r/compsci moderators told me to post here

Disclaimer for mods if you are about to delete this:
This post got deleted on r/compsci and r/math because apparently this is not related to computer science or math.

I believe that this topic has a lot of overlap with computer science, mathematical logic and universal systems.

I simply want to share something that I spent several hours of writing. I am here to have a civil conversation about universal models, their paradoxes and implications.
If you do delete this post. I’d appreciate where I can post this.

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Syntropos

Syntropos is an abstract causal universal computational model governed by intrinsic rules.

Goal

The original artistic concept was to have a world that allows the existence of any reality within itself, whether it is a fantastical world, Conway’s Game of Life, or our own universe. These subspaces could be interacted with and observed from the outside, beyond their bounds.
I wanted to have a world where emergent intelligence could arise if the starting state was white noise.

This artistic concept was expanded into an abstract model, which always has the possibility of a causal existence of any system in any subspace.

No concrete model is perfect, just like how physics is modeled in real life. This is why I started outlining what Syntropos is in abstract terms.

Axioms

The truths of Syntropos must be such that it is plausible to construct a concrete model of Syntropos using modern mathematical tools.
– Infinite but finite: Syntropos tessellates the space with an infinite number of states, with each state having a finite amount of information.
– State transition: States can only transition between neighbors.
– Dimension: Euclidean space with a finite number of states. The same relative state arrangement in higher dimensions can have a larger number of neighbors.
– Universality: The intrinsic rules are computationally universal. Given enough time, any system can emerge.
– Persistent: The universe never reaches a stable state. Otherwise it could stop being universal.
– Causal ordering: The speed of a state transition is globally constant. ^[1]
– Determinism: Locally deterministic, but beyond a critical volume ^[2], predictions become computationally irreducible from within Syntropos.
– Dimensional universality: Every k-dimensional cross-section of Syntropos is Turing-complete. ^[3]

From the axioms we can deduce the following

• The number of dimensions is finite. Otherwise you would have infinite information in a state.
• The data propagation is limited by the dimension and the number of neighboring states. Neighbors aren’t necessarily static.
• Persistence implies some conservation law. A global dead-end state can’t exist because then it wouldn’t be universal.
• ^[1]: The time is imperceptible from Syntropos perspective, as the speed to realize this fact depends on itself. Similarly to how deterministic systems behave the same regardless of the simulation speed. This is why the state transition speed is not relevant as long as it’s not 0 or infinite. Syntropos follows causal ordering in an infinite time scale.
• ^[2]: Critical volume is the size of the smallest irreducible system whose future can’t be predicted. It is possible to simulate the future of slower or lower-dimension systems because they are reducible. Due to data propagation speed, you can’t predict the future of Syntropos faster than itself.
• ^[3]: k-dimensional cross-sections along any axis remain Turing-complete. For example, if we take a 2D slice of Syntropos, it can simulate anything, even itself. But due to the reduced neighbor count, the computation would require more time.

Why these axioms?

• Syntropos is less abstract and more constrained than other universal models such as Stephen Wolfram’s Ruliad. These arbitrary constraints originate from the artistic concept of how I imagine Syntropos.
• Causality is enforced by the information propagation speed, which is a result of state causality in finite local Euclidean space. Without causality, all the systems would need to exist in a superposition, which goes against the original artistic concept.
• Inability to predict the future within Syntropos is a side effect of Causality. Similar to the halting problem.
• Syntropos has intrinsic universal rules. It can simulate any system with one global rule set, which is contained within itself. Similar to cellular automata.
• The dimensional hierarchy is an artistic view of how lower-dimension systems can exist independently while still being universal. A world within a world in a more concrete way.
• If a lower-dimension system was observed, its dimension would become the same as the observer’s. But an observer within a lower-dimensional system couldn’t interact with the higher dimensions on its own. Similar to how we don’t know what is beyond the real-life universe.

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Conclusion

Syntropos started as a novel thought experiment, but I didn’t expect to delve this deep into logical reasoning and universal systems.
I have only reasoned that such a system could be theoretically constructed, but it is not proven. There might be some paradoxes and edge cases where universality breaks.

Interestingly, the inability to predict the future doesn’t invalidate universality.
A future-predicting machine can exist, but it must predict the future slower than the time in Syntropos.
Semantically it’s not a future-prediction machine, but it exists.

Things start sounding philosophical when you realize that Syntropos as a universal system must contain itself. In fact, it does so infinitely many times because Syntropos is infinite.

The original artistic concept snippets:
The artistic concepts of Syntropos
Arktinu, the artistic ideology of an emergent intelligence

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There’s beauty in mixing art and mathematics, and I finally got to formalize what Syntropos is. In English, that is, because abstract axiomatic formalization goes beyond my knowledge.