I just finished reading the marvelous book, “Born on a Blue Day.” While I could easily write a very extended piece on the many ideas it suggests to me, I thought I would rather quote this passage, which is perhaps the most beautiful description I have ever read of the reasoning process that would usually lead to an explicit proof by induction:
One of the exercises in the book read like this: There are twenty-seven people in a room and each shakes hands with everyone else. How many handshakes are there all together?
When I read the exercise I closed my eyes and imagined two men inside a large bubble, then I imagined a half bubble stuck to the side of the larger bubble with a third person inside it. The pair in the large bubble shook hands with each other, then each with the third man in the half bubble. That meant three handshakes for three people. Then I imagined a second half bubble stuck to the other side of the larger bubble with a fourth person in it. Then the pair in the large bubble needed to shake hands with him too, and then the half-bubble men shake hands with each other. That would make six handshakes between four people. I continued in this way, imagining two more men in two other half bubbles until there were six in all and fifteen handshakes between them. The sequence of handshakes looked like this:
1, 3, 6, 10, 15…1
- Daniel Tammet : Born on a Blue Day : School Days↩
This demolishes Daniel’s whole argument that he just sees answers, he doesn’t have to work them out. Perhaps you will do well to read my detailed review of his book: OMISSIONS. He makes a number of mistakes in the book about me yet and claims to remember everything!