Embracing Curiosity: Ancient Mathematical Wisdom from a Truckstop in Cheonan

As I sit at a local truck stop in Cheonan on my journey to Seoul, I am struck by the bright blue above sky. It's a beautiful day here in South Korea and I am grateful to have time for reflection during my well-deserved vacation. While at the truck stop, I stumbled upon a small exhibition about Korean flags, which sparked my curiosity and inspired me to learn more. An experience that reminded me of my love for flags as a young boy and, in particular, the design masterpiece of the South Korean flag, known as the Taegeukgi; it consists of a white background with a circle of red and blue in the centre and four sets of black bars or trigrams.? The white background represents the land, the red and blue circle represents the people, and the black bars represent the government. The flag was created in 1882, but its symbols are some of the oldest found on any national flag.

The red and blue circle, known as the taegeuk in Korean or t'ai chi in Chinese, represents the dual forces of nature. The red part, representing yang (Chinese) or positive energy, is located above the blue part, representing um (Chinese) or yin or negative energy. This symbol is called the to (Chinese: tao) and represents the constantly changing and complementary forces or principles in all aspects of life, such as light and darkness, good and evil, active and passive, and masculine and feminine. The thick, round part of each comma represents the beginning of all things, while the tail section represents the end. The yang and um are constantly transitioning into each other, with the yang beginning where the um ends and vice versa.

The four sets of trigrams on the flag represent the dualism of the cosmos and the four cardinal directions. The three unbroken lines represent heaven, or the pure yang principle, while the three broken lines opposite it represent Earth or the pure um principle. The two lines with a broken line between them represent fire, and the two broken lines with an unbroken line in the middle represent water. These four trigrams also symbolize the seasons. The trigrams on the Korean flag are only four of the eight trigrams found in the I-Ching, a Confucian classic on Chinese cosmology.

But this wasn't always the case. The flag of the King of Joseon, also known as the Eo-gi, is a powerful symbol that has long been revered in Korea. It features eight trigrams that represent the eight principles of the I Ching, or Book of Changes:

1. Heaven: representing the pure Yang principle
2. Earth: representing the pure Yin principle
3. Fire: representing the transition from Yang to Yin
4. Water: representing the transition from Yin to Yang
5. Thunder: representing movement and action
6. Wind: representing penetration and flexibility
7. Mountain: representing stillness and contemplation
8. Lake: representing joy and pleasure.

Each hexagram in the I Ching is associated with one of these eight principles, and the text is used as a tool for divination, self-reflection, and decision-making.??

It also features the earliest known magic square. According to the tale, a turtle emerged from the overflowing River Lo with a pattern of dots on its shell. This pattern, described as a series of dots, indicated the correct amount of sacrifice that the people, who were in danger due to the flooding waters, should offer to the angry god to appease him and stop the river from rising further.

The Lo Shu magic square is so named because of the river from which it emerged and the word for "scroll" in Chinese (shu). It is a 3x3 grid in which every row, column, and diagonal equals the same sum, known as the magic constant. Magic squares such as this one are used for their perceived ability to hold great wisdom.

Magic squares have been a known mathematical concept for centuries, with evidence dating back as far as 650 BC. Latin squares, another mathematical concept, were also well-known by the 12th century. It was previously believed that the idea of orthogonal Latin squares, which are formed by superimposing two Latin squares and having each pair of symbols occur only once, was introduced by Euler in 1782.

However, this idea was first explored by Choi Seok-Jeong (a Korean politician and mathematician in the Joseon period) in his book "Gusuryak," which contains an example of two orthogonal Latin squares of order 9. This groundbreaking work predates Euler's by over 60 years and demonstrates Choi Seok-jeong's innovative approach to understanding mathematics through the lens of ancient Asian philosophy.

And on the topic of "turtles and Choi Seok-jeong" I started thinking about the Hexagonal Tortoise Problem, which also can be found in "Gusuryak". The problem involves assigning the numbers 1 to 30 to the vertices of a hexagon in such a way that the sum of the vertices of each hexagon is equal. This problem has continued to be of interest due to its connections to coding theory and can be generalized to other situations.

So the moral of this story is about indulging in curiosity. A natural human trait that drives us to seek new knowledge and experiences. Something often associated with children, who are known for asking endless questions and wanting to understand how and why things work, with almost infinite curiosity and desire to learn about the world around them. From an early age, they constantly ask "why, why, why" without any formal training in interview techniques such as the Five Whys. Just take this simple question:

Why is the sky blue???

Most of us can relate to the parent, stressed by various things saying something along the line of, why not, dont ask so many questions?

However, in this simplest of questions is a beautiful story:?The sky appears blue because light from the sun is scattered in all directions by the gases and particles in the Earth's atmosphere. When sunlight hits the atmosphere, it is made up of a mix of different colours of light, including red, orange, yellow, green, blue, indigo, and violet. These colours are all part of the visible spectrum, the range of wavelengths the human eye can see. The particles in the atmosphere scatter short-wavelength light (such as blue and violet light) more efficiently than long-wavelength light (such as red and orange light). This is because the size of a particle determines how much it can interact with a particular wavelength of light. When light hits a particle much smaller than the wavelength of the light, it is scattered in all directions, with shorter wavelengths being scattered more efficiently than longer wavelengths. This is why the sky appears blue most of the time - the shorter wavelengths of blue and violet light are scattered more easily than the longer wavelengths of red and orange light.

But the beauty of this simple question goes beyond just the scientific explanation. Asking, "Why is the sky blue?" sparks a sense of curiosity and a desire to learn more about the world around us. It encourages us to look beyond the surface level and seek a more profound understanding.

So what sparks your curiosity? Is it the beauty of the natural world or the mathematical mysteries of the universe?

Please share in the comments and whatever it may be, asking questions and seeking answers is essential to being human. It helps us to grow and learn and to better understand the world around us. So the next time you look up at the sky and wonder why it's blue, or if you have any other questions about the world, don't hesitate to ask (and share your learnings). The journey of discovery is half the fun!