Gary Marcus

Sure, but you do not understand Riemann sums innately - you learned about them. Humans clearly have some innate ability to learn about abstract systems that other species may not, but the learning is innate, not the concepts and relations themselves.

That's irrelevant though. Humans didn't evolve to learn those things. So there's unique innate machinery that's been repurposed. Eg permission schemas for abduction. Machinery for reasoning spatially with a graph based representation (easily confused for grids) for symbolic, coup

coupled with whatever allows us to learn recursive grammars and combinatorially compose atomic concepts. Once you have that, getting to a system that can derive Newton's Laws by looking at how things fall is a comparatively short step.

I think for example, the fact that cerebellum and motor cortex is recruited for even mathematical reasoning--and one may quibble over how innate is defined--suggests that at least the basis and initial stages are by analogy with/to innate capabilities.

I'm saying: brain does things it didnt evolve to, such as math or sewing. It's much more likely that existing nearby machinery was repurposed and then optimized in humans to be able to do or pick up recursive abstract reasoning than to have that capabiliity learned from scratch

Uh huh... I don't see how anything I said in this thread contradicts anything you've said here. My point is only: (1) there are some structural priors, but (2) we learn a lot, (3) we use distributed representations, and (4) this all fits with the general DL research program.

More degree than contra. I think instead, high precision to go from PushDA to TM. Such as,what is the arch that allows small toddlers but not adult chimps to pick up language? I am doubtful we learn a lot because developmental trajectories, common fallacies are too much shared.

I think, if just us humans have same limitations, strengths & develop in the same sequence, lack of dof strains what's meant by learn Specifically, I think existing unlearned machinery underlies our ability in say math. We learn to learn,fine-tune, learn facts & rules but