I turned to Neil and said: ‘Hey, look. We missed the whole thing!’

“When I was at summer camp they divided the campers into two groups,” Buzz Aldrin recalls. We are high up in a New York hotel — the city is one stop on a world tour to promote his new book, its publication tied to the 40th anniversary of first Moon landing. “It was called Trout Lake Camp. There were the Ts and the Ls, and they competed. And at the end, one team won: and they ate chicken and the other group ate beans.” He looks slightly rueful, despite the upright, West Point posture that hasn’t left him even at the age of nearly 80. “That’s not a good example,” he says, although to my mind it is, since I’ve asked him as politely as I can what the difference is between what it might have been to be the first man on the Moon, and to have been the second. Edwin E. “Buzz” Aldrin — he changed his name by deed poll to simply Buzz some years ago; it was the name his sister called him, a childish mispronunciation of “brother” — climbed out of the lunar module 14 minutes after Neil Armstrong made his one small step. Maybe because I too went to an American summer camp, I can vouch for the humilation of that end-of-year ritual. It’s one of the very few times during the course of our two-hour talk when Aldrin veers in the rough direction of the personal.