Scott Aaronson:

A biggest number contest is clearly pointless when the contestants take turns. But what if the contestants write down their numbers simultaneously, neither aware of the other’s? To introduce a talk on "Big Numbers," I invite two audience volunteers to try exactly this.

Who can name the bigger number? Whoever has the deeper paradigm. Are you ready? Get set. Go.

Have you read Rucker's classic?

A captivating excursion through the mathematical approaches to the notions of infinity and the implications of that mathematics for the vexing questions on the mind, existence, and consciousness.

It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations.

What about Penrose's The Road to Reality?

"What a joy it is to read a book that doesn't simplify (*), doesn't dodge the difficult questions, and doesn't always pretend to have answers."

Granted, it's not for everyone:

The film opens with her visiting a bookshop and fingering a copy of Roger Penrose's book, The Road to Reality. "Don't want to go there," she mutters to herself. Meanwhile, outside, her bicycle is being stolen.

(*) Ah, Lisa:

Grandma: I saw all your awards, Lisa. They're mighty impressive.

Lisa: Aw, I just keep them out to bug Bart, heh.

Grandma: [reproachful] Don't be bashful. When I was your age, kids made fun of me because I read at the ninth-grade level.

Lisa: Me too!

Grandma: You know, Lisa, I feel like I have an instant rapport with you.

Lisa: [gasps] You didn't dumb it down! You said "rapport".