Re: direction, dimension & Re: {soi}

[jorge@PHYAST.PITT.EDU]

And:
> > > That's right. But the sagging can be in one or both dimensions. The
> > > shape of the sag can be like half a sphere or it can be like half
> > > a cylinder. (I don't see that it depends on the object's symmetry;
> > > a square of corrugated cardboard would tend to sag "hemicylindrically".)
> > Yes, so does a sheet of paper, but the axis of the cylinder can be
> > any direction along the plane, if only one at a time. Which direction
> > is the sheet of paper tinsa in?
> Away from the plane defined by the paper's two principal dimensions.

So you agree that the direction place is redundant, since there is always
only one direction in which it can be tinsa, whether the object be of
spherical or cylindrical sag?

> I think we have two senses
> of dimension: (1) pertaining to the space within which the shape of x
> is defined;

A one dimensional object can have a shape in a three dimensional space
(a helix for instance), but I understand what you mean.

> (2) "axis". A person has 3 "axes"; a ball has none. Both
> are 3-dimensional.

How can you tell? A person has an up-down dimension thanks to gravity,
a front-back one thanks to movement, and a left-right one by virtue
of having the other two. But from a purely geometrical point of view,
the only interesting thing about a person is one plane of approximate
symmetry. Is this "axis" concept purely geometrical, or does it involve
things like gravity and movement?

Jorge