You’re probably sitting in a chair right now. You can move left, right, up, down, forward, and back. That’s it. That is the limit of your physical agency in a three-dimensional world. But what if there was another direction? Not a trick of the light or a perspective shift, but a legitimate, 90-degree turn away from everything you’ve ever known. When we talk about things to make and do in the fourth dimension, we aren't talking about time—at least not in the way Euclidean geometry defines space. We are talking about the "ana" and "kata" directions. It sounds like science fiction. Honestly, it feels like it too.
Mathematics doesn't care about your intuition. It treats a fourth spatial dimension with the same cold indifference it treats a triangle. If you add a coordinate ($w$) to the standard $(x, y, z)$, the universe opens up in ways that make our current existence look like a flat drawing on a piece of paper. You've probably heard of a tesseract, but actually conceptualizing what you would do inside one is a different beast entirely. It’s a place where you could look inside a sealed safe without opening the door or perform surgery without cutting the skin.
Making a Tesseract (and Failing to See It)
If you want to get started with things to make and do in the fourth dimension, the first project is usually a hypercube. Or a tesseract. Most people try to visualize this by looking at two cubes connected by their corners. That is a projection. It's a shadow. Think about a 2D shadow of a 3D cube; it looks like two squares smashed together. The real thing is much weirder. To "make" one in your mind, you have to follow a specific progression of logic that mathematicians like Rudy Rucker have championed for decades.
Start with a point. That's zero dimensions. Pull that point out to create a line (1D). Pull that line at a right angle to create a square (2D). Pull that square at a right angle to create a cube (3D). Now, here is the part that breaks your brain: pull that cube at a right angle to itself.
Where is that direction? It isn't there. Not in our 3D slice of the multiverse.
When you "make" a 4D object in 3D space, you are essentially taxidermying a higher reality. You can build a physical model of a tesseract’s net. Just like you can unfold a cardboard box into a cross shape, you can unfold a 4D hypercube into eight 3D cubes. If you’ve ever seen a "Dalí Cross" (like in his painting Corpus Hypercubus), you’re looking at a 3D blueprint of a 4D object. Making these models helps us understand the "surface" area of 4D shapes. A cube has 6 square faces. A tesseract has 24 square faces and 8 cubic "cells." It’s bulky. It’s crowded. It’s mathematically perfect.
Things to Do: The Geometry of a 4D Escape Room
Imagine being locked in a 3D room. No windows. No doors. In our world, you're stuck. But if you had the ability to move in the fourth dimension, escaping would be as easy as stepping over a line drawn on the floor. To a 2D "Flatlander" living on a piece of paper, a circle is an impenetrable wall. But you, a 3D being, can see over the circle. You can reach into the center of the circle and grab whatever is inside without touching the line.
Moving in 4D offers the same god-like perspective over 3D space.
- View internal organs: Since you are looking "down" from the fourth direction, 3D solids appear hollow. You could see a person's heart beating inside their chest as clearly as you see a circle drawn on a chalkboard.
- Knot untying: This is a wild one. In 4D space, most 3D knots simply don't exist. You could untie a knotted loop of rope without cutting it or passing the ends through the loops. The extra room allows the rope to "pass through" itself by moving around the obstacle in the $w$ axis.
- Mirroring yourself: If you stepped into the fourth dimension, turned around, and stepped back into 3D space, you would be mirrored. Your heart would be on the right side of your chest. You wouldn't be able to read English text anymore because it would all be backward. This is a real mathematical property of rotation in higher dimensions.
The Problem with Our Biology
We aren't built for this. Our retinas are 2D surfaces that map a 3D world. Our brains are hardwired to process parallax and shading to give us the illusion of depth. When we try to engage with things to make and do in the fourth dimension, we hit a hard biological wall.
Charles Howard Hinton, a 19th-century mathematician, actually obsessed over this. He spent years trying to "see" the fourth dimension. He invented "Hinton’s Cubes," a set of colored blocks that represented various cross-sections of a tesseract. He claimed that by memorizing the positions and names of these blocks in every possible orientation, he could eventually perceive the fourth dimension. Some accounts suggest he succeeded; others say he just became very good at a very specific type of mental gymnastics.
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Modern researchers like Marc Ten Bosch, who developed the game 4D Toys, argue that while we can’t "see" it, we can develop an intuition for it. By interacting with 4D physics simulations—where objects collide and rotate along four axes—you start to predict how they will behave. It’s like learning to ride a bike with an extra set of handlebars that move you through time's spatial cousin.
Why 4D Physics Matter Right Now
This isn't just for stoners or math nerds. High-dimensional geometry is the backbone of modern data science and machine learning. When an AI "learns" to distinguish a cat from a dog, it isn't looking at a 2D image the way we do. It’s mapping thousands of data points into a high-dimensional vector space.
In a sense, the most practical thing to "do" in the fourth dimension today is optimize an algorithm. If you have a dataset with four variables—say, temperature, pressure, volume, and time—you are working in a four-dimensional manifold. Mapping the "distance" between two points in that space requires 4D geometry. We use these "invisible" dimensions to solve real-world problems in logistics, weather forecasting, and even vaccine development.
Practical Steps for Exploration
If you want to move beyond reading and start "doing" things in the 4D realm, you have to bridge the gap between abstract math and physical intuition. You can't just wish your way into the $w$ axis. You have to use tools that translate that complexity into something your 3D brain can chew on.
- Interact with 4D Simulations: Download software like 4D Toys or play Miegakure. These aren't just games; they are mathematically accurate playgrounds where you can push 4D marbles and see how they disappear and reappear as they pass through our 3D "slice" of space.
- Study the Slice Method: Get a piece of paper. Imagine a sphere passing through it. To the paper, the sphere starts as a point, grows into a large circle, and then shrinks back to a point. Now, apply that to a 4D sphere (a glome) passing through our room. It would appear as a small sphere that grows and then shrinks. Visualizing "cross-sections" is the only way our eyes can process 4D objects.
- Build a 4D Projection: Use Zometool or even just pipe cleaners to build the 3D projection of a 24-cell or a 120-cell. These are the 4D equivalents of the Platonic solids. As you build them, try to identify where the "right angles" should be.
- Read the Foundations: Pick up Flatland by Edwin Abbott. It’s old, but it’s the best primer on the humility required to study higher dimensions. Then move on to The Fourth Dimension by Rudy Rucker for the heavy lifting.
The fourth dimension remains the ultimate "final frontier." It isn't somewhere far away in the galaxy; it's right here, potentially millimeters away in a direction we literally cannot point to. While we may never physically walk through a 4D portal, we can certainly build the mental structures to understand why we can't. Understanding things to make and do in the fourth dimension isn't about escaping reality—it's about realizing how much more reality there is than what we see.
To truly grasp the 4D experience, begin by sketching "Schlegel diagrams." These are wireframe representations that collapse higher dimensions into lower ones. By drawing a tesseract on a 2D sheet of paper, you are performing a double-compression of reality. Start with the "inner cube" and "outer cube" method, but as you draw, remind yourself that in a true 4D space, every single one of those connecting lines is the same length and every angle is exactly 90 degrees. That mental friction—the gap between what you see and what you know is true—is where 4D intuition begins to grow.