2017-11-30

[public] 77.0K views, 3.28K likes, 122 dislikes audio only

PBS Infinite Series

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What happens when you multiply shapes? This is part 2 of our episode on multiplying things that aren't numbers. You can check out part 1: The Multiplication Multiverse right here /youtube/video/H4I2C3Ts7_w

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The Multiplication Multiverse | Infinite Series

/youtube/video/H4I2C3Ts7_w

In our last episode, we talked about different properties of multiplication: associativity and commutativity are the most familiar, but they’re just two of many. We also saw it’s possible to multiply things that aren’t numbers, and in that case we may not have... associativity, for instance. But that’s not a bad thing. In fact, it’s a beautiful thing!

References::

More on the associahedra:

http://www.ams.org/samplings/feature-column/fcarc-associahedra

http://www.claymath.org/library/academy/LectureNotes05/Lodaypaper.pdf

https://arxiv.org/pdf/math/0212126.pdf

More on multiplying non-numbers:

http://www.math3ma.com/mathema/2017/11/24/multiplying-non-numbers

An introduction to operads:

http://www.math3ma.com/mathema/2017/10/23/what-is-an-operad-part-1

http://www.math3ma.com/mathema/2017/10/30/what-is-an-operad-part-2

Some applications in math and physics:

https://arxiv.org/abs/1202.3245

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.22.2871&rep=rep1&type=pdf

http://bookstore.ams.org/conm-227

http://www.springer.com/us/book/9780817647346

Richard Stanley’s book on the Catalan Numbers:

https://www.amazon.com/Catalan-Numbers-Richard-P-Stanley/dp/1107427746

Written and Hosted by Tai-Danae Bradley

Produced by Rusty Ward

Graphics by Ray Lux

Assistant Editing and Sound Design by Meah Denee Barrington

Made by Kornhaber Brown (www.kornhaberbrown.com)

Thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!

And thanks to Nicholas Rose and Mauricio Pacheco who are supporting us at the Lemma level!