I appreciate your oft-repeated sentiment along those lines. But, your shannon-communication definition of life, even if simple and elegant by itself, does not provide a clear or sharp demarcation between life and non-life. And that has nothing to do with a limitation of math nor a limitation of the physical world or a physical discription, nor, as you imply, a limited ability to communicate about it. It's quite simply that the model doesn't fit the data completely. Examples are simple organic molecules and artifical life systems. At any rate, this model brings one much closer to the fringes of life and greatly shortens the distance from life to non-life than most biological definitions. It's far easier to conceptualize, using your definition, how spontaneous generation of communication can occur in an molecular soup.
...Hence, the difficulty in our making a connection. Perhaps we ought to quit trying?
That's generous of you. Please feel welcome to jump in, again, any time. In any case, thank you for your posts.
When we were investigating abiogenesis using Shannon (which did give it a level playing field as you suggest) - we surmissed that there was no origin for information (defined by Shannon and paraphrased "successful communication") in space/time. We had looked at Kauffman and dismissed Maxwell's demon but we hadn't yet considered string theory or geometry.
It sounds like you have a idea how communications might have been bootstrapped into a primordial soup or primordial pizza. I'm very, very curious what you have in mind!