Conjecture (Math)

This conjecture asserts the inherent necessity of fundamental uncertainty for all state relativity in any complex, chaotic, continuous, or infinite system with intersecting or interconnected functional domains.

There is nothing inherently “virtual” about state relativity space, or relational superstates. They can often be more real and more tangible than the things they actually relate – depending on both the rules and the tools of relation employed, to both better and worse effect.

In other words, the relational states of objects around us are as real to us as we are able to project them, both outward and inward, within and without.

This is more or less a radical statement of essential relativism, or relative determinism.

The conjecture of deterministic relativity implies the fundamental uncertainty and complexity of all state relativity space in any real multi-clock domain of unit exchange or object flow, or in any applied theory with multiple infinite, continuous, or recursive functional domains.

Restatement I: This is basically just another way of saying that everything flows, so to speak, while adding that time itself is a relative and relational outcome of fractally intersecting unary flow entities that are arbitrarily detailed, complex, and uncertain. Because linear time can be formalized and mapped as a cross-section (or product) of interconnected sub-functional domains, the line of time itself must only be the surface of a deeper fractal relativity space.

Restatement II: This is a formalization of the idea that the motions of complex units in a given directional flow domain can be formalized and mapped as groups of chaotic and changeable morphisms between and among its sub-domains. Time within that domain then becomes regular and regulated as an outcome of the parent flow domain’s ability to coherently typecast all its primary functional entities and identities in accordance with its own complex identity morphism, within the constraints of its own parent clock domain.

I think this conjecture should actually be empirically verifiable, but that particular side of things is still a work in progress.

(But also, science actually might have me covered here.)

For now, the inherent uncertainty and complexity of state relativity is implied in the various parts of the conjectural correspondence.

First and second, it is implied in both a quantum correspondence and a digital correspondence, in the forms of quantum superposition and digital metastability.

That is, if you’ll accept a proof by Wikipedia. And you should – Wikipedia is awesome 😉

Third, it is also implied in a material correspondence, where continuous energy and continuous matter also share a spaciotemporal superstate that we call spacetime.

Like quantum particles and digital units, continuous matter also becomes unstable and volatile at the various boundaries of its relative superstates.

(In other words, you will inevitably encounter the limits and relative constraints of your state relativity space regardless of whether or not you handle the matter around you as waves or particles.)

Fourth, it is implied in an informational correspondence, where the informational unit and the transmission channel can share an entropic superstate, and where the relative entropy (or Shannon Entropy) can increase or decrease as a result of both information gain and loss from noise sources during unit transmission.

(Put another way, in practice entropic information and flow values are frequently gained and lost.)

Fifth, it is implied in a rulespace correspondence, where the rules and players in a complex game or drama share a relational superstate that can be measured as the system’s state-space complexity – and where a given ruleset increases in application difficulty as the game complexity approaches arbitrary limits.

And sixth, it is implied in a typespace correspondence, where the methods and units of typecasting can also share a relational superstate with their material constraints.

Note that in the classical sense, the casting of types can be both physically deterministic and virtually deterministic (i.e. it applies to both digital and mechanical type-printers), despite also being an inherently relativistic and uncertain method of empirical interaction.

And finally, and critically for my long-term project, it implies a new-ish parallel, a sociomaterial correspondence, where our complex social intentions and assertions can be held in a relativistic superstate within both our surrounding material and social contexts – a superstate which must always resolve to a valid internal state before the parent domain interjects, or which otherwise results in a social stack overflow.

In a certain sense, the socio-material extension is only a merger of the quantum, digital, material, informational, rulespace, and typespace correspondences.

I plan to develop an actual coded proof of this social piece. After all, gotta show your work.

The proof should help in showing how typecasting via source coding, channel coding, target coding, and line coding can all be extended into social theories of tight and loose norm systems. You know, the human side of things. This should provide an abstract social model that can be applied equally well to mindsets and singular minds, i.e. to both individuals and coalitions.

(I sometimes call this “the methods and practice of social annealing.” I also sometimes call it “building consensus.” And I also sometimes call it “exploratory problem solving,” or “collaborative discovery.” But at the most basic level, it’s really just one of many possible generalizations of how teams work together to get stuff done.)

Unlike classical systems of material interaction, this social “relativity stack flow-control” model should consider human actors and intentions in our social context as equally real alongside the matter and objects in our material context, even if dereferencing those intents within that context is inherently chaotic and uncertain.

It should also show how in practice, the continuous dereferencing of intent gets regulated and normalized into a consistent social structure, in spite of (or perhaps because of) the underlying chaotic processes of the individual unary elements.

And if I can get the base framework right, it might also become a useful tool to help regular people with generalized flow mapping, visualization, and design.

But this piece could take a little… time.

And I’ll need plenty of help along the way, too.

(Of course that shouldn’t be an issue, since helping each other is simply human nature.)

For now, all I’ve got is a short story, a dumb song, and a bunch of lazy aphorisms (see: this website). <lol/>

But don’t panic! We’ll get there eventually. I think.

Still, in the meantime I’ll have to settle for arguing that general state relativity and relative determinism are the best way to understand the world around us.

And for better or worse, building and fitting for better relational superstates is actually the only viable way to effectively project our current state outward in any truly complex system (i.e. using our best-fit representation of its “relational stack,” i.e. using whatever tools we have available within the systemic domain).

In fact, it’s what we’ve been doing all along.

I should also mention the various “indications,” which are just evidentiary patterns that I hope to describe, explain, and predict using this toolkit.

Indication I: Wave-particle typecasting.

The essential reality and inherent uncertainty of relational superstates – and time as an outcome or product of flow between and among the relational states in our domain of existence – is likely the whole reason we keep finding wave-particle dualities everywhere we look.

Well… at least everywhere that we keep trying to measure and test the nature of things as both waves and particles.

In the same way that the effective length of Mandelbrot’s ruler dictates the length of the measurements he finds in the coastline paradox, the particulate and waveform “rulers” that we use to measure, test, and typecast the world around us can also impact the measurements and outcomes we ultimately find in that very same world.

Indication II: State decoherence and accordion effects.

I call the process of unary unraveling at source-points in complex flow exchanges “state decoherence,” but it has many analogous concepts in many different domains: dereferencing pointers, decrypting hashed values, event parsing, or clock cycle arbitration.

In the same sense that dereferencing an inconsistency in software always carries a possibility of a fault, every time we forcibly break open a unit of “particulate wave” stuff, the howls of chaos inevitably come pouring out in one form or another, differing in effect depending on the nature of the relational constraints being broken open.

Accordion effects increase as you approach a relational limit, and when you actually hit the limit, well… that’s the whole friction>fission>stack overflow side of things that we run into when we try to rip and zip the truly deep flows around us.

We should probably be more careful about that sort of thing, just saying 😉

Indication III: Background radiance.

The recursive chaos and uncertainty of relational superstates is the reason why we always find fractal background radiation in every event field we try to extend and implement as a truly unary continuum. (Even if that “event field” is just a pretty fractal picture with words in it.)

Indication IV: Event horizons and eclipsing events.

Superstate uncertainty might also be able to describe and demonstrate the fractal self-similarity between event horizons in a black hole, the event boundaries in our own eyes, and the inherent event uncertainty introduced at the sources and end-points of a given chaotic flow, and the nature of systemic eclipses.

Side note: Why six correspondences? Because that’s all I can really handle for now. But really, if the conjecture holds, any system of complex unary flow exchange should exhibit the characteristic decoherence of unitary events at the thresholds of flow sources (i.e. flow exchange end-points or clock-cycle domain event horizons).

In other words, this is an n+1 type deal. Grocers offer two-for-one, but mathematicians like to offer… as many as you can “handle.”

I’m trying to act all math-y here, so that’s what I’m going with.

Side side note: I am NOT trying to build “univalent foundations” for all mathematics. Honestly I’m pretty sure that no such thing exists, and even if it did exist, mathematicians would do a much better job of building it than I ever could.

If anything, I’m just trying to build a “highly valent” foundation for human work and human flow. I’m assuming that if this project is possible at all, then all the pieces will either be relatively simple or already built. And I’m assuming I can find most of those pieces on Wikipedia.

Mostly, I’m just hoping to build an easy toolkit, and maybe a little philosophy to go with it, that people can actually use to make the things around them flow a little better. And if we do it just right, maybe we can all get a little more time back.

At least, that’s the plan. This branch of the project is really just a big, crazy attempt at doing something uniquely useful. And if by flowing through a ton of loopy mathematical stuff, I happen to prove one (already kinda obvious) thing for us humans – that humanity’s potential for goodness is a verifiably real thing that flows within each of us – then so be it.

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