The Measure of Things: Size matters: the long and the short of it

People always need to measure things. That’s how people are. They like to ask: How much? How many? How far? How long? When we gonna get there? A question from the back of the car.

To answer all these questions, numbers were “invented”. The earliest known evidence of human writing or reckoning are regularly spaced notches found on an antler bone from about 15,000 years ago. The notches were presumably made to count the cycles of the moon or the menstral cycle. Within a coupla thousand years in humankind’s march toward glory, people began to count the days, the years, and the seasons. Ah, to celebrate the coming of the seasons! We still like to do it. That’s why we have calendars. To measure time and to have holidays. When agriculture developed, and as people settled down in camps and villages, seamstresses and toolmakers were finally able to find gainful employment. And any good seamstress, toolmaker or carpenter will tell you that the measurements are everything. Farmers, of course, need to measure their fields and their produce, their bounty. Then they need to sell their crops, divy things up, trade things, open investment folios. What’s business without counting and measuring? Nothing.

What’s science without math? Also nothing. Once humans needed to keep better track of time, and/or once they began to carefully observe the stars at night and began to discern the great celestial patterns, mathematics, the great science of patterns, was born. Simultaneously, Astronomy, the first science, was born. And astronomers, as we all know, are also assidious measurers.


Tyro Brahe’s observatory
Tyro Brahe’s observatory in Copenhagen

Everyone needs to measure!

The problem, especially for the kids, and, OK, especially for me too, is that there are so many systems!

Personally, I always have trouble figuring out how many fluid ounces are in a liter bottle. And still, after all these years, I’m not exactly sure how big an acre is. Not to mention the cubit. And what’s with the angstrom unit anyway?

For today, let’s just talk about length, and restrict ourselves to Anglo-American culture. the question is: how do we measure length? To paraphrase Shakespeare, let me count the ways:There’s the obviously-anatomically-derived English foot, which equals twelve inches – an inch being the width of a man’s thumb, and derived in English from the Roman word uncia which means one twelfth. Thirty-six of those uncias make a yard, which is three feet. So far so good. But life always gets more complicated. There’s the mile, which is 1,000 Roman paces, or 5,280 feet. There’s the distance from your thumb to your pinky, a span (9 inches), the rod (16.5 ft), the furlong (220 yds or 1/8 mile), and then the Russian verst (.66 mile) just to mix things up. If you’re at sea, there’s the league, which is three nautical miles (a nautical mile equaling the length of one minute of latitude, or about 1.15 miles). The fathom is six feet, which I suppose is knot (nautical miles per hour) hard to fathom.

What’s tricky is the old cubit, the distance fron your elbow to the tip of your middle finger. Depending on your location and historical era, the cubit was anywhere from 19 to 21 inches. Noah’s built his ark 300 by 50 by 30 cubits. The Egyption “royal cubit” was about 20.1 inches. The base of the Great Pyramid (the gold standard for any discussion of measurement or for anything else for that matter) was apparently 440 by 440 of those royal cubits. The Pyramid inch was 1/25 th of that royal cubit, which is 1.001 British inches –


a “coincidence” not unnoticed by Flinders Petrie, the great 19th century Egyptologist, who was perhaps overly eager to discover connections between the “royal” British inch and the heroes of the Bible. Like a lot of other things, measurement and numbers can soon lead you down some strange paths.

A good point to stop, no? We’ve only just started to talk about length, and so far we’ve only touched on Anglo-Saxon measurement systems. What about weight, mass (which on the atomic level is expressed nowadays in terms of its energy equivalent in electron volts), and volume? What about measuring time? 

To conclude, scientists world-wide try (and they succeed on the whole) to use only the metric system, which was developed by the scientists of Napoleon’s revolutionary government specifically to replace France’s hodgepodge of regional measurement systems with one reliable standard that every Frenchman could agree on. For many years since that time, somewhere in a dark, temperature-controlled, vacuum vault in Paris sat on a fancy pedestal an (exactly!) one meter bar of platinum-iridium alloy. Any questions about the accuracy of your yardstick? Go to Paris. In actual practice today, the platinum-iridium bar has been replaced by the multiple of the wavelength of some element I forget. Like I say, these things are hard to fathom. Good luck with it.








18 thoughts on “The Measure of Things: Size matters: the long and the short of it

        1. This is a bit hi tech for me. A few years ago, I did re-order my serialized, sci-fi novella titled The Story of the P’s, which is in the header. It was a major project for me at the time. I’m generally too lazy to fix up the blog. Thanks for the visit!

        2. You shamed me into fixing it a bit! I changed the WordPress theme an hour ago. Someday I’ll try to play with the categories and the widgets. 🙂

  1. Bumba, newcomer here. Good history lesson. Thanks. I was reading that some languages make it easier to count and do arithmetic. Some Asian languages will say seven and twenty or three and forty, msking it easier to do calculations.

    They used an exanple that rice planters in Asia had to be good at math to calculate the needed water for the crop, a very hands on experience. Going further, it was noted rice planting was not as successful in the US , as the plantation owner would not get down and dirty in the rice paddies like his Asian counterpart.

    Being a math nerd, I found these two stories compelling. Keith

    1. Welcome! I got interested in math a few years ago. There are traces of the old measuring systems in all our modern languages. It’s an interesting subject.

      1. I also find it interesting. I was watching a piece on the History channel that said the first non-Roman emperor from Spain was an amateur architect. He hired a chief architect from Greece to help rebuild and expand Rome. Those mathematicians were essential to Rome’s growth and also revealed merit based promotion is beneficial. Keith

        1. Our first President was a surveyor. History is full of lessons. When I got into math a bit, I got fascinated by the Great Pyramid and the mathematics involved in that.

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