174 | Tai-Danae Bradley on Algebra, Topology, Language, and Entropy

174 | Tai-Danae Bradley on Algebra, Topology, Language, and Entropy

Mathematics is often thought of as the pinnacle of crisp precision: the square of the hypotenuse of a right triangle isn't "roughly" the sum of the squares of the other two sides, it's exactly that. But we live in a world of messy imprecision, and increasingly we need sophisticated techniques to quantify and deal with approximate statistical relations rather than perfect ones. Modern mathematicians have noticed, and are taking up the challenge. Tai-Danae Bradley is a mathematician who employs very high-level ideas — category theory, topology, quantum probability theory — to analyze real-world phenomena like the structure of natural-language speech. We explore a number of cool ideas and what kinds of places they are leading us to.

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Tai-Danae Bradley received her Ph.D. in mathematics from the CUNY Graduate Center. She is currently a research mathematician at Alphabet, visiting research professor of mathematics at The Master's University, and executive director of the Math3ma Institute. She hosts an explanatory mathematics blog, Math3ma. She is the co-author of the graduate-level textbook Topology: A Categorical Approach.


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179 | David Reich on Genetics and Ancient Humanity

179 | David Reich on Genetics and Ancient Humanity

Human beings like to divide themselves into groups, and then cooperate, socialize, and reproduce with members of their own group. But they're not very absolutist about it; groups tend to gradually (or...

10 Jan 20221h 13min

178 | Jody Azzouni on What Is and Isn't Real

178 | Jody Azzouni on What Is and Isn't Real

Are numbers real? What does that even mean? You can't kick a number. But you can talk about numbers in useful ways, and we use numbers to talk about the real world. There's surely a kind of reality th...

3 Jan 20221h 14min

Holiday Message 2021 | On Disciplines & Cocktails

Holiday Message 2021 | On Disciplines & Cocktails

As each December comes to a close, we wrap up another year of podcasts with the Mindscape Holiday Message. Nothing too profound, just some thoughts that wouldn't fit easily into a regular podcast. Thi...

20 Dec 202159min

AMA | December 2021

AMA | December 2021

Welcome to the December 2021 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). I take the large number of qu...

15 Dec 20213h 37min

177 | Monika Schleier-Smith on Cold Atoms and Emergent Spacetime

177 | Monika Schleier-Smith on Cold Atoms and Emergent Spacetime

When it comes to thinking about quantum mechanics, there are levels. One level is shut-up-and-calculate: find a wave function, square it to get a probability. One level is foundational: dig deeply int...

13 Dec 20211h 10min

176 | Joshua Greene on Morality, Psychology, and Trolley Problems

176 | Joshua Greene on Morality, Psychology, and Trolley Problems

We all know you can't derive "ought" from "is." But it's equally clear that "is" — how the world actual works — is going to matter for "ought" — our moral choices in the world. And an important part o...

6 Dec 20211h 26min

175 | William Ratcliff on Multicellularity, Physics, and Evolution

175 | William Ratcliff on Multicellularity, Physics, and Evolution

We've talked about the very origin of life, but certain transitions along its subsequent history were incredibly important. Perhaps none more so than the transition from unicellular to multicellular o...

29 Nov 20211h 26min

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