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The first nonabsolute number is the number of people for whom the table is reserved. This will vary during the course of the first three telephone calls to the restaurant, and then bear no apparent relation to the number of people who actually turn up, or to the number of people who subsequently join them after the show/match/party/gig, or to the number of people who leave when they see who else has turned up.
The second nonabsolute number is the given time of arrival, which is now known to be one of the most bizarre of mathematical concepts, a recipriversexcluson, a number whose existence can only be defined as being anything other than itself. In other words, the given time of arrival is the one moment of time at which it is impossible that any member of the party will arrive. Recipriversexclusons now play a vital part in many branches of math, including statistics and accountancy and also form the basic equations used to engineer the Somebody Else's Problem field.
The third and most mysterious piece of nonabsoluteness of all lies in the relationship between the number of items on the bill, the cost of each item, the number of people at the table and what they are each prepared to pay for. (The number of people who have actually brought any money is only a subphenomenon of this field.)
Life, the Universe and Everything. New York: Harmony Books, 1982.
Loci: Convergence
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Who's That Mathematician? Images from the Paul R. Halmos Photograph Collection
For more information about Paul R. Halmos (1916-2006) and about the Paul R. Halmos Photograph Collection, please see the introduction to this article on page 1.
Halmos in Hawaii
Paul Halmos served as chair of the mathematics department at the University of Hawaii in Honolulu during 1968-69 and he had many mathematical visitors during this time. (See page 2 and page 10 of this collection, for instance.) Four of his visitors during 1969 were Ivan and Crina Singer and Allen and Joan Shields. Allen Shields (1927-1989) visited the University of Hawaii for a semester from his home campus, the University of Michigan (where Halmos had been a professor from 1961 to 1968), while Ivan Singer visited UH for one week from much farther away, Romania. Actually, Singer was a Visiting Professor at the University of Iowa in 1969, and he and Crina traveled during the Winter Break to the West Coast of the U.S. so that he could give a series of talks and to Honolulu, Hawaii, for one week so he could work with Halmos. Besides doing mathematics, Singer remembers that he and Crina spoke Hungarian with Halmos because he wanted to practice it and that they had a wonderful time as tourists, taking in, for instance the Kodak Hula Show, and as guests of Paul and Virginia Halmos.
Left to right: Paul Halmos, Crina Singer, and Allen Shields at the University of Hawaii in Honolulu
Left to right: Paul Halmos, Allen Shields, Joan Shields, and Ivan Singer in Honolulu, Hawaii
Ivan Singer now is Research Professor and Honorary Member of the Institute of Mathematics of the Romanian Academy in Bucharest. He is a functional analyst currently researching geometry in semi-modules, and also interested in optimization, convex and discrete geometry, and operations research. Photographs of (and by) Singer appear on page 36 and page 58 of this collection, where you can read more about him. Allen Shields is pictured on page 48 of this collection, where you can read more about him.
Left to right: Paul Halmos, Crina Singer, Allen Shields, and Joan Shields in Honolulu, Hawaii
Left to right: Paul Halmos, Crina Singer, Allen Shields, and Joan Shields in Honolulu, Hawaii
Paul Halmos and Crina Singer poolside in Honolulu, Hawaii
Many thanks to Ivan Singer for the photographs on this page. For more information about Paul R. Halmos (1916-2006) and about the Paul R. Halmos Photograph Collection, please see the introduction to this article on page 1.
You may use the photographs on this page in your classroom; for all other purposes, please contact Ivan Singer, Institute of Mathematics, Romanian Academy, or MAA Convergence Editor Janet Beery so that she may seek permission for you from Prof. Singer.
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Beery, Janet and Carol Mead, "Who's That Mathematician? Images from the Paul R. Halmos Photograph Collection," Loci (January 2012), DOI: 10.4169/loci003801