Re: Deterministic systems.

guille2306 wrote:
[...]

I essentially agree with all you said, but I advocate a different
terminology. I think the basic problem is a category error in the words
used, starting with the subject of this thread: "Deterministic systems".
AFAIK there is no system in the world we inhabit that is deterministic
(meaning EXACTLY deterministic). Indeed, I doubt very much that the
adjective "deterministic" can sensibly apply to any real system.

Including even such simple systems as a pool cue for which
that end moves when I push on this end -- there is a minuscule
but nonzero chance that a thunderbolt out of the blue will
split the cue between push and movement. This is obviously an
artificial example to illustrate the basic point: in the real
world you NEVER know enough about the initial conditions to
obtain true determinism.

But "deterministic" does apply to our MODELS of many systems. Classical
mechanics is a theory that provides a framework for constructing
deterministic models of many systems of interest. Such models are always
deterministic IN PRINCIPLE, but applying the model to a real system
invariably reduces that to an approximation. For pulleys and inclined
planes that approximation is excellent, but in the case of chaotic
systems the approximation of determinism might be valid only for an
extremely short time interval.

So, for instance, a classical model of a pencil standing on its point is
deterministic. Ditto for a classical model of thrown dice. But upon
examination one finds that such classical models are inadequate to
predict the actual outcomes of real pencils or dice, because QM
inherently poses limits on the specification of the initial conditions
that are large enough to spoil the approximation of determinism for the
time scales on which we typically observe such systems (but for a few
microseconds that approximation is quite good :-)).

In short: it is important to not confuse the model with the system being
modeled. The former can be deterministic, but the latter cannot.

Tom Roberts

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Relevant Pages

  • Re: Deterministic systems.
    ... I think the basic problem is a category error in the words ... Determinism means: the theory that all occurences in nature ... invariably reduces that to an approximation. ... So, for instance, a classical model of a pencil standing on its point is ...
    (sci.physics.research)
  • Re: Deterministic systems.
    ... with determinism. ... Chaotic systems are deterministic. ... There are differential equations which show chaotic behaviour. ... Also those are only known by approximation. ...
    (sci.physics.research)