Unprovability and undecidability are fundamental features of our world. We can know that it is order when we see it. But we cannot know that it is not order just because we cannot see it and no mathematics, logic, or computers can help us. Order is order. The rest is undecided.
Information is associated with entropy, a measure of thermodynamic disorder.
Information cannot be defined without knowing the context. Not because there is anything wrong with our notion of information, but because the notions of order and randomness necessarily include an element of subjectivity. Complexity appears midway between the predictable and the unpredictable, the stable and the unstable, the periodic and the random, the hierarchical and the flat, the closed and the open. Between what we can count on and what we cannot. Complexity is to be measured not by the length of the message but by the work carried out previously.