[pegasus]

> From Shannon's theory, it's abundantly clear that "information" is just a mathematical description

That's a very narrow and technical definition of information. It's what people refer to by the word when they discuss things like: communication, medium, surprise, compression, etc. in a technical context. Otherwise one should refer to the dictionary definition, so we don't end up talking past each other.

If you'd like to get a better intuitive sense of what "it from bit" points at, check out David Deutsch's Constructor Theory and the Stephen Wolfram Physics Project. Also, Bernardo Kastrup, on the philosophy front.