Can a string of data be both random and meaningless?

[Yoni]

It is convenient to assign high randomness high information.
Random patterns, however, supposedly present no meaning. So how can information be meaningless?

What is "meaning" and is it relative to "the observer"?

 

[sophiecentaur]

One way to look at it is that a truly random string of data would need more information to transmit it faithfully than a non random string. With a non random string, it would always be possible (in principle) to send less information to reconstruct it perfectly.
The random sequence may have no 'meaning' to an observer but it could, for instance, be necessary to record or transmit that sequence. It has then 'acquired' a meaning or relevance to an observer.

To establish 'just how random' a string of data is, it would be necessary to analyse it. That would involve looking at a very long (infinite) string of data if you really wanted to be sure. Within a string of truly random data, it would be quite possible to find a string of 11001100110011001100110011001100, which, on its own, would not appear to be random.