Symbolics are really the tokens on which consciousness in almost all forms works, consciousness is intentionality and processing, a lever and a place to stand. I don't think it's coincidental that almost all tool-makers also have at least rudimentary languages - ravens, dolphins, apes, etc. They seem to go together.
Even in these systems though it's very difficult to understand multi-symbolic systems, consciousness as we experience it is an O(1) or O(N) thing and here are these systems that work in N^3 complexity spaces (or even higher... a neural net learning over time is 4D). And we don't even really have an intuitive conceptualization for >=5-dimensional spaces - a 4D space is a 3D field that changes over time, a 5D space is... a 4D plane taken through a higher-dimensional space? What's 6D, a space of spaces? That's what it is, but consciousness just doesn't intuitively conceptualize that, and that's because it's inherently a low-dimensional tool (even the metaphors I'm using are analogies to the way our consciousness experiences the world).
Anyway point being consciousness itself is a tool that our brains have tool-made to handle this symbolic/logical-thought workload, and language is (one of) the symbolics on which it operates. Mathematics is really another, both language and mathematics are emergent systems that enable higher-complexity logical thinking, maybe that's the O(N) or O(N^2) part.
And yeah it's inherently limited, and now we're building a tool that lets us understand higher-dimensional systems that are not computable on our conscious machines - a higher-complexity machine that we interface with, a bolt-on brain for our consciousness/logical-processing.
It seems like AI is going to let us cross another threshold of "intentionality" - if nothing else, we are going to be able to reason intuitively about brains in a way we couldn't possibly before, and I think there are a lot of "higher-order" problems that are going to be solved this way in hindsight. How do you solve the Traveling Salesman Problem efficiently? You ask the salesman who's been doing that area his whole life. The solutions aren't exact, but neither are a lot of computational solutions, they're approximations, and cellular-machine type systems probably have a higher computational power-category than our linear thought processes do.
Again, not rigorous, just trying to pour out some concepts that it seems like have been bouncing around lately.
With apologies to Arthur Clarke, what's going to happen with chatGPT? "Something wonderful". Like humanity has been dreaming about this for a long time, at least a couple hundred years in scifi, and it seems like Thinking Machines are truly here this time and it seems impossible that won't have profound implications analogous to the information-age change let alone anything truly unforeseeable/inconceivable, the very least change is that a whole class of problems are now efficiently solvable.
https://getyarn.io/yarn-clip/3755bfaf-c7e7-4142-a352-781b31a...
"computing power in the same computing-category as brains" is potentially a fundamental change to understanding/interfacing with our brains directly rather than through the consciousness-interface. Understanding what's going on inside a brain? And then plugging into it and interacting with it directly? Or offloading the consciousness into another set of hardware. We can bypass the public API and plug into the backend directly and start twiddling things there. And that's gonna be amazing and terrible. But also the public API was never that reliable or consistent, terrible developer support, so in the long term this is gonna be how we clean things up. Again, just things like "wow we can route efficiently" are going to be the least of the changes here, the brain-age or thinking-machine age is a new era from the information-age and it's completely crazy that people don't see that chatGPT changes everything. Yeah it's a dumb middle schooler now, but 25 years from now? And 10 years ago people's jaws would have hit the floor, but now it's "oh the code it's writing isn't really all that great, I can do better". The tempo is accelerating, we are on the brink of another singularity (which may just be the edge between these eras we all talk about), it seems inconceivable that it will be another 40 years (like the AI winter since the 70s) before the next shoe drops.
And honestly now that I am thinking about it, 2010 is such a rich book/movie with this theme of consciousness and Becoming in general... a really apropos movie for these times. That quote inspired me to re-watch it and as I'm doing so, practically every scene is wrestling with that concept.
https://www.youtube.com/watch?v=T2E7sxGAmuo
https://www.youtube.com/watch?v=nXgboDb9ucE
So was 2001 A Space Odyssey of course. Like I said this is a topic that has been grappled with in scifi, particularly Clarke and Asimov (Foundation, The Last Question, etc), or that episode of Babylon 5 about the psychic dude with mindquakes ;)
But I think we are on the precipice of crossing from the Information Age into the Mind Age. Less than 50 years probably. Less than 25 years probably. And it will change everything. ChatGPT is just an idiot child compared to what will exist in 10 years, and in 25 years the world will be fundamentally different in unknowable ways, any more than we could have predicted the smartphone and tiktok. 50 years out, we're interfacing with brains and directly poking at our biology and cognition
(did we have an idea that a star trek communicator or tricorder would be neat? Sure, but, it turns out it's actually a World-Brain In My Pocket. Which others predicted too, of course!)
Maybe in 100 or 200 years we are the David Bowman thought-being, moving our consciousnesses away from our biological hardware. From the moment I understood the weakness of my flesh, it disgusted me. ;)
Not necessarily. If you don't want to model every continuous thing possible, you can do a lot. Just look at how we use discrete symbols to solve differential equations; either analytically, or via numerical integration.