Understanding higher dimensions

Stuck in a 3d world, too boring?

Higher dimensions may be more accessible and simpler than you think it is :)

Just add another dimension and you enter the next realm of space

For beginners let's start with what a dimension is

Dimension means the constraint defined to space

On the contrary, higher dimensions will have less constraint and more freedom

Geometrically,

1)A fixed origin can be considered to be a point of 0 dimension obviously because it is totally constrained.





2)A point stuck on a line can be considered to be a 1-dimensional object because it can move only along the line

 Also, notice the number of line touching the vertex

3)A line in a plane can be considered to be a 2-dimensional object because the line can traverse anywhere in this plane marking length and width across space

Now guess what happens if a point enters a 2d world, would it be considered a 1d object or a 2d?
It would be a 2d because the dimension does not regard what type of object enters into it but it is all about the constraints for that object.

Also, think about what might happen if we keep 2 planes perpendicularly and allow 2d objects to move across the plane and thereby removing constraints further, would it lead to a new dimension?

The answer would be no! , although the object moves in a new direction, it is  constrained to move in a certain way in a plane and has not entered into the higher dimension

Amount of plane occupied by the object can be given by the area traversed


4)Things are getting interesting?

 Imagine planes stacked over one another  like the toppings in a burger and now objects are allowed to pierce through these planes

Guess what?

we are in 3 dimension baby!

cutting a new constraint and a new possibility of movement

This is the space where we live in




(Well, this burger is  3d  but  it is projected in a front plane hence it appears 2d)



Jokes aside,

The piercing through the plane added a new axis of a movement called height and it is represented by the axis y in the picture above.

Now you might wonder if is it necessary to remain 3d in a 3d world,
perhaps not, note that a shadow does not have any depth but still, it exists in a 3d world

It is also interesting to note that a 3d object would project a 2d shadow

5)Still here?  geometrically any no of dimensions is possible but what is it is the relevance?

All the interstellar fans, remember the wormhole in the movie  was made of 4 dimensions
The fiction says that wormhole can bend space and allow time travel

Maybe the warping movement that would allow this phenomenon





The fourth dimension can be created geometrically by drawing an axis perpendicular to the remaining three and here appears a new dimension

Since none of us have seen the 4 dimensions it is really a matter of choice, what to take the new dimension to be, the new movement of the fourth dimension could be moving in and out, whatever be the new dimension to be it has to be different from the 3 we have

Although some people refer to time as a 4th dimension
We know that time is a one-way street but  the dimensions can be traversed back and forth


Initially, I assumed that every dimension would have a closed object containing the same no of lines connecting the vertex as the dimension number be like,

1 line connecting the vertex for 1d, 2 for 2d,3 for 3d but what about 4d?
The figure below has 4 lines connecting every vertex but it did not require a new dimension to remain closed.

So maybe this analogy doesn't work

If we continue the analogy of shadow, a 4d object must project a 3d shadow
A shadow that would be real for us because it has depth

I also thought if this analogy works then why don't we see a shadow of a 2d object, but  I wonder if anyone has seen what a point is.