Algorithmic information theory
The first was generated with a random number generator, for example by throwing a coin. The second is easier to describe (eight times "1", then eight times "0"). For this reason, the first sequence has more algorithmic information, because it is harder to shorten ("compress") the description on how to generate it. Shortening the description may not be possible at all. The information value of a string is higher, if it is more difficult to shorten ("compress") its description. Random strings and white noise do not contain patterns that occur again. For this reason they cannot be compressed, and have a higher information value.