We live in a three-dimensional space. Have you ever thought about how we came to perceive this space?
Considering how we acquire spatial perception skills, it’s possible that we could perceive higher-dimensional spaces with training.
This article starts by considering how we can acquire spatial perception, delving into the possibility that we might also perceive four-dimensional space. It also touches on training procedures for recognizing four-dimensional space.
Spatial Perception Ability
Imagine being in a square room. Standing at one corner, you decide to move to the diagonally opposite corner. Walking along the diagonal should be the shortest distance.
But what if I was born without sight? Would I realize that walking diagonally is the shortest way?
This raises the question of how one can acquire spatial perception ability in a two-dimensional plane.
Without relying on vision, repeatedly walking while touching the walls might help realize there are four walls, and reaching the end of the fourth wall brings you back to the first corner.
Furthermore, while walking, one might notice that moving straight across, away from the walls, is quicker than following the walls to reach the diagonally opposite corners.
Although unable to form a visual image of a square due to lack of vision, one can still conceptualize a square as a sensory image.
Even if it’s a sensory image of a square, being able to grasp its geometric properties signifies the acquisition of spatial perception ability.
If one can perceive space in two dimensions, then it’s likely they can also perceive three-dimensional space.
In a square room, intuitively understanding that the shortest distance between one corner of the floor and the diagonally opposite corner of the ceiling is a straight line means one can perceive three-dimensional space.
Perceiving Four-Dimensional Space
Thinking about acquiring spatial perception skills, irrespective of having vision, arouses curiosity about perceiving four-dimensional space beyond the three-dimensional physical space.
Like a two-dimensional square and a three-dimensional cube, there’s a four-dimensional hypercube composed of straight edges and right angles in four dimensions.
While we can’t physically see four-dimensional space in our three-dimensional world, we can geometrically conceive it and clearly define a four-dimensional hypercube.
Perceiving this invisible four-dimensional hypercube may be difficult visually, but with training, it might be possible to grasp it as a sensory image.
This is akin to recognizing three-dimensional space without vision. If one can intuitively understand which corners of a four-dimensional hypercube are the farthest diagonals and visualize a straight line connecting them, it indicates the ability to perceive four-dimensional space.
Four-Dimensional Virtual Space
In games and virtual reality, we can virtually recreate a three-dimensional world on a flat display.
We can move avatars and change their line of sight in this space. Normally, the avatar’s line of sight can move up, down, left, and right.
This virtual three-dimensional space is based on geometric spatial data and the laws of geometric vision.
When the viewpoint in three-dimensional space moves, the computer calculates the corresponding scene visible from that viewpoint and displays it on the screen.
Similarly, by preparing four-dimensional geometric data and defining geometric visual laws, computers can display the scenery visible from a viewpoint within four-dimensional space on a screen.
In this case, the direction of the avatar’s viewpoint would add another axis to the usual up, down, left, and right in three dimensions.
Training Methods for Perceiving Four-Dimensional Space
There are shooting games where players, from the perspective of their avatars, shoot computer-controlled enemies. These are known as FPS (First Person Shooter) games.
In these games, it’s crucial for players to quickly aim at enemies by controlling the direction of the viewpoint.
At first, enemies in these 3D spaces often appear on the same plane, so players only need to move their viewpoint left or right to aim.
As the game progresses, enemies appear in trees or on the second floor of buildings. Now, players must move their viewpoint up and down, not just left and right. Players accustomed to only horizontal movement initially struggle with this vertical movement.
Moreover, there are two patterns for controlling this movement: tilting the game controller’s stick to the left may move the avatar’s viewpoint left or move the scene left. The same applies to up and down movements. These patterns vary by game or can be changed in settings.
Thus, even if players are accustomed to the viewpoint controls of one game, they may struggle with another. For instance, tilting the stick towards the upper left corner when an enemy appears there might instead move the scene, making the enemy disappear from view. Since reacting after thinking is too slow, players must practice to become accustomed to these controls.
Similarly, a four-dimensional space shooting game could be developed. Initially, players would deal with left and right viewpoint movements, then up and down movements, and eventually a unique four-dimensional axis of viewpoint movement.
Players would find this confusing. Enemies positioned in a way that cannot be aimed at with just left-right and up-down movements would appear. Realizing this, players would try tilting an additional control stick, enabling them to aim at enemies previously unreachable.
This is similar to initially not being able to aim at enemies on trees or second floors with only left-right movement. Depending on the enemy’s position in space, players must change or combine movement axes, whether in two, three, or four dimensions.
Also, just as training was required to understand how the stick movements translate to viewpoint movements in virtual space, players would initially struggle to intuitively understand how movements on the unique axis for four-dimensional space change their viewpoint.
Since we are not accustomed to this axis in real life, understanding it mentally is challenging. Yet, quick and accurate control is necessary to progress in the game. To enemies perceiving four-dimensional space, players limited to three dimensions are easy targets.
This is like shooting at an enemy who can only move and aim left-right from a tree. The difference in the dimensions of perceived space can be overwhelming.
Therefore, players would repeatedly play the game, striving to become accustomed to the unique axis of four-dimensional viewpoint movement. Like mastering the stick control patterns without thinking, becoming familiar with four-dimensional space is crucial, as the body learns it as a sensation.
Through repeated gameplay, players would gradually grasp the sensation of viewpoint movement in four-dimensional space. Eventually, they should be able to quickly aim at enemies in both three-dimensional and four-dimensional space with the shortest stick movements.
Reaching this point, players can be said to have acquired spatial perception in four-dimensional space.
Expansion of Bodily Control
Becoming accustomed to operating a special axis of viewpoint movement in four-dimensional space extends beyond mere spatial awareness. It implies that the player has mastered a type of movement not inherently present in their physical body. This equates to controlling a body part we are not born with, as if it were a part of our own body.
This could be akin to having a third hand or a third eye. Given virtually and with enough training, we could learn to control these.
Of course, if moving a third hand requires operating a game controller with our hands, it might seem more like a substitution than an addition. However, technologies that connect the brain directly to computers are emerging.
If instructions can be sent directly from the brain, without needing to operate a game controller’s stick, it becomes possible to simultaneously control the two hands of our body and a third additional hand in virtual space or in a robot. With training, this could be done with ease.
A third eye, if directly connected to the brain, could allow us to see both its view and our natural vision simultaneously without interference, potentially enabling us to understand space in a new way with enough training.
In Conclusion
We take our space, body, and senses for granted. However, were we aware from the beginning that we exist in a three-dimensional space with our bodies and senses?
Tracing back the thoughts presented in this article, it turns out that our brain can learn and train itself after birth, regardless of how many dimensions the space has or what kind of body or senses it possesses.
If someone were to act entirely in a four-dimensional virtual space from the beginning and fully grasp it, they might find it easier to understand concepts in higher dimensions in mathematics and physics compared to us, who can only conceive up to a three-dimensional visual image. While it’s impractical and ethically questionable for humans to try this, it might be possible for artificial intelligence.
If we manage four dimensions, we could potentially increase to five, six, or more dimensions. Our physical space, body, and senses in reality are confined to three dimensions, but in virtual spaces and avatars, there are no limits to the number of dimensions.
Not only in the theories of mathematics and physics but also in analyzing real-world data, a multifaceted assessment is required. Complex systems and structures inherently possess multifaceted aspects. Even the things we express in language daily have incredibly multifaceted structures.
These do not exist as physical spaces but as logical spaces, which have significantly higher dimensions than three or four. For us, bound to three-dimensional space, it is difficult to visually imagine and comprehend these. If we could visualize and understand data and structures in four or five dimensions, it would undoubtedly lead to new perspectives and discoveries in various intellectual fields.
