On Jun 10, 1:52 pm, "Nicolaas Vroom" <nicolaas.vr... at (no spam) pandora.be
wrote:



I have a problem in understanding the difference between
deterministic verus non-deterministic as axplained in the following url:http://en.wikipedia.org/wiki/Deterministic_system_%28philosophy%29

Are the following examples deterministic yes or no:
1. The movement of a round rubber ball with a certain weight,
dropped 1 meter above the centre of a round table.
After a couple of bounces the ball will come to rest at the centre
of the round table.
2. The same as #1 but the ball (same weight) has the same of an
american football.
The ball will not come to rest at the center of the table.
3. The same as #2 but the ball has the shape of a dice
4. The same as #1 but the ball (same weight) is made from glass.
The ball will come to rest, but not at the centre of the table.
5. The movement of the comet Schumacher Levy from just
before its break up into its 20 fragments, until each of those
fragments collided with the planet Jupiter.

IMO non of those examples is deterministic, but that opinion
is in conflict with the information in Wikipedia.

Nicolaas Vroomhttp://users.pandora.be/nicvroom/

Any classical system (i.e., where quantum mechanics plays no role) is
deterministic. Given the equations of evolution and the exact initial
conditions, you can predict exactly the evolution of the system. Of
course there will be problems: maybe you don't know the exact
equations or it is not possible to solve them in a reasonable time
(because of their complexity), and most probably you only have an
approximation of the initial conditions (which is specially bad in
chaotic systems). All of your examples (taken only as classical
systems and forgetting about QM) fall in one of those categories: for
example, even for a perfectly rigid "dice ball" on a perfectly rigid
flat surface, the rest position will depend strongly of the angle
between the first corner to hit the surface and the surface itself.
But, if you repeat the experiment with exactly the same initial
conditions, the ball will do exactly the same. It is, as stated in the
Wikipedia article, a matter of philosophy: you can't predict the
result for practical reasons, but it is predictable in theory.

When quantum mechanics enters the picture things change completely.
Even in theory, if you know the exact initial condition, the most you
can do is predict probabilities for the different results. But here I
have my own question to anyone: we can (in theory) predict the exact
evolution of the wave function of the system, does that means that
system is deterministic, or we should only apply the word
"deterministic" to systems where we can predict the result of the
measurement? I think that the second is the most correct approach, but
I would like to know if there is any consensus about this.

Guillermo

guille2306 wrote:

Any classical system (i.e., where quantum mechanics plays no role) is
deterministic.

This is far from the truth.

There are plenty of classical systems described by stochastic
differential equations, the simplest being Brownian motion.

Deterministic classical systems are only a convenient approximation
to the more realistic stochastic case.

For example, a deterministic damped harmonic oscillator is obtained
from a stochstic damped harmonic oscillator by completely ignoring
the damping mechanism.


Arnold Neumaier

Lou Pecora wrote:
Don't confuse difficulty in prediction, which is what you are saying,
with determinism.  Chaotic systems are deterministic.  Many can be
modeled well with differential equations which are deterministic.

Not many, but all.

By definition, a chaotic system is a system governed by an ordinary
differential equation which exhibits a specific form of sensitive
dependence on initial conditions. Such systems are therefore always
deterministic.

A pencil balanced on its point is not a chaotic system, although it is a
deterministic system.

A pencil balanced on its point is not a deterministic system,
although one can consider deterministic approximate models for it.
In that case it is chaotic, once you include forces on its point,
which are always present for a real pencil.

However, there is always some modeling error, which is not just
uncertainty in a constant, but uncertainties changing unpredictably
at each instant of time. Thus it must be modelled by a stochastic
term.

Of course, the uncertainty ultimately stems from quantum mechanics,
since a pencil balanced on its point is of course nothing but a
large quantum system.

I think I can say something a little bit more. We can tie in

Lou Pecora wrote:

Don't confuse difficulty in prediction, which is what you are saying,
with determinism. Chaotic systems are deterministic. Many can be
modeled well with differential equations which are deterministic.

Not many, but all.

By definition, a chaotic system is a system governed by an ordinary
differential equation which exhibits a specific form of sensitive
dependence on initial conditions. Such systems are therefore always
deterministic.

A pencil balanced on its point is not a chaotic system, although it is a
deterministic system.

A pencil balanced on its point is not a deterministic system,
although one can consider deterministic approximate models for it.
In that case it is chaotic, once you include forces on its point,
which are always present for a real pencil.

However, there is always some modeling error, which is not just
uncertainty in a constant, but uncertainties changing unpredictably
at each instant of time.

Thus it must be modelled by a stochastic term.

Of course, the uncertainty ultimately stems from quantum mechanics,
since a pencil balanced on its point is of course nothing but a
large quantum system.

Arnold Neumaier

[...]

guille2306 wrote:
Any classical system (i.e., where quantum mechanics plays no role) is
deterministic.

This is far from the truth.

There are plenty of classical systems described by stochastic
differential equations, the simplest being Brownian motion.

Deterministic classical systems are only a convenient approximation
to the more realistic stochastic case.

For example, a deterministic damped harmonic oscillator is obtained
from a stochstic damped harmonic oscillator by completely ignoring
the damping mechanism.

Arnold Neumaier

Do you consider all those systems deterministic ?

Just dont confuse "deterministic" with "predictable"
--
The question is what does each mean.

Lou Pecora wrote:

Don't confuse difficulty in prediction, which is what you are saying,
with determinism. Chaotic systems are deterministic. Many can be
modeled well with differential equations which are deterministic.

Not many, but all.

By definition, a chaotic system is a system governed by an ordinary
differential equation which exhibits a specific form of sensitive
dependence on initial conditions. Such systems are therefore always
deterministic.

A pencil balanced on its point is not a chaotic system, although it is a
deterministic system.

A pencil balanced on its point is not a deterministic system,
although one can consider deterministic approximate models for it.
In that case it is chaotic, once you include forces on its point,
which are always present for a real pencil.

However, there is always some modeling error, which is not just
uncertainty in a constant, but uncertainties changing unpredictably
at each instant of time. Thus it must be modelled by a stochastic
term.

Of course, the uncertainty ultimately stems from quantum mechanics,
since a pencil balanced on its point is of course nothing but a
large quantum system.

Is a computer deterministic?

Why?

You have remarked a few times that
things are only deterministic on a computer. But a computer is a
physical system. Is it deterministic?

Think that through.

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,
Models = mathematical equations are deterministic by definition ?
but applying the model to a real system
invariably reduces that to an approximation.
That is correct. This is the second part of the problem.

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

"Lou Pecora" <pecora at (no spam) anvil.nrl.navy.mil> schreef in bericht
news:pecora-89F83B.10195713062008 at (no spam) ra.nrl.navy.mil...

Is a computer deterministic?

Yes

Why?

Only in the sense that on the same computer every time when
you run the same program the same answer appears,
assuming that as part of program execution no human being is involved.

When you play the game of Golf on a computer, the program
becomes non-deterministic in the sense that every time
when you play the same game you get a different result.

On the same computer the same program will generate the same answer
almost every time. I think the OP has opened up the very interesting
question about how we label a physical system according to the the model
of the system we choose. That's at the heart of this discussion.

You call the computer deterministic because the model of the system is
deterministic.

Anyway this is not the issue. The issue is can we describe all systems
(the evolution of the total world) by mathematical equations
accuratelly. The answer is no

Pierre Simon Laplace was very much involved with the movement of the
planets. He confirmed that this motion could very well be calculated by
applying Newton's Law. In his view there is order in the planets and in
the total Universe. As such the Universe is determistic.

But is this reasoning correct if you consider all the complexities at
different scales finally going down to the level of electrons and
protons ? IMO the answer is no. You cannot describe all the details of
the Universe including the behaviour of humans by applying Newton's Law,
even stronger you cannot describe it by any form of mathematics.

Nicolaas Vroomhttp://users.pandora.be/nicvroom/

On Jun 25, 3:07 am, "Nicolaas Vroom" <nicolaas.vr... at (no spam) pandora.be
wrote:

Anyway this is not the issue. The issue is can we describe all
systems (the evolution of the total world) by mathematical
equations accuratelly. The answer is no

Pierre Simon Laplace was very much involved with the
movement of the planets. He confirmed that this motion
could very well be calculated by applying Newton's Law.
In his view there is order in the planets and in
the total Universe. As such the Universe is determistic.

But is this reasoning correct if you consider all the complexities
at different scales finally going down to the level of electrons and
protons ? IMO the answer is no.
You cannot describe all the details of the Universe including
the behaviour of humans by applying Newton's Law,
even stronger you cannot describe it by any form of mathematics.


OK, now I'm getting what you meant. Your first question ("Are these
system deterministic?") was too general. Now you have reformulated it
into "Can we totally describe the Universe through deterministic
models?" IMHO, those two question are different and that's why you got
two distinct group of answers here. For the second, I agree with you: in
practice there is no way that we could describe all the details of the
Universe, symply because there are too much details...

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