Tegmark's Platonia and TGD Platonia

Max Tegmark has published a book titled "Our Mathematical Universe" (see this about the idea that only mathematical objects exist objectively and mathematical object exists if this is possible in a mathematically consistent way.

Also TGD leads to this view. The basic problem shared with materialism is that the existence of mere mathematical objects does subjective existence. In TGD quantum jumps for the spinor fields in Platonia identified as the "world of classical worlds" consisting of space-time surfaces in $H=M⁴×CP₂$ obeying holography = holomorphy principle brings in consciousness and zero energy ontology solves the basic problem of quantum measurement theory and allows the experience of free will.

One of the participants of the discussion gave a short summary of the ontology of Tegmark. Tegmark proposes a multiverse with four levels, each more complex and abstract than the last:

1. Level I (Observable Universe): This is the most familiar level. In this view, the observable universe is just one of many pockets in an enormous (potentially infinite) space, all governed by the same physical laws.
2. Level II (Bubble Universes): Here, each universe (or "bubble") might have different physical constants and properties. It s like having different rules for physics in each universe one could have a different speed of light, while another might not have gravity at all.
3. Level III (Many-Worlds Interpretation): This level involves quantum mechanics. Every time a quantum event occurs, the universe "branches" into different outcomes, creating countless parallel universes. Think of it like a choose-your-own-adventure book that explores all possible story paths.
4. Level IV (Ultimate Mathematical Universe): This is where MUH comes in. Level IV is a collection of every possible mathematical structure, even those that don t resemble anything we would call a universe. According to MUH, each mathematical structure is a complete, self-contained universe. If a structure is logically consistent, it exists.

What about quantum Platonia according to TGD?

1. In TGD only the level I Universe expanded from real universe to adelic one to describe correlates of cognition is needed. The physical Universe is fixed by the condition that the structures involved exist mathematically. In the TGD framework the mathematical existence of the twistor lift of TGD fixes H=M⁴×CP₂ completely. Also number theoretical arguments fix H. Also standard model symmetries and interaction fix H. Space-time dimension is fixed to D=4 by the existence of pair creation made possible by exotic smooth structures as standard smooth structure with point-like defects identifiable as vertices for fermion pair creation. The mathematical existence of the Kähler geometry of the "world of classical worlds" (WCW) (space-time surfaces satisfying holography) fixes it. This was already observed by Freed for the loop space. Infinite-D existence is highly unique.
2. Level II Universe would be multiverse and is not needed in TGD since H=M⁴×CP₂ is fixed by mathematical existence and no spontaneous compactification leading to multiverse takes place. Inflation is replaced in TGD with the transformation of galactic dark matter as dark energy of cosmic strings to ordinary matter and there are no inflation fields forcing the multiverse (see this).
3. Level III Universe is not needed. The new quantum ontology, zero energy ontology (ZEO), leads to the solution of the quantum measurement problem and no interpretations are needed. It also leads to a theory of consciousness and a new view about the relation of geometric and subjective time. The implications are non-trivial in all scales, even in cosmology. One could of course call the hierarchy of field bodies as an analog of the multiverse.
4. Level IV Universe corresponds to WCW and WCW spinor fields M⁸-H duality relating number theoretic and geometric visions of TGD, holography= holomorphy vision, and Langlands duality in 4-D case implying that space-time surfaces are representations for complex numbers. Space-time surfaces can be multiplied and summed: this arithmetic is induced by the function field arithmetics for generalized analytic functions of H coordinates (3 complex and one hypercomplex coordinate).

   Space-time surfaces correspond to roots for pairs of this kind of functions and form hierarchies beginning with hierarchies of polynomials with coefficients in extensions of rationals but containing also analytic functions of this kind and even general analytic functions. The quantum counterparts of mathematical concepts like abstraction, concept, set, Hilbert space, Boolean algebra follow using the arithmetics of space-time surfaces.

5. Consciousness emerges from quantum jumps between quantum states as spinor fields of WCW representing quantum concepts. WCW spinors correspond to Fock states for the fermions of H and their Fock state basic forms a representation of Boolean algebra. One can say that logic emerges via the spinor structure of WCW which is a square root of geometry. Number theoretic vision implies the increase of algebraic complexity and hence evolution.

   ZEO allows the quantum Platonia to learn about itself by generating memory in SFRs and also makes memory recall possible: the failure of exact classical determinism for the space-time surfaces as analogs of Bohr orbits makes this possible. The seats of non-determinism represent memory sites (see this). Quantum Platonia evolves as a conscious entity as the WCW spinor fields defining conscious entities disperse to more and more algebraically complex regions of it.

See the article Space-time surfaces as numbers, Turing and Gödel, and mathematical consciousness and the chapter About Langlands correspondence in the TGD framework.

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.