Point and line
What I would like to do is to change our perspective. The problem is that we always start from what we know, and we endeavor to fit the experience of our world into this complex of what we already know instead of encouraging exploration to expand that knowledge to understand through acceptance of the reality that we actually encounter.
This is, in essence, contradictory, verging on the delusional in relation to our everyday lived experience. For, whatever I think of, and however I think about it, it is in terms of this 3d existence I am currently experiencing.
Close you eyes for a moment. Now imagine a point - which is a 0d object – in 1d space. Or a line, which is a 1d object in a 2d space. If we continue along this line of thought, we will arrive at the square – a 2d object in a 3d space, and finally the cube –- a 3d object in a 4d space!
The space containing the object is 1 dimension greater than the manifest structure of the object expressed by the space it contains. For instance, a soccer ball is defined by its skin, which is 2d, whereas it is, in essence, a sphere. To return to the realm of the imagination, upon asking you to “imagine a point”, what do you see? Was it like a period, a full-stop? Did it have length and breath? And thickness too? You have imagined a 0d point by approximating it with a tiny 3d representation.
Similarly, the line — a 1d object (in a 2d space) — would be imagined as a 3d object, having both length and breadth, and some depth – else I could not imagine it! And so on.
Everything we see (consciously) in our mind’s eye, we see as 3d.
And every 3d object contains (or is formed from) an infinite amount of 2d, 1d and 0d objects in it.
There are two ways to imagine this line we spoke of. The first is as an object, the line, that one sees as a thin black line (or rod) with a beginning and an end. The other is more derivative. Starting with a single fixed point, we extend another 0d point from it, till it reaches another point, or till we cease moving it.This is another way to see the 0d point at the end of line. In fact, the line is extended by adding 0d points to it!