Tally-Ho!

More on the history of numbers

Tally-sticks appeared as accounting devices sometime between the periods covered by my post on eleventh-century mathematical advances and my (somewhat tongue-in-cheek) post about my time as a quantitative analyst.

I will draw information from a review of the book By the Numbers, by Jessica Marie Otis, as well as from other sources. The book discusses “early modern England” beginning around the end of the fifteenth century. Tally-sticks had been in widespread use before that time. [The following quotation and later ones are taken from the review by Tom Johnson.]

Tallies were long, squared-off pieces of wood – often hazel – cut with horizontal notches to represent quantities of money or goods that had changed hands between two people. After the transaction, the tally was split in half along the length, into a ‘stock’, for the creditor to hold on to, and a ‘foil’ for the debtor. When the debt was settled, stock and foil were matched to demonstrate that the amount was correct.

The stock part of these tally-sticks were often used as a form of currency, since they represented debts. They could be traded, often at a discount, for hard cash (meaning coins — paper money came later). These transactions may have led to our term “stock market.”

Each notch, or “score” on the stick represented twenty units of whatever was owed. That word retains its meaning in modern times. A score of paper is twenty sheets — not to be confused with a quire (twenty-five sheets). There are a score of quires in a ream. You may go into the local Stapes and buy a ream of paper without thinking too much about the origin of that word (defined as “large quantity” from the Arabic rizma meaning bundle).

are the opening words of the Gettysburg Address. The word “score” has a myriad of meanings, and one verb form retains the sense of scoring the tally-sticks — “to make a mark or cut on the surface of something.“

With his popular textbook The Grounde of Artes (1543), Robert Recorde made a polemical claim for arithmetic as the foundation of all human knowledge. ‘Without nomberynge a man can do almost nothynge,’ he wrote, but ‘with the helpe of it, you maye attayne to all thyng.’ In many respects, what Otis describes [in her book] was a documentary transformation: in these two centuries, cheap printed materials, technical education and Arabic numerals combined to flatten the hands-on world of object-based reckoning into the abstract arithmetic of pen and paper. Counting with things became old hat. Less than two centuries after Recorde was writing, a treatise entitled The Gentleman Accomptant disdained tallies as ‘obsolete’, except for ‘ordinary Use in keeping Accompts with illiterate People’.

A couple of asides here: (1) “Arabic” numerals, as noted in my earlier post, are actually Hindu numbers, conveyed to Europe via Arabia. (2) Norman words such as “account” and “controller” are sometimes still spelled in the old style to honor their origin (or outright misspelled), but are (and presumably always have been) pronounced, as in French, with a nasal “m” not with a labial “m” so that comptroller sounds like kuhn·trow·lr. One of my pet peeves is hearing radio announcers mangle this word.

Johnson goes on the explain how mechanical counting became more sophisticated, though the use of Roman numerals persisted well into the seventeenth century.

The mechanical aspect of accounting lay in a knowledge of the counting board, or ‘reckoning cloth’, chequered with black and white squares – the origin of the name for the royal ‘Exchequer’. Clerks pushed metal counters across the grid to represent quantities.

Eventually, Arabic numerals gained sway.

Arabic numerals allow the conception of ‘zero’ as a natural number. … In early modern England, this was their defining quality: the use of Arabic numerals was called ‘ciphering’, from șifr, the Arabic word for zero, or ‘algorism’, after the Persian astronomer al-Khwarizmi.

Then, other advances came rapidly:

The 16th and early 17th centuries yielded vital breakthroughs, both in theory and in practical application. The Scottish mathematician John Napier discovered logarithms, and also devised a calculating machine called ‘Napier’s Bones’, a set of rods inscribed with numbers which made it possible for users to perform complex multiplication and long division via the simpler operations of adding and subtracting. Edmund Gunter drew on logarithms to design measuring devices with trigonometric functions for navigation at sea and land surveying.

See my post on my early exposure to calculating devices. About halfway through is a picture of the last slide rule made in America.

Johnson’s review goes on with some entertaining stories drawn from the book. He concludes:

Ideas cast from objects take a long time to die. Twenty, or thereabouts, is still a score – a notch on the old tally. When in 1783 the Exchequer finally replaced tallies with a system of paper cheques, it gave them indented edges that mimicked the form of a stock and foil. Well into the 20th century, dockers and miners continued to be issued with brass ‘tallies’ as a means of clocking in at work. Some numbers are still odd.