Special Seminar on Napier's Promptuary Event as iCalendar

(Science Event Tags, Seminars, Computer Science)

16 August 2017

1 - 2pm

Venue: Building 303S, Room 561

Host: Computer Sciences

Cost: Free

Speakers: Garry Tee, Nevil Brownlee, and John Butcher

On Wednesday, 16 August from 1pm we will convene a special seminar to celebrate the transferal of the University of Auckland’s replica of Napier's Promptuary to Napier University (UK), to commemorate the 400th anniversary of Napier’s death.

The Promptuary was the first mechanical calculator, and it facilitates the multiplication of numbers with up to 10 digits each. Garry Tee, with introduction and summary statements from Nevil Brownlee and John Butcher, will describe the device (see description below) and provide a demonstration.

John Napier (Laird of Merchiston, 1550-1617) published his invention of logarithms at Edinburgh in 1614, and the mathematicians of Europe instantly acclaimed him as the greatest of them all. In 1617 he published his small book Rabdologiae. That describes his inventions of a  pocket-size multiplication table for decimal multiplication (Napier's Bones), binary arithmetic (as far as square root extraction) and his Promptuarium Multiplicationis (Lightning Calculator). That was an almost-wholly mechanical multiplier for numbers with up to 10 digits each, giving the exact product (up to 20 digits). It displayed conveniently the pair of digits for each product of digits from the 2 numbers being multiplied, with the user mentally adding the single-digit numbers displayed. Napier's Promptuary was almost completely ignored. Very few mentions of it got published, and almost all of those confused it with Napier's Bones (which are trivial).

Garry Tee supervised William Francis Hawkins for his Ph.D. (1982) on The Mathematical Work of John Napier. When Hawkins translated Rabdologiae from Latin to English, neither of them initially could understand the Promptuary. When Tee did succeed in understanding Napier's account, his admiration of Napier as a brilliantly original mathematician was greatly enhanced. Ray Myer (Dean of Engineering) agreed to get the Engineering technicians to build a Promptuary from Hawkins's English translation. Napier declared that the 20-digit product of a pair of 10-digit numbers could be produced in 1 minute by using the Promptuary. Hawkins and Tee found that, after a little practice, each could do it in 45 seconds.

Hawkins first publicly demonstrated our Promptuary at the 1979 NZ Mathematics Colloquium (University of Waikato). In 1980 Hawkins (then a vigorous youngster of 74) carried that Promptuary (c10kg) and demonstrated it at various universities in England, Scotland and the USA. Several universities ordered similar Promptuaries from our School of Engineering - but the cost of making our specimen was much higher than anticipated, and the Dean would not agree to manufacture any more of them.

Napier University in Scotland was named after John Napier, and his castle at Merchiston (west of Edinburgh) is the centre of its Merchiston campus. Garry Tee has now arranged for the University of Auckland to present the Auckland Promptuary to Napier University.