What better way to expand your mind than into more dimensions. Here's are some simply things we do every day that are a little different in four or more (or many more) dimensions.
Beware. It's not just statistics that lie. So do percentages and numbers in general when you misinterpret them. Zach provides a few examples where the numbers we usually use in certain situations don't provide an accurate picture of what's going on.
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.
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.
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.
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.
Your odds of reaching your winnings goal in a fair game, versus the house's edge, are dependent on how much you have to risk and the size of your bets. Fewer bigger bets give you better odds than lots of little bets.
Zack explains the initially intimidating but oddly artistic Smith chart that is used to determine the degree of signal reflection between loads of different impedance.
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.
