The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. To be sure, his art originated in the necessity for clothing such creatures, but this was long ago; to this day a shape will occasionally appear which will fit into the garment as if the garment had been made for it. Then there is no end of surprise and delight.
Loci: Convergence
Counting Boards
A Counting Board in a Strasbourg Museum
Have you ever seen a counting table? The question occurred to me when I came across a very fine example in Strasbourg and wondered why I had never seen one before in any museum in Europe.
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
