Some thoughts on Four-dimensionalSpace

some time ago, I was chatting with a friend and mentioned a game called “4D Miner”, and he gave me a science popularization by the way

of course refers to Four-Dimensional Space, not to time

Because I have not referred to any relevant materials and have no knowledge of the relevant field, the following is my personal understanding

Introduced from low dimensions to high dimensions

First Dimensional

In the 1-dimension, things only exist on a single axis (e.g. X Axis)

That is, the object exists in a straight line.

Imagine a single-line railroad track, with the main character’s perspective being a train

Character’s maximum movement: only front and back (i.e. X++, X–)

So the upper limit of the protagonist’s cognition: only before and after (i.e. X=N)

Second Dimensional

In 2 dimensions, things exist on two axes (e.g. X Axis, Y Axis)

Because two axes can form a plane, that is, the object exists in a plane.

Imagine a blank piece of paper with the main character’s perspective on a black dot that can be moved

The main character’s upper limit of movement: only up, down, left, right (i.e. X+N, Y+N)

So the upper limit of the protagonist’s cognition: only up, down, left and right (i.e. X=N, Y=N)

Third Dimensional

In the 3 dimensions, things exist on three axes (e.g. X Axis, Y Axis, Z Axis)

The three axes form a space, so the object exists in a three-dimensional space.

That is, in our world, the protagonist is yourself

The upper limit of the protagonist’s movement: only up, down, left, right, front and back (i.e. X+N, Y+N, Z+N)

if you don’t understand the upper limit of exercise at this point, you may be able to understand it at this point

you can change the state of movement: you can indeed run in any direction (X+N, Y+N) and jump (Z+N),
but they are all confined to three-dimensional space

can also change the way of movement: walking, riding in a car, or even riding a rocket can be marked by the XYZ triaxes

but you can’t change the upper limit of movement: you’re not on the fourth axis and you can’t have more movement

The upper limit of the protagonist’s cognition: only up, down, left, right, front and back (i.e. X=N, Y=N, Z=N)

also better understand the upper limit of cognition at this time, as mentioned above, the upper limit of exercise cannot be changed.
even if you were told that you could have a new axis for you to move, you wouldn’t know where that axis was for a while
this is the upper limit of cognition, and it is not natural to think of movement patterns beyond three dimensions

more vivid example, the ant has always been known as a cognitive two-dimensional creature, and for humans it is a three-dimensional individual
But for ants, crawling on another plane, there are only two axial movements of XY
That’s why if you draw a circle to enclose an ant, it will hesitate when it touches it

Summary

Having said a lot, let’s take a look

We can find some fixed patterns:

The existence of a dimension is irrelevant to the existence of such a dimension in a biological cognition
A high-dimensional worldview that cannot be naturally cognitive
When a dimension is upgraded to a higher dimension, only one coordinate axis is added to it

The Four-Dimentional Space

Okay, so I’ve built some settings upfront, and then here’s my 4th Dimentional Space understanding

Now it’s the tricky part hehe

Based on the 3D, add one more axis (W axis), which is now XYZW four axes

Imagine a 3D coordinate system with three axes XYZ centered on the origin
But you’re looking at this 3D coordinate system on a screen (2D).
Imagine a square with X=0 Y=0 Z=0
Then this screen itself is W=0
Then we overlay the front and back of this side of the screen
It’s basically what a four-dimensional coordinate system looks like

It can also be understood as: the directional superposition of a three-dimensional object

It is also conceivable if you are playing a 3D puzzle game:

You pick up an object that can be rotated
Imagine the rotatable object facing you and facing you in the opposite direction (i.e. W Axis)
In fact, there are countless of the same objects superimposed
But when it is mapped to your eye, you can only see this one because it overlaps
When you rotate, each piece on the W axis rotates because it is the object itself
In the end, it was still the object that was mapped
You can’t see what it looks like in 4D

Cross-dimensional display

I’ve thought about what if 3D could be mapped to 2D and be well understood
(For example, if you play a 3D game on a 2D screen, you can still understand the depth information well)

Does it mean that 4D can also be mapped to 3D well?

For example, the Apple Vision Pro is a spatial computing platform

Later I was reminded by a friend that this would be a better form of expression

But it doesn’t become a way to break down dimensional understanding

Because the upper limit of the human eye itself is three-dimensional, the cognitive range is only three-dimensional.