[TChris]

As you get closer, or look closer with binoculars, it then becomes apparent that there's another dimension, or direction of freedom of movement, the ant has, in the circular dimension around circumference of the wire.

There is no "circular dimension" though! This is just a circular pathway traveled through the three physical dimensions. The footsteps of an ant are not a dimension. I still don't buy / get it.

[longshadow]

There is no "circular dimension" though! This is just a circular pathway traveled through the three physical dimensions.

The hypothesized "extra dimensions are orthogonal to the three physical dimensions with which you are familiar. The ant in the example is walking around one of those curled up extra dimensions; his coordinates in the standard 3-dimensional space with which we are familar don't change at all while it traverses the extra dimension.