  Ever since its foundations were laid nearly a century ago, quantum theory has
provoked questions about the very nature of reality. We address these questions
by considering the universe, and the multiverse, fundamentally as complex
patterns, or mathematical structures. Basic mathematical structures can be
expressed more simply in terms of emergent parameters. Even simple mathematical
structures can interact within their own structural environment, in a
rudimentary form of self-awareness, which suggests a definition of reality in a
mathematical structure as simply the complete structure. The absolute
randomness of quantum outcomes is most satisfactorily explained by a multiverse
of discrete, parallel universes. Some of these have to be identical to each
other, but that introduces a dilemma, because each mathematical structure must
be unique. The resolution is that the parallel universes must be embedded
within a mathematical structure, the multiverse, which allows universes to be
identical within themselves, but nevertheless distinct, as determined by their
position in the structure. The multiverse needs more emergent parameters than
our universe and so it can be considered to be a superstructure.
Correspondingly, its reality can be called a super-reality. While every
universe in the multiverse is part of the super-reality, the complete
super-reality is forever beyond the horizon of any of its component universes.
