Life isn’t black and white. It’s a million gray areas, don’t you find? – Ridley Scott
In Boris Jardine’s paper “State of the field: Paper tools” the author tells a story about Edmund Halley, the guy that found the comet, who was asked by John Houghton to figure out the area of England and Wales.
That’s actually quite hard to do, when you think about it. Most of us can work out the area of a circle or a rectangle, but how to you work out an irregular shape like the outline of a map?
It’s also quite an important question because the areas of places have implications for what can happen there – what kind of industry might arise, how many people can live there, and what sort of taxes you can raise.
The technique Halley used was one that is a little unexpected, although it was well known in the 1600s, called “cut and weigh”.
Halley selected a map that he felt was a good representation of the country and cut it out. Then he cut circles from the same paper as the map until the cut out map and a circle weighed the same. Now, he could work out the area of the circle and based on the scale of the map calculate the area of England and Wales. He came up with the number 38.7 million acres, which is not far off the modern number of 37.3 million acres.
We think of paper as just a place to hold ink, but it turns out it can do more than that, and sometimes its weight matters more than you might think.