Kaye Stacey
When I was a child there were no supermarkets and no
cash registers in our town. When we went
shopping, the shop-keeper got what we asked for from the shelves behind the
counter. He wrote down the prices of the
things we bought with a pencil, kept behind his ear, and then added them up on
paper. Some of the prices had to be
worked out first too, like one and a half pounds of apples at so much per
pound. We had to be careful that we
weren’t overcharged, so we checked by adding up the prices as well as we could
mentally. When the shop got a cash
register, the adding up didn’t seem so important, but we still needed to be
careful that the right prices were put in and that we were being given the
right change. Arithmetic and shopping were clearly linked.
Nowadays, there is little reason to associate routine
shopping with arithmetic. The bill is added up automatically and the amount of
change appears on the screen. Sometimes, you
need to estimate how much something will cost, perhaps if you don’t have
quite enough money for what you want to buy - but usually asking for a subtotal
solves the problem.
Most people would probably agree that routine shopping
does not now require many calculations for most people. It once was an activity where many people
used or saw being used both simple and complicated arithmetic (try finding the
price of one and three quarter yards of material at twelve shillings and six
pence per yard). Today, it is not.
However, the surprising fact is that there are many more calculations going on
in a supermarket today than ever before. Mathematics has gone underground,
invisible, embedded into the machines – the cash registers, the EFTPOS links
and the many other components of the supermarkets computer systems.
The obvious arithmetic in the supermarket is still in
adding up the prices although even the cash register now clearly does a lot
more: telling how much change to give, perhaps calculating a discount, working
out the number of customer loyalty scheme points, etc. Even so, most of the
calculations being done are not happening there. In this article, I will outline one way in
which important but hidden calculations are being done for the communications
in commerce. Two key concepts will be explained – error detecting codes and
error correcting codes - and illustrated with two familiar examples – barcodes
and ISBN numbers.