On 08 Dec 2013, at 21:59, Ali Polatel wrote:

I have been following this list for a while and some idea popped up to my mind today which I'd like to ask/share. I don't know if there are resources about this and I'd love to read any reference you can direct me to. (I am eager to learn so I thought finding something to read about this is a miraculous idea to start :) - The predictability of a random system is dependent on its limits. (You roll a dice, the limit is 1-6 so it has a higher predictability than a dice which has more surfaces and numbers than a common dice.)- If there is no limit defined for the system to restrict therandomnessand thereby making it predictable to a certain degree it can not bepredicted. No conclusions can be drawn so no rules or knowledge canbe.- If the system is infinite there is no single rule which isabsolutelytrue because there is no functioning boolean values for the reference system in question.

`Use sigma_algebra. or lebesgues measure. The only problem is that`

`infinite intersection of subset would define an event, with Boolean`

`algebra. But the probability to send an arrow on a circular target, at`

`the point (sqrt(2), sqrt(2)) does not make sense, so it is preferable`

`to not making a singleton (like you can get with infinite`

`intersection) into an event. Work with open interval, or more`

`generally with a sigma_algebra.`

If it is possible to deduce: - When a system is infinite, either it is either an illusion of our truth determining facility (perception, belief etc.) or anything we know about it has no absolute true/false value. Is it possible to determine if anything is infinite?

`No, but even in the finite case, probability will often use laws of`

`large numbers, indicating that a treatment with integral on infinite`

`space will be more handy and efficacious than the use of a finite`

`space and its boolean structure. Measure theory is the name of the`

`theory handling those infinities.`

`For example, If you take the n-iterated self-duplication, up to n =`

`30, the statistical distribution is the finite binomial, but above (n`

`bigger) you will use the continuous Gaussian distribution.`

Bruno

-- Ali Polatel

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