The greatest mystery of mathematics is, to me, that all of these patterns and logical systems appear to almost (and autonomously) seek higher-dimensional self-representations. In category theory or combinatorics we can relatively simply determine and demonstrate the way a set of properties or relationships seeks something of an implicit, intrinsic and endemic higher-dimensional geometry.
The question becomes not one of how, so much as why and to what extent material (as much as cognitive) reality also reflects this endlessly unfolding geometric metamorphosis towards autonomously self-propagating recursive and endlessly extensible system evolution. If the natural orientation of distributed patterns of information and energy is itself towards abstract forms of geometric dimensionality, then what is the effective endpoint to such a hyper-inflating referential space of relationship and possibility?
Are we missing something fundamental about the nature of identity and information? Is there some sense in which distributed patterns of similarity and encoded structural or systemic behaviour indicates that information systems need not always be causally-connected to possess unity, or – otherwise rendered, is it the case that there exists forms of system unity and subtle presence of encoded structure that is not dependent upon physical, material proximity? Is there, in short, another form of information and reality in some sense inside this one, mysterious and distributed across the entire surface of this world? Is information, artefact or entity (and sentience) actually a property that is not discernible in its parts but only ever in its inexplicable and incomprehensible, entangled wholes?
Finding the right words is difficult but, for what it’s worth, I am not certain that these things can ever be directly, unproblematically or reductively captured by symbolic logic, either.