[extropy-chat] what is probability?
gts
gts_2000 at yahoo.com
Tue Jan 16 18:20:55 UTC 2007
On Tue, 16 Jan 2007 12:23:35 -0500, Benjamin Goertzel <ben at goertzel.org>
wrote:
> How does this help with the PI and so forth? Not at all as far as I
> can tell, it's just the only work I know that formally addresses the
> issue of defining randomness ;-)
In 1928, Richard von Mises published _Probability, Statistics and Truth_,
which pretty much started the frequentist revolution in probability.
In that book he developed two supposed 'empirical laws of probability':
The first law was not entirely original to him (he was following after
Venn, famous for Venn diagrams, and after someone else whose name I don't
recall). This first law is the law that relative frequencies converge as
the number observations increase. As everyone knows, if you flip a fair
coin enough times the % of heads will converge on 50% to any degree of
precision.
Von Mises' second law was his own 'discovery': it is about the definition
and meaning of randomness, what I have called here "The Law of Excluded
Gambling Systems".
Principle of the Impossibility of a Gambling System
http://www.philosophyprofessor.com/philosophies/impossibility-of-a-gambling-system-principle.php
I don't think the frequency definition of "random" has changed very much
since then, though Popper and some other people have attempted to improve
on von Mises' theories.
-gts
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