Here's a question I've been fruitlessly pondering a long time.
Where does information come from and is there even such a thing as "new" information? In other words, when someone writes down a mathematical theorem, have they just created new information or was the theorem always "out there" waiting to be discovered? What about the specific arrangement of molecules that we call the Mona Lisa or the silly limerick I composed yesterday?
Put another way: is information a form of energy and therefore does it obey the laws of thermodynamics, implying that it can neither be created nor destroyed, and can only be changed from one form to another? If it is, then when I composed that limerick, what other information did I change, destroy or use up in composing my limerick? On the other hand, if information isn't a form of energy, does that mean we can create something out of nothing?
There's a related question in maths: is maths invented or discovered? Do numbers have a meaning and existence independent of our own perception of them? I come down on the side of it being discovered but it's a weakly held view. To my knowledge, there isn't a consensus answer to this question.
After posing this question to a few people (and not yet having received an answer), I came across John Wheeler's "it from bit" information-theoretic view of physical reality. This might be related to and even answer my question. I'm not sure yet as I'm still digesting what Wheeler was getting at. It's also possible that his characterisation answers a different (opposite) question, namely, where does physical reality come from, and not, where does information come from.