Exploring the Rotational Properties of Zero and One-Dimensional Points

[atomicgrenade]

Fairly simple question I s'pose. If I've a perfect disc and I spin it about its centre, does the zero-dimensional point at its very centre actually rotate?

On the one hand, if I imagine being at the centre and looking out in one direction, if the disc rotates 180°, I would've thought that I should be facing in the opposite direction.

On the other hand, although obviously everything either side of it rotates, the central point itself has no sides, which suggests that if one were to rotate it 180° it wouldn't have changed at all, because a point would not seem (to me at least) to be facing in any particular direction. If it did rotate 180°, then this would imply its 'north face' would now be facing south and vice-versa.

Same question for a one-dimensional line going through the centre of the disc.

 

[HallsofIvy]

What do you mean by a point rotating? I think you have answered that question and your entire question with "it wouldn't have changed at all, because a point would not seem (to me at least) to be facing in any particular direction".

There is a difference between you being at the center and "looking out in a particular direction" and a point being at the center!

 

[atomicgrenade]

By 'me' looking out from the centre, I was imagining my perspective were I the central point itself.

 

[apeiron]

The issue for a point on a line may be even worse. Can it be crossed from one side to the other? Can there be a path that hits one side and leaves from the other?

An actually zero-D could not be oriented in this fashion. But then does this challenge the idea of zero-D points?

Of course the Euclidean foundational approach was constructive. Assume the point just exists (stop worrying about it). Then adding many points (infinitely) makes a line. Etc.

But there could also be a reverse-Euclid story based on constraint. So constrain a 2D plane (infinitesimally) and it would make a line. Constrain a line and you can create a 0D point. But where things may get interesting (in a Planckian soliton sort of way) is that this point could not be completely 0D. It would retain some (infitesimal) orientation to the wider world of which it is a constrained part. A quantal spin, so to speak.