re: Nuit's definition of shadow
I'm not sure I agree with
your description of a shadow. True, usually the visible part is two-dimensional.
But next time you have a lot of smoke in your home, go next to a two-paned
window. Look at the support in between the panes -- It casts a very
clear three-dimensional shadow, since the smoke isn't illuminated by
Now, as for the two-dimensional objects casting
a one-dimensional shadow, I think you're half right. If we had a two-dimensional
world we had breadth and depth in, then we had a lightsource and an
object, we'll have only one important measurement -- breadth -- in determining
the size of the shadow. The depth will be however far the light goes,
since there's no height for the light to possibly go over. But the overall
area is two-dimensional.
| |SSS| |
| |S| |
L = Lightsource
S = Shadow
O = Object
| = Light boundary
A one-dimensional shadow would look like this.
| | |
| | |
| O |
Finally, a one-dimensional shadow:
Anyone living within these scenarios would see one
less dimension than they have, but that's how it always is. We see a
flat image, a resident of our two-dimensional land would see lines,
and a resident of our one-dimensional land would see points.