[FoRK] Re: [physnews@aip.org: Physics News Update 765]

Dave Long < dave.long at bluewin.ch > on > Fri Mar 10 14:21:11 PST 2006

> The Stock Market Criticality piece is interesting... I wonder if it 
> suggests that the crash of '87 was
> engineered? If so, can it be mathematically proven (like applying 
> Benford's Law to detect accounting fraud)?

I don't think it implies there was any fraud.  Sure, gaussian normal 
distributions are common, but there's no reason why lack of one implies 
any underhandedness[0].

Often, a normal distribution occurs because there's a deviation about 
some value which has restoring forces that tend to preserve the 
distribution.  It's perfectly possible to have distributions which 
don't tend to any expected value, and even diverge the longer one looks 
at them[1].

Phase transitions, as the article discusses, are areas where one leaves 
the domain of one set of stable values and enters a different domain -- 
and switching from one set of restoring forces to another is a natural 
place to get all manner of fluctuations.  Applied to the stock market, 
it's likely that '87 was just the 20th century equivalent of switching 
from a phase where just about everyone thought high-end turnips were 
valuable to a phase where the beliefs were the opposite.

Maybe check out Thom and Catastrophe Theory.  In the early 70's he 
catalogued several of the simplest generic phase transitions 
("catastrophes"), and also observed that close to the transition 
points, one would observe behavior at all scales.  I don't believe 
anyone's done much practical with this work, but it's a much more 
formal treatment of the commmon "tipping point" meme.


[0] "Everybody firmly believes in [the central limit theorem] because 
the mathematicians imagine it is a fact of observation, and observers 
that it is a theory of mathematics" -- Poincare

[1] I owe to Schroeder the idea that software projects can be a good 
example: often the longer a large project has gone without a stable 
release, the less likely one is to have a clear timeframe as to when 
the release will actually occur.

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