Topology

Topology is beautifully simple, yet understandably complex" ~ Joshua

Lets just look at the link between Topology and video games :)

1d

Suppose you are a 1 dimensional creature, if you were to travel on a line segment AB. When you travel out through B, you come in through A. And vice versa.

We can connect the two points together to form a circle.

2d

Now suppose you are a little point on a 2d square. If you move up out of the page, you enter from its bottom, if you go out through the right side, you re-enter from its left. We can connect all the edges to form a donut or torus.

3d

I believe this forms a 4d torus that cannot be visualised. So don't bother

What is Topology

Topology aims to understand that given a line, a square or a cube, if you connect its edges, how many holes would the new shape possess. A circle has 1 1d hole, while a torus has 1 1d hole (its centre) and a 2d hole inside the donut.

I've no idea how, but mathematicians managed to find a formula to quantify the number of holes any object at any dimensions would have.

Single cell

Source:
https://www.youtube.com/watch?v=MURzTFRRuJQ&list=LL&index=2&t=8s