Is there a good book that is similar in spirit, but doesn't require the maturity of GEB? I know an 8th grader that would be a great target, but I don't know if they have the mathematical/logical maturity to get through it.
+1
Penrose's The Emperor's New Mind Timothy Ferris Coming of Age in the Milky Way and the Zen and the Art of Motorcycle Maintenance, previously mentioned.
Maybe not the most current thinking (but perfectly fine as an introduction), but the writing is more accessible than GED.
His 2007 book, "I Am A Strange Loop" is a bit of an answer to this. It's mostly the same ideas in GEB about the self and strange loops, but without all the meandering and interludes. It's been a while but I remember it being less logic/mathy than GEB. I did enjoy it.
But the meandering and the interludes are part of the enjoyment of GEB. So if you're looking for another book to capture that spirit of GEB, I'm drawing a blank, hopefully someone else knows one.
Barely related recommendation, but I remember reading "A Brief History of Time" around that age. Very doable for a young teen if they have a passion for that sort of topic.
Ah - interesting. It took me several readings to tease-out what I thought the central theme was. As it happens, it led to a position that I objected to (and still object to). So discovering that central theme brought the book down a peg or two in my estimation.
I still think it's one of the most entertaining books of popsci that I've ever opened.