He Used Sticks To Calculate The Circumference Of The Earth In 200BC | by Eric Brown | Aug, 2022

Eratosthenes of Cyrene reminds us technology can be a comfort trap

Eratosthenes Teaching In Alexandria (1635) — By Bernardo Strozzi Via Wikimedia Commons

TTechnology fools us. It wraps us in a blanket of comfort we find it hard to wiggle out of. In fact, in many ways we can’t see a world without it. The ease by which it simplifies processes also tends to bias our thinking, particularly with ancient cultures.

For instance, we refer to the times the ancient Greeks and Romans lived as “Antiquity.” It’s base root: “antiquated.” So, even our terminology for them points out they’re primitive. After all, they didn’t have computers, GPS, the internet, or the internal combustion engine, and they lived in glorified huts.

Seriously, how intelligent could they be? What tremendous advance could you make without a machine to help you, electricity, or modern technology?

Well, you might be surprised to learn you can make mind-blowing discoveries with simple tools and some imagination. History has many examples.

While these feats may appear amazing, they’re nothing compared to the work of Eratosthenes of Cyrene over two-thousand years ago. He calculated the circumference of the Earth. The tools he had available for this project were sticks, shadows, and logic, yet he made it happen.

Not only did he make it happen, but calculated the circumference so closely NASA confirmed he was only off by one percent.

How’s it possible and how’d he do it? Well, before we break down the “how,” we need to examine the “who.”

You’ll see the word “polymath” overused in the modern day, however, Eratosthenes couldn’t be explained any other way. He was born in Cyrene. This Greek-founded city, in modern day Libya put him in contact with a collection of higher thoughts from the ancient world.

First, he studied philosophy in Athens. Zeno of Citium and his ideas expressed in Stoicism caught his early attention. Then, he moved on to Plato’s Academy. James T. Chambers in his Dictionary Of World Biographynotes Eratosthenes wrote his first scholarly text Platonikos, investigating the mathematic base which drove Plato.

He also studied and wrote poetry which attracted attention. He later penned various chronologies dating the reigns of royalty and Olympic victors. Eventually his body of work caught the eye of Egypt’s Ptolemy III.

The Pharaoh invited him to be librarian of the Library of Alexandria, the greatest repository of knowledge in the ancient world at the age of thirty.

In his new role, fate put a book in his hands that would forever cement the name Eratosthenes into human history.

Reconstruction Of Eratosthenes’ Map Of The World (Zoomed In By Author) — By EH Bunbury (1883) Via Wikimedia Commons

Astronomer Carl Sagan in his Cosmos Eratosthenes explains read a random scroll in the library describing a strange meteorological event in a small outpost town in Syene. It happened on the longest day of the year at high noon. Shadows from a temple column or a stick in the ground disappeared and the sun shone directly down a well always cast in shade.

Sagan says most might think this a curious account and move on, but not Eratosthenes. He tested it out in Alexandria. On the longest day, the sun cast a shadow of a little over seven degrees.

But the image of a shadow vanishing fixed his mind. It didn’t happen in Alexandria, why would it be different in a town far to the South? If the world was flat, all shadows should be equal. Unless…the Earth curved.

Equal Shadows Cast By The Sun (My Lamp) On A Flat Plane (Note Paper) — Picture By Author

Eratosthenes had heard from Aristotle and other Greeks a theory that the Earth was a sphere. Curves, shadows, spheres, and distance opened a window. It was a mathematics problem, similar to the type Plato in his Academy gave reverence to.

With another data point, Eratosthenes could calculate the circumference of the sphere we call the Earth! He hired a bematist. This was a professional pacer, who walked out distances. Seriously, this is what you did before tape measures.

The bematist measured a distance of five thousand stadia or eight hundred kilometers between Alexandria and Syene. Plus, Eratosthenes already had the degrees of the shadow cast in Alexandria. The seven degrees out of a three-hundred sixty-degree circle equated to one over fifty.

Now, the complex problem worked out with simple multiplication.

Break Down Of Eratosthenes’ Calculation — Via NASA [Public Domain]

Two-hundred fifty thousand stadia converts to forty thousand kilometers. NASA explains the modern accepted value of the Earth’s circumference is only seventy km different. In other words, Eratosthenes figured out this NASA sized question with sticks, a human measuring tape, shadows, and common sense.

Not resting here, the ancient Greek Sherlock Holmes also calculated the tilt of the Earth’s axis. Rumor has it he used a toothpick, a toga, and olive oil. Alright, I just made that up. But after the whole circumference thing, you might be tempted to believe it.

While Eratosthenes provides us with a fascinating story, he also gives us a valuable lesson for our present day.

When I was in college, during a computer-information-technology course there was a final where we had to do a presentation. We took on the role of consultants. The project involved giving a corporation business advice for the future to help their operations.

Our teacher was an IT guy that had years of experience working at the highest levels of large companies with names you’d recognize. He tore us all apart. I had several classmates compliment my presentation; one even copied it. Well, my teacher wasn’t a fan and graded me similar to everyone else.

Obviously, students complained. His quick reply: everyone focused way too much on technology and computer systems. And this came from an IT guy.

He explained in every profitable company he worked for, older people sat at the head. They weren’t computer geeks or overly tech savvy. Yet, they got things done, created well-functioning organizations, and sustainable businesses with happy employees.

Tech comes and goes, along with computer languages. But the logical thinking which profit creates capable enterprises and solves problems isn’t dependent upon technology.

Pushing buttons is a comfort trap much easier than the struggle of deep thought. But proper logic is the ultimate equalizer.

  • Eratosthenes could think through a method to get the circumference of the globe in ancient times with no modern equipment
  • The ancient Egyptians aligned their pyramids to true North with only plumb lines as guides
  • Admiral Stockdale didn’t need a graphics calculator for his algorithms, just a stick
  • Archimedes discovered a principle still used today with a rudimentary bathtub

It’s something to think about as we’re more integrated and distracted by the technology we find it impossible to separate from. Deep thinking must be exercised like a muscle. And it’s hard to do this while we’re asking Google for the answer to everything.

Technology should be an aid, never a crutch. Otherwise the comfort will separate us from our ultimate tools — logic and thought.

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