santosh said:
Possible, though I would've thought that presented with a sequence
that's apparently random you cannot conclude that it *is* random since
reading more of the sequence might reveal a pattern or organisation.
And for a sequence of fixed length to say definitively that it's random
would be to close the door to a possibility that future mathematics
could find an organisation not apparent now.
I don't think you have to look at quantum effects in physics to
find something that for all intents and purposes is truly "random".
Consider, if you will, a drunk at a craps table...you can't be sure
he won't fling the cubes right off the table, drop them right in front
of himself, or actually make a legal throw to the back of the table,
hitting those little bumps that send them spinning unpredictably
to their final resting place...
And yet, with a sufficiently high-speed camera(s) to record
the approach of the dice to the wall, a super-fast super-computer
dedicated to calculate the trajectories of the dice based on the
inputs from the camera(s) and a model of the countours of the
table, could you "predict" in a split-second the result of the dice
throw AFTER the dice were thrown? Be aware that just such
a (sometimes human) system was developed to predict the
quandrant where the ball would land in roulette ("wheel clocking"),
resulting in tremendous profit for the players of the "system"...
And also, some people allegedly can or at least try to "set the
dice": hold them in a pre-determined position, and throw them in
such a way that they can somewhat predict the result. This is
so potentially profitable it is totally illegal in all casinos; if they
catch you holding the dice and throwing them in a certain way,
you will be asked to change your behavior, leave, or be arrested...
In those cases, an apparently random system becomes "non-random"
(read "predictable") due to information about or control of the
"randomizing"
process. In cases where the result was predicted by high-speed
analysis of the process, the tests that the math wonks apply to
determine randomness would still apply; of course, when the process
is "controlled", the tests will show the process is no longer "random",
at least from that perspective...
So it's always actually a matter of how you look at it, how much you
know about the process, how deftly you can analyze and/or control
the process, that is the final test of whether something is truly "random",
as in "unpredictable". History shows many examples of "unpredictable"
series of events becoming "predictable" as greater knowledge of the
underlying process and/or better analytical capabilities were developed,
and perhaps this will be the case someday for "quantum physics" as
well (Einstein: "God does not play dice with the universe").
But right now, predicting what a drunk in Vegas is going to roll BEFORE
he rolls it can be pretty safely called "impossible"...