It really is a paradox - to a physicist.

It's not so much of a paradox to a mathematician, who's only care is
obtaining a sequence of digits where each successive digit cannot be
determined from the sequence itself.

There are other definitions, I think that I found at least six
different definitions in various texts from different fields from
statistics to information theory.

But in physics, you have to wonder if randomness could possibly
manifest itself in this world, and what that would look like. The most
common thing to do is resort to the fallacy of equivocation. To
equivocate unknowability of an outcome with disorder. This argument is
really just determinism in disguise.

Lets say that you're a mathematician. You define a sequence of random
digits. You could have defined random points, but you selected digits.
Why digits ? Digits are different than points. By specifying digits,
you impose order. By specifying points, you impose a different order.
The mathematician does not care, because he has his sequence and IT
WORKS the way he wants it to, but the paradox is that this process is
NOT completely disordered - even in the abstract case. At this point, I
become a mathematical heretic, and nobody would even bother to debate
the point. But the paradox remains.

The weird thing is that if pure randomness does not exist, even in the
abstract case, then why does statictis work so perfectly ?!?!?

Certainly - a random sequence in R1 is different from random points in
R2, R3, Rn, etc etc.

There is ALWAYS some logical structure present to corrupt the disorder.
I think it's a paradox. But, mathematicians are'nt really going out
intentionally looking for inconsistencies - are they.

LEFTY wrote:
It really is a paradox - to a physicist.

It's not so much of a paradox to a mathematician, who's only care is
obtaining a sequence of digits where each successive digit cannot be
determined from the sequence itself.

There are other definitions, I think that I found at least six
different definitions in various texts from different fields from
statistics to information theory.

But in physics, you have to wonder if randomness could possibly
manifest itself in this world, and what that would look like. The most
common thing to do is resort to the fallacy of equivocation. To
equivocate unknowability of an outcome with disorder. This argument is
really just determinism in disguise.

Lets say that you're a mathematician. You define a sequence of random
digits. You could have defined random points, but you selected digits.
Why digits ? Digits are different than points. By specifying digits,
you impose order. By specifying points, you impose a different order.
The mathematician does not care, because he has his sequence and IT
WORKS the way he wants it to, but the paradox is that this process is
NOT completely disordered - even in the abstract case. At this point, I
become a mathematical heretic, and nobody would even bother to debate
the point. But the paradox remains.

The weird thing is that if pure randomness does not exist, even in the
abstract case, then why does statictis work so perfectly ?!?!?

Certainly - a random sequence in R1 is different from random points in
R2, R3, Rn, etc etc.

There is ALWAYS some logical structure present to corrupt the disorder.
I think it's a paradox. But, mathematicians are'nt really going out
intentionally looking for inconsistencies - are they.

You confuse *balance*, the condition every force in the
universe tries to achive, with *randomness*.

A loaded coin or die violates the predictions of
probability to seek a balance of *all* the forces
that it is subject to.

So... It will will not be necessary to sacrifice
three handicapped fighting cocks to
the god of randomness this week. ;-)

Sue...

LEFTY wrote:
It really is a paradox - to a physicist.

[I assume you have switched topics and are now discussing
randomness.]

Not really. Models for the decay of unstable particles assumt perfect
randomness, and agree quite well with observations. There are, of
course, many other instances of randomness in physics....

Bottom line: there's no reason to expect the world to be deterministic
(in the classical sense). And there are observations that imply such
determinism cannot apply to the world we inhabit.


Tom Roberts

Order vs. disorder is just determinism with with a new suit and a bad
wig. We could debate randomness all day long, and at best we'd generate
a huge pile of philosophy, nothing that would lead to any kind of
proof.

Would'nt it be better if there were a more rigorous answer to this ?

Well, I think that we might get more rigor by finding a way to
implement a change to the Lorentz Transform. The statement I want to
insert into the transform, algebraically, is that "Time and Length are
unobservable on extreme scales".

The expected result is trivial space, a tangible nonexistence. The
philosophy makes perfect sense - but can it make sense mathematically ?
All it needs is some algebra. I know it can be done, but the whole
"observability" thing - how do you put symbols on that ?

I'm sure that there would be lots of weird and unexpected results of
using such a space in physics. It might turn out that it makes no sense
whatsoever, and then it could be junked. But if it made sense, and it
seems like it might, the result is a whole new cosmology and many
opportunities for explorations and research.

Trivial space. Nonexistence. Call it what you like - it is now
constructible, at least philosophically. I need to put some algebra on
this thing otherwise it's just more silly words.

"Time and length become unobservable at extreme large and small scales"
+ algebra = [ ? ]


I am confident that there are respectable solutions to whether
randomness exists or not, but you need trivial space to get those
answers. You can also get some respectable answers regarding continuity
of spacetime. Probably tons more. We need some algebra.

http://www.cs.auckland.ac.nz/CDMTCS/...n/sciamer.html

Randomness and Mathematical Proof
Scientific American 232, No. 5 (May 1975), pp. 47-52
by Gregory J. Chaitin

"Although randomness can be precisely defined and can even be measured,
a given number cannot be proved to be random. This enigma establishes a
limit to what is possible in mathematics. "

--------------------------------------------------



Limits to what is possible in mathematics ?

What he's saying here is that determinism is still unsolved as of (May
1975).

LEFTY wrote:
http://www.cs.auckland.ac.nz/CDMTCS/...n/sciamer.html

Randomness and Mathematical Proof
Scientific American 232, No. 5 (May 1975), pp. 47-52
by Gregory J. Chaitin

"Although randomness can be precisely defined and can even be measured,
a given number cannot be proved to be random. This enigma establishes a
limit to what is possible in mathematics. "

--------------------------------------------------



Limits to what is possible in mathematics ?

What he's saying here is that determinism is still unsolved as of (May
1975).

No ... you said that.
He said:
"...a given number cannot be proved to be random"

Or automobiles cannot be shown to have other that
four wheels so locomotives can't either.

Einstein and others perhaps thought that this was a
defect of the theory that should eventually be removed,
by a supplemental hidden variable theory[6] that restores
determinism; but subsequent work showed that no such
hidden variables account could exist. At the microscopic
level the world is ultimately mysterious and chancy.

So goes the story; but like much popular wisdom, it is
partly mistaken and/or misleading. Ironically, quantum
mechanics is one of the best prospects for a genuinely
deterministic theory in modern times! Even more than in
the case of GTR and the hole argument, everything hinges
on what interpretational and philosophical decisions one
adopts. The fundamental law at the heart of non-relativistic
QM is the Schrödinger equation. The evolution of a wavefunction
describing a physical system under this equation is normally
taken to be perfectly deterministic.[7] If one adopts an
interpretation of QM according to which that's it -- i.e.,
nothing ever interrupts Schrödinger evolution, and the
wavefunctions governed by the equation tell the complete
physical story -- then quantum mechanics is a perfectly
deterministic theory. There are several interpretations
that physicists and philosophers have given of QM which
go this way. (See the entry on quantum mechanics.)

More commonly -- and this is part of the basis for the
popular wisdom -- physicists have resolved the quantum
measurement problem by postulating that some process of
"collapse of the wavefunction" occurs from time to time
(particularly during measurements and observations) that
interrupts Schrödinger evolution. The collapse process
is usually postulated to be indeterministic, with probabilities
for various outcomes, via Born's rule, calculable on the
basis of a system's wavefunction. The once-standard,
Copenhagen interpretation of QM posits such a collapse.
It has the virtue of solving certain paradoxes such as
the infamous Schrödinger's cat paradox, but few philosophers
or physicists can take it very seriously unless they are
either idealists or instrumentalists. The reason is simple:
the collapse process is not physically well-defined, and feels
too ad hoc to be a fundamental part of nature's laws.[8]
http://plato.stanford.edu/entries/determinism-causal/

IWO... our inability to understand a mechanism does
not force nature to roll dice. We may 'choose' to
roll dice so we can collect data using statistics
to substitute for unknown mechanisms.

Sue...

Well, when I think of "complete" disorder, I think that everything must
be up for grabs - including form.

An absolutely disordered system will have no preference whether it
produces numbers, geometry, waves, particles, text, dimensions, or
anything else. This is what I visualize when I think of absolute and
total disorder. The problem is that it would not be of much use to
anyone.

So, we have ways to produce constrained disorder with dice, roullette
wheels, etc. But the disorder is not absolute. And I suspect that the
absolute disorder that I'm thinking of can only live in trivial space -
i.e. does not exist.

Chaitin points out a dilemna of random numbers, and there are others. I
think that it is a genuine paradox that the act of defining disorder
actually imposes order upon it, thereby negating it. No statistician
wants to hear that - and I dont blame them. They have disordered
sequences and processes which clearly work properly and I'm not saying
that they are wrong.

As for the universe, I dont believe that absolute disorder can exist in
it. I think that you can get very, very close to absolute disorder, but
cannot achieve it. Same thing with order. I dont think that absolute
order can exist. You can get pretty close, but cannot achieve absolute
order.


I personally cannot achieve the greek expression descrbing
non-observability of time and length..... : )

I can get very close, but an absolute solution is impossible ? ...... :
)

LEFTY wrote:
Matter of fact, if you could use relativity to demonstrate quantum
weirdness, then this would be a huge advancement for the relativists.

I think that it CAN be done, the philosophy is now in place, just needs
some algebra.

I dont give a damn about medals, money, or tenure. I like science
because I want to know how this place works. If you feel that way too,
then post some algebra and we'll beat the truth out of this thing
collectively - like a big collective brain.

So, science = getting at the truth? What truth?

And it's strange that it seems so dependent on scale.

Consider the collision of two billiard balls. The more time elapses,
the less order you have. In the immediate instants which follow the
collision, Newtonian mechanics gives extremely accurate results. The
process is almost completely ordered because the time interval is so
short.

But if you let the balls collide and then come back and check on things
100,000,000 years later, then chaos has taken over and the dynamics are
considered to express randomness in certain ways !!

And this difference is the result of scale on the t axis. Scale and
order are related in spacetime. Very surprising result when viewed that
way.

LEFTY wrote:
Well, when I think of "complete" disorder, I think that everything must
be up for grabs - including form.

That is mathematics... not physics.


An absolutely disordered system will have no preference whether it
produces numbers, geometry, waves, particles, text, dimensions, or
anything else. This is what I visualize when I think of absolute and
total disorder. The problem is that it would not be of much use to
anyone.

Order is what a mathematician defines it to be.


So, we have ways to produce constrained disorder with dice, roullette
wheels, etc. But the disorder is not absolute. And I suspect that the
absolute disorder that I'm thinking of can only live in trivial space -
i.e. does not exist.

The concept you just created... does not necessary exist.


Chaitin points out a dilemna of random numbers, and there are others. I
think that it is a genuine paradox that the act of defining disorder
actually imposes order upon it, thereby negating it. No statistician
wants to hear that - and I dont blame them. They have disordered
sequences and processes which clearly work properly and I'm not saying
that they are wrong.

As for the universe, I dont believe that absolute disorder can exist in
it. I think that you can get very, very close to absolute disorder, but
cannot achieve it. Same thing with order. I dont think that absolute
order can exist. You can get pretty close, but cannot achieve absolute
order.

You are defining order and disorder so you can certainly
pass judgement on what complies.



I personally cannot achieve the greek expression descrbing
non-observability of time and length..... : )

For length this seems to work:
http://hyperphysics.phy-astr.gsu.edu...ic/elefor.html

Mass:
0.511 megaelectron volts = 8.18712172 × 10-14 joules
http://van.hep.uiuc.edu/van/qa/secti...1005144616.htm


Time:
http://www.glenbrook.k12.il.us/gbssc...aws/u2l3a.html

Speed of light:
http://physics.nist.gov/cuu/Images/alphaeq.gif
http://physics.nist.gov/cuu/Constants/alpha.html


I can get very close, but an absolute solution is impossible ? ...... :
)

Try looking beyond the space between your ears. )

Sue...