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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.

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# Counting Boards

## A Very Brief History of Counting Boards

Surfaces marked with lines were used for calculation with counters since antiquity and the early printed arithmetics commonly show illustrations of them being used.

From Jakob Koebel's Rechenbiechlin, Augsburg, 1514

The practice of using a table dedicated for the purpose continued in northern Europe long after it had died out in favour of written methods elsewhere in Europe; the table in Strasbourg appears to be as late as the end of the 16th century. My suspicion that the Strasbourg table is a rare surviving example is strengthened by the fact that it is the only one used to illustrate counting tables in Pullan's History of the Abacus.

There must have been many hundreds of these tables at one time, in which case it is surprising not to find any remaining. Admittedly the Strasbourg example comes from a former Merchants' House where the wealth of the guilds is still evident. Furthermore, the lines are not cut into the surface but are made with inlaid ivory and so the table would have been thought worth preserving.

Does any reader know of other examples?

References

Musee de l'Oeuvre Notre-Dame, Strasbourg

J. M. Pullan, History of the Abacus, ch. IV, Hutchinson, London: 1968

D. E. Smith, History of Mathematics, vol. II, Dover, New York: 1953

Contact: chrisweeks@eurobell.co.uk

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