A earthworm crawls on a piece of paper, and the world it perceives only has "front-back" and "left-right". For it, there is no such thing as "up-down". One day, a child pokes through the paper with a pencil, and a never-before-seen "point" suddenly appears in front of the earthworm, only to disappear instantly. It cannot understand that this "point" came from an "above" that it could never imagine.
If you feel sorry for the earthworm, let me tell you - we humans in three-dimensional space are just another "earthworm".
We live in a three-dimensional world composed of "length, width, and height", which seems very natural. But scientists have long proposed a startling idea: our world may be far more than three-dimensional. In addition to the obvious three directions, there is another direction that we cannot see or touch, yet it is constantly affecting our lives.
This direction is called the "fourth dimension".
What exactly is a "dimension"? Don't be fooled by science fiction movies
Speaking of the "fourth dimension", many people think of the mysterious space in "Interstellar" that can "go through walls into the past", or superpowers in certain TV shows that allow people to "walk through walls and doors".
But we have to put those aside for now. A "dimension" in science is a very serious concept; it refers to a "direction in which one can move independently". In a one-dimensional world, you can only move forward or backward. A two-dimensional world adds "left-right". In three dimensions, "up-down" is added, forming our familiar three-dimensional world.
What about the fourth dimension? It's not simply "going up another level", but adding a new direction that is completely independent of the previous three. That is to say, if you are a three-dimensional creature, no matter how you move or turn, you cannot directly "enter" the fourth dimension. You have to be "lifted out", just like we lift an earthworm off the paper.
Why can't we see it?
The reason is simple: our brains and senses don't have this function.
Just as a two-dimensional earthworm cannot understand "up", we three-dimensional creatures cannot truly "see" the fourth dimension. We can imagine, calculate, and even draw mathematical models, but we can only ever see its "projection" in the three-dimensional world.
For example, there is a geometric shape called a "hypercube" or "tesseract", which is the extension of a cube into four-dimensional space. You can imagine it as a cube nested inside another cube, connected by strange lines. It will "rotate and deform" in our three-dimensional world, folding like a Rubik's Cube. This is not an illusion; it's a projection of a high-dimensional structure that we don't understand in the three-dimensional world, just like when a two-dimensional world sees a sphere pass through a plane, it will only see a "point" turn into a "circle" and then disappear.
Mathematics has long played with the fourth dimension
In the world of mathematics, the fourth dimension has long been "implemented".
A point in three-dimensional space is represented by (x, y, z); in four dimensions, you just need to add a "w" coordinate, becoming (x, y, z, w). Then you can write the four-dimensional distance formula, like extending the Pythagorean theorem:
Distance = √(x² + y² + z² + w²)
This is not just theoretical; many theories of higher dimensions are based on this representation, such as "multidimensional scaling" in statistics, "high-dimensional vector features" in machine learning, and one of the most core theories in physics: Relativity.
Einstein: You mean time isn't part of space?
In the early 20th century, Einstein did something earth-shattering: he incorporated time into space, forming what we know today as "spacetime".
In his General Relativity, the universe is not a static three-dimensional backdrop, but a four-dimensional structure that can be bent, stretched, and even distorted - three dimensions of space + one dimension of time. This structure is called "spacetime".
In this model, the Earth is not held by "gravity", but is because the Sun "bends" the spacetime around it, and the Earth orbits in this curvature. The trajectory of an object's motion is not a line, but sliding along the "spacetime surface".
And this "time" becomes the "fourth dimension" in our real world.
Scientists still aren't satisfied: Let's make it ten dimensions!
Did you think scientists were satisfied with four dimensions? Wrong.
There's a theory called "String Theory" that attempts to unify gravity, light, electromagnetism, the weak force, and the strong force with a single mathematical formula. This theory boldly claims: the universe we live in actually has ten, or even eleven dimensions!
Where did the extra dimensions go? Scientists say: they are curled up. Yes, curled up, like a strand of hair curled into a circle, shrunk to an extremely small scale that human instruments cannot detect.
These are called "compactified dimensions", and they may be hidden within the internal structure of every atom, only becoming "visible" under extremely high energy.
Besides space, could time also have more than one dimension?
Here we enter the truly brain-burning territory.
Some people propose that we have always treated time as a single straight line, but in fact, time may also have multiple directions - even multiple "versions". This is called the "multi-temporal theory", which speculates that time can also have multiple dimensions like space, and that there may be multiple timelines, multiple universes, and even that the "you who is experiencing this now" is not the "only you".
This theory has not yet been experimentally verified, but it is widely discussed in quantum mechanics, the many-worlds interpretation, and even science fiction novels.
Invisible ≠ Non-existent
If you think this is all fantasy, then consider this: you can't see air, but you know it's there; you can't touch a magnetic field, but it makes a compass needle spin; you can't even "see" time itself, but you can feel it flow.
The meaning of science has never been to give you a world that is "seen is believed", but to help you understand the "truths" you cannot see with your naked eyes.
Higher-dimensional space and four-dimensional structures may never be fully presented to human senses, but mathematics and physics have built a complete system in this invisible world. And we, perhaps, are just "two-dimensional creatures" who have not yet awakened. Once a breakthrough arrives, we will realize that the reality we perceive is just the tip of the iceberg.
You think the world is three-dimensional, but in fact, the world may be far deeper than you imagine. Perhaps, as you read this article, something is brushing past you from the "fourth dimension", you just haven't perceived it.