Comment by observationist
1 day ago
In principle - if you're able to scale appropriately, using technology to augment capacity, then in principle, there's no abstraction for which we lack the capacity to comprehend, because calculation is calculation. Turing Computers can calculate anything which can be calculated given enough time and memory. Brains are Turing complete.
It's not just a tautology, it's a feature of the universe- if it can be computed, it's comprehensible. Even quantum physics is just computation - truth tables and counterintuitive operators interacting over time in ways that are strange to our embodied norms, but nonetheless following rules and limits strictly defined by mathematics.
But again, that's in principle. It might be completely impractical - taking a million years for an individual human - to hold a particular idea in their head, while an advanced AI can have such thoughts many times a day. Such things would remain mysteries, but in principle, an augmented human, or a series of interfaces with the relevant abstraction levels of such an idea, theory, or system, would in principle give us comprehension.
In practice, we'll never run out of mystery or ignorance or mistakes.
Inconsistent logic.
You've made a grave assumption in treating this as a binary problem: comprehensible or incomprehensible. The truth is that this lies along a spectrum. I can "comprehend" a color which my eyes can't see but this is different than trying to comprehend red. Or as a variant, I can comprehend a color that I can't see naturally but if I go into a lab and they simulate those cones in very specific ways I won't ever be able to really imagine it. Seeing it will be clearly a different level of comprehension.
I fully agree with this but also for some reasons unmentioned. Truth has infinite precision, a thing we will never achieve. Similarly my namesake showed there are limits to axiomatic systems.
And there are problems that can't be solved by Turing complete machines. That only means they can solve computable problems but there's plenty that aren't. Very famously the halting problem isn't. And in the real world there's many problems which are intractable. And some are more intractable than others