Sure, I'm a veritable genius when I'm on the grid, but am I mentally crippled when I'm not? Does an overreliance on machine memory shut down other important ways of understanding the world?

Very cool clip!
Like many people, I can do pretty complicated computations in my head, but I almost lost that. I learned a valuable lesson about technology. Just because you have technology doesn't mean you HAVE to use it.
When I first opened a business, I proudly purchased an electronic calculator and used it for all computations. Within a few months, I could no longer do simple arithmetic problems with more than one digit in my head.
Once I stopped using the calculator, my old computational skills returned....over the next few months. That was scary and amazing.

extended mind theory interesting (Chalmers et al). The use of a notebook or an abacus or a knot in the hankie are earlier 'technologies'. McLuhan talked in the 60s of new electronic media as 'extensions of the nervous system'.

I don't necessarily think that we're "remembering" less....i think we know less. A very small example of this would be phone numbers. I don't anyone's phone number. Not because i can't remember them, but because i never need to know them. They're all just programmed into my phone. Anyway, just a theory.

A very good theory. I sometime feel really bad when I have to think a bit for my own home phone number, that is, when I'm away from my cell phone (for some odd reasons of course).