No non-human animals are in the club that's marked by having a language with an infinitely generative syntax and a large (100,000+ words) and always-growing vocabulary.
Intelligence might be a spectrum, but powerful generative language is a step function: you have it or you don't. If you have it, then higher intelligences can communicate complex thoughts to you, if you don't they can't. We have it, so we are in the club, we are not cockroaches.
there are many humans who could study mathematics for a lifetime and not be able to comprehend the current best knowledge we possess. i'm one of them. maybe it takes 2 lifetimes. or many more.
a human-level AI operating at machine pace would learn much more than could ever be taught to a human. our powerful generative language capabilities wouldn't matter - it's far beyond our bandwidth. especially so for a superhuman-level AI.
The fact that AIs will have some information that we cannot understand, or will have more information than they can transmit (or we can absorb) does not make us cockroaches.
The AIs will deliver to us truly massive quantities of information, every minute, until the end of time, much of it civilization-changing. Thus the AIs relationship to us will thus be nothing like our relationship to cockroaches, where we essentially cannot tell them anything, not even the time or the day of the week, let alone the contents of Wikipedia.
I think Hofstadter is having an emotional reaction to AI. He says so as much. And it'a a common one, it's the woe is me phase. But I think he's totally wrong about the analogy. I'm 100% sure we will not feel like cockroaches when AI is in full swing, not in the slightest.
Intelligence might be a spectrum, but powerful generative language is a step function: you have it or you don't. If you have it, then higher intelligences can communicate complex thoughts to you, if you don't they can't. We have it, so we are in the club, we are not cockroaches.