In a way, the relation between “physics space” and “information space” is one of the topics I address in my work on inquiry driven systems. Here is a pertinent place in medias res, from which point one may happily sample both backwards and forwards:
Part of my task in the projected work is to make a bridge, in theory and practice, from simple physical systems to the more complex systems, also physical but in which new orders of features have become salient, that begin to exhibit what is recognized as intelligence. At the moment it seems that a good way to do this is to anchor the knowledge component of intelligent systems in the tangent and co-tangent spaces that are founded on the base space of a dynamic manifold. This means finding a place for knowledge representations in the residual part of the initial factorization. This leads to a consideration of the questions: What makes the difference between these supposedly different factors of the total manifold? What properties mark the distinction as commonly intended?
From a naturalistic perspective everything falls equally under the prospective heading of physis, signifying nothing more than the first inklings of natural process, though not everything is necessarily best explained in detail by those fragments of natural law which are currently known to us. So it falls to any science that pretends to draw a distinction between the more and the less basic physics to describe it within nature and without trying to get around nature. In this context the question may now be rephrased: What natural terms distinguish every system’s basic processes from the kinds of coping processes that support and crown the intelligent system’s personal copy of the world? What protocols attach to the sorting and binding of these two different books of nature? What colophon can impress the reader with a need to read them? What instinct can motivate a basis for needing to know?