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.


Episoder(416)

255 | Michael Muthukrishna on Developing a Theory of Everyone

255 | Michael Muthukrishna on Developing a Theory of Everyone

A "Theory of Everything" is physicists' somewhat tongue-in-cheek phrase for a hypothetical model of all the fundamental physical interactions. Of course, even if we had such a theory, it would tell us...

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254 | William Egginton on Kant, Heisenberg, and Borges

254 | William Egginton on Kant, Heisenberg, and Borges

It can be tempting, when first introduced to a deep concept of physics like Heisenberg's uncertainty principle, to draw grand philosophical conclusions about the impossibility of knowing anything prec...

23 Okt 20231h 6min

253 | David Deutsch on Science, Complexity, and Explanation

253 | David Deutsch on Science, Complexity, and Explanation

David Deutsch is one of the most creative scientific thinkers working today, who has as a goal to understand and explain the natural world as best we can. He was a pioneer in quantum computing, and ha...

16 Okt 20231h 42min

AMA | October 2023

AMA | October 2023

Welcome to the October 2023 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). We take questions asked by Pat...

9 Okt 20232h 58min

252 | Hannah Ritchie on Keeping Hope for the Planet Alive

252 | Hannah Ritchie on Keeping Hope for the Planet Alive

Our planet and its environment are in bad shape, in all sorts of ways. Those of us who want to improve the situation face a dilemma. On the one hand, we have to be forceful and clear-headed about how ...

2 Okt 20231h 15min

251 | Rosemary Braun on Uncovering Patterns in Biological Complexity

251 | Rosemary Braun on Uncovering Patterns in Biological Complexity

Biological organisms are paradigmatic emergent systems. That atoms of which they are made mindlessly obey the local laws of physics; even cells and organs do their individual jobs without explicitly u...

25 Sep 20231h 11min

250 | Brendan Nyhan on Navigating the Information Ecosystem

250 | Brendan Nyhan on Navigating the Information Ecosystem

The modern world inundates us with both information and misinformation. What are the forces that conspire to make misinformation so prevalent? Can we combat the flow of misinformation, perhaps by lega...

18 Sep 202357min

249 | Peter Godfrey-Smith on Sentience and Octopus Minds

249 | Peter Godfrey-Smith on Sentience and Octopus Minds

The study of cognition and sentience would be greatly abetted by the discovery of intelligent alien beings, who presumably developed independently of life here on Earth. But we do have more than one d...

11 Sep 20231h 28min

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