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.


Gephi

Gephi is an open-source software for network visualization and analysis. It helps data analysts to intuitively reveal patterns and trends, highlight outliers and tells stories with their data. It uses a 3D render engine to display large graphs in real-time and to speed up the exploration. Gephi combines built-in functionalities and flexible architecture to: explore, analyze, spatialize, filter, cluster, manipulate, export. Gephi is based on a visualize-and-manipulate paradigm which allow any user to discover networks and data properties. Moreover, it is designed to follow the chain of a case study, from data file to nice printable maps.


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.



Cosmic Queries: Time and Higher Dimensions

Wormholes, hypercubes, Flatland, and more – Join Neil deGrasse Tyson as he explores time and higher dimensions with comic co-host Harrison Greenbaum and mathematician John Allen Paulos. To start off, Neil explains the concept of a fourth spatial coordinate. Then, our trio compares our knowledge of a possible 4th dimension to the Flatlander’s knowledge of the 3rd dimension in Edwin Abbott’s book Flatland. Ponder the idea that we’re prisoners of our three-dimensions, echoing the shortcomings of Abbott’s two-dimensional beings. You’ll also investigate the film Interstellar and its use of wormholes and the 5th dimension. Physicist James Kakalios, returning guest and Read More


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