I met a voodooist when I was eight years old, young enough to believe anything anyone said, yet old enough to trust my instincts.
The voodooist was sitting – maybe crouching is more exact – on the edge of the pavement as I walked down the street. Her clothes seemed to be scavenged from odds and ends. Noticing my gaze, she introduced herself as a voodooist, which intrigued me enough to sit with her for a while.
She gave me an odd contraption that she proudly referred to as a “bottle,” although it resembled no bottle I had ever seen. Abrasions covered the cloudy glass, and its neck curled like a swan’s. At the end of this curvature, the bottle slipped inside itself.
Seeing that I was unimpressed by her “precious” gift, the voodooist spoke: “This bottle,” she winked, “is a key – a key to a secret. Not just any secret,” she added when she saw my indifferent expression. “It is the key to the secret. If you figure out the inside and the outside of this bottle, you will be granted the secret.” The mystery intrigued me, so I accepted the bottle.
From then on, the key and the secret troubled me like a curse. I would run my fingers over the bottle whenever I could. My mission was to distinguish between the inside and the outside of the bottle – if it had an inside and an outside. I spent countless hours, always beginning on the outer surface of the bottle but ending up on the inner surface. It seemed to violate the laws of geometry.
My wondering continued unanswered until I saw a picture of a similar bottle on the cover of a book; it had the same elegant swan neck but shone in liquid brilliance. The curvature penetrated itself just like mine. I was awestruck.
The book’s name was General Topology, by Stephen Willard. The bottle was called a Klein bottle. In the following weeks, I learned that things such as Klein bottles and Mobius strips have only one side, yet are two-dimensional. From then on, I delved into math to gain knowledge about homeomorphism, and I took interest in how Euclidean polygons are different from fundamental polygons. I learned many other equally amazing things, but none of them seemed to be the secret.
Frustrated to unravel the secret, I showed the bottle to my father. He displayed little interest in the bottle itself because, as an engineer, he already knew about topology, but he did seem amused by the “voodooist” who gave it to me. “Based on your description, this voodooist seems to be the infamous madwoman who lived in our old neighbourhood, in those shacks in Taiyuan. I wonder how she got a Klein bottle.”
I was not sure if Daddy wanted his little girl to feel sorrow or contempt for the “unfortunate neighbour,” but I experienced something more than sympathy. I had believed in the voodooist, had faith in her secret. Now I am no longer sure of either, but my fascination with topology continues. Perhaps that is where the secret lies.