Let's imagine. Spatial dimensions.

in #english3 years ago


We are honored to live in a world that appears to us as three-dimensional. Each object is characterized by his length, width and height. These are so-called spatial dimensions. We also have time dimension without which it is difficult to imagine our existence, but today we will deal with the description of dimensions thanks to which we are able to study geometries. We are accustomed to the way that we observe the world. We usually don't wonder what would happen if we lived in a world with a different number of dimensions. So let's start from the beginning.

Dimensional capacity


0-dimensional world

Imagine a world that has no spatial dimension. We will quickly notice that it is boring.
Nothing happens in it because nothing can happen. We can represent it by a geometric point which, as we know, is not characterized by any dimension.
So it is not a world that we can analyze deeply. Practically that is all. So let's move on to more interesting examples.

1-dimensional world

If we have two points and connect them, then we get a straight line. It is our example of a one-dimensional world. Note that in this worlds we have the ability to move right and left.
Because we can characterize the length of the straight line. It is more interesting than a point, which allows for a deeper analysis. Imagine one dimensional beings (let's call them liners)
living in a one-dimensional world without borders (unlimited line on both sides). What is their life like? Extremely boring! Suppose they have eyes at both ends of their body.
The only thing they see throughout their lives are the eyes of their neighbors. They can neither walk around nor jump over them, as they have length only and for that, additional dimensions would be needed.
They only move right and left. Not a very wide range of possible moves, but it's still much better than in a 0-dimensional world, where you could do practically nothing!
We can look at it as if a 1-dimensional world consists of an infinite (if the line is unlimited) number of 0-dimensional worlds. I invent the term dimensional capacity.
So if the length of the line which is a 1-dimensional world equals n then it consists of n 0-dimensional worlds (without going deeper into details of countable and uncountable sets).

2-dimensional world

Suppose one of the liners discovers in his one-dimensional world that he may be immersed in some other strange dimension.
He can thus simply move in the second dimension to see all the other liners (move to the side).
Thanks to this, he is not constrained to watching his neighbors throughout his life. But strange things are happening in the world of liners.
A liner who has not discovered the second dimension, and has a neighbor who can dive into it, will suddenly notice that his neighbor disappears.
And then it appears on the other side of it, for example. This is incomprehensible to liners because they know that they are not able to teleport through neighbors.
Moreover, a liner submerged in the second dimension sees the entrails of its companions! (liners have no skin to cover their insides between his two eyes because they are neither wide nor tall!). The 2-dimensional world is simply a flat two-dimensional space, like a sheet of paper,
whose thickness is zero. Plus, it's unlimited. So let's imagine this space.

Creatures living in two dimensional space will have length and width (let's call them flaters).
How will liners see flaters? They will see them as if they were a line that appears for some time depending on the speed of the plane traversing a 1-dimensional world,
which will disappear after a while. Of course, as before, the 2-dimensional world is much richer in new possibilities than the 1-dimensional world.
If a 2-dimensional world has a length and width equal n, then it is composed of n 1-dimensional worlds or n^2 0-dimensional (n*n).
The flaters lives on the plane and it is their natural world. They cannot jump because they do not have height, and if they come across buildings,
they must avoid them by going around. The flat ones don't realize there are other dimensions either, until one of them discovers that he can jump!

3-dimensional world

What happens when the flater immerse into the third dimension? Like before, he will see his whole world from above!
She will be able to walk through flat walls of buildings, appear in a 2-dimensional world and suddenly disappear, she will be able to see everything at once.
Like a God of a 2-dimensional world. We are the beings * higher than Flaters living in the 2-dimensional world.
If we were to observe a two dimensional world, we would see everything at any moment. Every action of every flater, or their guts.

And how could a flater observe three-dimensional objects in its two-dimensional world?
Depending on the shape of the three-dimensional object, if it passed through the world of flaters surface, they would observe a changing shape line
(imagine a ball passing through a flat piece of paper, and a growing circle appears on its surface, which after a while it shrinks and disappears).
The 3-dimensional world is therefore even more capacious than the 2-dimensional world. When a 3-dimensional world has a length, width, and height equals n,
then it is composed of n 2-dimensional worlds, n^2 1-dimensional worlds or n^3 0-dimensional worlds. It is therefore enormously more capacious and richer than
worlds with fewer dimensions. What if you discover tomorrow that you can immerse yourself in the fourth spatial dimension?

4-dimensional world

It would be something transcendental. Considering what happened with the increasing dimensions in the previous worlds, here too we can conclude that it will be similar.
If you immerse yourself in a 4-dimensional world, You would just see everything. All the people around you, whether they are behind the wall or not.
You could appear and disappear into our world. You could walk through walls and you would see the insides of our organisms. I can't imagine how
4-dimensional beings would look like in our three dimensional world. It would probably be some complicated shifting shape that would appear and disappear.


Thanks for your attention. I hope this short article evoked positive emotions in you.

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