Marcelo Herreshoff over at Overcoming Bias claims that visualizing math is easier than symbol manipulation because “visualizing things is part of the brain’s native architecture”. It’s great to see other people making this point, but then the question is: are we (the vis people) out of a job as soon as we convince the rest of the world of this? Reaching over to the data producers at the other side of the fence is important: it gets our work noticed, and it really does help them deal with all the data. However, it’s sort of obvious we should be visualizing data. The important question is: how do we do it well?
What’s exiting is scivis, I think, is finding ways that make the visualizations obvious. I love the idea of digging deep into the math of a problem, and then find something that makes sense to look at. After you have the infrastructure, visualizing the data should be simple. Here’s a great example in CFD: when two fluids mix together, how do you tell that something is a bubble, and how can you look at a coherent piece of a bubble as a simulation progresses? Even though we can usually tell right away, it’s much harder to describe one to a computer.
The answer to that question comes from Laney et al’s paper a couple of years back. It requires some math, but the results are surprisingly “simple”: the bubbles segmented with topological persistence (coming from Morse theory) look just like they should. Even better, they can then do quantitative analysis on the number of bubbles, etc. By the “I would love to have been on a paper” measure of paper quality, this one is right up there for me. Solid math, great results, and pretty pictures!