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No. 3271:
An Obsession with Round Numbers

by Roger Kaza

Today, an obsession with round numbers. The University of Houston presents this program about the machines that make our civilization run, and the people whose ingenuity created them.

The other night I found myself watching a documentary about Kenyan runner Eliud Kipchoge and his amazing sub two-hour marathon. His record isn't "official", since he ran behind a team of elite runners blocking the wind and a car setting the pace. His custom Nike shoes weren't "legal" either. But with these small hacks, he clocked in at one hour 59 minutes, 40 seconds. Wow.

Eliud Kipchoge
Eliud Kipchoge
  Photo Credit: Denis Barthel, CC BY-SA 4.0 , via Wikimedia Commons.

Later on though, I couldn't help but ponder the obvious: what is so magically different about a marathon finished in slightly under two hours, vs one slightly over? Both times are astounding. Have we humans made idols out of round numbers?

Yes, you killjoy, I thought, we have indeed. The examples are countless. Breaking the four-minute mile. Turning fifty. Making six figures. The 70s, 80s, your decade. The millennium? How many generations get to experience one of those?

But maybe once in a while, we ought to humble ourselves contemplating the sheer arbitrariness of these milestones. The numbers in nature are often unround: think of pi or the days in a year. So decades or centuries or millenniums--these spans are all just artifacts of our base 10 counting system. We're told that base 10 is somehow "natural" since we have ten fingers and ten toes. The ancient Sumerians, who were some of the first mathematicians, thought otherwise. They counted using multiples of 12 and 60. The Babylonians did as well.

It turns out we get all of our time units from those ancient cultures: 60 minutes, 60 seconds. And the Sumerians decided a day should consist of, what else, twelve hours. So each of their hours was the equivalent of two of our modern hours. Just think if that had stuck. The twenty-hour workweek! I like it already. Kipchoge's record, a Sumerian sub one-hour marathon. Sounds even more impressive, right?

Complicating this medley of time measurements are the ones we use for distance. In 1896 at the first modern Olympics, the marathon was 25 miles, a nice round number. That was roughly the distance between the ancient Greek cities of Marathon and Athens. According to legend, a messenger once ran that route at a blistering pace to report a battle victory, after which he expired from the exertion. But in 1908 the British Royal Family requested that the Olympic marathon start at Windsor Castle, so they could watch. The distance from the castle to the finish line at the stadium happened to be a very unround 26.2 miles, but that number stuck. And how did the mile itself come to be? Long story, but the word comes from the Roman mille passus, or "one-thousand paces." Clearly our love of round numbers goes way back.

So, when you add it all up, Kipchoge's amazing feat is an odd mishmash of ancient Sumerian and Babylonian time-counting units, with a Greek legend, Roman miles and British Royal Family decree thrown in for good measure. However you measure it--round or, as I prefer, unround, a remarkable achievement.

The Battle of Marathon, painted by Georges Rochegrosse
The Battle of Marathon, painted by Georges Rochegrosse
  Photo Credit: Georges Rochegrosse, Public domain, via Wikimedia Commons.

This is Roger Kaza, from the University of Houston, where we're interested in the way inventive minds work.

The documentary about Kipchoge and the quest for a sub-two hour marathon is Kipchoge: The Last Milestone. Kipchoge also holds the official world record for the men's marathon, at 2:01:39. For comparison, the Olympic record in 1908 was 2:55:18.

The ancient Sumerians and other base 12 cultures counted using the following method: using your thumb as a pointer, count each of the digits of your four fingers of the same hand. That's 12. Do that five times, using your other hand's fingers and thumb to tally them. That's 60. But wait, there's more! 60 x 6, 360, is of course used in degrees of a circle or sphere, another Babylonian contribution.

12 is also a much handier number than 10, because it has more factors or divisors. Think if you had a dozen eggs to divide evenly. You can do so with 2,3,4, or 6 friends, so it divides four ways. 10 divides only two: 2, 5.

Why 60 is a great counting number.

Wikipedia entry on the first modern marathon in 1896.

Why a Marathon is 26.2 miles.

Why we find comfort in round numbers.

The Roman mile is not the same distance as our modern mile, but is the origin of the word and concept. Coincidentally, a marathoner with a stride of 5.28 feet over one thousand paces would indeed add up to a modern mile.


The author's 60th birthday cake, counted in Sumerian twelves.
The author's 60th birthday cake, counted in Sumerian twelves.
  Cake Credit: Julie Thayer.


This episode was first aired on May 25, 2022