> was a nice change of pace.
> Jeff
>
>
> John Conover wrote:
> >
> >While we are on the subject of good books about things fractal and
> >chaos, here are a few of my favorites:
> >
> > "Mind Tools", by the logician Rudy Rucker, (more noted as a
> > science fiction author, and a world renowned mathematician-he
> > personally worked with Kurt Goedel,) Houghton Mifflin Company,
> > Boston, Massachusetts, 1993, ISBN 0-395-46810-8, (paperback.)
> > Rucker is at the forefront of science in the 21'st century,
> > (looking after the formal issues,) and the book is about
> > complexity, and how information theory, math, logic, and
> > randomness are all tied together. It is non-technical, but that
> > doesn't mean the reader does not have to think. If I were king,
> > all high school diplomas would be issued only after a student had
> > demonstrated competency with the content of this book.
> >
> > The Stewart book, (mentioned previously,) "Does God Play Dice?:
> > The Mathematics of Chaos", Ian Stewart, Blackwell Publishers,
> > Cambridge, Massachusetts, 1992, ISBN 1-55786-106-4. It is very
> > heartening that a mathematician of the stature of Stewart would
> > set down and write a book about randomness for the lay
> > person. This book addresses predictability, randomness, and
> > entropy, and how they are related, (and how they are not.) Note
> > that we really don't know what the word random means. (Could you
> > explain it?)
> >
> > "The Jungles of Randomness: A Mathematical Safari", Ivars
> > Peterson, John Wiley & Sons, New York, New York, 1998, ISBN
> > 0-471-16449-6, a good introductory book on simple fractals, with
> > real-life examples, and how fractals, chance, and randomness work.
> > Perhaps available now in paperback.
> >
> > "What is Random?: Chance and Order in Mathematics and Life",
> > Edward J. Beltrami, Springer-Verlag, New York, New York, 1999,
> > ISBN 0-387-98737-1, (I don't know about paperback.) A bit more
> > technical and formal approach to randomness, and how it is tied
> > into information theory.
> >
> > John
> >
--
John Conover, john@email.johncon.com, http://www.johncon.com/