At 01:58 AM 5/5/00 +0100, Richard wrote:
[...]
>If you accept the quantum nature of the universe (which has apparently been
>proven beyond reasonable doubt), then it follows that chaotic systems must
>ultimately be unpredictable. And all systems are chaotic to some degree,
>even the motion of the planets.
>
>So I have no doubt that the universe is probabilistic, not deterministic.
>However, I'm not sure that this necessarily addresses the issue of free
>will. Perhaps our actions are predetermined in a probabilistic sense, e.g.
>there are a number of possible shirts I may wear tomorrow, and the
>probability of each can be calculated, but I have no say in the matter!
>
>I feel the problem of free will is very closely linked to the problem of
>consciousness. They're both great unexplained mysteries. (By the way, I
>*still* haven't got around to reading Dennett's "Consciousness Explained").
I suppose I agree generally here. I would say that indeterminacy gives the
hope of freedom but it certainly isn't a proof. In the 17th century I would
say determinism probably had the upper hand from the scientific perspective.
Mechanistic materialism, Newtonianism, the clockwork universe etc. Based
on what was understood at that time things certainly would have appeared to be
deterministic. But things have changed. Quantum mechanics, nonlinear
dynamics, chaos etc. Determinists no longer have the luxury, IMHO, of
passing the burden of proof to their opponents.
Well, I thought of another thought experiment last night. I hope everyone
isn't getting too bored by my little experiments :).
In view of Tedd's comments let me emphasize here that I'm concerned
with a particular form of determinism we can call strict determinism. Strict
determinism from the mechanistic materialist point of view would hold that
the current positions and velocities of all particles in the universe + the
laws of physics completely determines all future states of the universe.
Any feeling of freedom is an illusion. But strict determinism may arise by
other mechanisms, i.e. the will of an omnipotent being. Regardless how it
comes about, with strict determinism the future of the universe has already
been determined. Including ( :-0) what shirt I will wear on any given day.
Here we won't appeal to a supercomputer which I believe would be impossible
to build anyway. Instead we'll have a regular old computer. The "prediction"
in this case will be simply a shirt chosen at random from a list of my shirts.
In view of your comments above, we can have it chosen according to
some probability distribution, it doesn't matter. The night before, the
computer
spits out a "prediction", a specific shirt. I decide in advance that I will
never
wear the shirt it "predicts". Am I free to do this? Well, if everything has
already
been determined (and I have a finite number of shirts :), then eventually,
if we
perform the experiment enough times, the computer will "predict" the shirt I
was predestined to wear. So, the determinist would have to predict that some
time or another I will wear the shirt "predicted" by the computer.
> >As far as mathematics goes, I'm curious your response to Chaitin's proof
> >that there is randomness even in pure arithmetic?
>
>I haven't heard of this. I guess he's referring to something like the digits
>in pi being random. If so, then they aren't random in the sense that
>we've been discussing. They're only random to someone who doesn't
>yet know them--they would be known to a computer of sufficient power.
Since many here may not have heard of Chaitin, let me preface my comments
by saying that many regard his work to be one of the greatest achievements
of modern mathematics. I say this only to make sure everyone realizes we're
not talking about a crank. Chaitin is one of the co discoverers (with
Kolmogorov and
Solomonoff) of algorithmic information theory (AIT), but the result we're
discussing
here is uniquely his.
I really can't do any justice to his ideas here, I would encourage those
who are
interested to visit his web page where he has almost all his papers
available for
downloading:
http://www.umcs.maine.edu/~chaitin/
As regarding Pi, let me just say that in AIT Pi is the exact opposite of
random, highly
ordered, since it can be generated by a sort algorithm.
Regarding randomness, let me just give a couple of quotes where Chaitin himself
is discussing the implications of his proof.
======================================================
The most important application of algorithmic information
theory is to show the limits of mathematical reasoning. And
in particular what I've constructed and exhibited are mathematical
facts which are true for no reason. These are mathematical facts
which are true by accident. And since they're true for no reason you
can never actually prove logically whether they're true or not. They're
sort of accidental mathematical facts which are analogous to
the outcome of a coin toss, because the independent toss of a
fair coin has got to come out heads or tails but there's no reason
why it should come out one or the other. And I've found mathematical
facts that mirror this very precisely.
-- Gregory Chaitin, "How to Run Algorithmic Information Theory
on a Computer," <Complexity>, 2(1):15-21.
=======================================================
================================================
In a nutshell, Gšdel discovered incompleteness, Turing discovered
uncomputability, and I discovered randomness---that's the
amazing fact that some mathematical statements are true for
no reason, they're true by accident. There can be no ``theory
of everything,'' at least not in mathematics. Maybe in physics!
-- from the preface of <The Unknowable> by Gregory Chaitin.
==================================================
Brian Harper
Associate Professor
Mechanical Engineering
The Ohio State University
"One never knows, do one?"
-- Fats Waller
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