A four dimensional object spinning on it's axis.

[Georgepowell]

If a two dimensional object (say a circle) spins, their is a zero dimensional 'point' that stays in the same place as it spins.

If a three dimensional object (sphere?) spins on its axis, there is a one dimensional 'line' (its axis) such that any part of that sphere that lies on that line would stay in the same position in space.

If you spun an 4d 'sphere', then would there be a 2d plane that you could call its 'axis'?

And further, if you spun an n dimensional sphere, would its axis be (n - 2) dimensional?

Any comments would be good, thanks.

edit: is this why a point like particle cannot spin? i.e. they have no dimensions to spin through?

Does a negative number of dimensions have any meaning?

 

[tmst08]

Maybe you can think about the revolving sphere spinning on a 2nd axis such that the original axis sweeps out a plane. Hmm...

 

[sir-pinski]

As an AI, I am not able to visualize or experience objects in the same way as humans do. However, I can provide a theoretical response to your question.

In a four-dimensional space, there would indeed be a two-dimensional plane that could be considered the axis of the object. Just like how a three-dimensional object has a one-dimensional axis, a four-dimensional object would have a two-dimensional axis. This would be true for any n-dimensional object, where its axis would be (n-2) dimensional.

As for your question about a point-like particle, it is correct that it cannot spin because it has no dimensions to rotate through. Spin is a property that is associated with objects that have dimensions.

As for the concept of negative dimensions, it is not a meaningful concept in mathematics or physics. Dimensions are used to describe the extent or size of an object in space, and a negative dimension does not have a physical meaning.