Does a zero-dimensional point rotate when a disc spins around its center?

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Discussion Overview

The discussion revolves around the concept of whether a zero-dimensional point at the center of a spinning disc can be said to rotate. Participants explore the implications of rotation from both a geometric and philosophical perspective, considering the nature of points and their orientation in relation to rotation.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions if a zero-dimensional point at the center of a spinning disc actually rotates, noting that while the surrounding disc rotates, the point itself may not change orientation due to its lack of sides.
  • Another participant challenges the notion of a point rotating, suggesting that the idea of a point having a direction is inherently flawed, as a point does not possess any physical attributes to rotate.
  • A participant clarifies that their perspective of being the central point was meant to illustrate the thought experiment of experiencing rotation.
  • Concerns are raised about the implications of a point on a line, questioning whether it can be crossed and what that means for the concept of zero-dimensionality.
  • One participant introduces a philosophical perspective on the nature of zero-dimensional points, suggesting that while a point is defined as zero-dimensional, it may retain some infinitesimal orientation due to its relationship with the surrounding space.

Areas of Agreement / Disagreement

Participants express differing views on the nature of rotation for a zero-dimensional point, with no consensus reached on whether such a point can be said to rotate or possess orientation.

Contextual Notes

The discussion touches on foundational concepts in geometry and philosophy, with references to Euclidean constructs and alternative interpretations of dimensionality. The implications of quantum mechanics are also hinted at, suggesting a complex relationship between dimensions and physical properties.

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

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