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?