Dear Pragmatic,
very pleasant read indeed. A message that builds up during reading but also, it seems, during writing! Nice narrative idea and style.
Perhaps my favourite passage is the one in which you admit to ignore why the All displays recurrent, reproducible, often self-similar subsystems, but identify in these features the key for an effective coupling with the mathematical language, which delivers simplified universal models that are reproducible and reusable. So, the marriage between a world with much regularity and a language with much 'universality' (absence of human baggage) and reproducibility appears, at least at first sight, very possible, although your treatment, being necessarily concise, cannot dig into the details, where the devil is often hidden (in marriages in particular...).
With respect to the question of why features such as regularity and self-similarity, interspersed with chaotic ones, are so frequently observed in the subsystems of this world, let me just point out that the assumption of a fundamentally algorithmic nature of the universe appears to some physicists, e.g. S. Lloyd, as a very attractive explanation (the last figure in my essay illustrates the idea).
Your essay is one of the few I've read so far that offers - starting from the title - a generous attempt to address the very hard question about possible alternatives to mathematics for modelling the observable world. The requirement for such an alternative model to support predictions beyond the 'wait and see' barrier, and to describe many subsystems, not just one, is also very well stated in several passages.
The answer you provide to this hard question is appealing, at least at first sight: use subsystems for modelling subsystems - establish a reproducible link between them. It's also a very economic solution, in that it does not bring on stage new actors. The example of Analogue Gravity explains well the idea.
But your proposal triggers a question.
The marriage between mathematical model and physical subsystem is asymmetric, in the sense that the model abstracts away the details of the modelled object: it represents an equivalence class of phenomena (subsystems), each happening at different places and times. In the subsystem-subsystem marriage, this is lost: both subsystems have fuzziness, so to speak. One might suspect that mathematics is still necessary, for extracting the universality behind BOTH of them.
Thanks and best regards
Tommaso
P.S. Is there not any Pragmatic Computationalist in your wider family tree?