What's the Meaning of a Fire Truck?

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Will: How do i get useful work out of knowing that the set of relationships between my object and every other conceivable object tells me everything there is to know about it? Will: I like to answer this question back in the context of language, which we were thinking about earlier. It's really interesting that large language models only have access to the context, you know, in which a word appears. They just sort of see what goes with what in the language,. together with the statistics, and somehow from that can glean semantic information about words. And how is this useful? Well, it goes back to sort of this experimental motivation we were talking about earlier. We don't know if these tools

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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