Thoughts on the Book of Sand.
This occurred to me: open the book on a certain page, shut the page again, and you will never again be able to open at your earlier page. More: the pages cannot be numbered--there are an infinite number of them between the front and back boards; which means that, open it roughly in the middle, there are an infinite number of pages on either side.
But (and this is the part that troubles my head): let's say the book is an inch thick, and you took a half-inch paintbrush and painted the ends of the first half of the stack of pages gold. Afterwards, and whilst it would still be perfectly impossible for you to open the book at the same page twice, you could be 100% sure of opening the book in the first half. This puzzles me, because it suggest (counterintuitively) that it is possible to narrow down an infinite range of options. My sense is that this is no paradox: that half of infinity if still infinity, but it feels weird. It prompts me to ask: how far is it possible to narrow things down like this?