Random algorithm

[Randall Reetz]

Thank you Francois,

Can statistics be rigorously derived from proability math?  I hope so.  Both are heavily dependent on what appears to be statistics ("both" refers here to my twin gods).  I am a self admitted thermodynamics and information science freak.  I'd hate to think that my whole world was anecdotally argued.  I do see a strange but familiar symmetry between the finite/infinite distinction that seperates probability theory and practice, and the open/closed system maths that seperates the thermodynamic engineering from pure science.

Randall

-----Original Message-----
From: "Eric Chatonet" <eric.chatonet at sosmartsoftware.com>
To: "How to use Revolution" <use-revolution at lists.runrev.com>
Sent: 11/13/2008 9:51 AM
Subject: Re: Random algorithm

Bonsoir François,

Great post indeed :-)
I fully agree.

Le 13 nov. 08 à 18:47, François Chaplais a écrit :

>
> 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.


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