Modeling Reality
Below is a rough draft trying to explain Langan’s CTMU in brief. It’s not as accessible as I had hoped it would be, but it’s a work in progress. I also take a more confident tone but should not be taken for a serious authority on the matter (in all honesty, there is but one). I am happy to answer any questions I can.
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The mind ordinarily models new phenomena by selecting a similar, known phenomenon and corresponding formalism, and applying this to the new phenomenon as a metaphor. It then makes any necessary permutations, occasionally generalizing the original phenomenon and formalisms to subsume the original and new phenomenon. Waves are an example of this. We intuitively understand waves from experience, and apply this intuition when studying acoustics or mechanical action. We discover all of these describable as solutions to a second order partial differential equation. This gives us a new wave concept of which water, acoustic, and mechanical waves are specific implementations. Our minds encountered a phenomenon, borrowed and applied a metaphor, generalized its intuition and formalisms, and subsumed new and old phenomena under the generalization.
Electrons are another example of this. The Ancient Greeks imagined matter composed of indivisible, variously shaped objects moving randomly, semi-randomly, or deterministically. Electrons, similarly flung around by electromagnetic forces, aren’t fully describable by such billiard ball models. Scientists added wave and billiard ball formalisms to effect a new quantum mechanical description of particles. In this case, the mind combined concepts, effecting a more effective concept.
We think similarly about Reality[1]. Sometimes Reality is an egg, a balloon, or a rubber sheet; sometimes billiard balls riding pilot waves. This completely fails. Reality must self-contain. Langan argues this convincingly: If there were something relevant outside Reality it would be included in Reality by definition. This prevents Reality from being a set; sets have self-containment issues. Mental tools such as billiard balls cannot self-contain or self-explain; Reality must do both.
Langan uses a different approach: Reject the mind’s subservient tools and take mind itself as the metaphor; take language as the corresponding formalism[2]. Language, being the most general meaningful mathematical structure available, still fails in describing mind and reality; we must augment it for self-processing and self-containment. Langan achieves this by replacing language’s terminal and non-terminal symbols, and grammatical transformation rules, with objects containing both called syntactic operators. He’s infamous for neologisms like “syntactic operator”, but the term fits. Self-configuring, self-processing language (SCSPL) results from this augmentation[3].
Symbols cannot self-process and don’t contain their grammatical substitution and transformation rules. Grammatical rules alone don’t contain the symbols they govern. Theories built from languages separating symbols and grammatical substitution and transformation rules typically prescribe an external space containing objects governed by external rules. Self-containment precludes this situation from adequately describing Reality. Self-containment permits and obligates us to merge grammatical rules and symbols into “self-dual” objects; they are inductively defined and lack full definition apart from mutual reference. Hence, we arrive at syntactic operators. Self-processing syntactic operators in place of grammatical symbols, and substitution and transformation rules are SCSPL’s objects. It’s worth pointing out this includes non-terminal and start symbols in addition to terminal symbols.
We complete the process saying any being, happening, or object formally equivalent to a syntactic operator is a mind. Reality is a mind equivalent to the syntactic operator acting as its start symbol; you are a mind equivalent to a non-terminal syntactic operator; an electron is a mind equivalent to a terminal syntactic operator.
Langan took mind itself as the metaphor for Reality in place of billiard balls, eggs, or rubber sheets. He applied mind and linguistic formalism, developed a new (meta-)formalism resolving the resulting discrepancies called SCSPL, generalized the concept of mind, and declared Reality a self-contained mind containing all others; applying the process above at a higher level. This gives us a theory of reality in the form of SCSPL. Unapplied theories are meaningless, so we must apply SCSPL theory to Reality. The branch of mathematics dealing with applying theories is called model theory.[4] Model theory’s main objects are languages, theories, universes, and models. A language is a collection of symbols combined with formation rules determining valid and invalid strings of symbols. Theories are built from languages by adding additional axioms and rules of inference further restricting valid expressions. E.g. A first order language augmented with the Peano axioms is the theory of arithmetic. Langan makes the argument a theory can be considered a language with further grammatical restriction. A universe is a (co)domain containing objects our theory applies to. A model is a mapping from language to universe. The reader may find better explanation elsewhere.
SCSPL and the Real Universe are respectively the CTMU’s theory and universe. In the CTMU’s abstract Langan writes:
“...the goal of providing a scientific model and mechanism for the evolution of complex systems ultimately requires a supporting theory of reality of which perception itself is the model (or theory-to-universe mapping).”
Generalized perception interprets SCSPL theory in the Real Universe, the Real Universe comprising all perceptions. This correspondence makes the CTMU “supertautological”: “Tautological” because it must be true that Reality’s measurements interpret its correct theory; “super” because this is a language and system level construction, not a statement or measurement level construction. Perception maps SCSPL syntactic operators to objects, events, or processes in the Real Universe, interpreting the theory and explaining the universe. This gives scientific progress firm foundation without hindering it - SCSPL mandates only meta-linguistic axioms and leaves full room for empiricism.
[1]: Reality means ultimate or maximal reality, not merely some subreality within it e.g. an ancestor simulation.
[2]: Personally I suspect wrapped in some kind of topos theory.
[3]: Presumably, anyway. This part is a bit hazy for the rest of us sometimes.
[4]: Yes, this is a real branch of mathematics, no, it’s not easy.
