Mathematical Enchantments, or “Jim Propp’s math blog” is about “adventures in fantastic realms you can build inside your head.” The blog has been discussed a few times on this blog in recent years. Welcome to my tour of a few interesting posts on the blog.

I appreciate when the purpose and focus of a blog are well-defined, and this post really delivers on that front.

Propp wrote about math as “a consolation for living in a world without magic.” As someone who never believed in magic (even as a child) but wished for it’s existence, I relate to that sentiment.

“Lots of people (most notably Martin Gardner and more recently Arthur Benjamin, Persi Diaconis, Ron Graham, and Colm Mulcahy) have written and talked about the links between math and magic tricks, but hardly anyone talks about the way that math, for many people who do research in it, satisfies a craving for the fantastic that most of us haven’t outgrown (even if we’ve persuaded ourselves that we have). Indeed, I think that most children get glimpses, all too easily forgotten, of math as a wondrous ticket to other worlds,” Propp wrote.

“My goal in Mathematical Enchantments is to reawaken in my readers this childlike relationship to the subject, and to make this view of math enticing and even natural. And if you are an actual child, or an actual mathematician, and your sense of mathematical wonder is already awake and active, all the better! There’ll be lots of new games you can play. These things are fun, and fun is good,” he added.

“The Paintball Party Problem and the Habit of Symmetry”

Propp wrote about time he was “the showrunner” of his son’s ninth birthday party. He had to decide how to configure seven games of two “four on four” paintball teams so that each boy attending the party would be on his son’s team the same number of times, and ideally, would also be teammates with each of the other party attendees the same number of times.

He describes how the notions of randomness and quasirandomness, the geometry of cubes, finite fields and other mathematical ideas informed his solution. The team schedule “took me under five minutes, if you leave out the time I spent learning abstract algebra and coding theory thirty-plus years earlier,” Propp wrote.

This post starts with the idea of portals similar to those in *The Chronicles of Narnia* books by C.S. Lewis and the *His Dark Materials* trilogy by Philip Pullman. Propp then shows how to use “mathematical scissors and glue” to construct different types of wonky, complex portals. His post includes a link to an older video of Bill Thurston (1946-2012) discussing similar ideas.

I love *A Wrinkle in Time* (the classic book by Madeleine L’Engle and the 2018 film), so this post especially appeals to me. Propp begins with a discussion of forth dimensional space, which he defines as “a space that at every points admits four mutually perpendicular lines, in no particular order, but not five.” He then delves into a discussion of tesseracts, hypercubes and music as a tool for thinking about higher dimensions.

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