What measures the ruler? A 4,600-year-old bar and a puzzle from Wittgenstein
Every metre stick was once checked against a single official bar kept in Paris. Philosopher Ludwig Wittgenstein noticed an odd gap: nothing could prove that the bar itself measured one metre. It simply was a metre, by agreement. The humble ruler hides surprisingly deep questions, and an ancient pedigree.
The oldest surviving measuring rod is a copper-alloy bar from around 2650 BC, dug up by the German Assyriologist Eckhard Unger at Nippur, a Sumerian city in present-day Iraq. The Indus Valley civilisation was carving rulers from ivory before 1500 BC. One from Lothal, around 2400 BC, is marked in steps of roughly 1.6 millimetres. Ian Whitelaw argues that a ruler from Mohenjo-daro divides into units of 33.5 millimetres with decimal subdivisions accurate to about 0.13 millimetres, and bricks across the region match those units.
Early measures leaned on the body, such as the cubit, hand and foot, and their lengths drifted from place to place and century to century. The metric system, introduced in the late 18th century, gradually replaced most of them. Wittgenstein's point in his Philosophical Investigations of 1953 was that the Paris bar could not be measured against itself; calling it a metre was a move in what he called a language game.
Rulers also shape geometry. With only an unmarked straightedge and a compass you can split any angle neatly in half, yet dividing an arbitrary angle into three equal parts is impossible, unless you cheat by putting two marks on the ruler. Anton Ullrich invented the folding rule in 1851, and Frank Hunt followed with a flexible one in 1902. For curves, draughtsmen use rigid French curves or bendable splines, while masons once shaped a flexible lead strip to mouldings; it was called a lesbian rule, after the island of Lesbos.
Source: Ruler
