How Do You Predict the State of a Quantum System?

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i just did a podcast with anil seth who is a nero scientist, but he also writes papers about emergence. How do you combine different variables into a smaller number of variables so that you still get a predictive theory? Write like, what is the information you can ignore and still be marcovian in the sense that the state now predicts the state next? Ah, so that's one. And the other example is, i just wrote a paper with my student, my former student, ashmead sing, called quantum mereology. So these are word, you know, in a word, t is new. The oneta lima am is a very, a well

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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