... wherein Peter posts a Weekly Media Update.
Books: Euler's Gem
Movies:
TV: Game Changer (season six)
Courses: How the Great Migration Changed America (audiocourse)
Euler's Gem: The Polyhedron Formula and the Birth of Topology by David S. Richeson
If you take just about any polyhedron, you can count the number of vertices (V), the number of edges (E), and the number of faces (F), and this formula will hold:V + F - E = 2
Euler's Gem is a book about this formula - what preceded it, how it was discovered, and how it was the solitary tumbling pebble that would eventually avalanche into the whole field of topology. "Topology" is what's left of geometry after you say "sorry, all of these shapes have gone all stretchy." Suddenly you can't say anything useful about how long such-and-such a line segment is, or how big such-and-such an angle is - you're left studying more fundamental facts, like "what is attached to what?" or "how many vertices does this polygon have?"
It's a whole world of fundamental truths about the nature of shapes that we never really dug into until the 1800s. It's like a handful of Greeks got really obsessed with length-measuring and then math got permanently distracted by that superficial level of study.
The shocker of this book is that we had polyhedra kicking around for thousands of years before somebody (Leonhard Euler, arguably the best mathematician who ever lived) even noticed this equation. That's... weird. You can quickly look over the Platonic solids and literally count edges, faces, and vertices until the relation leaps out at you.
The further shocker is that it's possible that nobody noticed this before because, with respect to polyhedra, nobody really had a concept of an 'edge'. But then, so much of the history of math consists of smart people putting words to concepts that have been right in front of us the whole time.
-
You can think of Euler's Gem as two books.
The first half is historical, leading us up to the polyhedral formula and exploring some of the ways you can prove it, along with some of the confusion about exactly which shapes it applies to.
That first half, I highly recommend. It tells a wonderful story about how ideas slowly come into focus - like, it was a good long time until people settled on what a 'regular polyhedron' was, and then a longer time until people realized there were five Platonic solids. (And then the Archimedean solids got discovered, lost for about a thousand years, and then re-discovered. It was a whole thing.) Then once that infrastructure is in place, we see a generation of mathematicians almost playfully explore the space, discovering all the things about polyhedra that it seems like we should have always known. The proofs that come up are tricky but followable.
-
And then... there's the second half. The second half of Euler's Gem is basically a 100-page overview of... all of topology. Mr. Richeson does what he can, but he's facing an iron triangle: he can cover the material concisely, thoroughly, or clearly - choose two.
His compromise moves through the material too quickly to be clear. Or more precisely, the book segues from being a "math for the lay reader" book to just a "math book". Sure, you don't need prior training to keep up, but the density of the material skyrockets, to the point that you have to digest every sentence, *and make sure you thoroughly understand it*, to move forward. For instance, he introduces the concept of a "boundary" in a paragraph or so - it has a specific set of definitions in topology - and if you glaze over slightly in that paragraph, you're screwed for understanding the whole rest of the book.
It makes you realize how much redundancy is built into lay public science communication. If a concept is important, you hammer away at it for pages, explaining it from different angles, using different metaphors, showing additional examples, and then briefly re-explaining it when it comes back into play. Math texts, on the other hand, often pride themselves on conciseness; I suspect that, when mathematicians write for wider audiences, they have to fight an urge to express things in as few words as possible.
So in a way, Euler's Gem reflects both what I like and what I dislike about math books. I'm annoyed at its ambition: if it had stuck more strictly to its topic (Euler's polyhedral formula), and not used it as a tenuous excuse to breathlessly summarize ~125 years of topology, the material could have (appropriately enough) stretched out more, and breathed a bit, and I would have unabashedly loved it.
As it is, I'm not sure how to recommend it. "Read the first half?" "Read it 'til it gets confusing, and then stop, because the book will only get monotonically more confusing from there?" "Read the whole thing, but only if you already kind of understand the topic?"
It's a fun read for math nerds, and perhaps a near miss for everyone else.
Game Changer (season six)
This is the 2024 season of the dropout.tv game show that changes its concept every week, leaving its comedian contestants scrambling to figure out how this week's game works, let alone how to win it.
So there's this moment with a ladder.
It happens about midway through the season. I'll be vague to avoid spoilers: there's a game mechanism they've set up where the players have to obtain something from a high shelf next to the podiums. A contestant immediately darts backstage and comes back with a big blue industrial ladder.
And the host, Sam Reich, stops the show. He explains that the ladder breaks the game mechanic they had in mind. They remove the ladder and continue with the show.
In a weird way, this moment sits at the heart of season six for me. This show that crosses off a new game-show premise every single episode has seemingly burned through all the easy and simple ideas. Game Changer also gets more *ambitious* with each passing season. The show that was invented as a quick way to churn out cheap content now has spinoffs, wild popularity, and (I would guess) more of a budget.
They've started to employ game and puzzle designers as consultants, and the results are intricate, complicated, big, and impressive. Gone are the days of "roll in a fake machine that goes 'ding' and pretend it's a lie detector for half an hour."
But they're building these convoluted structure around, essentially, improvisors doing improv. So there's always this improv show that's trying to break free from the structure of the episode. But at this point it *can't*, really, because the structure, while brilliant and meticulously worked-out, is fragile. There are a lot of moving parts, and they're all designed to interconnect precisely.
Ultimately, the show loses, for me, a lot of the joy of improv. It *can't* be truly spontaneous. It can't go where the moment leads it, in the moment. There are rails and there are rules. And darting backstage to get a ladder ¹ doesn't fit within them.
To be clear, I still like Game Changer.
I think hiring game designers has been the right way to go for season six, and the dizzying heights of game design at play here are fascinating in their own right. And it's often fun to watch this chaotic improv energy slam against the format of the show. Sam Reich asks the players "who is the lead character of The Lord of the Rings?" and Erika Ishii does not say "Frodo", but responds with a small dissertation about the trilogy's narrative structure while her two competitors breeze into the shot and perform interpretive dance around her. It's a delight, and it's a delight largely because they are *so* not supposed to be doing that.
Improv so often benefits from parameters, but improv as an art form truly sings when it lifts itself free of the predefined boundaries. A great improv show shifts from "the thing you planned out" to "the thing you couldn't have planned", the unique performance art that only made sense in that moment, for those people, in that room, at that time. Game Changer never quite balances out the rules and the chaos to my taste; I'm betting there is no way to truly balance them.
That said, "Second Place" was one of my favorite episode concepts of the whole series.
How the Great Migration Changed America by Professor Davarian L. Baldwin (audiocourse)
This is the 2024 Teaching Company course about the Great Migration, when Blacks moved en masse from the southern states to the northern cities.
I fear that late-period Teaching Company courses are all tending towards the same assessment: "amazing concept, just-okay execution".
The Great Migration is an S-tier pitch for a Teaching Company course. It's a vital part of American History; it's a key to understanding where the country now (uneasily) stands with respect to race. It has inherent drama. It sits just beyond the edge of living memory. And yet it gets short shrift in most history education - or at least it barely got a mention in my high-school textbooks. ²
This makes it a perfect topic for the Teaching Company to tackle. It even follows the reliable formula of recent courses: you take a broader topic (in this case, Black history), but you find a specific subtopic (i.e., the Great Migration) to provide your 'way in'. It's a little like how "what Darwin didn't know" provided an excuse to talk about modern evolutionary theory.
And yet. The Teaching Company has transitioned from traditional filmed lectures - get a university prof to stand up behind a lectern and just *go* - to basically having someone read an essay on-camera. It's my understanding that the presenters write every word of every lecture, then let the company thoroughly fact-check it, and then read it off a teleprompter. The spontaneity is squeezed out, the rhythm feels off, and you find yourself wondering why you don't just read a book instead.
I feel like this is what gets in the way of How the Great Migration Changed America. Professor Baldwin covers a broad topic effectively, but the Great Courses is mostly employing him as an audiobook reader, and he's less good at that. To his credit, he conveys the emotion of the story, recounting how his own relatives were part of the migration, and hammering home just how dire it was in the Jim Crow south. ³
Other times, I found myself getting lost because I didn't already have enough of a grounding in Black history. I noticed this especially when the lectures went into lists, when I'd hear something like, "This neighborhood was home to many great artsits, including..." and then there's a list of ten names I've never heard of. It worked better for me when it went into detail about individuals, like C. J. Walker and her beauty-product empire, or Louis Armstrong making the hard choice to move north.
In the end, this is a *good* course, in that it conveys how interesting and important this subject matter is. But I don't know if I can recommend the course - it's more like you should find a great book about this subject and read that instead.
For next week: ugh, so much in the backlog (this is what happens when I travel, right?). So I need to write about season one of Shōgun, season six of Game Changer, Turning Red, and a math audiocourse. I'm now reading that history of the MCU and a book about the Harvard Longitudinal Study. I'm listening to the Blank Check miniseries about Kevin Costner and an audiocourse about our relationship to digital technology.
____
¹ I wrote, and deleted, the phrase "ladder-al thinking".
² That said, I grew up in a small town in Kentucky in the 1980s, so
³ One of my favorite points from the course: we're told that the Great Migration was about finding opportunities in the factory towns of the North, but it was at least as much about escaping a violent, fascist, oppressive society.
Movies:
TV: Game Changer (season six)
Courses: How the Great Migration Changed America (audiocourse)
Euler's Gem: The Polyhedron Formula and the Birth of Topology by David S. Richeson
If you take just about any polyhedron, you can count the number of vertices (V), the number of edges (E), and the number of faces (F), and this formula will hold:V + F - E = 2
Euler's Gem is a book about this formula - what preceded it, how it was discovered, and how it was the solitary tumbling pebble that would eventually avalanche into the whole field of topology. "Topology" is what's left of geometry after you say "sorry, all of these shapes have gone all stretchy." Suddenly you can't say anything useful about how long such-and-such a line segment is, or how big such-and-such an angle is - you're left studying more fundamental facts, like "what is attached to what?" or "how many vertices does this polygon have?"
It's a whole world of fundamental truths about the nature of shapes that we never really dug into until the 1800s. It's like a handful of Greeks got really obsessed with length-measuring and then math got permanently distracted by that superficial level of study.
The shocker of this book is that we had polyhedra kicking around for thousands of years before somebody (Leonhard Euler, arguably the best mathematician who ever lived) even noticed this equation. That's... weird. You can quickly look over the Platonic solids and literally count edges, faces, and vertices until the relation leaps out at you.
The further shocker is that it's possible that nobody noticed this before because, with respect to polyhedra, nobody really had a concept of an 'edge'. But then, so much of the history of math consists of smart people putting words to concepts that have been right in front of us the whole time.
-
You can think of Euler's Gem as two books.
The first half is historical, leading us up to the polyhedral formula and exploring some of the ways you can prove it, along with some of the confusion about exactly which shapes it applies to.
That first half, I highly recommend. It tells a wonderful story about how ideas slowly come into focus - like, it was a good long time until people settled on what a 'regular polyhedron' was, and then a longer time until people realized there were five Platonic solids. (And then the Archimedean solids got discovered, lost for about a thousand years, and then re-discovered. It was a whole thing.) Then once that infrastructure is in place, we see a generation of mathematicians almost playfully explore the space, discovering all the things about polyhedra that it seems like we should have always known. The proofs that come up are tricky but followable.
-
And then... there's the second half. The second half of Euler's Gem is basically a 100-page overview of... all of topology. Mr. Richeson does what he can, but he's facing an iron triangle: he can cover the material concisely, thoroughly, or clearly - choose two.
His compromise moves through the material too quickly to be clear. Or more precisely, the book segues from being a "math for the lay reader" book to just a "math book". Sure, you don't need prior training to keep up, but the density of the material skyrockets, to the point that you have to digest every sentence, *and make sure you thoroughly understand it*, to move forward. For instance, he introduces the concept of a "boundary" in a paragraph or so - it has a specific set of definitions in topology - and if you glaze over slightly in that paragraph, you're screwed for understanding the whole rest of the book.
It makes you realize how much redundancy is built into lay public science communication. If a concept is important, you hammer away at it for pages, explaining it from different angles, using different metaphors, showing additional examples, and then briefly re-explaining it when it comes back into play. Math texts, on the other hand, often pride themselves on conciseness; I suspect that, when mathematicians write for wider audiences, they have to fight an urge to express things in as few words as possible.
So in a way, Euler's Gem reflects both what I like and what I dislike about math books. I'm annoyed at its ambition: if it had stuck more strictly to its topic (Euler's polyhedral formula), and not used it as a tenuous excuse to breathlessly summarize ~125 years of topology, the material could have (appropriately enough) stretched out more, and breathed a bit, and I would have unabashedly loved it.
As it is, I'm not sure how to recommend it. "Read the first half?" "Read it 'til it gets confusing, and then stop, because the book will only get monotonically more confusing from there?" "Read the whole thing, but only if you already kind of understand the topic?"
It's a fun read for math nerds, and perhaps a near miss for everyone else.
Game Changer (season six)
This is the 2024 season of the dropout.tv game show that changes its concept every week, leaving its comedian contestants scrambling to figure out how this week's game works, let alone how to win it.
So there's this moment with a ladder.
It happens about midway through the season. I'll be vague to avoid spoilers: there's a game mechanism they've set up where the players have to obtain something from a high shelf next to the podiums. A contestant immediately darts backstage and comes back with a big blue industrial ladder.
And the host, Sam Reich, stops the show. He explains that the ladder breaks the game mechanic they had in mind. They remove the ladder and continue with the show.
In a weird way, this moment sits at the heart of season six for me. This show that crosses off a new game-show premise every single episode has seemingly burned through all the easy and simple ideas. Game Changer also gets more *ambitious* with each passing season. The show that was invented as a quick way to churn out cheap content now has spinoffs, wild popularity, and (I would guess) more of a budget.
They've started to employ game and puzzle designers as consultants, and the results are intricate, complicated, big, and impressive. Gone are the days of "roll in a fake machine that goes 'ding' and pretend it's a lie detector for half an hour."
But they're building these convoluted structure around, essentially, improvisors doing improv. So there's always this improv show that's trying to break free from the structure of the episode. But at this point it *can't*, really, because the structure, while brilliant and meticulously worked-out, is fragile. There are a lot of moving parts, and they're all designed to interconnect precisely.
Ultimately, the show loses, for me, a lot of the joy of improv. It *can't* be truly spontaneous. It can't go where the moment leads it, in the moment. There are rails and there are rules. And darting backstage to get a ladder ¹ doesn't fit within them.
To be clear, I still like Game Changer.
I think hiring game designers has been the right way to go for season six, and the dizzying heights of game design at play here are fascinating in their own right. And it's often fun to watch this chaotic improv energy slam against the format of the show. Sam Reich asks the players "who is the lead character of The Lord of the Rings?" and Erika Ishii does not say "Frodo", but responds with a small dissertation about the trilogy's narrative structure while her two competitors breeze into the shot and perform interpretive dance around her. It's a delight, and it's a delight largely because they are *so* not supposed to be doing that.
Improv so often benefits from parameters, but improv as an art form truly sings when it lifts itself free of the predefined boundaries. A great improv show shifts from "the thing you planned out" to "the thing you couldn't have planned", the unique performance art that only made sense in that moment, for those people, in that room, at that time. Game Changer never quite balances out the rules and the chaos to my taste; I'm betting there is no way to truly balance them.
That said, "Second Place" was one of my favorite episode concepts of the whole series.
How the Great Migration Changed America by Professor Davarian L. Baldwin (audiocourse)
This is the 2024 Teaching Company course about the Great Migration, when Blacks moved en masse from the southern states to the northern cities.
I fear that late-period Teaching Company courses are all tending towards the same assessment: "amazing concept, just-okay execution".
The Great Migration is an S-tier pitch for a Teaching Company course. It's a vital part of American History; it's a key to understanding where the country now (uneasily) stands with respect to race. It has inherent drama. It sits just beyond the edge of living memory. And yet it gets short shrift in most history education - or at least it barely got a mention in my high-school textbooks. ²
This makes it a perfect topic for the Teaching Company to tackle. It even follows the reliable formula of recent courses: you take a broader topic (in this case, Black history), but you find a specific subtopic (i.e., the Great Migration) to provide your 'way in'. It's a little like how "what Darwin didn't know" provided an excuse to talk about modern evolutionary theory.
And yet. The Teaching Company has transitioned from traditional filmed lectures - get a university prof to stand up behind a lectern and just *go* - to basically having someone read an essay on-camera. It's my understanding that the presenters write every word of every lecture, then let the company thoroughly fact-check it, and then read it off a teleprompter. The spontaneity is squeezed out, the rhythm feels off, and you find yourself wondering why you don't just read a book instead.
I feel like this is what gets in the way of How the Great Migration Changed America. Professor Baldwin covers a broad topic effectively, but the Great Courses is mostly employing him as an audiobook reader, and he's less good at that. To his credit, he conveys the emotion of the story, recounting how his own relatives were part of the migration, and hammering home just how dire it was in the Jim Crow south. ³
Other times, I found myself getting lost because I didn't already have enough of a grounding in Black history. I noticed this especially when the lectures went into lists, when I'd hear something like, "This neighborhood was home to many great artsits, including..." and then there's a list of ten names I've never heard of. It worked better for me when it went into detail about individuals, like C. J. Walker and her beauty-product empire, or Louis Armstrong making the hard choice to move north.
In the end, this is a *good* course, in that it conveys how interesting and important this subject matter is. But I don't know if I can recommend the course - it's more like you should find a great book about this subject and read that instead.
For next week: ugh, so much in the backlog (this is what happens when I travel, right?). So I need to write about season one of Shōgun, season six of Game Changer, Turning Red, and a math audiocourse. I'm now reading that history of the MCU and a book about the Harvard Longitudinal Study. I'm listening to the Blank Check miniseries about Kevin Costner and an audiocourse about our relationship to digital technology.
____
¹ I wrote, and deleted, the phrase "ladder-al thinking".
² That said, I grew up in a small town in Kentucky in the 1980s, so
³ One of my favorite points from the course: we're told that the Great Migration was about finding opportunities in the factory towns of the North, but it was at least as much about escaping a violent, fascist, oppressive society.