Hosted by Gabriel Hesch and Autumn Phaneuf, who have advanced degrees in EE and industrial engineering/operations research respectively, come together to discuss mathematics as a pure field al in its own as well as how it describes the language of science, engineering, and even creativity. Breaking Math brings you the absolute best in interdisciplinary science discussions - bringing together experts in varying fields including artificial intelligence, neuroscience, evolutionary biology, physics, chemistry and materials-science, and more - to discuss where humanity is headed. website: breakingmath.io linktree: linktree.com/breakingmathmedia email: breakingmathpodcast@gmail.com
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59: A Good Source of Fibers (Fiber Bundles)
Mathematics is full of all sorts of objects that can be difficult to comprehend. For example, if we take a slip of paper and glue it to itself, we can get a ring. If we turn it a half turn before gluing it to itself, we get what's called a Möbius strip, which has only one side twice the length of the paper. If we glue the edges of the Möbius strip to each other, and make a tube, you'll run into trouble in three dimensions, because the object that this would make is called a Klein flask, and can only exist in four dimensions. So what is a fiber? What can fiber bundles teach us about higher dimensional objects?
All of this, and more, on this episode of Breaking Math.
[Featuring: Sofía Baca, Meryl Flaherty]
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