Engineering lives on a continuum from almost pure maths to pure cookbook canned solutions, with a much smaller arrow going in the opposite direction from unexplained observations to theorising and model building.

Things like Shannon's description of information-as-entropy were certainly a mathematical discovery about engineered systems, and led directly to a lot of coding and data compression theory.

There wasn't a whole lot of interest in quantum channels at the time, so the fact that the theory fed something back to mainstream physics was a bonus.