Associahedra: The Shapes of Multiplication

What happens when you multiply shapes? This is part 2 of our episode on multiplying things that aren’t numbers.

The Multiplication Multiverse

Multiplication of numbers is an associative property and we can make sense of “multiplication” between things that aren’t numbers but that’s not considered as associativity.

Telling Time on a Torus

What shape do you most associate with a standard analog clock? Your reflex answer might be a circle, but a more natural answer is actually a torus. Surprised? Then stick around.

Times Tables, Mandelbrot and the Heart of Mathematics

The good old times tables lead a very exciting secret life involving the infamous Mandelbrot set, the ubiquitous cardioid and a myriad of hidden beautiful patterns. Time for the Mathologer to go on a serious fact-finding mission.

Stochastic Supertasks

Supertasks allow you to accomplish an infinite number of tasks in a finite amount of time. Find out how these paradoxical feats get even stranger once randomness is introduced. What happens when you try to empty an urn full of infinite balls? It turns out that whether the vase is empty or full at the end of an infinite amount of time depends on what order you try to empty it in.

Making Probability Mathematical

Throughout much of human history, people consciously and intentionally produced randomness. They frequently used dice – or dice-shaped animal bones and other random objects – to gamble, for entertainment, predict the future and communicate with deities. Despite all this engagement with controlled random processes, people didn’t really think of probability in mathematical terms prior to 1600.

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