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.



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.


Simplicial Complexes: Part 2

Last episode we saw that your neural network can be modeled as a graph, which — we’ll show in this episode — can be viewed as a higher-dimensional simplicial complex. So… what is a simplicial complex??


Your Mind Is Eight-Dimensional: Part 3

Last episode, we learned that your brain can be modeled as a simplicial complex. And algebraic topology can tell us the Betti numbers of that simplicial complex. Why is that helpful? Let’s find out.


ˆ Back To Top