More on stained glass Necker cubes

A commenter below, RBH, told a great little story about a stained glass piece he made, which got into a curated show. I was already impressed, but now I know enough to be even more impressed.

my second was a 3-D wall sculpture (glass mounted to copper posts standing out from a plywood back, etc) that was a fool-the-eye, incorporating Necker Cubes in both 2-D and 3-D. That one got into a curated show at a gallery, and I promptly retired!

Trompe-l'oeil ("fool-the-eye") is a kind of art illusion, usually creating a very vivid depiction of 3D objects on a 2D surface, such as a painting or a mural, like below.



There are a lot of trompe l'oeil images used to illustrate points in psychology and cognition, because they provide interesting explorations in how the eyes and brain process information. I had to look up Necker cubes to make sure I was thinking of the right thing; here is an example (Mathworld is a wonderful resource for math definitions and bibliographies; both of these examples are from Necker cube there.):



and the following tile floor, excavated at Pompeii:



So from this, we can get an idea at a very low level of the basis of RBH's stained glass; no idea what colors he used, but the basic pattern is the 2D rhombi above and the 3D analogue.

Now for why I am further impressed--I went to the stained glass store where I take my lessons, and saw a Necker cube (2D only) piece for sale. The woman behind the register is the one who made it; it was one of her early pieces. I mentioned that I was struck by how easy it looked from the simplicity, yet how hard it must have been to make: the illusion is maintained by the precision of the lines and angles. It is not a forgiving design at all; my parrot, on the other hand, acquired some occasional curves it hadn't had, but absorbed them seamlessly. But this one--either the lines are perfectly straight, or you might just as well not bother.

Having developed a new appreciation of how the lead came can fight back through the time I spent trying to keep already-assembled pieces from escaping while I was adding new ones, I said that it must have been hard to assemble. It was--the precision required and the number of pieces to keep in their exact place made this a formidable project. If you just look at it as rhombi, it looks very simple; if you appreciate how much work it is to assemble the rhombi, it becomes clear that the simplicity is deceptive, and RBH's design becomes even more impressive (even without knowing all the details).

I can only extrapolate how much work it must have been to add the 3D Necker cubes to the 2D ones--RBH, if you have a picture of your piece, I'd love to see it! Even though it would be a representation in only 2D, still it would be cool.

Also, I have to wonder about something, and I'd love to check it out: the illusion of the 2D Necker cube stimulates our brains to see 3D. What do the 3D Necker cubes stimulate our brains to see? Even though we are restricted to 3D space, still, the illusion has to "flicker" through something as it changes, much like the 2D cubes "flicker" through the illusion of 3D. Although we cannot really see 4D, I would love to see what the illusion of it--created by a 3D Necker cube--looks like to our perception.