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.


Again, what does this have to do with mathematics?
Really, I fail to see how you can get anywhere (at
least, logically) without comprehending that the
mathematical language is adapted to studying propositions
of the form, A --> B.

"The basic concept is this: Once you entomb mathematics
in an artificial language a la Hilbert, once you set up
a completely formal axiomatic system, then you can forget
that it has any meaning and just look at it as a game
played with marks on paper that enables you to deduce
theorems from axioms. Of course, the reason one does
mathematics is because it has meaning. But if you want
to to be able to study mathematical methods, you have to
crystalize out the meaning and just examine an artificial
language with completely precise rules." ~ Gregory
Chaitin, Metamath!, Pantheon 2005, p. 164.

If you have actually read Chaitin, I think you need to
read a bit more carefully. If he thought that your
context for "trivial" has any mathematical meaning at all,
he would merely have written off Omega as a nonsensical
result, an artifact of the computing art.

Tom
.

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