Phil,
I am digging deeper into your essay, and getting a better understanding of the necklace algebra you are proposing: "it can be interpreted as the emergence of
string field theories in continuous space and time from algebras based on quantised information,"
I think I am in agreement with the general idea. In my definitions, I associate information with uncertainty (which is consistent with Shannon). I am associating knowledge with what most people view as information, which is the sense of Wiener. In any case, the relative information, e.g. shared knowledge is what we are interested in. That is limited by quantum mechanics. In my interpretation of what you are saying, the idea is that we could build algebras based on the quantization of mutual information, which must be limited, which I am taking to mean there is a least element that can be defined. I like the idea of algebra building in general, so I find your essay to be very helpful.
On another note, what are your thoughts on the apparent similarity of ideas that seem to be popping up from different corners?