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.
Bruno
--
Ali Polatel
http://iridia.ulb.ac.be/~marchal/
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