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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30 | Derek Leben on Ethics for Robots and Artificial Intelligences

30 | Derek Leben on Ethics for Robots and Artificial Intelligences

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21 Jan 20191h 28min

29 | Raychelle Burks on the Chemistry of Murder

29 | Raychelle Burks on the Chemistry of Murder

Sometimes science is asking esoteric questions about the fundamental nature of reality. Other times, it just wants to solve a murder. Today's guest, Raychelle Burks, is an analytical chemist at St. Ed...

14 Jan 20191h 15min

28 | Roger Penrose on Spacetime, Consciousness, and the Universe

28 | Roger Penrose on Spacetime, Consciousness, and the Universe

Sir Roger Penrose has had a remarkable life. He has contributed an enormous amount to our understanding of general relativity, perhaps more than anyone since Einstein himself -- Penrose diagrams, sing...

7 Jan 20191h 35min

Holiday Message 2018

Holiday Message 2018

There won't be any regular episodes of Mindscape this week or next, as we take a holiday break. Regular service will resume on Monday January 7, 2019. In the meantime, here is a special Holiday Messag...

24 Dec 201844min

27 | Janna Levin on Black Holes, Chaos, and the Narrative of Science

27 | Janna Levin on Black Holes, Chaos, and the Narrative of Science

It's a big universe out there, full of an astonishing variety of questions and puzzles. Today's guest, Janna Levin, is a physicist who has delved into some of the trippiest aspects of cosmology and gr...

17 Dec 20181h 8min

26 | Ge Wang on Artful Design, Computers, and Music

26 | Ge Wang on Artful Design, Computers, and Music

Everywhere around us are things that serve functions. We live in houses, sit on chairs, drive in cars. But these things don't only serve functions, they also come in particular forms, which may be emo...

10 Dec 20181h 10min

25 | David Chalmers on Consciousness, the Hard Problem, and Living in a Simulation

25 | David Chalmers on Consciousness, the Hard Problem, and Living in a Simulation

The "Easy Problems" of consciousness have to do with how the brain takes in information, thinks about it, and turns it into action. The "Hard Problem," on the other hand, is the task of explaining our...

3 Dec 20181h 22min

24 | Kip Thorne on Gravitational Waves, Time Travel, and Interstellar

24 | Kip Thorne on Gravitational Waves, Time Travel, and Interstellar

I remember vividly hosting a colloquium speaker, about fifteen years ago, who talked about the LIGO gravitational-wave observatory, which had just started taking data. Comparing where they were to whe...

26 Nov 20181h 19min

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