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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266 | Christoph Adami on How Information Makes Sense of Biology

266 | Christoph Adami on How Information Makes Sense of Biology

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AMA | February 2024

AMA | February 2024

Welcome to the February 2024 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 Pa...

12 Feb 20243h 24min

265 | John Skrentny on How the Economy Mistreats STEM Workers

265 | John Skrentny on How the Economy Mistreats STEM Workers

Universities and their students are constantly being encouraged to produce more graduates majoring in STEM fields -- science, technology, engineering, and mathematics. That's the kind of training that...

5 Feb 20241h 20min

264 | Sabine Stanley on What's Inside Planets

264 | Sabine Stanley on What's Inside Planets

The radius of the Earth is over 6,000 kilometers, but the deepest we've ever dug below the surface is only about 12 km. Yet we have a quite reliable idea of the structure of the Earth's interior -- in...

29 Jan 20241h 12min

263 | Chris Quigg on Symmetry and the Birth of the Standard Model

263 | Chris Quigg on Symmetry and the Birth of the Standard Model

Einstein's theory of general relativity is distinguished by its singular simplicity and beauty. The Standard Model of Particle Physics, by contrast, is a bit of a mess. So many particles and interacti...

22 Jan 20241h 26min

262 | Eric Schwitzgebel on the Weirdness of the World

262 | Eric Schwitzgebel on the Weirdness of the World

Scientists and philosophers sometimes advocate pretty outrageous-sounding ideas about the fundamental nature of reality. (Arguably I have been guilty of this.) It shouldn't be surprising that reality,...

15 Jan 20241h 20min

261 | Sanjana Curtis on the Origins of the Elements

261 | Sanjana Curtis on the Origins of the Elements

In mid-20th-century cosmology, there was a debate over the origin of the chemical elements. Some thought that they could be produced in the Big Bang, while others argued that they were made inside sta...

8 Jan 20241h 7min

260 | Ricard Solé on the Space of Cognitions

260 | Ricard Solé on the Space of Cognitions

Octopuses, artificial intelligence, and advanced alien civilizations: for many reasons, it's interesting to contemplate ways of thinking other than whatever it is we humans do. How should we think abo...

1 Jan 20241h 10min

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