Re: real random


"Richard Heathfield" <rjh@xxxxxxxxxxxxxxx> wrote in message
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In <h964tt$fsd$1@xxxxxxxxxxxxxxxxx>, BGB / cr88192 wrote:


"Richard Heathfield" <rjh@xxxxxxxxxxxxxxx> wrote in message
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In
<7cc69756-f72f-4d40-a895-41253a9238b5@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
websnarf wrote:


<snip>

So first you have to start with the definition of "random". It
just means the opposite of deterministic.

You can mean that if you like, but it's a very humpty-dumpty way of
looking at randomness.


"indeterministic" is the opposite of "deterministic" as I see it.

as I see it, a deterministic system is a system in which the results
can be generated from a finite (and typically known) set of rules.

And *therefore*, whether a system is deterministic depends on how much
knowledge you have about that system. For example, here is a set of
numbers, the last of which I have concealed from you. But *I* know
it.

40041 87595 86455 20463 74627 56958

To you, the rule for generating these numbers is unknown. To me, it is
known. So, for you, this system is non-deterministic. But for me, it
is highly deterministic. One might say that the randomness of the
sequence can be measured by one's inability to predict the next
number in that sequence. Thus, for me, what I might call the
"coefficient of randomness" [1] of the above sequence is 0.0, but for
you it is (probably) 0.99999 (i.e. you have one chance in 100,000 of
guessing it correctly). Of course, you might step outside the system
by guessing the rule. If your guess is correct, the randomness drops
to 0.0 for you, too.

[1] I am not sufficiently up on information theory to know whether
this "coefficient of randomness" is an exact analogue of the concept
of "entropy", but it is surely very close.


I disagree here, namely, I believe that whether or not a system is
deteministic is a part of the system, rather than a part of the observers.

just because a system is deterministic does not mean all observers will know
the state, or be able to draw predictions, but it will effect how the system
will behave in the long run...


hence, if you could know the complete state of the system at a given
moment, you could also know all possible future states as well
(whether or not this "can" be done in practice is another issue).

however, a deterministic system can be "chaotic", as is typically
the case with PRNGs.

Typical PRNGs are in fact not chaotic in the mathematical sense of the
word. A chaotic process is unpredictable in the long run, no matter
how much (finite) knowledge you have of the starting state. A typical
PRNG gives you 100% predictability if you know the algorithm and the
start state.


AFAIK, this statement is incorrect.

http://en.wikipedia.org/wiki/Chaos_theory

would seem to be in agreement with my understanding of the issue.

it would be a non-deterministic process which would be unpredictable, and
not a chaotic process, where a chaotic process remains deterministic, and
thus may be predicted given sufficient information (in much the same way as
a PRNG).


as I see it, a PRNG is a choatic deterministic process.


granted, then there is the philosophical issue of "global" or
"universal" determinism or indeterminism, however, in this case this
is not my focus of concern. we can just assume that chaotic patterns
in physical reality are non-deterministic.

Um, no. Chaos is not randomness. Chaotic processes /are/
deterministic. They're unpredictable (in the long run), but not
random. (That doesn't mean you can't have a process that is partly
chaotic and partly random. As Ian Stewart rightly said, "chaos and
randomness are two sides of the same coin, except that it isn't a
coin and it doesn't have only two sides.")


as I say, we can "assume" this, regardless of the actual "universal" state
of things...

personally though, I believe that the universe is itself non-deterministic,
however, I also believe that the past/present/future distinction is
ultimately meaningless, as all exist essentially at the same time, but the
process is essentially a sort of asymmetric "cone" WRT entropy, which
essentially forces us to "move" along in a single direction WRT time (AKA:
the past has not "gone away", and the future is not "being made", rather it
just seems like this is the case...).

not that I believe in fatalism though, since, as I see this, this would be a
rather incorrect interpretation of the process (AKA: even if all of the
future and all of the past exist at the same time, there may exist far more
futures than there exist pasts, or it could be that the universe has already
"collapsed" onto a single outcome, and as such the eventual "fate" of
everything is already been decided, but even as such, free-will and freedom
of outcome will at least "appear" to exist...).

or, stated in another way:
there is no "guiding hand of fate" to force any particular output, and
infact people have full free will, only that the entire future state (every
decision to ever be made, everything to ever exist, ...) may already exist,
only that they are invisible from the present state.

(or something like this...).


(or, even if not, that
they reprsent a MUCH larger state than is typically available to a
computer...).

Right.


either way, this was not the point of distinction, as I was saying, either
way, we can "assume" that the process is essentially random (or, at least,
it is very unlikely that this exact chain of events will be happening at
several different locations as to allow the RNGs to accidentially end up
with the same state).


<snip>

But if you mean that randomness
depends on how much information the user has or can gain about the
sequence that assists in predicting future numbers, you are
correct.


nevermind that none of this makes it "random" in a strict sense.

Well, I think it does, actually.


(I think an important piece of context has been lost here...).


but, as I see it, randomness is not purely observer specific, and hence, as
I see it, a PRNG is not "random" even if it appears to be.

even though the sequences from a PRNG and TRNG may "look" exactly the same
(from a statistics POV), I have often observed that computationally, there
are many more subtle differences.

similarly, many specific algos may demand one but prohibit the other in
order to work correctly.

consider, for example:
GUID generation (kind of sucks with a PRNG);
permutative hashing/caches (totally breaks with anything other than a PRNG,
as a TRNG would essentially make it impossible to retrieve the information
again, since the ability to locate the information again depends purely on
the particular pseudo-random sequence...).


similarly, I use limited PRNGs in things like the code-generator for my
compiler (related to optimization and register allocation), however, any
variation from the strict deterministic sequence would essentially break the
compiler (by throwing passes out of sync, essentially throwing the whole
process into chaos...).

(granted, this sort of dependency between compiler passes is not exactly a
good thing, but to do things better at present would require essentially
re-engineering this whole section of the compiler...).


determinism vs non-determinism is not a matter of observervation
(how much the observer knows or does not know).

But how much the observer knows - even if it's only in a meta-sense -
will affect whether he considers a process to be deterministic.


potentially, however this may not matter, since he may guess one way or
another, and still be incorrect.


<snip>

--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
"Usenet is a strange place" - dmr 29 July 1999
Sig line vacant - apply within


.

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