My recent trip to Canada got me thinking about Canadians and hypercubes. I realize that may sound like an odd association, but I have empirical evidence to back it up.
When I visited Montreal a while back, and had the good fortune to get a tour of the National Film Board, I saw a large mural drawn by Norman McLaren himself — the pioneering and enormously influential animator. In fact, the building I was visiting was named for him.
As part of this mural, McLaren had drawn a line, then a square, then a cube, then a hypercube. Essentially, a progression of “cubes” in successively higher dimensions. And then he continued the visual sequence on to even higher dimensions.
I was reminded of this mural when I visited Autodesk in Toronto. One the many brilliant people who works there is Jos Stam — a genial giant, and the genius responsible for some key computer animation techniques you see in movies.
On the wall outside his office, he had drawn a line, then a square, then a cube, then a hypercube … continuing onward to seven dimensions. When I met with him, I meant to ask him whether he had seen McLaren’s work at the NFB. But once we got to talking, our conversation quickly wandered to so many topics that I completely forgot about my question.
Interestingly, I have my own association with Canada and hypercubes. Back in 2010 I built one of the first things I ever made on a 3D printer, during a summer I spent at the Banff Centre for the Arts.
It was a zoetrope of a tumbling hypercube. In a way it contained five dimensions, since it expressed four spatial dimensions plus time. Here is the blog post I wrote about it.
Maybe easier access to higher dimensions is just one of those Canadian things, like their easier access to affordable healthcare.