Episode list

Zach Star

Parity Puzzles

Fri, May 08, 2020
Zach shares some puzzles that have odd or even solutions but not both. They are parity puzzles. Recognizing a puzzle as a parity puzzle makes the existence of a solution more obvious.
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These changed how I think about higher dimensions
Mathematicians developed the field of topology to explore the manipulation of objects in space. Zach find it helpful for visualizing higher level dimensions and the shapes of alternative universes. Even the mathematical operations help in visualization.
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We likely live in one of these 18 universes
Mathematics offers a multitude of different geometries our universe might have. Astronomers think we live in a universe with Euceidean rather than spherical or hyperbolic geometry. But that still leaves 18 Euclidean universes to choose from.
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What would we see if we lived on a hypersphere?
The shape of our universe is still an open question. But what does this mean? Zach takes a look at what our universe would be like if our three dimensional universe was the surface of a four dimensional hypersphere. But he shrinks the universe to approximately the size of the earth so the effects are more obvious.
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The Poker Paradox

Sun, Aug 14, 2022
Adding a joker to a poker game does something weird to the probabilities of winning hands and hence their rankings.
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Probability is just...really weird
The Monte Hall paradox wasn't controversial enough for Zach. But not to worry. He has a selection puzzle that it too confusing even for social media because even it you guess right it's probably for the wrong reason.
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