"I Ching is Number" -- The story of how Onmyoji 1000 years ago calculated the universe with counting rods
This note is inspired by the first installment of our Wasan (traditional Japanese mathematics) exploration series, "Were Onmyoji STEM majors!? -- Abe no Seimei, the man who calculated the universe with counting rods," and explores the human wisdom of "physically handling numbers" and the "learning through experience" approach that Sangaku Juku values.
Please see this blog for more details on the class.
"If you learn arithmetic, you can cure people's illnesses or cast curses on them."
This is a passage from the Konjaku Monogatarishu, a collection of tales from the Heian period. When I first read these words, which are quoted in the teaching material "The Path to Becoming a Mathematician" No. 2 by Mr. Naoto Shimagami, director of the Sangaku Juku Lab, I couldn't help but laugh.
"Cursing people with mathematics."
But while laughing, I felt like I had remembered something important.
■ The true nature of the feeling that "math is scary"
When working with children who struggle with arithmetic and mathematics, I sometimes encounter those who have a feeling that "math is scary."
"What if I make a mistake?" "The teacher will get mad at me." "It's not for me."
That sense of fear might be surprisingly similar to the feeling of people in the Heian period who considered arithmetic to be a form of sorcery.
A fear of "things that are unknown" or "things that are beyond one's control."
But Abe no Seimei understood those "scary things" more deeply than anyone else. That is why he is still talked about 1,000 years later as someone who "deciphered the rules of the universe."
The reason Sangaku Juku values the phrase "It's okay not to know. That is the beginning of the power to think" is because we know the true nature of this "scary" feeling.
■ The "essence of numbers" that counting rods taught us
The "counting rods" (sangi) that the children experienced in this class are tools for representing numbers by arranging thin sticks.
"Instead of writing numbers as symbols, you place them as physical objects."
This is the essence of counting rods.
As someone who taught geography and history in high school and studied pedagogy in graduate school, when I started reading math books after turning 40, I was surprised many times, thinking, "I never knew there was this perspective." One of them was this concept of the "physicality of numbers."
We use the symbol "3" as if it were natural. But the fact that a line in the shape of "3" came to represent the quantity of "three things" is the result of inventions accumulated little by little over the long history of humanity.
Counting rods are tools that allow you to feel the process of their invention right in your hands.
Place a rod. Move it. Remove it. Cancel it out.
It is not the sensation of "calculating numbers," but rather "finding the answer by moving objects." This was the method of thinking used by genius mathematicians 1,000 years ago.
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■ Rather than "the person who invented zero," the "person who struggled without zero"
There is one moment in the lesson where the children are most perplexed.
It is the moment they try to represent "105" using counting rods.
Place a rod in the hundreds place. Place a rod in the ones place. So, what about the tens place?
"In an era without the symbol for zero, how do you think they represented this emptiness?"
The children fall silent for a while.
When they realize the answer is "to place nothing there," I follow up with another question.
"Then, when representing 203 and 2003 with counting rods, how do you distinguish between them?"
Through this question, the children experience the "greatness of zero" for the first time.
Even if a textbook says "zero was invented by the Indians," it only enters as knowledge. When the knowledge that "zero was invented by the Indians" is introduced after the experience that "without zero, we couldn't distinguish between 203 and 2003," a realization emerges that "this is why human history changed."
What Sangakujuku values is this sequence of "providing knowledge after the experience."
■ The common ground between Onmyoji and modern computers
There is something I told the children at the end of the lesson.
The "principle of place value (decimal system)" that Seimei and his peers used with counting rods is the same fundamental principle that modern computers use for calculation.
Computers process information using the binary system of "0 and 1." However, the principle of place value—where you place one number in each digit and the weight of that digit determines the overall value—is based on the same concept as counting rods.
The mechanism by which Seimei calculated the universe with counting rods 1,000 years ago lives on inside today's smartphones.
The wisdom once feared as "learning arithmetic allows you to curse people" is now held in the palms of all humanity.
I always feel a shivering sense of awe at this continuity.
■ The Fact That "People of All Ages and Genders Were Enthusiastic"
There is a reason why I did not name this series "A Battle of Wits Among Samurai."
In the Edo period, it was not just samurai who enjoyed mathematics. Farmers pondered it on the ridges between fields, merchants solved problems beside their account books, and women dedicated sangaku (mathematical tablets) to shrines. The arithmetic book "Jinkoki," written by Mitsuyoshi Yoshida, was a bestseller in the Edo period. Its readers were "anyone," regardless of status or occupation.
Arithmetic was neither a "scary thing" nor something "only for geniuses"; it was enjoyed by people of all ages and genders as a game. I want to bring that culture to children in Sangaku Juku classes. That is the reason I designed this series.
"It is okay not to understand. That is the beginning of the power to think."
Just as Onmyoji 1000 years ago moved counting rods, the children at Sangaku Juku touched the world of numbers with their fingertips today.
Next time, we will challenge the survival game called "Mamako-date" (Stepchild Selection) that appears in the Edo bestseller arithmetic book "Jinkoki." A circle of 30 people, every 10th person is removed—we will experience the thrill of logic and regularity.
#SangakuJuku #AbeNoSeimei #CountingRods #Wasan #Onmyoji #PlaceValue #InventionOfZero #Arithmetic #Mathematics #ThinkingSkills #ElementarySchoolStudents #EducationalPhilosophy #InquiryBasedLearning #EdoPeriod
Sangaku Juku Principal Yosuke Yamashita
Thank you for reading until the end.
At Sangaku Juku, we hold classes themed around arithmetic every week.
Details of the classes can be found on the Sangaku Juku website blog.
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