Brainstorming!
We sat down as a group and thought about what we were actually going to during this project. Every one of us had slightly different ideas of what mathematical VR meant, what can we actually do with it, who are we targeting, and so on. It seemed impossible to find a good solution, so we decided to employ some of the "idea tools" that we were taught on our lecture.
As the next step, we tried thinking what we would do with unlimited time, money and all other earthly resources. This actually produced some interesting ideas, but we had to discard all of them after we brought reality back into the game. Whatever we had planned with unlimited resources did infact require far too much time and research to be feasible to implement.
Just trying to force ourselves into these fixed molds seemed to limit our thinking, so we tried a different approach: we would talk freely, but employ some of the tools from the "negative brainstorming". And with this way, we had great successes. Our discussion progressed quickly as we are able to freely discuss new ideas and then think what does and does not work in them. With this, our idea reached it's (currently) final form.
The tools
We started out with some freeform discussion, but that progressed quite slowly, so we tried the Me-We-Us-process. We had individual thinking, followed up with discussion on pairs, after which the two pairs (4 persons in total) discussed their results. And to be honest, that did not help us at all. The only progress we had was in the "us"-phase, and I feel that locking down the discussion/thinking into smaller groups or individual persons limited the collective thought flow of our group. We concluded that this was not the right tool for our group, and moved on.As the next step, we tried thinking what we would do with unlimited time, money and all other earthly resources. This actually produced some interesting ideas, but we had to discard all of them after we brought reality back into the game. Whatever we had planned with unlimited resources did infact require far too much time and research to be feasible to implement.
Just trying to force ourselves into these fixed molds seemed to limit our thinking, so we tried a different approach: we would talk freely, but employ some of the tools from the "negative brainstorming". And with this way, we had great successes. Our discussion progressed quickly as we are able to freely discuss new ideas and then think what does and does not work in them. With this, our idea reached it's (currently) final form.
The ideas
 |
| Six of our ideas placed in an uncertainty diagram. |
As our project is still finding it's exact form many different ideas have been thrown around. Our group is very mathematics oriented and has a lot of computer know-how, thus most of the ideas are focused around some kind of visualization software. Here I will give a brief rundown of each of the ideas.
Hyperbolic Space Visualization Software
The idea here is to experience hyperbolic space in VR. This has been implemented already, so we would be looking some way to expand this, maybe by building a new interesting environment where one could roam.
Hyperbolic Games
As hyperbolic virtual reality has already been implemented, we tried to think of fun ways to experience it. VR games could prove to be an ideal medium for that. The games should have moving projectiles, preferably in 2D, so the current equipment could be used to its full extent. Examples of such games would be pool/billiards, tennis or maybe bowling.
Hyperbolic Rotations of Euclidean Objects
To study non-euclidean spaces one does not necessarily have to leave euclidean space. It might be interesting to see how rotations through hyperbolic space would affect familiar objects. We could for example, add a fourth hyperbolic dimension which we would rotate objects through and project the changes in to 3D objects (similar to 4D Rubik's cube). However, since we are using VR, not utilising full hyperbolic space might be a waste.Relativistic Visualization Software
In the theory of relativity there are multiple applications for non-euclidean spaces. For example black holes are known to stretch space-time. When space is stretched, it is euclidean no more. Maybe we could visualize black holes in a new interesting way? We could focus on phenomena like gravitation lenses and orbits of planets.
Second possibility in relativity could be the visualization of Minkowski space. Minkowski space is an essential construction in theory of special relativity and it is essentially hyperbolic. Lorentz transformations are essentially rotations in this space, maybe we could visualize this idea in more understandable way for students?
VR Plotting Tools
There are already plotting tools in VR, but as of now we have not come across any hyperbolic ones. It might be interesting just to create tools to draw plots in VR with hyperbolic axes. Another implementation could be hyperbolic 3D objects that could be studied in VR.
Hyperbolic Network Visualization
When researching the applications for hyperbolic geometries, I found that hyperbolic spaces are often used in network visualization. The effect of hyperbolic spaces is similar to a magnifying lens, meaning that the centre is focused and edges are blurred. Examples of such networks could be a large website, some neural networks or even the brain.