The Pythagorean Ensemble is ontologically the first layer of the structure of reality. It includes primordial Phase-1 of the Two-Phase Cosmology.
The Void (0|∞) is not an empty space or a physical vacuum. It is a pre-physical background from which all consistent mathematical structures may emerge. Because there are no spatio-temporal constraints yet, it “contains” all coherent and unchanging mathematical forms – all sets of internally consistent mathematical relationships, which includes the totality of all physically possible universes, histories, and processes except those that encode conscious organisms. This is a strong form of what is usually referred to as mathematical Platonism: any logically coherent structure exists, in a timeless and spaceless way, within the realm of formal possibility. I prefer to call it Pythagoreanism. This is because Plato didn't stop at mathematical structure, but also included a whole range of “forms”, such as the “perfect table” from which all other tables are ultimately derived. There are no tables in the ensemble I'm describing – there are informational structures that resemble tables, but nothing can actually be a table without a conscious being such as a human assigning that specific meaning to it. There's no perfection in the ensemble either, for the same reason.
Within 0|∞, every mathematically valid but non-conscious cosmos exists in superposition. Not “in parallel universes” in the physical sense, but as informational structures with complete internal logic. Some correspond to universes with no stars, some to universes with strange physics and some to our own universe, including the entire history of our cosmos from Big Bang to Earth’s early biosphere. These are not “happening”. There is no time or change yet, only possibility. They simply exist as coherent totalities in the Pythagorean sense.
This is a structural and logical starting point, not a temporal one. In some ways it is similar to the Many Worlds Intepretation of QM, and the multiverse of all cosmoses. It is structurally identical to Max Tegmark's mathematical multiverse, apart from one thing: MWI and Tegmark's multiverse are both essentially materialistic notions, which have nothing to say about consciousness. Therefore they contain all possible timelines, and all possible cosmoses, including (since no exceptions are made) all possible timelines involving conscious beings. Conscious beings in these models are just “along for the ride”. Our own lives, as we experience them, are nothing more than random walks through a meaningless multiverse. There is no difference between possibility and actuality – all worlds are actual.
So there is a crucial difference in the model I am describing: the Pythagorean ensemble is only a collection of possibilities, not actualities. If all of these possibilities were as real as the reality we actually find ourselves in, then the standard anthropic solution to the fine-tuning problems in cosmology would apply: all possible realities exist, and only in those which contain intelligent beings such as humans does anybody ever ask questions about how they came to exist. This would leave us with no new scope for progress on the other problems on our list, including the mind-splitting problem of MWI.
We are now talking about a very different situation to wondering how our particular reality can come from nothing. The entire problem space has been turned on its head, and we are left with a very different question: if only a small proportion of these possible worlds become actual worlds, what determines which of the possibilities are actualised? Instead of needing to explain how reality can be constructed from nothing, according to a set of laws we can't explain the origin of, we need some sort of “mechanism” which selects specific realities from the vast range of possibilities.
Next section: The Embodiment Threshold | Two-Phase Cosmology