This video was a Math Improv in that I sat down and filmed for about four hours without any script or detailed plan… I knew I wanted to hot glue them into polyhedra or something but the twist classification and woven polylink were arrived at through play. I’d wondered about color frequency and the Smartie Sandwichability Problem before and probably didn’t represent them as neatly as I would’ve if I went script-first, but that’s the kind of thing that makes videos take a long time to make! I think about all the things all the time, and have thought a lot about Smarties in my life.
In a way, I’ve been working on this video for 7 years. Back in 2010 I blogged some Smarties platonic solids:
…as well as Smartie Skeleton…
…as part of a series of Halloween math candy blogposts that also included candy corn Sierpinski triangles (which showed up as a video some number of Halloweens ago). It’s faster to blog photos than to make videos, so I’m still catching up video-wise on work I did many years ago. On the other hand, I’m much better at it now! I’ve been wanting to do a smartie video of some sort for a long time, and thanks to going full-time on Patreon it was a good time to finally do it.
The voiceover was written based on the footage I’d shot, and then the footage edited to the voiceover. So not quite my usual process, but same editing process in the end.
It’s another way in which video can be used as a tool for thought… I capture one aspect of a thought-process as I film, and then use the footage as a scaffold to write out a clearer version of the thought-process, and finally put the two together to hopefully capture and communicate what’s going on in my head a bit more effectively than conventional communication can. I capture thinking with my hands, not just with my brain, which is evident in things like feeling the clockwiseness or widdershinsness of a twist.
Some parts of math are easier to feel than to think, especially with practice. We need a curriculum for getting an embodied understanding of mathematical concepts, beyond just “hands-on learning”. I’ve got to start keeping a list.
Ok, I started the list: http://vihart.com/embodied-math/ Someone remind me to keep adding things to it if I forget!
Oh, one more thing: did you know that while regular polyhedra have been around FOREVER (like thousands of years), regular polylinks were discovered relatively recently and are still being explored? Check out Alan Holden’s 1980 paper on them.
The first polylink I tried to make in the Smarties video was of 6 squares. I’ve made it out of balloons and other things through the years:
Regular polylinks are in my repertoire of go-to shapes at almost the same level as polyhedra, fractals, lattices, and other canonical mathematical forms.
The polylink of 4 triangles, despite being one of the simplest ones by number and sides, is quite difficult to weave correctly. A balloon version from 2008 or 2009:
…which reminds me, mathematical balloon twisting is another thing I’m many years past due on making a video about!
That’s it for now.
P.S. Here’s my new video studio, now with camera arm and hyperbolic planes! Really half the reason I made the smarties video was to play with my new setup.