A Journey into Dimensions: A Lingering Mystery

About nine years ago, I stumbled upon a YouTube video that left an unexpected impression on me. It featured a teenager, standing with the kind of casual confidence that makes complex ideas feel approachable. He was explaining the concept of dimensions, something I hadn't really given much thought to before. With a simple cube in his hand, he demonstrated how it existed in three dimensions—length, depth, and height. He called it a 3D object, and I remember nodding along, feeling like I was grasping something fundamental yet profound.

He went further. To explain 2D, he picked up a book, and with a flick of his finger, pointed to its flat surface. "This is the 2D world," he said, as if inviting us into a universe I’d never imagined. In this world, he explained, shapes like squares, triangles, and circles lived, but they could only perceive each other as lines. It blew my mind to think of a universe so limited, yet so full of possibility.

Unfortunately, I don't remember the title of the video or the creator's name. It's lost somewhere in the endless abyss of the internet. But the idea stuck with me.

Later on, I stumbled upon another video, this time featuring the physicist Michio Kaku. In it, he described a childhood experience that captured my imagination in a new way. He spoke about visiting a Japanese tea garden in San Francisco and staring into the fish pond. As he watched the fish swimming below the surface, he thought about them living in a 2D world. They could move forward and backward, left and right, but the notion of "up" didn't make sense to them. Moving vertically, into the third dimension, would be as unimaginable to them as stepping into a fourth dimension is to us. That image—the fish, gliding in their limited world—was haunting.

A little while later, another video caught my attention—this time from TED-Ed. It was called Exploring Other Dimensions by Alex Rosenthal and George Zaidan. I clicked on it, thinking it would give me more clarity, and it did. The video was based on an 1884 novella by Edwin Abbott called Flatland.

Through vibrant animation and rich storytelling, they expanded on the idea of the 2D world. They reiterated that in this dimension, all shapes—squares, triangles, and circles—could only see each other as lines. However, there was an added nuance that intrigued me: closer objects appeared brighter. This fact implied that even in their limited world, these 2D beings could perceive a sort of depth. Suddenly, they could differentiate between shapes. They weren't completely blind to the differences between a square and a triangle, after all.

But here's the thing that's bugged me ever since. If these 2D beings could perceive depth and collide with each other, are they really two-dimensional? I couldn't shake the feeling that they weren't. In my mind, if they could bump into each other, then they must have a tiny bit of thickness—just enough to make them more like flattened versions of 3D beings, rather than purely 2D. True 2D beings, as I imagined them, should pass through each other like ghosts. No sides, no depth. Just flatness.

This question gnawed at me, a paradox that made the concept of dimensions even more fascinating. As 3D beings, we view the 2D world from above or below, seeing it with an outsider's perspective. But what if those 2D beings lived in a way we couldn't fully comprehend? Were we over-simplifying the nature of dimensions just to make sense of them?

I've yet to find a satisfying answer. Maybe I never will. But this curiosity, sparked from a random YouTube video and later deepened by Flatland, has stayed with me. It's one of those ideas that makes you question not just other dimensions, but the very nature of reality itself.

p.s. The cover image is by Janesca on Unsplash. Unfortunately, LinkedIn doesn't allow me to add a caption to the image.