Necker Cube

["Mark E. Shoulson" <cbmvax!uunet!CTR.COLUMBIA.EDU!shoulson>]

I write, after drawing an ambiguous picture:

>  Well, you get the picture.  Those two spots where the two squares intersect
>  are ambiguous, in that you don't know which line is in front, and that
>  means you don't know which square is in front.  If you draw it so you can
>  tell, but with the disambiguation in an impossible fashion, you get the
>  famous irrational cube (q.v. various Escher prints.  _Belvedere_ is a good
>  example, as the guy in the dungeon is holding an irrational cube and
>  there's a picture of a Necker Cube on the floor with the key intersections
>  circled).

To which Ivan responds:

>Haud a wee.  If I remember correctly, the cube in _Belvedere_ is not
>an ambiguous one, because you can tell which line is which, only they
>go in a way that makes it impossible for the cube to exist in real
>life, like so:
[picture of irrational cube]

Yes, Ivan, the cube the guy is holding isn't ambiguous, just impossible.
But that wasn't the one I said was ambiguous.  On the ground in
_Belvedere_, in front of the dungeon window there's a scrap of paper on
which is drawn the Necker cube, all ambiguous, with the interesection
points circled.

'Course, the building in _Belvedere_ is irrational, too.

~mark, the Escher fan.