Student's Choice: Hyperbolic Space in Virtual (Un)reality

For this week I'll be reviewing Group 18, Sandeep Joshi's presentation on hyperbolic visualization in virtual reality.

I thought this use of VR technology was interesting and memorable 1) because of the colorful presentation demo and 2) because it reminded me of a time back in one of the calculus courses where we were working with functions that had graphs in 4 dimensions. Obviously, visualizing or even imagining something in 4 dimensions is difficult because we only know the 3 dimensions, x, y and z. I remember looking at pictures of graphs that wove into and through itself and, though I knew the math behind it, I couldn't quite grasp what I was trying to look at or achieve. I thought that being able to looks at it in fully immersive 3D rather than a 2D picture would be an interesting experience for those who learn about it in their math classes.

Like what Sandeep said in his presentation, hyperbolic geometries exist in nature (lettuce leaves and crochet patterns) but we as humans can only easily understand euclidean geometry. I think this method of visualization would be most applicable in education. Like I touched on before, it's sometimes difficult to grasp a mathematical concept when there is no visualization. Because a computer, with the right mathematical input, can generate a hyperbolic space, being able to look at it in an immersive way would bring more life to the calculus functions we learn in school. And this visualization of hyperbolic space could also lead us to a better understanding of the nature and physics surrounding us. The demos we saw in class reminded me of that one scene in Interstellar where Matthew McConaughey got trapped inside this 4th dimension time-space cube. I feel like this is a step closure to bringing that sort of thing into reality, and we may possibly make another huge mathematical discovery within our lifetime with this technology, which is super exciting to look forward to.