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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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Euler Squares
Euler Squares
Euler squares are created when two orthogonal Latin squares are overlaid to include two attributes in each cell of the array. Orthogonal Latin squares ensure that each and every possible pairing of the two attributes appears exactly once in the array. Now known as Graeco-Roman squares or Euler squares, these arrays are classified by their “order”, or the number of items along one side of the square array. For example, a 3x3 Euler square has order three.
In 1694, Jacques Ozanam [6] posed the problem of arranging 16 playing cards in a 4 x 4 array such that no row or column contained more than one card of each suit and each rank (Figure 2). The solution forms an Euler square of order four with the attributes ofcard rank and suit. There are 144 possible solutions, not including symmetrical transformations [7].
Figure 2: One solution to the playing card problem