Saturday, August 04, 2007

Fun with Numbers!

In recent years I've developed the habit of poking through thrift shops and acquiring some of the more peculiar relics I find. Some months back, I stumbled across and bought an old Burroughs hand-cranked adding machine, for the lordly sum of three or four dollars. What made this one interesting to me was the extremely odd key layout, which is easier shown than described, so I won't even attempt to do so here — that, and the seemingly unfathomable mathematical principles upon which it appeared to operate.

A few weeks ago, after a power outage at work knocked all our networks down for three hours, I decided to redecorate my office by bringing in this adding machine and an old manual typewriter and putting them on my desk, as a sort of silent ironic commentary. Two weeks later, after dealing with a steady stream of visitors to my office who kept popping in to punch some buttons, pull the handle (If only it was a slot machine and I got a quarter each time!), and then ask, "What is it?" "Where did you get it?" "What on earth is it doing to those numbers?" — I finally decided to get serious about researching it.

Guess what?

It turns out that what I have here is Burroughs Portable financial calculator, which was made for the U.K. colonial market. It's in perfect operating condition and the computations it performs make perfect sense, provided you already know that sixteen quarter-farthings make a pence, twelve pence make a shilling, and twenty shillings make a quid. (Sorry, it doesn't do groats.) Once I made that leap, and brought it to the attention of some of my co-workers who are U.K. ex-pats and old enough to remember life before Decimalisation, they all looked at it and said, "Oh yes, of course," and confirmed that those were exactly the sorts of Dickensian computations it was performing.

What apparently identifies this thing as a colonial-market machine are the rows of ha'pence, farthing, and quarter-farthing keys, as those denominations fell into disuse in the U.K. long before the advent of mechanical calculators but remained in use in Ceylon, Malta, and the West Indies until comparatively recently.

What fascinates me most now, though, is the idea that the operating principles embodied in this machine express an entire cogent and coherent system of mathematics that is right on the very brink of extinction. There are still people around today who remember being taught this system as children and can add and subtract such sums as if by reflex. But in another generation or two the triumph of Decimalisation will be complete, and then this sort of math will be utterly unintelligible.

Oh, what glorious headaches this machine will give some future archaeologist!