Topological Spaces in Robotics

5min Snip

00:00

Play full episode

Summary

Transcript

Episode notes

Topologists don't care so much about individual bumps and wiggles like geometry cares about. Pnemology is more lucy goosey. And what it cares about exactly, y ave, very lucy goosy. So there are topological spaces that we care about. Well, maybe they're inspired by real physical situations, but you might think that, well, physical space is three dimensional,. Therefore tere's some topological spaces to think about, but not that many. There are complicated situations where the space of all possible configurations of something is an interesting topological space. The product of two circles are the points on the surface of a taurus again

“A way that math can make the world a better place is by making it a more interesting place to be a conscious being.” So says mathematician Emily Riehl near the start of this episode, and it’s a good summary of what’s to come. Emily works in realms of topology and category theory that are far away from practical applications, or even to some non-practical areas of theoretical physics. But they help us think about what is possible and how everything fits together, and what’s more interesting than that? We talk about what topology is, the specific example of homotopy — how things deform into other things — and how thinking about that leads us into groups, rings, groupoids, and ultimately to category theory, the most abstract of them all.

Support Mindscape on Patreon.

Emily Riehl received a Ph.D in mathematics from the University of Chicago. She is currently an associate professor of mathematics at Johns Hopkins University. Among her honors are the JHU President’s Frontier Award and the Joan & Joseph Birman Research Prize. She is author of Categorical Homotopy Theory, and co-author of the upcoming Elements of ∞-Category Theory. She competed on the United States women’s national Australian rules football team, where she served as vice-captain.

See Privacy Policy at https://art19.com/privacy and California Privacy Notice at https://art19.com/privacy#do-not-sell-my-info.