A Simplex, Is It Possible to Explain a Simplex?

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Ogy: Is it feasible to explain how this concept of a simplex helps us understand the topological structure of complicated spaces? Ah, i see. And you mentioned sore that the two simplex is a little part of the plain, and therefore there's some topology going in there. But there's more topology than that, right? Like the not like is tad. Ogy: Not all topological spaces can we see with our real, you kno, with our eyes,. There are other spaces that aren't key rings. You know, they're very abstract, and they're in some text book, buried deep in the pages. How can i understand that object?

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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