Innovation Tournament

Pitting ideas against each other in the innovation tournament.

Our goal this week was to clarify the end goal of our project as well as figuring out what our prototype should look like. We achieved this by devising an innovation tournament, where we studied the opportunities and uncertainty associated with each of our ideas.

After the brainstorming phase, we had some ideas for the first round of the tournament, which are described below. Some ideas were merged, transformed and developed further during subsequent rounds.

ROUND 1

After the brainstorming phase, we had the following ideas:

Hyperbolic minigolf

Minigolf game in hyperbolic space. We could build on Henry Segerman’s work. Could be fun and interesting. The math could make it hard to implement it.

Hyperbolic pool

Pool game in hyperbolic space. Would work very similarly to a minigolf game.

Hyperbolic darts

A darts game with hyperbolic geometry. For games to be interesting in hyperbolic space, they should incorporate objects moving along something other than straight lines. In the case of darts, this only applies in the z-direction, but having the z-axis to be hyperbolic causes issues, as described by Segerman. In this sense this isn’t a very promising concept.

Hyperbolic frisbee

A frisbee game in hyperbolic space. Could be interesting as it does not only move in a straight line. The physics of a frisbee complicates the implementation very much.

Hyperbolic Mario Kart

A Mario Kart like cartoonish racing game (as opposed to a racing simulator) but set in hyperbolic space. Driving around in hyperbolic space is probably very interesting (at least to mathematicians) or, at the least very weird.

Hyperbolic Trackmania

Trackmania is a racing game where the tracks have loops and other kinds of crazy stuff. This would definitely crank up the craziness of the previous idea to the next level.

General relativity

We could use VR to help visualize the effects of general relativity. These include the gravitational lensing caused by a black hole, lorentz contractions and doppler shift. This isn't a really explored topic and there is definitely a lot of room for innovation.

Rotations

Applying hyperbolic rotations to euclidian objects is unintuitive and hard to visualize on a two-dimensional screen. Hyperbolic rotations arise naturally in physics in the study of general relativity.

Network visualization

According to this article, tree-like networks map naturally to hyperbolic spaces. We could somehow utilize this to help visualizing complex networks.

Hyperbolic space

Here the idea was to simply extend Henry Segerman’s work to e.g. different geometries or tilings.

Plotting tools

Some sort of plotting library that utilizes VR. Could be very useful. Some basic VR plotting tools already exist, although they often do not take full advantage of the opportunities offered by VR. Making a better tool than existing ones might still be challenging.

Brain visualization

A VR tool for visualizing and mapping out the brain. The distances between neurons naturally map to a hyperbolic space and VR could possibly help visualizing these.

Minkowski space

Non-Euclidean Minkowski spaces are studied in special relativity. VR could be used by researchers to visualize and gain better intuition of these.

VR OpenRelativity

OpenRelativitiy is a Unity plugin that incorporates Lorentz contractions and other relativistic effects. This is something that would benefit a lot from the addition of VR, but surprisingly enough, nobody seems to have tried doing this.

ROUND 2

In the second round, we got rid of several ideas.

Darts has only objects traveling in straight lines in the x-y-directions so it’s not so interesting in hyperbolic space. Implementing a physics engine might also turn out to be difficult. The difficulty of implementing a physics engine also led us to give up on the frisbee idea. Hyperbolic rotations, network visualization and Minkowski spaces all involve complicated math and would require quite a lot of research as the whole group is unfamiliar with the topics. We thus dropped them at this stage in favor of more plausible ideas.

The following ideas survived through to the third round:
Hyperbolic minigolf
Hyperbolic pool
Hyperbolic Trackmania
Hyperbolic Mario kart
General relativity
Hyperbolic space
Plotting tools
Brain visualization
VR OpenRelativity

We merged the minigolf and the pool games into a general ‘ball game’, as they would be pretty similar to implement. We also decided to merge the Trackmania and Mario Kart ideas to an overall driving game set in hyperbolic space.

ROUND 3

At this point, we discussed our ideas a bit further.

We got rid of the hyperbolic ball game and racing game ideas, as we found these to be not interesting enough for less mathematically inclined people. We also want to do something that is more educational rather than purely for entertainment.

Additionally, we talked about brain visualization, as this was an interesting-sounding topic that we had already discussed earlier. We discarded this idea as too research-intensive compared to the other remaining topics.

We split the general relativity topic into separate optical and geometric parts. Although on a fundamental physical level these two things are interlinked, from a simulation standpoint they would require quite different approaches. The two new topics were simulation of optical effects such as the gravitational lensing of black holes and geometric deformations caused by Lorentz contraction. Although we gave up on the racing game idea as too game-y, we considered a racing game that implements relativistic effects as a new idea.

By the end of the third round, we were left with the following ideas:
Gravitational lensing
Lorentz contractions
Relativistic racing game
Hyperbolic space
Plotting tools
VR OpenRelativity

ROUND 4

In the last round, it was time to choose our final topic.

After a bit of pondering, we came to the conclusion that relativistic effects wouldn't add that much to a racing game, and dropped this idea. We also concluded that simply extending Henry Segerman's hyperbolic VR visualizations is not an ambitious enough task, and the non-physicists in our group didn't find it that interesting overall.

We also got rid of the plotting tools idea at this point. Although this could be something useful, this feels like more of an engineering tool than something that is innately mathematical. We would also have to compete with existing VR plotting solutions.

In the end, we were left with ideas involving visualizing special relativity concepts. We realized that the OpenRelativity framework would provide a great starting point for visualizing Lorentz contractions, so the first prototype could be built on top of that.

The complete innovation tournament in graph form is shown in the picture below.