I can’t imagine what a four-dimensional space looks like — just as a straight line can’t imagine what a square looks like. That frustration made me pick up Flatland. The book is thin. It was written over a hundred years ago. The author was a pastor. I thought it would be a dry geometry science lecture. After a few pages, I realized it was a social satire novel wrapped in the clothing of mathematics.
By the time I was halfway through, I noticed that I was no longer reading with just my eyes. Some region of my brain that had been unused for years suddenly lit up. That feeling was like discovering a door in a room where you have lived for decades — a door you had never noticed before.
A World of Only Length and Width
Flatland is a two-dimensional world. The residents are various geometric shapes. Women are line segments. Men are isosceles triangles, equilateral triangles, squares, pentagons, and hexagons. The more sides you have, the more noble you are. Circles are the highest class. This premise sounds like a fairy tale. But the author, Edwin A. Abbott, wrote it like a cold and stern social investigation report.
In this world, identifying a person’s class is done through touch and hearing. You cannot use your eyes, because from the front, everyone looks like a straight line. You have to feel his angles. Sense his side proportion. Or listen to his voice. Lower-class triangles have rough voices. Upper-class circles have smooth, rounded voices.
This method of identification sends a chill down your spine. Because it is too similar to those social codes in our world that tell people who you are before you even open your mouth that tell people who you are before you even open your mouth. Clothing style. Accent. Watch brand. Which street you live on. In any human society, these things are just variations of angles and sides.
The women of Flatland are line segments. From the front, they look like a single point. Extremely sharp. Ready to stab at any moment. So the law requires women to sway left and right as they walk and to utter warning sounds. On the surface, this rule is meant to protect public safety. But underneath, it is fear of women and discipline imposed on them.
A Square’s Awakening
The protagonist of the book is a square. A respectable middle-class resident of Flatland. One day, he dreams of going to Lineland, a one-dimensional world. The residents there are line segments. They do not know what width means. They certainly do not know what height means. The square tries to explain to them the existence of two dimensions. They treat him like a lunatic. When he wakes up, he thinks he is ridiculous. He criticized the people of Lineland for being narrow-minded. But was he not the same?
Later, a sphere descends from the three-dimensional world into Flatland. The moment the sphere passes through the plane, the square is terrified. Because he cannot understand how something can appear out of nowhere and then disappear. The sphere patiently tries to explain the concept of three dimensions to him. Height. Above. Below. These words simply do not exist in the square’s dictionary. He tries hard to understand. But he makes no progress. We mock the ignorant people of Flatland. And we mock those of Lineland, too. But in front of beings from higher dimensions, we are exactly the same as them.
This Book Is a Hammer Built to Smash the Walls of Your Thinking
On the night I finished Flatland, I lay on my bed staring at the ceiling. I was thinking about one thing: of all the common sense that we deeply believe in today, how much of it is only true because we have never been taken to a higher dimension? Abbott used geometric allegory to criticize everything about his era: class stratification, gender discrimination, intellectual restriction, and the suppression of dissenters.
More than a hundred and forty years later, the things he criticized have just changed their clothes. They are still here. But this book installed an alarm clock inside my brain. From now on, whenever I cannot help mocking someone’s ignorance, that alarm clock will go off. Then I will remember the square from Flatland mocking the line segment from Lineland. Then I will remember the sphere mocking the square. Then I will remember that higher-dimensional being.
The best gift this book gave me was making me more humble. Humble enough that before I say anything, I ask myself one question first: Am I that line segment in Lineland, mocking the very concept of width?
