It is actually a video about Topology, but it shows something about how brains work, too. If you are already familiar with Topology then you need only watch the last 4 minutes (where my link to the video starts), so then just follow 'Click here to see the end'. If you aren't familiar with Topology then watch the whole thing.
There is a very nice book called 'The Shape of Space' by Jeffrey Weeks that does some of this low dimensional topology in a way a lay person can understand.
I would also say that the 'shrink to a point' concept of a hole is only one of many possible ways to define a hole. This is known as the 'homotopy' definition of a 'hole of dimension n'.
There is another way that looks at parts of the space with no 'boundary' that are not themselves 'boundaries' of some other part of the space. This is called the 'homology' definition of a hole.
So, for example, if you draw a circle on a sphere, there will always be some area that the circle you drew will be the boundary of *in the sphere*.
But, if you draw a circle around a hole in a torus (donut), there will NOT be an area that it is the boundary of. That means there is a 'hole' there. In this case, there is a one-dimensional hole since the curve is one-dimensional and there is no two-dimensional piece for which it is the boundary.
In the same way, for the surface of a sphere or torus, there is an *area* (two dimensional) that is not the boundary of any *three dimensional* piece.
It turns out that the torus has a 'two dimensional hole' when working with homology but NOT when working with homotopy.
