Re: Proof that Randomness is trivial. Zero explained in complete detail.


T.H. Ray wrote:

T.H. Ray wrote:

T.H. Ray wrote:

T.H. Ray wrote:


Even sharks have to have something to chew> on,
before
they can chew. Merely throwing out
opinions is
not
equivalent to feeding.

What, for example, do you mean by "absolute
disorder?"

Tom


In a sequence of fair coin tosses, each
succesive
outcome is disordered
with respect to all the others. Absolute
disorder
means that there is
no order whatsoever in this process.

Really? What do you call the perfect
information
that you possess (two sided coin, fair weight,
fair
toss)? What you should have said is that the
outcome
of any single toss is independent of the
outcome of
the previous toss. Where does that leave your
definition of "absolute disorder?" -- dead in
the
water.
The coin toss algorithm is ordered, i.e., not
random.

Tom


In fact that is precisely my position. Exactly.
You
have nailed it.

So, this property of "randomness" is quite
elusive.
Yet, we can define
it in such a way that it has meaning, and the
presence of disorder is
bolstered by tons and tons of probability and
statustic which seems to
validate it's presence.

This seems paradoxical. The only way to resolve
it is
to let the
property itself be trivial. Existence is
problematic,
nonexistence is
also problematic, and the compromise is
triviality.
The existence of
randomness is indeterminate.


Your conclusion does not follow from your premises.

Tom


Because we are dealing with existential issues, it
would be expected
that some things might seem contradictory at first
glance. Even the
very idea that existence could be indeterminate, this
seems quite
utterly preposterous on the face of it.

Yet - we are talking about an existential boundary
condition and you
would expect logic to do some wierd things.

There really is no way to tell if an object is
itself, or if it is a
trivial clone of itself. This cannot be determined.

Mathematical indeterminacy is very interesting, but
there really is'nt
much info on it except for what we know about
"randomness".


While it is true that one cannot differentiate between
a perfect emulation of a computer program and the original
-- to mathematics, it doesn't matter. Mathematics is the
language in which the program is written, not the thing
being described.

We know that when we describe random events by some
program, we are only describing a pseudorandom sequence,
because the algorithm is smaller than the thing it
describes. The question of whether the thing that we call
the universe is algorithmically compressible, is an open
question.

You are confusing the language, mathematics, with the
properties of the world that it seeks to describe. The
language is, of course, far from random.

Tom


Well, thats great criticism. So, let me start by saying that physics is
an abstract mathematical model of physical reality, and yes it is
distinct from that reality, even though it is embedded somehow in the
universe vis-a-vis the mind. Nevertheless, it is a representation. What
I think we're doing here is providing a representation which is much
closer to describing what's really happening, so much so that reality
and math become difficult to distinguish, but certainly they are
distinct.

Questions about randomness and determinism are very old, and I think
that the property of randomness is itself inherently paradoxical. This
is not to say that randomness is useless. Rather, that the existence of
paradox implies something which has not been understood because we have
a tendency to reject paradox as scientific junk.

Even Chaitin acknowledges that there is no way to determine if a given
number is random or not. You simply cannot determine if the number was
generated by a random process, or a deterministic one. I dont think
that Chaitin realized the depth of what he said.

In saying this, he actually stated that there is indeterminacy with
respect to the presence of this property of randomness. He did'nt say
it that way, but this is precisely the content of that result.
Unfortunately, mathematicians are trained to think in a logically
deterministic way and so when you find indeterminacy it looks like a
dead end and you move on to other things. I dont think that he realized
that he actually held the solution, but he was missing just one thing -
triviality.

Existential triviality is not considered a very valuable thing
mathematically, and so it's not surprising that he missed the
connection. Mathematicians use existence is a somewhat contorted way.

Anyway, to say that randomness is trivial, what that implies is that
the presence of randomness cannot be determined. You can argue that it
does exist, and also that it does not. I'm not suggesting that
randomness is mathematical junk. Rather, that it has this amazing
aspect of indeterminacy, and why.

.

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