Comment Re:Every so often (Score 1) 140
Not "In fact" but rather "Additionally", because those two observations about randomness are independent of each other.
There is a clear difference between
1. very occasionally "a pattern appears" randomly in the random data sequence (and yet it is apparently still perfectly random) ...
and
2. a perfectly random sequence can nonetheless be an encoding (representation) of something else that is non-random.
I must admit it is hard to think clearly about the semantics of "randomness".
For example, does an infinite-length random sequence necessarily contain non-random subsequences, in fact, ALL non-random subsequences?
This is the Boltzmann brain issue generalized to non-physical random sequences.
I guess, when we "check" a sequence for randomness, we have to ASSUME we are not so terribly unlucky as to be checking during the infinitesimally rare time period of the sequence generation in which it's generating regularity purely by accident. How many times its it sufficient to sample different parts of the sequence to be sure it is not "usually somewhat regular". What if we are extra unlucky and are in the middle of a very long accidental regularity in the sequence?
So can we ever be sure something is random just by looking at the random data sequence?
Or must we instead analyze its generation process and say nothing could predict that process exactly, so we may as well say its output data is random.
There is a clear difference between
1. very occasionally "a pattern appears" randomly in the random data sequence (and yet it is apparently still perfectly random)
and
2. a perfectly random sequence can nonetheless be an encoding (representation) of something else that is non-random.
I must admit it is hard to think clearly about the semantics of "randomness".
For example, does an infinite-length random sequence necessarily contain non-random subsequences, in fact, ALL non-random subsequences?
This is the Boltzmann brain issue generalized to non-physical random sequences.
I guess, when we "check" a sequence for randomness, we have to ASSUME we are not so terribly unlucky as to be checking during the infinitesimally rare time period of the sequence generation in which it's generating regularity purely by accident. How many times its it sufficient to sample different parts of the sequence to be sure it is not "usually somewhat regular". What if we are extra unlucky and are in the middle of a very long accidental regularity in the sequence?
So can we ever be sure something is random just by looking at the random data sequence?
Or must we instead analyze its generation process and say nothing could predict that process exactly, so we may as well say its output data is random.