Stories for Maths Teachers - why is a meter not a meter?

Stories are great ways to teach about concepts. This is a great story that talks about where a metercomes from, why it the length it is and why it is actually wrong and is too short!

I took these notes when reading The Measure of All Things – the seven year odyssey and hidden error that transformed the world, Free Press by Alder, Ken 2002. I recommend this book to all maths teachers.  

Introducing: Jean-Baptiste-Joseph Delambre, the north going astronomer and Pierre-Francois-Andre Mechain, the south going astronomer.

The plan was to have the meter equal a ten millionth of the quarter meridian from pole to equator.

These two measure from Dunquerque to Barcelona through Paris by triangulation over 7years during the French Revolution.

Their meter is 0.2 mm too short because Mechain made a mistake - about the width of 2 sheets of paper. 

Today’s satellite surveys have the meridian of pole to equator as 10,002,290 meters

Which is 500,500,000 inches (John Hershell)

In their time precision was paramount and error was thought to be possible to avoid. They were savants, not scientists as the scientific method recognizes error. One baseline measured by Delambre was found to be 1 cm short. A discrepancy error of .0001%, over a ten km stretch.

In 1960 an international bureau redefined the meter “in terms of the wavelength of light emitted by a specific energy transition in the krypton-86 atom.

International Bureau of Weights and Measures redefined the meter in 1983 as the distance traveled by light in a vacuum in 1/299,792,458 seconds, time defined by the atomic clock (Atomic Clock  Isidor Rabi (1898-1988), atomic clock in 1949 Natural resonance frequency of atoms. National Institute of Standards and Technology started using an atomic clock called NIST F-1 in Boulder Colorado 1999) A second is defined as 9,192,631,770 vibrations of a cesium atom. The clock will lose 1 second every 20 million years.

Delambre’s archive meter was a platinum bar, platinum-iridium (10%) alloy in the end,

The French “under the cover of some 800 names, the Ancient Regime of France employed a staggering 250,000 different units of weights and measure” p 2

French experimented with the metric system but it failed (even Napoleon turned against it) and it was not until 1840 that it was restored. By then Holland and Belgium had been using it for 20 years. It was legally adopted in Chile 1848, Colombia 1853, Ecuador 1856, Mexico 1857, Brazil 1862, Peru 1862, Argentine 1863.

Legal enactment of the metric system has followed in the wake of revolution or war, upstart regimes legitimizing their rule

Britain tried it in 1863, by a House of Commons vote 110 to 75 but it never became law.

US never joined the system because of its ‘freedom from feudal institutions’. It already has common standards and is big enough internally to maintain them. But problems arise and can be embarrassing. The 1999 Mars Climate Orbiter, NASA, failed because one team of engineers used traditional American Units, another had used metric units, Result was a trajectory error of 60 miles and a waste of $125 million .

Notes by Derek Pugh