Mathematical moments of wonder like Cantor's diagonal method

June 8, 2014 3:57 PM

I've been reading Godel, Escher, Bach and I want to find more mind-expanding concepts that give the sense of understanding some fundamental truth.

While I can't always follow the specifics of the mathematics in GEB I have experienced some jaw-dropping moments of understanding, e.g. when Cantor's diagonal argument clicked into place. I want to find more mind-bending mathematical concepts like this, explained in a way that I as a non-specialist can understand (even if there is some work required). Books / websites / anything else welcome. Thanks in advance!

posted by StephenF to Science & Nature (14 answers total)

Perhaps Proofs from the Book.
posted by hoyland at 4:00 PM on June 8, 2014

The Mind's I
posted by Sal and Richard at 4:37 PM on June 8, 2014 [3 favorites]

Best answer: GEB is one of my favorite books, and one of the few I've read three times (not a big re-reader). I didn't get it the first time, but had the experience you describe on the second.
A book that also did this for me is Umberto Eco's Kant and the Platypus. the first chapter is puzzling and daunting, but do not be discouraged, from the second chapter onward Eco lays stone upon stone to a path of understanding how we define and categorize information. it bears on how we communicate, how we learn, and how we gain understanding of things we've never encountered before. it's great stuff.
I may have read one of his books on semiotics prior to this, but IIRC it is not necessary to understanding KatP.
posted by OHenryPacey at 5:09 PM on June 8, 2014 [1 favorite]

Everything and More: A Compact History of Infinty by David Foster Wallace, which is more or less all about Cantor. I haven't read GEB, so I'm not sure how much overlap there is in the material.
posted by BrashTech at 5:47 PM on June 8, 2014

I Am a Strange Loop and Metamagical Themas, also by Douglas Hofstadter.
posted by ostranenie at 5:57 PM on June 8, 2014

Asimov wrote some non-fiction on math, I remember first learning about Euclid's fifth postulate from him. I don't remember any specific math-related collections of his, but they probably exist.
posted by vasi at 7:10 PM on June 8, 2014

Understanding the Monte Carlo algorithm for approximating pi was a "lightbulb" moment for me.
posted by edguardo at 8:49 PM on June 8, 2014

Martin Gardner's books. Raymond Smullyan's books. Vi Hart's videos. Rudy Rucker's nonfiction.
posted by Schmucko at 10:30 PM on June 8, 2014 [2 favorites]

Response by poster: Thanks all!
posted by StephenF at 1:10 AM on June 9, 2014

"The Origin of Consciousness in the Breakdown of the Bicameral Mind," Julian Jaynes. Not math, but original thinking.
posted by fivesavagepalms at 6:54 AM on June 9, 2014 [1 favorite]

There are a couple of books in the series Proofs Without Words that show interesting geometrics proofs. If you google that term you'll also find some other links and images on that theme.
posted by stp123 at 8:59 AM on June 9, 2014 [1 favorite]

A Thousand Plateaus, by Gilles Deleuze and Felix Guattari...
posted by Joseph Gurl at 8:49 PM on June 9, 2014

The Turing Omnibus covers 66 different computer-sciency topics with a few pages per topic -- some of the same stuff covered in GEB, though more succinctly (perhaps overly so) and with less flowery prose. Most of it pretty fundamental, though.
posted by RobotVoodooPower at 4:42 PM on June 13, 2014

Also: Who Can Name the Bigger Number?
posted by RobotVoodooPower at 4:52 PM on June 13, 2014