Stephan Mertens reviews a popular mathematics book on networks by Peter M Higgins titled Nets, puzzles and postmen for Science:
In every network, there are at least two nodes that have the same number of links. Translated to a social network, this means that at any party there will be two people with the same number of friends at the gathering. For a proof of this fact, party style, suppose that there are n guests at the party. The number of friends that a guest can have at the party ranges from 0 to n -1. Label n martini glasses with these numbers, and ask each guest to put an olive in the glass that represents the number of his or her friends. Now there are n olives and n glasses. Glass n -1 will contain an olive only if there is a guest X who is a friend of everybody else. In this case, glass 0 must be empty, because everybody is friends with X. If, on the other hand, someone put an olive in glass 0, there can’t be anyone who is friends with everybody, and glass n -1 must be empty. In effect, there are only n -1 glasses for n olives, so at least one glass will contain more than one olive. The guests who put their olives in this glass have the same number of friends. QED. The book rarely gets more complicated than this, even when Higgins (a mathematician at the University of Essex) explains quite sophisticated facts about networks.
Looks like a nice read, from the review at least.
In the same issue of Science, Joseph N Pelton and John Logsdon pay their tributes to Arthur C Clarke:
Scientific giants give us powerful understanding of how nature works. Newton identified gravity; Curie provided knowledge of radioactivity; Einstein, the space-time continuum; Hubble, a yardstick to measure the size of the “Big Bang universe.” Other powerful figures in human history contribute primarily by their insights into what might be. They span an incredibly broad range of art, literature, invention, and scientific inquiry. Leonardo Da Vinci is an obvious prototype, whose work and thoughts have transcended time.
Sir Arthur C. Clarke was clearly one of these “others.” He was able, decade after decade, to generate prescient insights into the scientific and social worlds. He skipped merrily and with equal aplomb from the world of imagination to that of science and technology. He was the essence of wit. But there was more than wit and insight to his work. Unlike his contemporaries–Ray Bradbury, Isaac Asimov, and Robert Heinlein among them–Arthur Clarke remained an optimist about the human ability to make life better through the peaceful use of science and technology. That he was often disappointed in reality did not temper that optimism. Though he was not a religious man, there was an underlying positive spirituality to his writings that set him apart. He was convinced that human destiny involved leaving the Earth for other places in the solar system and beyond, and that the results of space exploration would improve the human condition.
The obituary also mentions some facts about Clarke that I did not know of:
Now, after 90 full years, Arthur C. Clarke is launched into the cosmos for a welldeserved rest. This is no mere literary allusion. Clarke, who had no false sense of modesty about his achievements, arranged for a lock of his hair to be launched into space so that he could share his DNA with the universe.
Take a look!
Tags: Arthur C Clarke, Nets, Peter M Higgins, puzzles and postmen
