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 the randomness
and thereby making it predictable to a certain degree it can not be
predicted. No conclusions can be drawn so no rules or knowledge can be. - If the system is infinite there is no single rule which is absolutely
true 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.


Ali Polatel


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