The Tesseract

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The Tesseract

Without dimension, you have a point. With one dimension, you have a line. Two dimensions of equal magnitude gives you a square. And if you extend that into three dimensions, you get a cube.

Every schoolchild can tell you that much. When I was a schoolchild myself, it fascinated me. It’s why I went into physics.

The thing with truly advanced physics — the exciting kind where you’re creating theories out of whole cloth, trying to make the pieces fit together — is that it often starts to sound a lot like philosophy. It’s the same struggle for a higher level of understanding about a lower level of reality than you can perceive. Indeed, levels are what it’s all about.

My name is Dr. Sarah Howatson, and this will probably be my final message. I hope they allow it to be found.

So you have the point, and the line, and the square, and finally the cube when you get up to three dimensions. But the universe has more to offer. If you expand to a fourth physical dimension, even if you can’t visualise it, you arrive at a shape with many names. A 4-cube, or a hypercube of the fourth degree, or the name that captivated me since I first read it decades ago.

The tesseract.

A tesseract is to a cube as a cube is to a square. Conceptually, it’s relatively simple. To make a cube in three-dimensional space, you take two identical squares, make them parallel to each other, move them apart in the new third dimension by the same distance that separates each of their corners, then connect the corresponding corners. Now you have a cube. Every schoolchild has drawn one in that exact way, using perspective instead of physical separation.

It’s the same with a tesseract, but most people’s minds fall down at this step. The instructions haven’t changed: take two identical cubes, move them apart in parallel in the fourth dimension so they’re uniformly separated in 4D, then connect all eight pairs of corners across that new fourth dimension. It’s fine until you start trying to picture it, and then you fail — because we picture things in 3D or less.

Did you know you can spend an entire career chasing the ability to truly see the tesseract?

I did. I embraced physics, and geometry, and mathematics. I dabbled in philosophy. I even admit that I dabbled in psychoactive drugs. I had my periods of despair and disillusionment, but I persisted. In the end, the breakthrough came as they all do: when it’s least expected, and when you’re not really working on it.

I was tired. I think that was the key. I’d been awake for most of the previous night, starting with insomnia and progressing through a couple of glasses of whisky. I make no apologies for that. I finally got to sleep at around five in the morning, and I woke up less than four hours later. I was in the lab all day, but it was just busywork and dealing with my doctoral students. By the time 8pm came, I just wanted to go home and sleep for a week.

I remember that I took my glasses off and set them on the desk. I stretched, tilting my head back and to the side, and I caught sight of the fluorescent light fitting on the ceiling from a strange angle. The metallic housing was partly reflecting the setting sun, and for a moment it seemed like the housing was not only non-rectangular, but also built upon a different plane than the ceiling itself. For some reason, my brain made a new connection.

I saw the tesseract.

It was a flash of intuition, visible in my mind’s eye for only a moment, but it was enough. I almost fell to the floor.

Instead, I stood up, and I remember that my heart was suddenly racing. I tried to see it again, and it was still there, still accessible. I put my glasses on and it went away, but then I took them off again and I could bring it back. I stood there, breathing noisily, and I checked all of my assumptions against the four-dimensional object in my mind. It was the tesseract, sure enough. I had seen it. I could see it. I typed some no-doubt crazed notes on my computer, and I went home.

It took almost no time at all to get to sleep, but my dreams were all of falling into strange geometries, inside and behind the everyday reality I knew, conspicuous and vulnerable to something I couldn’t quite perceive.

The notes were gone from my computer the next morning, and I assumed I’d just failed to save them in my excitement. Now, I know that I made no such mistake. Now I know a lot of things that had previously remained hidden to me.

By lunchtime the same day, I had began to see the strangers.

They were people, certainly. People in the sense that cubes are squares, and that squares are lines. They were everything that people are, but they were more — in a way that I can only describe via that analogy.

They were in my office when I returned from my morning coffee break. There were two of them, or perhaps two-squared, or some higher number. It’s difficult to tell. But I know that there was a man and a woman, at least at my own dimensional level. And then they were gone.

They came back many times. I had the sense that they were sometimes trying to speak to me, but their message was over at the same time that it began. I couldn’t understand, and when I tried to say so, they already seemed to know.

I could never quite see them clearly. I had the impression of seeing something that was vast, but that was very nearly edge-on from my perspective. I knew that I should move around in some way, but I had no more dimensions to move around in. At least, I didn’t at first.

They began to show me. Sometimes by a suggestion of movement in my peripheral vision. Sometimes by whispering things into my mind. And one afternoon, after a caretaker had just emptied the wastebaskets in my lab, they appeared again — those two or four or eight or sixteen hyperpeople — and they handed me a tesseract.

I can’t describe it to you. Our language lacks at least one full dimension of capability. But I could perceive it, as much in my mind as in my hands, and I understood. I grasped its nature, and then I saw the edge that marked the boundary of our own fourth dimension.

That was where they’d gone to, and come from. That was where they lived. They’ve always lived there, above and around, beneath and within. Anything that is hidden here in our three-dimensional world is laid bare to them. Distance means nothing, and so nor does time. They’re simply other planes in which to manoeuvre.

They want me to go with them, or perhaps to come with them. To be with them. I’m going to do it.

I see the edge of the next plane, and I still have the tesseract; it’s in my left hand as I write this, and my left hand is in it too. It’s time to go. I don’t think I’ll return, because I’ve sought this for my entire life. I doubt that anyone who reads this will ever be able to perceive me again.

To those I’m leaving behind, I’m sorry. But if it helps, try to remember just one thing.

I’ll be right here.

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