What Does the Fourth Dimension Actually Look Like? | PODCAST: The Joy of Why

We know all about how things exist in the three dimensions of length, width, and height. Physicists often talk about time as a fourth dimension, but what if there were a fourth spatial dimension — another direction entirely? How on earth would we picture that? Mathematician Maggie Miller explains why our intuition about three dimensions breaks down in four, and how she visualizes 4D spaces as a reel of three-dimensional snapshots.' Watch the companion video "How to 'See' the 4th Dimension with Topology" to learn more: https://youtu.be/MURzTFRRuJQ “The Joy of Why” is a Quanta Magazine podcast about curiosity and the pursuit of knowledge. The mathematician and author Steven Strogatz and the cosmologist and author Janna Levin take turns interviewing leading researchers about the great scientific and mathematical questions of our time. For more episodes visit Quanta Magazine: https://www.quantamagazine.org/tag/the-joy-of-why/ -------- 0:00 Introduction: Topology and the Möbius Strip 2:47 Maggie Miller on Art and Math 5:58 Understanding Topology and Dimensions 11:00 Why Four Dimensions Defy Intuition 17:39 Knots, Surfaces and Building Spaces 26:19 Inside, Outside and What Makes a Hole 29:05 Seifert Surfaces and Untying Knots in 4D 35:31 When Are Two Shapes the Same? 37:59 Is Math Invented or Discovered—and Why Does It Matter? 42:02 Physics, Higher Dimensions and the Joy of Discovery --------- Mathematicians use topology to visualize abstract spaces in higher dimensions. Maggie Miller at the University of Texas at Austin explores what happens when knots encounter an extra dimension. Familiar tangled loops behave in unexpectedly complex and counterintuitive ways in 4D: Knots can always come undone, while ordinary surfaces like spheres can — surprisingly — become knotted in ways that can’t be undone. In this episode, Miller explains to co-host Janna Levin why 4D is the lowest dimension that mathematicians still don’t fully understand, how she and her collaborators resolved a question about knotted surfaces first posed by mathematician Charles Livingston in 1982, and how her interest in art has helped her develop the visual techniques she uses to picture 4D spaces. --------- The Joy of Why is produced by PRX Productions; the production team is Caitlin Faulds, Jade Abdul-Malik, Genevieve Sponsler, and Merritt Jacob. The Executive Producer of PRX Productions is Jocelyn Gonzales. Edwin Ochoa is our project manager. From Quanta Magazine, Simon Frantz and Sam