Thought Experiment: Operational Incompleteness — A Physicalist Deduction and Formaliz

[Drashner1]

[Reply to post #17]

Hi, Drashner1

Thanks for adding this — it maps very cleanly onto what I’m trying to do, even though I’m pushing the discussion toward civilizational dynamics rather than the internal psychology of individual minds.

On (a): I’m fully aligned with OA’s “quantitative/brute-force incomprehensibility” framing. A sufficiently large quantitative gap can push the interaction surface into a regime where the projection and verification burden exceeds what the human observer class can realistically sustain. At that point, the distinction between “quantitative” and “qualitative” differences becomes practically secondary, because the interface behaves as if we were dealing with a different cognitive order altogether.

Agreed - Over the years, we've found it much easier to discuss quantitative differences, including those growing to this kind of level, because they are easier to think about than trying to come up with a truly qualitative difference (let alone 6+ of them). We still try from time to time because it's fun/interesting to think about and discuss (well really, both kinds are).

On (b): OA’s discussion of diminishing returns, instability, and paradigm shifts between S-levels is especially valuable. It highlights that capacity expansion is neither smooth nor indefinitely scalable. It involves plateaus, fragility zones, and the risk of internal breakdown. From a civilizational perspective, that matters because verification and augmentation do not expand in a clean linear fashion; they encounter friction, structural limits, and transitional instability.

Thanks! We're actually rather proud of that aspect of the setting. Back when OA started, a lot/most science fiction that included a singularity treated it as something that happened pretty smoothly or inevitably and led to a smooth and rapid ascent to some sort of apotheosis that was only dimly described (if it was described at all). The founders of the project wanted to both do something different and felt it was more realistic that there would be challenges and problems and potential downsides to the whole thing (as well as much else in the setting, despite initial appearances).

Where I’m focusing is the downstream consequence: once capability scaling and verification scaling decouple for long enough, coordination migrates away from shared understanding and toward interface governance (protocols, disclosure grammars, audit rights, access thresholds). Uneven augmentation then turns into structural stratification: different groups end up living inside different effective verification horizons, and that divergence can become hard to reverse.

So in that sense, I see no contradiction between OA’s model and the framework I’m sketching here. They operate at different descriptive layers. OA focuses more on cognitive architecture and individual or transapient development. I’m trying to focusing that into long-term institutional and coordination consequences once incomprehensibility becomes structurally persistent rather than episodic.

This is an area that OA probably needs to explore more fully than we have so far. Not just in terms of what we refer to as 'intertoposophic relations' between different singularity levels, but relations between beings of the same singularity level but different (possibly radically different) body and mind types and type and degree of augmentation. In OA it is entirely possible for a human not so different from people in real life to have a best friend who is a self aware tapeworm and a brother-in-law who is a starship (or vice versa) and to live in an environment surrounded by dozens to thousands of different intelligent species who are both varying types of human (some entirely non-human) and employing various types of genetic and cybernetic augmentation/alteration. All of these people may think very differently than we do, but also somehow manage to all get along together pretty well.

We do have various articles that address how this works as well as a lot of community knowledge/norms that aren't written down (but should be). But there is definitely room for more info and detail in this area around how it all works.

What you're aiming to do might be at least tangentially (and sometimes directly) applicable to addressing parts of this wider issue.

Please feel free to share/discuss as you develop ideas around this - and possibly OA might develop some ideas you find useful as well as we go along.

Todd