random

[Nick Perkins]

"Alex Martelli" <aleaxit at yahoo.com> wrote in message
news:9fb0ju01a8a at enews2.newsguy.com...
> "David C. Ullrich" <ullrich at math.okstate.edu> wrote in message
> news:3b18ea18.332276 at nntp.sprynet.com...
>     ...
> > I said you cannot have complete information about
> > a physical system. You can't. An algorithm is not
>
> Let's take your original sentence again, snipless:
>
> """
> A physical RNG can have the property that one cannot make
> any prediction about the value of the next bit even given
> _complete_ information about how the numbers are being
> generated.
> """
>
> This says "GIVEN _complete_ information".  Now you say
> you CANNOT "have complete information".  The two
> statements are in contradiction.  If you cannot have it,
> how can it be given?  I don't see why you keep denying
> this obvious contradiction.


This is not a contradiction.

if we define predicates:
I : have complete information
P : can make prediction

then the first statement is:
I implies (not P)

and the second is:
(not I)

The conjuction of these axioms implies that I is false,
but says nothing about P.
Both of these statements can be true regardless of whether P
is true or false.

The second statement renders the first irrelevant,
but does NOT contradict it.