Ostensibly resembling Marcel Duchamp's Water Mill, this object
was first inspired by conversations with algebraic geometer Loring Tu
and then with topologist Ken Baker. One way to make new spaces out of
existing spaces is to "multiply" them together; the resulting
space is then known as a product space. That's interesting, but kind of
flat; so another thing that we can do is to put torsion or a twist into
it. Here, there's a 180 degree twist.
Being an object that exists in four dimensions, this piece is well-known
to the average Tralfamadorian*. In fact, we believe that it was a key
component in the machine that allowed them to experience time as we do.
This would be akin to a contraption that would put us squarely (literally!)
*This was brought to my attention when an insightful student of mine claimed
that I was from Tralfamadore. Though I did not contradict her, I was surprised
to learn that in her eyes I appeared to be a two-foot tall green-colored
being. So it goes.