It may not surprise anyone here on the forum, but I disagree with Brian Greene concerning infinite dimensionality existing no matter how someone thinks they can divide the indivisible Multiverse into an infinity of finite universes. An infinity of fractal self-similar multiverses, yes, that I can see, but to tear apart a build up of dimensional complexity into a infinite number of pieces of that singularity, including pieces where complexity just keeps on piling on complexity to an infinity of dimensional complexity, from exactly the same base, that I cannot see whatsoever.
As an amateur complexity theorist, of which 'Chaos Theory' is a subsidiary of 'Complexity Science', I'm thoroughly tied to the realization that complexity, including multi-dimensionality which is simply a build up of complexity, collapses in on itself, or flattens out, at some finite point nowhere even close to infinity. So all of those bubble universes in his program would largely be "fractal self-similar", or as Will Durant said concerning history's physics, "history always repeats itself in large aspect, though rarely, if ever, in its fine detail."
All of the dimensionality of Multiverse will be recursive (repetitive) throughout an infinity of finite bubble universes (infinitizing multiverse self-similarity), but rarely, if ever, exactly duplicating in its fine grain detail (in other words, Multiverse -- as large aspect-- is not a constituent -- fine detail -- multiverse element of the set Multiverse). All of them will have zone dimensions of lifelessness on the way to zone dimensions of life capability and zone dimensions of life capability on the way to zone dimensions of lifelessness. That they can and will intermingle in lumpy mixes should be a given, as Stephen Hawking foresaw when he wrote of life possibly migrating always to stay in life zones.
Multiverse multi-dimensional possibility was also put on display in a Star Trek segment when the crew is all members of a totalitarian state and some of the crew accidentally cross-switch rails and trains (so to speak) between paralleling universes. Now that is Multiverse multi-dimensionality on full display.... Large aspect repetition to infinity, difference in fine detail to infinity, localized fractal self-similarity (but not quite exact duplication (for reasons given long ago exact duplication of detail does occur in an infinity but would never be realized to actually exist as such because exact duplicates overlay and inlay to exactitude; to just one and the same)).
Brian Greene, to me (as an amateur complexity theorist), blew it at that point. He wants a numbers game to infinity regarding infinite Universe, try this base2 binary (('1') and/or ('-1') / ('1') and/or ('0')). Those infinities of [divided] finite bubble universes are infinities (plural) for the simple reason that energy is conserved thereby in the finitude. The infinite Universe needs no conservation since it has no energy (one might say of its own) to it and, therefore, no time (of its own) to it. Relativity breaks down. Complexity collapses. Entropy is inexorable. Building dimensionality on dimensionality, on dimensionality; or shoveling dimensionality into dimensionality, into dimensionality; will burn it out, blur it out, deforming and doing away with the very existence of dimensionality as such (thus a dimensionless point, an infinity of point infinitesimals, an infinitely flat-smooth surface Universe (an infinite Big Crunch Vortex (Big Hole Vacuum) (Big Mirror Mirroring ('1') ('-1').... Multiverse).
It seems I need to at least partially explain my whole model every time simply to fulfill explanation of the why and how of disagreement with how such things as multi-dimensionality is visualized. Even with the premise of the thing being visualized. Brian Greene essentially said that a string is a superpositioned singularity: Or more likely pairs of them pairing to spring strings, which is then their transformation and endings. He didn't say it outright, but I think it is what he said without saying it. Now that part I would heartily agree with (even though he didn't say it outright), since I've already modeled such a possible transformative relationship myself.
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