I found this list of 20 Strange Books over on the book club at House Arrest. The lister, John Cartan, writes:
A complete catalog of my library would be tedious; a list of my favorite books would be mostly titles you already know. More interesting by far would be a short list of books that took me by surprise and then changed me, odd little books you may never have heard of. After several decades there are only a handful that stick out in this way. Some are truly wonderful and cry out to be shared. Others, frankly, aren't as good - but are genuinely strange.Looking over the list, I'd read a quarter of them -- The Mysteries of Harris Burdick, Flatland, Borges' collection Labryinths, Maze, and Gödel Escher Bach.
I wasn't a fan of Christopher Manson's Maze, described as a "paperback Myst", but mostly because it was just too hard! [This was before you could just look up the answers online. There's an online version, but the pictures are unfortunately too small.] And Chris Van Allsburg's Mysteries, a book of illustrations in search of stories, was a later (but welcome) addition to our library. The other three, though, were definitely well-thumbed as a kid, and helped warp me into the strange person I am now. I think my copy of GEB nearly disintegrated by the 8th grade, and somewhere I may still have the bad philosophical dialogues it inspired me to write. If you're nice to me I won't share them with you.
Fans of the Maze should check out Masquerade, equally beautiful and unsolvable. And if you liked Flatland, you should read the Planiverse, a computer scientist's take on 2-dimensional life.
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