Reply #84: I think your understanding of the word "chaos" here is the problem. [View All]

[Nihil]

You have a tendency to group the words "chaos" and "randomness" together
when they are actually two different things.

Chaos means an non-periodic deterministic behavior that is incredibly
sensitive to its initial conditions. This means that a tiny difference
in initial conditions for a chaotic system can produce huge differences
in the subsequent output.

Chaotic systems may look random but they aren't. They are repeatably
deterministic systems - ones whose results are predictable if you
have enough information (or control) at the start as they operate
by formula (often simple) or physical laws but which are very *very*
difficult to predict accurately if there are *any* variances in that
startup data.

Randomness is "a lack of order, purpose, cause, or predictability".
A random process is a repeating process whose outcomes follow *no*
describable deterministic pattern. Although, for a large enough sample,
they may follow a probability distribution (i.e., the expectation that
a certain percentage of the results will fall within certain limits)
the result of a single operation will not be predictable.

Truly random systems are not repeatably deterministic and thus their
results are not predictable regardless of the control or information
that you possess at the start of the operation.

Hence your comment:
> But if chaos and randomness have pasterns they are no longer chaotic
> and random
... is wrong. Chaos *does* (in fact *must*) have patterns and chaotic
systems will *always* result in such patterns. Only random systems do not
possess patterns (although human perception will often overlay a random
display with a false pattern as that's just the way that perception tends
to work with normal humans - but this is a different argument!).

Hope this helps.

:hi: