Re: real random

In <h964tt$fsd$1@xxxxxxxxxxxxxxxxx>, BGB / cr88192 wrote:


"Richard Heathfield" <rjh@xxxxxxxxxxxxxxx> wrote in message
news:HfWdnXAh4MuY4yvXnZ2dnUVZ8l2dnZ2d@xxxxxxxxx
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.

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.

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.")

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

Right.

<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.

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.

<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
.

Relevant Pages

  • Re: real random
    ... One might say that the randomness of the ... A chaotic process is unpredictable in the long run, ... PRNG gives you 100% predictability if you know the algorithm and the ... "universal" determinism or indeterminism, however, in this case this ...
    (comp.lang.c)
  • Re: Does True Randomness Exist?
    ... fundamental randomness at the core of reality. ... In a purely deterministic universe, ... and the classicist insistence on fundamental determinism. ...
    (talk.origins)
  • Re: Free will
    ... What determines what you imagine? ... So if you don't fully understand it, how can you exclude randomness? ... seems you're as interested in determinism as I am to indeterminism. ... sense of choice or responsibility with randomness, ...
    (comp.lang.lisp)
  • Re: PI random? Debate running in circles (you try making math jokes)
    ... underlying bedrock of determinism somehow. ... at the beginning of the universe quantum mechanics was NOT random at ... The indeterminacy which you ... what this means for understanding randomness? ...
    (sci.math)
  • Re: signs of life in martian meteorite?
    ... [SNIP] ... it a third time as well. ... Not only do mathematicians know no such thing, ... specialise in randomness. ...
    (talk.origins)