Le 13 nov. 08 à 03:39, Randall Reetz a écrit :
And another problem is that a random and unique solution actually
reduces randomness as it is run. Each time you eliminate a number,
the set of numbers left is reduced. This is even true of an
infinate number randomizer. Sometimes i wonder if this fascination
with random number generation isnt a good diagnosis of severe case
of the geeks.
maybe it is just a lack of mathematical background
-----Original Message-----
From: "Randall Reetz" <[EMAIL PROTECTED]>
To: "How to use Revolution" <[email protected]>
Sent: 11/12/2008 6:18 PM
Subject: RE: Random algorithm
There is a huge difference between random and unique. If you are
after unique then just use the counting numbers. If you need both
random and unique you will have to check each number generated
against a saved list of every previous number. There is nothing
wrong with a random number generator that spits out duplicate
numbers. Random is blind to history (and future). Random is not
nostalgic. A coin with two sides is just as good at random as a
pair of thousand sided dice.
actually, random is so little nostalgic that a random sequence of
zeros and ones (with equal probabilities) can produce ones for a
zillion consecutive ones without invalidating the probabilistic model.
This fact holds (mathematically) as long as the number of events is
finite (which is always the case in practice). The central limit
theorem only holds for an "actual" infinite number of values.
Of course, some may object that having a zillion consecutive ones is
unprobable; however, this assumption itself can only be verified by
repeating the experience an actual infinity of times, so we're back to
the same modelling problem.
In practice, people do not refer to probabilities but to statistics.
As far as I know there are two schools of statisticians (at least when
it comes to teaching)
1) the "clean" statisticians present statistics as an offspring of
probabilities; it is mathematically clean but has the same weaknesses
when to it comes to confronting the model to the experiment.
2) the "dirty" statisticians admit that if your random process
produces a zillion ones, then you have to pull the trigger on the
model, arguing that modelling the sequence by a constant is closer to
what happens and as economical as the flawed statistical model. A
zillion or two zillion limit: you chose.
Now, if you admit that computers are deterministic, then, knowing the
initial state of your machine (which may be LARGE), you are able to
predict every output of it provided you know the inputs. Relying on
unmodelled input (such as the time at which you computer is turned on)
only makes the thing unmodelled; it does not garantee randomness.
If you go further, if all comes to a problem of semantics: what people
want with random series is a user triggered event that will defeat
prediction (that's what the las vegas folks want). However this
definition is severely hampered the the limitations of the existing
languages (man or machine language). You should consider the
possibility that one will produce a language/model that can predict
what happens.
cheers,
François
P.S. on the lighter side, my wife's experience with M$ Word on the PC
suggest that a large amount of Word's behaviour is unpredictable.
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