On Jul 6, 9:10 pm, j.wilki...@uq.edu.au (John Wilkins) wrote:

My understanding is that the correct way to interpret this is to think
of the information that is required in a message to know the outcome.
For example if I am about to flip a coin and you know nothing of the
method that I am going to use to flip it, then the outcome of the flip
will be random even if the process of flipping has been mechanically
constrained to only yield heads. It would take a message of one bit
communicated to you in order for you to "determine" what the outcome
will be.

There is an inherent ambiguity in the meaning of the word "determine".
It can mean that I am able to state what will be and it can mean to
cause what will be. It is like when we say determine what color the
car is. In one case I go and look. In another I go and select a paint.

However, as you collect statistics (assuming I have a machine that
flips coins precisely yielding only heads) it becomes possible to
posit a "theory" about the flipping namely that it does not yield
tails. According to that theory you now "know" something and the
process is no longer ... at least if you believe the theory....
random. It would then take 0 bits to communicate the outcome (again
assuming the theory is correct - that becomes the role of the
"prediction". The output of the theory replaces the information you
would have needed. It informs you as to what the outcome will be). In
other words the theory you have come up with says that the process is
completely not random (deterministic) because if you believe the
theory you would not need any message at all to determine the outcome.
It will be, according to the theory, in fact a head. You would then be
able to "determine" in advance without a message what the machine
"determined". You would not even have to witness the flip.

It is of course possible that even after 1000000 heads that the theory
will be disproved as it was based on a statistical anomaly - meaning
that you never will really be able to determine with 100%% confidence
that in fact the machine is not random. After all... we really don't
know that the sun will rise tomorrow.

My understanding is that if you know enough about the rnd() function
that the output is not random in the sense that it is completely
predictable even if you have received no information about what the
next number will be. Technically its lack of randomness is based on a
predictive physical theory and its subtheories that constitude the
meaning of "a computer" and "a function" and "the rnd() function. It
is that physical theory that is where the "determinative-ness" of the
"machine" is derived.

It remains random in the limited sense that one can not easily
determine from its output a theory on which to base a conclusion about
what number will come next. Absent that theory you require information
to determine the outcome.

The interesting thing about quantum theory is that it does not
completely allow a prediction of the outcome and so it is called non-
deterministic. You can't "determine" the outcome from the theory - you
need some message with information in it - information only available
in the result of the experiment. That is why randomness and
probability is inherent in the theory. It turns out that at our size
the quantum effects are so small that the "deterministic" theorys can
be posited that will tell you the outcome with such reliability that
the result of all experiments of all history will "probably" not
invalidate the theory. Technically this means that the physical theory
with which you predict that the physical device executing the rnd()
function is deterministic is not correct according to modern physics
and there is some possibiliy that in fact it will fail to give the
predicted numbers and either give an incorrect number or even explode.

The statement "...we just do not have the math to describe subquantum
determinacy yet.." is incorrect if quantum theory is correct. The
problem is not a mathematics problem. It is the uncertainty principle
which, if it is valid, states that the there can never be an
experiment that will reveal a "subquantum determinacy". The quantum
theory states that there is no such thing as a subqantum determinacy.
In other words the the quantum theory states that physics is
inherently uncertain. The uncertainty principle is just the a
consequence of the wave particle duality. It is not a consequence of a
lack of mathematics. It is a question of the physics itself. If the
theory is correct then no amount of mathematics will result in a
deterministic theory. It will just result in more pure mathematics not
a new physics. What would be necessary to defeat quantum mechanics
would be a new physics, a new theory that does not have the wave
partical indeterminacy. It would require that we have a physical
theory that is for example a pure particle theory or something like
that.

So in a sense, a process that is nondeterministic can be approximately
determinstic in the sense that it would "probably" take more
experiment than can be done to invalidate a theory that predicts the
outcome. Likewise, a deterministic algoritm can result in approximate
randomness because the amount of experiments that it would take to
determine the algorithm is prohibitive. Try to derive the output of
the rnd() function emperically by just reading its result. Take the
first 999 numbers and try to predict the next.