Sometimes applications of mathematical fields can leave me boggled. Topology is about deformation of one shape into another, and include insights into which shapes can never be reached from a starting shape. This comes from “Shape Shifters,” Devin Powell (Discover, October 2018), which also includes this:
For a long time, these bizarre shapes — and others revealed by topology — were mere curiosities. But then they started showing up in surprising places, like black-and-white digital photographs. About 10 years ago, [Gunnar] Carlsson, the Stanford mathematician, was analyzing photographs a colleague had cut up into 9-pixel blocks when a pattern emerged. Plot the blocks as points on a graph with nine dimensions, one for the value of how dark each pixel is, and a shape emerges that looks like a Klein bottle. Carlsson applied this knowledge to invent a new way to digitally compress images to smaller sizes. A company he founded, AYASDI, has used topology to look for patterns in genes involved in different cancers, for instance, and bank transactions that indicate fraudulent activity.
Wait, what? How does this work? I can’t even guess, no intuition on this one at all.
But for all those who whine about the money that goes into obscure scientific investigations, results like this should be a redoubtable retort.
