Does a random sequence contain information? I certainly hope so:
Regularly, in most of my lectures, I refer to a "random sequence" of
random variables. If they do not contain information, then I, and my
fellow statisticians, have done a fantastic job of hoodwinking the world.
(I'll keep my paycheck, thank you. :-)) The entire subject of statistical
inferences is based on the premise that random sequences CAN be gleaned
for useful information ("information" used in a nontechnical sense). Apart
from this reality, most of modern science could shut down. (And Glenn
could stop telling his company where to dig its next oil well -- allowing
him even more time for the reflector. :-))
It is true that most statistical models assert that a random sequence
contains a COMPONENT of "noise" -- devoid of information. Perhaps this is
what some discussants are thinking about. Beyond this, any useful model
contains a component for "signal" or "the true measurement" - apart from
noise, or whatever, depending on the context. Sometimes the "signal,"
itself, is permitted some randomness as well.
Gordon Simons