# Tag Archives: math in real life

## Bob, Gwen, and Lines of Best Fit

I have no excuse for this article. Except the new Fosse/Verdon ads are showing up. Also, consider “lines of best fit” a descriptive, not technical, term.

“Hey, Gerardo. Take a look at this.”

Gerardo, my new TA, reluctantly removed his air pods. Like all my graders, he’d been my student for three classes before asking if I could take him in third block, but the rest of my TAs were chatty folks. Gerardo grades with fantastic efficiency, but the rest of the time he’d really rather be somewhere else working on his English essay.

“What the hell…heck is that?”

“Well, this is an image from a famous dance. I took some images from it and started comparing movement lines for fun.”

Gerardo shot me a look. “Fun? You’re so weird.”

“Yeah. But it beats grading. So take a look. What do you notice?”

“You mean, what are the red lines telling me?” Gerardo did look, and think. But shook his head. “I don’t see anything.”

“Who’s taller?”

“What, that’s a trick question? The guy is.”

“Yep. The guy is Bob Fosse, one of the most famous choreographers in history, and Google says he’s 5’8″.  The woman is Gwen Verdon, his wife, and she’s 5’4″.”

“So what does….wait a minute. Gerry looked again. ” You’ve got the other lines at their butts and knees.”

“Yep.”

“And they’re, like, the same.”

“Exactly. So what does that mean?”

“She has to have really long legs. Yeah, I see it now. Look how far below her shoulders are. Her body’s a lot shorter.”

“Good! Try this one.”

Gerardo was interested, now. “Okay, I get this. Her hips are way, way out. His aren’t. But what’s the line for…oh, I see. You have the lines right on their hips, and there’s all this space between her body and the line. But the line goes right through his body. So that means…he can’t push his hip out as far.”

“Nice. Now here’s two at once. What do they have in common?”

Gerardo was hooked, now, leaning into my desk closely. Ideally, my trig students were getting some work done, but we were pretty intent on this.

“Okay, so the top red line on this one is about their height…it’s the same. How is that happening?”

“Good catch.”

“Their knees are lined up, their heads are lined up…wait. Their…what, hips? His is lower!”

“Look at his feet.”

“Oh, wow. He’s got way more give in his feet. So he’s using his feet to push up while his knees are bending down. Oh, you have it circled in the next one. So he’s able to bend down to her height on his toes using only his knees.”

“It’s unusual, because she’s clearly more flexible than he is in the hips, but he’s got very bendy feet. Try this one.”

“Okay, those vertical lines are showing the distance.”

“Yeah. Later on I do slopes to show the difference.”

“What, you’ve got more?”

“No, no. But on this one, I can’t figure out what it means. Her leg is straight up and down. His is all bent forward…oh, I see. He has to bend forward, to do that thing with the shoulder. But she can keep her whole body straight.”

“Neat. Next up.”

“Oh my god. How does she do that with her leg? And she’s almost straight up. She is straight up. He’s kind of tilted just to try and get his leg up nearly as much. Not that I could lift my leg more than an inch.”

Despite his complaints, Gerardo had moved far in to check out the pictures.

“He’s way higher.”

“Yep. Fosse was a jumper.”

“But the other lines show his leg is below his waist. Hers is above…hey, she’s lower than he is in the air, but her leg is higher–not just relatively, but like higher than his. ”

“These are getting easy. She’s standing straight up, while he’s having to bend to get the same results. And this one, she’s got the flexible hip thing going, while his is straight.”

“Here I was trying to show that she is turning faster. But I honestly don’t know if that’s a problem, if they’re supposed to time it perfectly, or what. I was just trying to show the turn.”

“Yeah, you can see he’s barely started when she’s halfway around.”

“So he’s having to bend to get the same positions that she can do standing straight up. What part of the body allows that?”

“Hips, definitely. Knees? Good question. Here’s a sequence of three that probably look strange, but it’s like a fake exaggerated run.”

“Jeez, her leg is at 90 degrees, and her body is tilted over. What is she holding herself up with–just her foot?”

“And some pretty impressive legs and abs, I’m thinking.”

“He’s solid on that one, too. But in the next ones, her body is practically an L.  He’s balancing. Like throwing his weight forward to get his leg up. In the last one, he has his leg up as high as hers but tilts over a bit to do it.”

“Well, keep in mind that on relative terms, she outranks him. Gwen Verdon was probably the best dancer ever seen on Broadway, and the rest of the best were trained by her. In her prime, no one was better at that time. Fosse was a groundbreaking choreographer and an excellent dancer, but not in the same league as a performer or star. I know nothing about dancing, so I can’t tell you how the two of them are rated by others, nor do I have any clear idea of who was “better”.

“So this was a long time ago?”

“Yes, Damn Yankees is sixty years old. Try this group of pictures of a sequence of two jumps.”

“He’d have been a damn good basketball player.”

“I know, his vertical jump stats had to be amazing. ”

“You know what else? And you didn’t red line it, so maybe I’m getting good at this. He’s the one who’s straight up. She’s the one bending to balance and get more flight.”

“Whoa. I didn’t catch that. You’re right.”

“Unless maybe the middle picture is just her on the way down?”

“No, I caught the first two on the way up and the last one, after they’d switched sides, at as close to peak as I could. That’s another sign that he’s much more comfortable at jumping than swinging his hips.”

“Well. As it is for most guys.”

“Ha. True.”

“This is obvious. She’s got a straight leg, up and down, and then just a tilt of her body. He’s tilting his body one way to get the hip out, then the other way for the…whatever you call it, the show. Hey, you know, this really is a good use of slopes.”

“Thanks.”

“What the fuck…oh, sorry. What is happening with her leg!”

“I love this one, because it’s related to the reason I became fascinated with this dance.”

“But man, look at it! He’s at his highest point and she’s got a whole additional gear yet!”

“And the funny thing is it makes Fosse look almost clumsy, which he wasn’t. Not many male dancers could do anywhere near as well.”

“How come you got so interested in this dance you’re breaking it down image by image?”

“My interest was first.  I made the images for math class, but much later.   I was watching a documentary once years ago where Gwen was talking about this dance and how Bob Fosse was always yelling at her to jump! because she can’t fly like he does.  I’ve been watching musicals my entire life, but I never really considered comparing dancers. When I was a kid, I always wondered why Cyd Charisse was brought in to dance with Gene Kelly…”

“Who?”

“Remember that movie we watched with Princess Leia’s mom at Christmas?”

“Oh, and then  she died! Yeah, the musical about silent movies. That was good.”

“So you remember how in the big dance number at the end, it wasn’t Princess Leia’s mom?”

“The brunette lady with the legs.”

“Exactly. I used to wonder why they brought her in. But when I grew up, I realized it was because Debbie was a  movie hoofer, while Cyd Charisse rivals Verdon as the best there is. So when I found the dance on Youtube, I analyzed the whole dance and noticed differences that went both ways.”

“You do that with a lot of dances?”

“No. Most famous dances with men and women aren’t doing identical steps–and most of the ones that do exist are tap dances.”

“I was having trouble sleeping one night and  watched Cabaret, which he directed. That got me thinking about this dance, and wondering if I could capture their differences in a way a student could analyze.”

“For class?”

“Yeah, maybe. It was just a whim.”

“How does she hold that balance? Even for a second? I mean, he looks good, but normal.”

“Here’s another spin. This time, it goes from a spin into her going on the floor into a goofy tug and him pulling her by the leg. I should say that some of their spins were perfectly synchronized. I was more curious as to what it meant.”

“Ha, I like that little arrow you put! He just jumps like it’s nothing.”

“Wanna see the actual dance?”

“Wait. That’s all the pictures? You mean, there aren’t like, five hundred?”

But Gerardo watched the clip closely, despite the clear implication that I’m a tad, oh, obsessive.

“OK, I get it now. If I’d watched this first, I’d say they were completely identical. But looking through those pictures lets me see the differences.”

“Thanks. Now. You’ve been a really good sport, but can you do me one more favor?”

Gerardo looked warily skeptical. “What?”

“These pictures are from a recreation of that dance from a new show coming out on their lives. I don’t have any red lines drawn, but do you notice anything?”

He snorted. “Yeah, right, like I’m going to see any  differences…wait a minute. Their hips and knees aren’t even. She doesn’t have the long legs.”

“And?”

Gerardo sighed, but complied. Suddenly he leaned forward, and smiled. “Got it. He’s the one dipping his hips! She’s holding them straight.”

I startled him, and the class, by thumping my desk. “I am justified.”

“What?”

“That’s the whole reason I asked you to look through those pictures. Because when the new trailer came out, all I could think was hey, they’ve got it backwards! and I wanted to have someone else know. Thank you, Gerardo. I’ll give you an A.”

“All TAs get an A. Is the guy a better dancer than the lady, or just more flexible?”

“Well, they’re both actors, not dancers. But Sam Rockwell, who’s playing Fosse, has danced in almost all of his movies and you can see he’s really loose-limbed, with hip action. Michelle Williams famously recreated one of Marilyn Monroe’s dances and got nominated for it, but it may or may not be significant that they cut away during a lot of the dips and weaves. Or maybe these few seconds aren’t representative, of course.”

(Note: I didn’t bore Gerardo with this picture, but hey, this is my blog so I’ll bore you. Here’s one example:

Williams, on the right, has to turn her entire body back to kick backwards. Monroe, who had been well-trained to use her body in dancing, can turn her head and neck, kick her leg back–farther, no less– while keeping her body straight.)

I’d like to tell you that Gerardo then asked me dozens of questions about movie lore, but instead he went back to modern music on his air pods. But I felt better for the validation, and got some grading done. While I told the story uninterrupted,I did take some time for student trig questions, pesky though they were.

If you’re unfamiliar with the story, “Who’s Got the Pain” is a throwaway number from “Damn Yankees”. For years, it was considered a time-waster and often cut out of TV broadcasts. But dancers and choreographers treat the scene like the Talmud, studying it endlessly. And over time, “Who’s Got the Pain” became known as the only time Fosse and Verdon danced together in a production movie number. Definitely watch the dance all the way through if you’ve made it this far into the read.