> does an analog to Godel's incompleteness apply

not GP but this seems like quite an attractive idea that many people have reached: a brain of a given "complexity" cannot comprehend the activity of another brain of equal or higher complexity. I'm positive I'm cribbing this from scifi somewhere, maybe Clarke Or Asimov, but, it's the same idea as the Chomsky hierarchy, and the Godel theorems seem like a generalization of that to general sets of rules rather than mere "automata".

For example, you can generalize a state automata to have N possible actors transitioning state at discrete clock intervals, but each actor can keep transitioning and perhaps even spawn additional ones. The machine never terminates until all actors have reached a termination state. That machine is probably impossible to model on any kind of a Turing machine in polynominal time. And a machine that operates at continuous intervals is of course impossible to model on a Discrete Neural Machine in polynomial time (integers vs reals categorization). There are perhaps a lot of complexity categories here, similar to alephs of infinity or problems in P/NP, and when you generalize the complexity categorization to infinity, you get godel incompleteness, just an abstract set of rules governing this categorization of rule sets and what amounts to their computability/decidability.

Everyone is fishing at this same idea, a human has no chance of slicing open a brain (or even imaging it) and having any idea what any of those electrical sparkles mean. At most you could perhaps model some tiny fraction for a tiny quantum, with great effort. We have to rely on machines to assist us for that - probably neural nets, a machine of equal or greater complexity. And we will probably have to rely on machine analysis to be like "ok this ganglion is the geographic center of the AI, and this flash here is the concept of Italy", as far as that even has any meaning at all in a brain. Mere line by line analysis of a Large Language Model or other deep neural network by a human is essentially impossible in any sort of realtime fashion, yeah you can probably model a quantum or two of it statistically and be like "aha this region lights up when we ask about the location of the alps" but the best you are going to do is observational analysis of a small quantum of it during a certain controlled known sequences of events. Unless you build a machine of similar complexity to interpret it. Just like a brain, and just like a state machine emulating a machine of higher complexity-category. They're all the same thing, categories of computability/power.

This is not in any way rigorous, just some casual observations of similarities and parallels between these concepts. It seems like everyone is brushing at that same concept, maybe that helps to get it out on paper.

For an actual hot take: it seems quite clear that our computability as a consciousness depends on the computing power of a higher complexity machine, the brain. Our consciousnesses are really emulated, we totally do live in a simulation and the simulator is your brain, a machine of higher complexity.

Isn't it such a disturbing thought that all your conscious impulses are reduced to a biological machine? Or at least it's of equivalent complexity to one. And the idea that our own conscious and unconscious desires are shaped by this biological machine that may not even be fully explicable. That has been a science fiction theme for a very long time, or the Phineas Gage case, the idea that we are all monsters but for circumstance and we are captives of this biological machine and its unpredictable impulses. We are the neural systems we've trained, and implacable biology they're running on - you change the machine and you also change the person, Phineas Gage was no less conscious and self-cognizent than any of us. He just was a completely different person minus that bit, his conscious being's thought-stream was different because of the biological machine behind it. It's the literal plato's cave, our conscious thoughts are the shadow played out by our biological machine and its program (not to say it's a simple one!).

It's not inherently a bad thing - we incorporate distributed linear/biological systems all over the body in addition to consciousness. reflexes fire before nerve impulses are processed by the conscious center, your eyes are chemical photosensors and can respond to extremely quick instantaneous (high shutter speed) "flash" exposures like silhouettes. And the brain is a highly parallel processor that responds to them. But logical consciousness is a very discrete and monodirectional thing compared to these peripheral biological systems and its computational category is fairly low compared to the massively-parallel brain it runs on. but, we've also mastered these other AI/computational-neural systems now to be a force multiplier for us, we can build systems that we direct in logical thought for us (Frank Herbert would like to remind us that this is a sin ;). Tool-making has always been one of the greatest signifiers of intelligence, it may be quintessentially the sign of intelligence in terms of evolution of consciousness between certain tiers of computation.

And humanity is about to build really good artificial brains on a working scale in the next 25 years, and probably interface with brains (in good and bad ways) before too many more decades after. But it doesn't make any logical sense to try and explain how the model works on a line by line level, any more than it does with the brain model we based it on. Completely pointless to try, it only makes sense if you look at the whole thing and what's going on, it's about the brainwaves, neurons firing in waves and clusters.

/not an AI, just fun at parties, condolences if you read all that shit ;)