[geewee]

Having danced for around a decade, I would say the hand positioning example is a bit reductive. The most obvious example is that there's only one variant of "both hands crossed over" - while it's true that the hands might only fit together one way, the things you can do with the hands depending on what arm is on top varies significantly.

Having said that I'm pretty excited about the topic and what the author can do with it.

[viraptor]

It is, but also it's a helpful simplification, I believe. It's kind of like a cup and a ring being topologically equivalent. Helps you talk about some generic thing without overloading with details.

Then there are many more layers on top: palms facing up/down/side, cupped or pressed against, which part of the hand/arm/body are you holding, which one's on top, compression or stretch, at what height, etc.

[knuckleheads]

To me, it's explicitly about being topologically equivalent. I brushed up on my topology and knot theory when working on this to make sure I had it right. The post is considering two social dancers as connected components of two topological objects and the 15 different ways are all the different ways specific points of the surface (hands reduced to points that is) are able to connect.

There's more topology as well when you start bringing in other characteristics of a position, like relative distance and orientation of the dances, you can find more equivalence classes for the other types of equivalences that fall out of that.