vocabulary
before we continue, a quick check on the words being used to describe the stuff we're dealing with.
so far we only have one type of thing in the void (there are two of them, but they the same type of thing).
the word has been mostly given as 'point', however, it has come to be known that in geometry there is word 'vertex' (pl. 'vertices') which seems to describe the thing that we are describing.
dimension
remember the first vertex created in the void? it had no width, no height - and this is still true. we went on to create another vertex, and it is also is without width and height, for that is the nature of vertices, they occur at a place without occupying any space. ah! there's an interesting word - 'space' - see what has happened:
now that there are two vertices, something else has come into consciousness - a spatial dimension.
where ever our two vertices may be, there can be seen between them a line...
the line has come into being because of the two points, but it is not limited by them. thus the line is infinite, and both vertices are upon it.
well, maybe you saw it coming, but that took me by surprise. we created one type of thing, duplicated it - just the same as the first, only separate to it and poof -- a completely different type of thing appeared! perhaps even two things; there is now an infinite line that we can recognise as a spatial dimension, and also there is a finite part of the infinite line that is in-between the two vertices. there's enough here to keep me thinking for a while...
