Random algorithm

[François Chaplais]

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" <randall at randallreetz.com>
> To: "How to use Revolution" <use-revolution at lists.runrev.com>
> 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.