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Image a hotel room with infinite rooms. And it's full. And you want a room. Well, guess what - you'll get one. Because it's infinite. And if an infinite number of people show up wanting rooms, they'll all get one. Even though the hotel is full. If you think that's wild, read on.
The book starts off by talking about how creativity is essential for knowledge creation. Deutsch stresses a good explanation above and beyond everything else - especially mere faith. A good explanation can open up entire realms of discovery, such as the theory evolution did. As a physicist, Deutsch uses many physics and mathematical examples as well, including the one about the above-mentioned infinite hotel, by David Hilbert. One of the cooler things mentioned about the hotel was its "trash disposal system". Management makes an announcement on the PA that says, "within the next minute, will all guests please bag their trash and give it to the guest in the next higher-numbered room. Should you receive a bag during that minute, then pass it on within the following half minute. Should you receive a bag during that half minute, pass it on within the following quarter minute", and so on. Nobody works infinitely fast, or handles infinitely many bags. Every action is finite. and yet, at the end of two minutes, nobody has any trash left. All the trash in the hotel is literally gone from the universe. This is also known as singularity, or what we speculate to happen inside black holes.
If you are wondering what the point of the book is, I can't tell you - I didn't even finish it. As with any other book - if I find myself really struggling to continue to read it after a few sessions, I typically stop reading it. A book you don't enjoy reading anymore is a sunk cost and we should move on. That was one of the best lessons I learned in a speed reading class I took (read faster by reading stuff you enjoy - go figure). When I did understand certain parts, I found myself day dreaming about the differences between countable and uncountable infinities and not really reading the book at all. Even statements that are written in simple English forced me to think way too hard. Such as this nugget: “Feeling insignificant because the universe is large has exactly the same logic as feeling inadequate for not being a cow.”
If you have the tenacity to read the entire book, please let me know how infinity ends :)