Where Does the Meter Come From

Originally published on substack.

A while ago I’ve read “Antifragile: Things That Gain From Disorder” by Nassim Nicholas Taleb, and I found the argument laid out in it overall compelling, but there was one passage that felt wrong to me:

… few realize that naturally born weights have a logic to them: we use feet, miles, pounds, inches, furlongs, stones (in Britain) because these are remarkably intuitive and we can use them with a minimal expenditure of cognitive effort—and all cultures seem to have similar measurements with some physical correspondence to the everyday. A meter does not match anything; a foot does.

Setting aside the overall argument for “metrology bad”, “A meter does not match anything” is simply not true (or mostly not true).

Meter was supposed to match a ten millionth of a quarter of the Earth’s polar circumference. Due to measurement errors, the original definition of meter was slightly off, and that error is forever ingrained in all the following standards. The decision on how to define a meter was laid out in the “Report to the Academy of Sciences on a Unit of Measure” (translation to English).

One of the reasons to use Earth’s polar circumference was that it is relatively easy to calculate. Eratosthenes calculated earth’s polar circumference around 240 BCE with impressive precision.

How to calculate the “meter” like Eratosthenes

1. Believe that Earth is round.
2. Believe that the sun is so large and so far away that its rays that reach the Earth are parallel.
3. Figure out when solar noon is.
4. Figure out when summer solstice is.
5. Have access to a place where sun is directly overhead on summer solstice at solar noon (see Northern Tropic). Let’s call it “point S” (because Syene was the city used in Eratosthenes calculation).
6. Have a way of figuring out where north is.
7. Have access to a place “sufficiently” far to the north from point S. Let’s call it “point A” (because Alexandria was the other city used in Eratosthenes calculation).
8. Have professional step measurers measure distance between points A and S.
9. Measure length of the shadow of an object of known height at point A on summer solstice at solar noon.
10. Use shadow length and object height to calculate the angle at which sun rays fall on the object. That angle is the same as the angle ACS (where C is centre of the Earth).
11. Multiply distance between points A and S by number of times angle ACS would fit in a circle. That is the Earth’s circumference.
12. Divide a quarter of the Earth’s circumference by ten million, that is the meter.

This diagram from Wikipedia illustrates the reasoning behind this calculation:

Using this approach, Eratosthenes calculated the Earth’s polar circumference to be 252000 stadia, but given that we don’t have a precise value for stadia, we don’t know exactly how close Eratosthenes has been to the “real” value. If stadia used by Eratosthenes is assumed to be 157.5 meters (apparently “Griechische und Römische Metrologie” by Friedrich Hultsch is the definitive source here), the error between value calculated by Eratosthenes (39690 km) and real value (40008 km) is 0.8%, and so if he decided to use the same ten millionth of a quarter of the Earth’s polar circumference as a unit of measurement, that unit of measurement would be within 0.8% of the value we use today.

Far from not matching anything, a meter matches something that all people of all countries share and (with some effort) can agree on, a part of the Earth.