While making the Venn Diagram House, a few mathematical toys started popping up. And then more math toys. Until it seemed that they wanted their own interactive math museum, which of course should itself be shaped like a venn diagram with the math toys categorized by field. It’s public on Anyland in the area called “Venn Diagrams”, or if you don’t have a Vive you can get an idea of it in this video:

I spent some time trying to decide what categories would make sense for the current toys and future toys. In the end I went with geometry, topology, and algebra, which creates some nice overlaps what with geometric topology, geometric algebra, and algebraic topology all being mathematical subfields. This organization not only brings some order to the exhibits, but also I’ve found it helpful for my own mental map of mathematical subfields. Most people don’t know much about the different areas of pure mathematics, and they can be difficult to explain, but having this room-based organization could help give an embodied understanding that makes it all seem more natural.

There’s also exhibits outside the museum on things outside those topics: light and sound. (Not that you couldn’t also have some overlap and do an exhibit on the geometry of music or whatever, but as I didn’t make one, I don’t have to worry about that yet.)

It’s amazing how much clearer my mental model of these concepts is after starting to place them in the virtual museum. When I was sketching using pencil on paper, whenever I wasn’t looking at my notebook I’d find myself going “wait, did I have something for algebra and topology yet? How many things are in geometry? What do I have that’s just topology again?”. But working in virtual space, I have a clear instant mental map of where every exhibit is. I don’t have to actively remember what’s going on in the museum, I just know. I not only know where the exhibits are now, I have this timeline in my head of knowing how they evolved and moved and relate to each other, as I added to them and sometimes even modified them to change to a different room.

What’s exciting to me is the potential of bringing that feeling of “I just know” to concepts that are difficult to understand through traditional means. A short stroll through a virtual exhibit could give a student an “I just know” understanding of something they’ve been struggling to understand out of textbooks for weeks. That’s one reason I’m practicing designing embodied explanations.

The audience for these explanations, for now, is mostly myself. I’ve tried to design the museum partly with public accessibility in mind, but the major goal was to practice mapping out my own ideas and associations in an interactive, animated, embodied way, rather than the notebook sketches I’m used to. It wasn’t my original goal to create an interactive museum, but that ended up being the sketching medium that made sense and felt natural to me.

More about all that in the future, but for now here’s some advantages I’ve learned that virtual museums have over real ones:

Firstly, having some experience with actual math museum exhibit design, one of the biggest problems is making things robust enough to survive heavy handling by children, as well as safe enough that no fingers get caught in moving parts or cut by pointy edges. The Exploratorium has an entire staff working full time with a shop in-house to be able to repair, clean, and modify exhibits as needed. Not a problem in our VR world, though! Every single object can be grabbed and manipulated, held and looked at from many angles, passed around, and thrown. Materials can’t be lost or stolen, but they can be copied and added to your own collection! Beautiful delicate-looking pieces with moving parts don’t need to be kept out of reach.

Objects in VR can float, morph, animate, and otherwise disobey the laws of physics. Our topology exhibits especially benefit from the ability of virtual objects to change shape and volume. In topology, shape doesn’t matter, but traditional representations are forced to choose one or more specific shapes. I wanted to be able to explain topology using constantly morphing wobble objects, that can nonetheless be held and manipulated, and VR is perfectly happy to comply!

Exhibits can also be seen from all angles without any extra bits having to be added to mount or display them. When the mathematics relies on the specifics of connections or symmetry, it’s helpful to have the object just floating by itself. The current exhibits have a very wall-based arrangement, but I’d like to explore building interactives in a larger environment to see how the design might change when you don’t have to worry about using wall mounts to help you defy gravity. Then again, our familiarity with walls means that even when they’re not physically necessary, we might want to use them anyway to aid our mental map.

VR does have its downsides, and there’s plenty of things that would do better as a real exhibit than a virtual one. In fact, some of these objects so want to be real that I’ve made them real, which I’d like to talk about in a few weeks. So if you have a museum that needs interactive math exhibits, or are simply interested in how VR can be used as a design tool, stick around!

Vi Hart