Re: Chaos Theory & Statistics
- Dear Roger,
Pleasure to talk with you.
Consider my questions little provocations, not that I haven't
mastered the fields of either science.
I humbly say I haven't, but who may arrogantly say he has?
In principle I believe (but I cannot prove my belief mathematically)
that the universe is deterministic materially speaking (foreseeable
Sometimes the number of variables involved is so great (or not even
yet entirely known) rendering its determination impossible exactly
(at least using the numerical methods known).
More efficient mathematical methods may be invented in the future to
solve what's nowadays unsolvable.
On the other hand in cases where the will of the creatures is
involved the universe is non-deterministic: nobody knows whether
I'll raise my index finger now or not (that depends on my will alone
and not on anything material) or whether the dog next door will bark.
So the world is a combination of deterministic and non-deterministic
things and we're immersed up to our necks in this chaos.
Statistics only partly explains the worldly phenomena.
In other words I fully agree with you that Statistics is incapable
to give solutions to all things what-will-happen-next.
As I see Chaos Theory today is still in its tender infancy.
Much more will come in the next centuries/millennia to enrich this
gemstone of the human thought.
What, for example, will be equivalent of the invention of the
logarithms, the set theory, the calculus, etc. (things that
transformed Mathematics radically) in the field of Chaos Theory?
Your comments (and from other colleagues as well) are much welcome.
--- In email@example.com, ROGER L BAGULA <rlbagula@...>
> --- Geraldo de Bem <gdb@...> wrote:
> > Gentlemen,
> > Relatively new to the field I presume, by the
> > examples I saw, Chaos
> > Theory is a rather statiscally-biased science.
> > 1) Are they really intertwined or is it only my
> > impresion?
> > 2) In what sense is Chaos Theory is a body of
> > knowledge of its own that
> > makes it different from Statistics?
> > Best,
> > Geraldo
> Geraldo de Bem
> Statistics more or less deals with smooth probability
> distributions ; mostly normal or Gaussian.
> Chaos deals with the systems processes on a
> deterinistics level.
> it is true that the best pseudo-random algorithms are
> usually from some known chaotic process,
> but chaos starts very near an ordered smooth process
> and diverges from there.
> In stocks, for instance, the sharp ups and downs are
> better mapped by a cut off fractal process or
> a multifractal over a smooth probabilistic function.
> Essentually what Statistics fails at due to sharp
> edges or
> uneven/ disjoint distributions that involve complex
> processes, chaos and fractal theory can handle.
> Actually chaos is due to the failure of
> Statistics/probability theory
> to explain the real world.
> Your reaction is due to the fact
> that you haven't yet mastered either field
> I think.