Schools & libraries minus students times pandemic = many variables in where we learn.
Andrew Tan/ Pixabay

Math Connections Across Cultures

Every September, billions of students around the world go back to school. But in 2020, “back to school” favors logging on from home. Fortunately, remote learners can still enjoy everybody’s favorite subject—math.

Oh, it’s not your favorite?  Well, before you count math out, please join me on a virtual math field trip. No masks, no calculus required.

We’re off to discover how people have made math connections across cultures. We’ll count on traditional number systems and weigh in on the world’s most unusual units of measurement.  We’ll even collect souvenirs—cross-cultural math tips that quickly translate equations into solutions.

Guess the missing numbers <10: Are you at 6s & 7s with math or is it easy as 1-2-3?
High 5 if doing math puts you on Cloud 9!

When History Subtracts Cultures

Many of us grew up with a Euro-centric idea of math’s origins. It’s as if mathematical concepts never occurred to anyone until one sunny Greek day when Pythagoras swaggered into show-and-tell with his right angles, theorems, and proofs.  This was 6 BCE—not that anyone, even Pythagoras, could have known that. (Think about it.)

However, as historians like Sally Ragep and George Gheverghese Joseph have pointed out, by that time ancient scholars in Egypt, Iraq, India, and China had already turned in thousands of years’ worth of math homework.

Even math tools go back 35,000 years, to the Lebombo bone of Swaziland (now the kingdom of Eswatini). Archaeologists discovered the bone had been carved into a 29-notch measuring stick. Whether someone used it to tally things or to measure time (like the lunar cycle), we’ll never know. But this artifact shows that we’ve been counting on math throughout human history—no bones about it.

This water clock found in Iran has been measuring time for 2,500 years.
Photo by Maamaah

Countless Ways to Count!

Today, most people count using the base 10 number system. Historians say it’s because fingers were the first math tools. Ancient Mayans developed a sophisticated base 20 system, leading scholars to surmise that they also factored in toes.

In New Guinea, the Oksapmin have preserved a traditional base-27 counting system. Counting starts at one thumb, touches the wrist and forearms, goes up to the neck and nose, and continues down the other side of the body to the pinky of the other hand. Try it!

In France, counting begins as base 10 (“une, deux, trois . . .”). But once you pass 71— voila!—it switches to base 20. For example, 72 is soixante-douze, “sixty twelve,” and 80 is quatre-vingts, “four twenties.”

The Danish system throws in fractions. For instance, 50 is halvtreds, an abbreviation of “half third times twenty.”

The West African Yoruba number system ups the ante. In every set of ten numbers over 10, you add to express the fist four numbers. (The word for 14, męrinla, means “10 + 4.” ) Wait, there’s more! You then subtract to express the last five numbers in the set. (The word for 17,  étàdílógún, means “20 – 3.”)

Like 1970s calculators, a 1920s German “Addiator” reflected
the assumption that everyone used base 10.

Something from Nothing

Let’s zip back to zero. More than 36,000 years ago, the Mayans developed a concept of it, using the symbol of an empty shell. Yet zero remained a placeholder until the first century BCE.

That’s when a Persian mathematician, Mohammed ibn-Musa al-Khowarizmi, used zero to do breakthrough calculations. Al-Khowarizmi’s rules became known as algorithms, and the title of his published work, Kitab al-Jabr, gave us a whole new subject: algebra.

Once the concept of zero finally reached Europe, it caused a sensation. Among scholars, zero was suddenly Number 1. How slowly did zero travel? According to Daniel Tammet, author of Thinking in Numbers, William Shakespeare became one of the first English schoolboys to learn about it.

And if you think that nothing in math class made an impression on Shakespeare, you’re right. “Nothing” made such an indelible impression that it inspired extensive wordplay in at least six of the dramatist’s best plays. When it comes to zero, or cipher, as it was then called, Shakespeare really did make much ado about nothing.

Plays performed in-the-round let Shakespeare “zero” in on cypher-space wordplay.

Let Us Count the Weighs

Virtually all cultures count and measure, but how we do this encompasses a world of variables. For example, which three countries still use a system of units that has ancient Roman and Old English roots? According to the not-at-all-secret CIA Factbook, it’s Liberia, Myanmar, and the United States.

Americans’ use of the terms feet and miles derives from the Latin mille passus, “a thousand paces” as marched by Roman soldiers. Latin also produced uncia, which Old English called ynch, giving us “inch.” Yes, give us an ynch and we’ll take a mille.

Ancient Romans coined the word libras, for “pounds,” abbreviated as lbs.
Then they invented tasty ways to gain them.
© Joyce McGreevy

In 1795 France established the system that most of the world uses, introducing the word mètre, from the ancient Greek word for “measure.”(Some countries, like England, are mostly metric but occasionally nod to the older system by using miles on road signs.)

Today, as the metric system gains ground in American culture, tourists have adapted to using it overseas. Mostly. One U.S. traveler at a charcuterie placed an order using kilomètre instead of kilo. Fortunately, the butcher knew the traveler meant 2.20 pounds of ham, not .62 miles’ worth.

How Many Square Smoots in an Oxgang?

Over centuries, different cultures invented unusual units of measurement:

• Ireland: A cow’s grass was the amount of land it took to support a cow.
• Scotland: An oxgang was the amount of land tillable by an ox.
• Massachusetts: A smoot is 5 foot 7 inches, the height of one Oliver Smoot. In 1958, Smoot’s college buddies used him to measure the Harvard Bridge. It’s 364.4 smoots, “plus or minus one ear.”
• Finland’s measurements once included poronkusema, the distance a reindeer can travel without stopping to, um, take a break (about 6 miles). Also, peninkulma, the distance a barking dog can be heard in still air.
  

  Farmers once used traditional cow-culations.
  © Joyce McGreevy

• In Australia, the sydharb is an official unit of measurement, equivalent to 500 gigalitres—the volume of water in Sydney Harbour.
• Britain: British journalists used Wales (8,194 square miles) to report on everything from an iceberg in Antarctica (“one-quarter the size of Wales”) to a mangrove swamp in India (“half the size of Wales”). Comedians had a Welsh field day with this. One news-parody show reported a fictitious earthquake in Wales that affected “an area the size of Wales,” while a BBC radio show coined the fishy term kilowales—an area 1,000 times the size of Wales.

Every Culture Counts

Feeling down for the count about math? To solve your problem, make math connections across cultures. Italy’s method of lattice multiplication makes navigating numbers as easy as pi.

Many Italian students still use the lattice method first documented in 1478.
© Joyce McGreevy

And as you explore connections across cultures, you’ll also discover how many different and valid ways to accomplish something. For a quick proof, just compare how you count on your fingers to the approach in these cultures: Japanese, Russian. The starting points or gestures may vary, but they all add up to something that works.

As our virtual math field trip concludes, may your interest in math grow exponentially. After all, math intersects with every culture’s daily activities and extraordinary endeavors.

Oh, I see: Math is the sum of diversity plus discovery throughout history. To apply an idealist’s math model, don’t divide by cultural differences—factor in more cultural wisdom. What it adds up to may totally inspire you.

Discover more diversity in how different cultures count: Filipino and German, and Maasai.

See the impact of math on German classical music here and Senegalese fashion design here.

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