Our external physical reality is a mathematical structure. That is, the physical universe is mathematics in a well-defined sense, and in those [worlds] complex enough to contain self-aware substructures SAS [they] will subjectively perceive themselves as existing in a physically 'real' world (- Max Tegmark's mathematical universe).
Although it was not the original intention, as this model progressed over the past 13 years (I began in 2003) the axioms began to resemble those of the ancient philosophers and teachers, particularily the Greeks, and so to make this theory more interesting to the non-technical reader I began to weave this theme into a book, what began as a series of notes eventually becoming a text entitled Plato's Cave, after Plato's Allegory of the Cave (from Plato's The Republic) for Plato also casts doubts on our space-time world-view (our cave-wall).
Strangely these axioms of the Ancient Universe, although starting as a mere curiosity, began to direct the theory itself, leading finally to this mathematical universe, why this should be so has become an interesting question in itself. Likewise the philosophical implications are also most intriguing for the simplicity of the theory suggests the role of an Intelligence. Could physics be forced to accept that the most probable explanation for our universe is as a simulated (programmed) environment and thus the universe itself becomes evidence of Intelligent Design? ... for a programmed virtual universe suggests a Programmer.
Nevertheless, to separate the physics and philosophy debates I have set up two independent websites, the other website for the non-technical introduction, that site also links the ebook (online) which discusses the points raised here in much greater detail and so may serve as a reference to those who are interested in this model...