When I was in grad school I noticed that Gödel, Escher, Bach was the book about mathematics that non-mathematicians had on their coffee table. The one that the mathematicians had was The Mathematical Experience.
If I had to name only one other book, for this audience I'd have to go with Code Complete.
I first read it years ago, 1979 or 1980. It was the first time I ever thought about how math related to music, art and nature. I had never heard of recursion or self-reference, never programmed a machine to do anything, never thought about how it could be done, or why I might want to do it.
So the book opened up new worlds for me. It changed the way I think.
How do you think you'd rate it today, already knowing about all those things? It's sitting on my table in my to read stack but I haven't managed to get to it yet.
My (potentially unpopular) feeling about GEB is that it's a book that explores some very interesting areas but that doesn't say all that much of interest itself. Reading it I felt like different sections could be put into two categories: (good and somewhat romantic) exposition about something interesting, and observations that seem profound until you think about them and realize that they're stupid (e.g. Hofstadter spends some time discussing how a Bach piece that ends up one semitone higher than it starts [and can therefore be repeated to form an infinite ascension] embodies self-referentiality and that this is the critical component of self-awareness, and that therefore the two are connected; of course, this is all just more-or-less meaningless fluff).
To give an alternate opinion. You should read through the first dialogue and the following chapter, then decide for yourself. Maybe skip ahead a bit. I read half of it sitting in a library when I didn't really have time to read it, it presented ideas I hadn't thought before. I hadn't heard of figure and ground, at least not generalized, so I enjoyed noticing that my conversations jumped around the subject rather than being on the subject. I also hadn't heard about recursion before, so...
If the writing engages you then you and presents interesting ideas, to you, in a non-obvious way, then it is worth reading.
>Been wanting to read "Godel ..." for years...
Me too. I have the book but every time I try to read it I go to sleep. (May be I just get in an infinite loop)
Fiasco - Stanislaw Lem