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Hey OListers,
Randomness is a negative property; it cannot be proven only disproven.
Best,
Bill
----- Original Message -----
From: "Alex Matulich" <alex@xxxxxxxxxxxxxx>
To: <omega-list@xxxxxxxxxx>
Sent: Friday, January 10, 2003 1:45 PM
Subject: Re: FW: Random walk
> Brent wrote:
> > I know that randomness can be proven. Can non-randomness be proven?
>
> Yes. I've done graduate study in Chaos Theory. Many seemingly random
> phenomena have deterministic causes, and sometimes that determinism
can be
> derived from observing the 'random' data. There are even universal
> constants associated with chaos theory which can be derived from
dynamical
> systems that are truly deterministic yet chaotic. Fractals play a big
> role, and the fractal nature of markets was demonstrated over two
decades
> ago (see an early book by Edgar J. Peters for example) as an
alternative
> to the Efficient Market Hypothesis (the 'random walk theory').
>
> I can give you a simple real-world example of random events for which
one
> can derive a deterministic relationship. Set up a faucet to drip from
a
> small orifice; preferably the drops should come from a small tube, but
not
> so small the the flow rate causes the water to spray out rather than
drip.
> You start out with drip, drip, drip, drip. Increase the flow rate
slowly
> and you eventually get a bifurcation: dripdrip, dripdrip, dripdrip.
> Increase some more, and if your drops are small enough to resolve, you
get
> another bifurcation: dripdripdripdrip, dripdripdripdrip,
dripdripdripdrip.
>
> Increase the flow rate some more, and at some point the drips become
> completely random; you can make a histogram of the time interval
between
> drips and find a reasonably uniform distribution of random numbers.
For
> all intents and purposes you could use them as random numbers.
>
> But wait! Is it really random? If you generate a list of time
intervals
> between successive drops, t1, t2, t3, t4, etc., it looks like a list
of
> random numbers, but if you PLOT the points (t1,t2), (t2,t3), (t3,t4),
etc.
> on a graph, you get a bunch of dots that eventually fill into a smooth
> curve. This means that the any given time interval is determined by
the
> one preceding it! Voila! You have derived the deterministic nature
of
> these chaotic "random" events. Therefore they're non-random.
>
> You asked "can non-randomness be proven?" The answer is yes.
>
> > If you doubt it, just tell me what the exact price of the Dow will
be 5
> > days from today at 9:00est.
>
> Chaotic systems don't work that way. There's this aspect called SDIC,
or
> sensitive dependence on initial conditions. You can't predict a time
> interval between two drops at 11:43:02 tomorrow just from knowing a
time
> interval today and iterating the nonlinear function you derived from
> observations. A time interval of 0.15224 seconds might imply a time
> interval of 0.02386 seconds at that time tomorrow, but any uncertainty
in
> that last decimal place can mean huge differences in tomorrow's
> prediction, so 0.15223 seconds would predict 0.19000 seconds tomorrow.
>
> My example with the drops is a really simple "map" between one event
and
> the next. Theoreticians have tried to derive a similar "map" for
markets.
> It's not one-dimensional like the drip map. And it's not necessarily
> discrete either. And it's polluted by noise in the data. So it's a
tough
> problem.
>
> > Could the truth be that the markets are both random and non-random?
I
> > guess that you didn't think of that.
>
> Insofar as noise is random, markets have a random nature, yes.
>
> > On a cloudy day you can see shapes in the clouds, like ships, faces,
>
> What I see is a number of levels of fractal similarity.
>
> -Alex
>
>
>
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