Money problems without decimals
By Frederic Friedel
“How much is a packet of chewing gum?” “Eight cents.” “Okay, I’ll take 100.” “Great, that will be eight dollars.” That was easy, you’ll admit. Even taking 50 would have caused nothing more than a two-second hesitation: “That will be four dollars.”
I spent early childhood in India, where my father, a German who had fled the Nazis, had taken up residence and been granted British citizenship — by King George, during the war! India, at the time, ran on Rupees, annas and pice (or “pies”, as they were often called). And this is how they converted:
1 Rupee = 16 annas
1 anna = 12 pice
So the purchase of chewing gum for a child’s birthday party went like this: How much is one packet? Seven pice. Okay, I’ll take 100. And Ramanujan needed to be called in for the shopkeeper to figure out how much the child should pay. Remember, there were no electronic calculators at the time. With my modern device I make it at 2 rupees, 11 annas and 9 pice, though I could be wrong — I am no longer able to handle such complex calculations. How did the country survive, how was it able to gain independence?
Well, it gained independence from the British, who had an almost equally convoluted system. The Pound Sterling, written like this: £, was divided into twenty shillings, and these were twelve pence each. I went through that system as well, where the problem was the same: you couldn’t find out how much things cost. Try it: a chewing gum is 4p (that’s how they wrote pence). How much do 100 cost? Call Alan Turing.
There is one more preposterous detail: Britain had, at the time, a coin called a Guinea. Would you like to guess how many pounds, shillings or pence that was worth? The answer is given at the end.
Now you may think that the British overlords were responsible for the madness of Rupees, annas and pice. Nothing of the kind. The Rupee traces back (hold your breath) to the 6th century BC, making it the oldest coin in the world. The pound is just 1200 years old—it came into existence in the eighth century AD, when “sterlings” or silver pennies were the main currency in the Anglo-Saxon kingdoms.
In the meantime both nations have adopted the decimal system — though the British have not agreed to drive on the right side of the street (they still use the wrong side, as I keep telling them). But at least they are abandoning miles and Fahrenheit. I still know by heart that there are 1760 yards to the mile, and that water freezes at 32°F, a random temperature. Daniel Gabriel Fahrenheit called the coldest temperature he had measured zero degrees, while 32° was the temperature at which water happened to turn into the solid white stuff. So what is the temperature at which it turns into steam? 212°F! We had to know that as children, and live with it. It was only after it was hard-wired in my brain that I converted to the simpler 0° and 100° Centigrade used in Europe.
There is one thing which is even more drastic, one place where in fact all communication breaks down. In Germany, we specify fuel efficiency by giving the amount of petrol (which the Americans erroneously call “gas”) in the number of decimal litres required to drive 100 kilometres. The Americans, on the other hand, tell you how many miles they can drive on one “gallon” (don’t get me started on that!). Once I told a friend visiting from the US that my car ran at “6.4 litres”, leaving him completely mystified. How many gallons for a mile? Unfortunately, no advanced mathematician was present to resolve the problem.
A quick aside before I reveal the guinea secret: the British still talk about their weight in rocks. Instead of saying “I weigh 72 kilograms, they say eleven rocks and 5½ pounds. Sorry, correct that: it’s not rocks, its stones. So eleven stone five and a half pounds. Can you guess how many pounds there are to the stone? Give up, you’ll never get that one: fourteen. And the pound, which is in use in the United States as well, is equal to 453.59265 grams or 0.45359 kilogram. Of course the kilogram is 1000 grams, and the metric pound is exactly half a kilogram (500 g). Oh yes, and finally, g is the common abbreviation of gram, kg stand for kilogram, while pounds (you won’t believe it) are “lb”. As in “you need to buy 2 lb meat.”
So now back to the Guinea: that golden coin was worth 21 shillings, or one pound and one shilling. A very useful denomination, don’t you think?
Above is a drawing by John Tenniel for Lewis Carroll’s marvellous Alice in Wonderland. The mad hatter is wearing a hat with the number 10/6 written on it. You know why? Because it cost half a Guinea, or ten shillings and sixpence. Really!