Why does fashion repeat in 20-year cycles? Math has the answer

A mathematician analyzed 150 years of women’s fashion to understand 20-year trend cycles, and how “optimal distinctiveness” drives change.

Speaker names marked ? are inferred from speaking time and the show’s known hosts — they are not voice-verified.

• 0:03Flora Lichtman?

  Hey, I'm Flora Lichtman, and you're listening to Science Friday. Fire up TLC, get out your bucket hats, your low-rise jeans, your Furbies, the original Labubus, because, as you may have noticed, Y2K fashion is in right now. They say fashion moves in 20-year cycles, and it turns out it does, according to math. Here with us now is Dr. Emma Jaidela, a mathematician at Princeton University who analyzed over 35,000 images of women's clothing spanning back to the 1860s to confirm this theory. She uses mathematical models to understand complex systems. Emma, welcome to Science Friday.

• 0:48Speaker 01

  Great to be here.

• 0:50Flora Lichtman?

  This must be a gigantic field, math-fashion.

• 0:53Speaker 01

  Oh, definitely not. I think quite the opposite. Most mathematicians really don't think about fashion. There's actually a joke in the math community, which is, how do you know that a mathematician is well-dressed? And the answer is because his t-shirt doesn't have holes.

• 1:13Flora Lichtman?

  Okay, so why did you take this on?

• 1:16Speaker 01

  I've always been really interested in patterns around me as a mathematician, and in general, this idea that fashion comes back, or history repeats itself. So I started to think, is it just a perception that fashion comes back, or is it actually true? And could we prove this mathematically?

• 1:34Flora Lichtman?

  Do you have any connection to fashion? Any personal connection?

• 1:38Speaker 01

  I do, a little bit. I grew up in Paris, France, which is the capital of fashion, as many people would say.

• 1:43Flora Lichtman?

  So you're like, I know about fashion. I grew up in Paris.

• 1:45Speaker 01

  I love fashion. I definitely do. My mom also has worked in fashion. She worked for Nina Ricci at some point. So I definitely grew up, at least being a lover of fashion, myself.

• 1:57Flora Lichtman?

  What were you looking at specifically with this study?

• 2:00Speaker 01

  Well, when we first set out to do this, we wanted to figure out a way to even quantify fashion, because what does that even mean? There's so many dimensions to fashion: color, pattern, shape. So we looked at women's dresses, because there's this kind of idea that's been going for a while, that hemline is inversely related to the economy, hemline length. So this actually came from the 1920s, when women used to wear silk stockings. And when they could afford real silk, they would wear short dresses to show off their silk stockings. And when they couldn't, they would wear longer dresses. So there's been kind of this idea floating around. We also teamed up with a fashion historian at Northwestern University, Alicia Katice,

• 2:44Speaker 01

  and she's the one who helped us decide on the measures of women's fashion that we looked at. So what we did is we measured neckline, waistline, and hemline of women's dresses over about 100 years. Like you mentioned earlier, 35,000 images that we analyzed for this. And we found something really exciting to us, which was that there actually are cycles in fashion. And not only that, these cycles are 20 years long. We found this in the data, and we had no idea that this was something that was well-known in the fashion industry. We only found this out about six months later, and we were, wow, this is so crazy, that we find exactly in the data what's been pretty well-known in the industry for a while.

• 3:29Flora Lichtman?

  Yeah, it's backed up, right, by the data.

• 3:31Speaker 01

  Exactly.

• 3:32Flora Lichtman?

  For this particular, at least this particular case study. I mean, why did you focus on hemline and neckline and wa-- like, was there a math reason to focus on these variables in particular?

• 3:44Speaker 01

  Yes, definitely. So as mathematicians, we typically try to simplify systems as much as possible. And we wanted to try to analyze fashion along one dimension. So we did it along what I like to call the vertical axis, from the head to the feet. What do you have? You have neckline length, waistline, and hemline.

• 4:06Flora Lichtman?

  And then the images, where did they come from? What were you looking at?

• 4:11Speaker 01

  We used two data sources for these images. The first one is this amazing dataset called the Commercial Pattern Archive, or COPA. This is a dataset of sewing patterns archives from 1869 till 2015 is the latest one. So that was about 25,000 of the images that we used, but there was a sparser data in more recent years. So we turned to Vogue runway images. And there's actually two kinds of runways. The first one is what's called couture or high fashion. That might be what you think of typically like Dolce & Gabbana or Ralph Lauren. So we used some images from that. And then the other was Vogue ready to wear.

• 4:56Speaker 01

  That might be something like H and M clothes that you would wear, that more typical people would wear.

• 5:03Flora Lichtman?

  Okay, so how should I imagine these trends mathematically? Is it like a sine curve or something where you sort of have like short dresses, long dresses, short dresses, long dresses over a 20-year span?

• 5:14Speaker 01

  Yeah, pretty much. It's a little bit more complicated than that, actually. And this was something else that was surprising to us. So if you imagine the data, there's first of all, one cluster of floor-length dresses that's just always existing. And maybe that's for events or just the maxi skirt. Yeah, basically. Maxi skirt is always in, always has been. That's one cluster. And then there's a secondary cluster, which is the shorter dresses. And from about the 1920s to the 1980s, that looks exactly like a sine wave. But what happens is, starting in the 1980s, we see a split in this upper cluster of dresses. So it splits into two and you start having the coexistence of three kinds of styles.

• 5:59Speaker 01

  Mini skirts, meaty, which is kind of this ankle or calf-length skirts, and the floor-length dresses at the same time.

• 6:06Flora Lichtman?

  How do you interpret that? The sort of emergence of these, of another category?

• 6:12Speaker 01

  I think there's two main reasons that we find based on our model that explains why there's a split. The first reason is just that there's an acceleration in trends overall. So trends are changing faster and faster, and this could lead to the split. And this is not only true in fashion, but actually there's scientific evidence of this across many other domains in society that there's an acceleration of trends.

• 6:35Flora Lichtman?

  You mean like acceleration of trends, like they move in and move out faster?

• 6:40Speaker 01

  Exactly. Also, as people are consuming more, so people are buying more and more clothes, which means that it needs to be different faster and faster. And reason number two is what you pointed to, which is that there's just a greater diversity of styles, which maybe reflects this greater diversity in society and also the fact that there is less conformity in society, where in the past, women were kind of all expected to wear the same clothes. But then, starting from the mid 1980s, there was a greater diversity in the kinds of styles that were acceptable for women to wear.

• 7:14Flora Lichtman?

  Does this tell us anything about predicting future fashion? And like, what about outside of the realm of hem length?

• 7:21Speaker 01

  Definitely. So, we developed a model to explain these trends. And this model is actually based on a very simple idea from psychology called optimal distinctiveness. And optimal distinctiveness is this idea that for innovations to succeed, they need to be different, but not too different. Because if you're too different, you're just weird. And if you're just different enough, then you can be cool.

• 7:48Flora Lichtman?

  I'm familiar with the former, personally. Yeah.

• 7:52Speaker 01

  Yeah. So, optimally distinct. And we find that there's three aspects of this optimal distinctiveness that explain these trends. The first one is that you need to be different, but not too different from the past. So for trends to keep being fashionable, they need to be different from what happened last year. That's number one. Number two, you need to be different from others, but not too different. So there's kind of this social aspect to it. And then third, you need to be, there's some physical constraints, because obviously dresses can only be so short or so long. Although, fun fact, we actually find trains, for example, in the 1850s. So there's kind of very long, you know, you can kind of extend in some ways past floor length.

• 8:34Speaker 01

  But typically, there's more or less some of these physical constraints. So you need to be different, but not too different from a reference point of some sort, like the knee. And these three ingredients are enough for us to replicate the dynamics that we see. So these cycles, this split, this acceleration of trends. And we think that this model could help us understand future trends as well, not just in fashion, but also trends in other aspects of society as well.

• 9:02Flora Lichtman?

  I mean, it actually makes perfect sense when you describe it that way because it's like you'll have people who are sort of pushing to be slightly different, but they'll get to a max where the skirt can't get any shorter or whatever, and then you have to sort of come back down the slope again. So is that the idea?

• 9:17Speaker 01

  Yeah, that's exactly what we think is happening, that because you have these boundaries and you have this fact that you need to be different, the system wants to oscillate and the system wants to create cycles because at some point, there's nowhere else for it to go but back up.

• 9:32Flora Lichtman?

  All right, hang on for just a stitch, we'll be right back. We're going to talk about how math helps us understand everyday life, even outside of fashion.

• 9:44Speaker 02

  And from the Alfred P. Sloan Foundation, working to enhance public understanding of science, technology, and economics in the modern world.

• 9:56Flora Lichtman?

  Okay, so I want to talk about your work with cycles and sort of complex systems generally. What is that field and why are those things interesting to mathematicians?

• 10:08Speaker 01

  Complex systems is this field that's been taking off, I would say, a little bit lately. And what's really cool about complex systems is this idea that the whole is greater than the sum of its parts. So in the case of fashion, for example, you have a lot of different designers, a lot of different consumers, they're all interacting individually. But on the whole level, we get these cycles, we get these clusters that we're able to understand mathematically. Some other examples of kinds of things that mathematicians are interested in are groups of animals. So you can imagine flocks of birds flying Around in groups, they have these really interesting patterns. Geese kind of forming these V shapes, for example, or schools of fish.

• 10:51Speaker 01

  If you've ever seen these videos of fish that are swimming around and you sometimes have a shark that comes, the fish, the whole group of them manages to do this very fast. So this is what complex systems is about, looking at these systems where you have a bunch of different individuals interacting to form some greater pattern.

• 11:09Flora Lichtman?

  And the idea with the math is to understand what that greater pattern might be?

• 11:14Speaker 01

  Exactly. So in our model, for example, for the fashion, we don't necessarily need to understand what's happening with every single individual. What we want to understand is why are there clusters? Why are there these cycles in fashion over time? And math allows us to do that.

• 11:32Flora Lichtman?

  Do you think math has been underutilized to help us understand culture or everyday life?

• 11:39Speaker 01

  I think so. For me personally, it was really mind blowing when I first heard about the fact that we could use math to understand human behavior. Because I find people extremely puzzling. People are very complicated, very unpredictable. But I find math very simple and elegant, and one plus one is always two. Which is why I was really excited about this idea that we could use math to understand human behavior. And that might be for fun things like fashion or culture. But it's also the case for healthcare, for example. The idea that we need to understand not just, in a pandemic, for example, how the epidemic is spreading itself, but how people interact so that we can make better decisions as a society.

• 12:24Flora Lichtman?

  Emma, you work in, you know, one of the most male dominated research fields. I think it's something like 30% of PhD mathematician grads are women. Did it feel radical in any way to take on fashion?

• 12:44Speaker 01

  Actually, we've had a really positive response from pretty much everyone that I've talked to about this. And the math that we've done for this is actually very rigorous math that's applicable to a lot of other fields. The model that we developed, this optimal distinctiveness model, is actually, I think, gonna have implications in many other different fields. I also think for women, it's been a lot of fun to see men, as you said, that are dominating this field, get really excited about something that's maybe typically associated more with women, which is fashion and specifically women's fashion. That's been a lot of fun. This is what's cool about this kind of topic,

• 13:27Speaker 01

  that you can use very elegant, very rigorous math to study any variety of systems. And if you do it in that way, I think people generally get pretty excited about it.

• 13:39Flora Lichtman?

  OK, one more burning question for you on Y2K fashion. Have you embraced the bucket hat personally?

• 13:47Speaker 01

  I have embraced the bucket hat. I have a bright yellow bucket hat. I don't know how good it looks, to be honest, but I love it.

• 13:56Flora Lichtman?

  Do you have any takeaways from these mathematical models on how to be stylish?

• 14:02Speaker 01

  The takeaway is this idea of optimal distinctiveness, I think. So if you're constructing an outfit, you want to be different but not too different, which means maybe you wear a pretty standard outfit, so some jeans and a white shirt, but then you pair it with your yellow bucket hat. Or maybe you wear, in a more professional context, a blazer, but then you put kind of a cool vintage pin on it or a cool pair of earrings. Just accessorizing is a really good way to distinguish yourself without going into the a little too far category.

• 14:35Flora Lichtman?

  The weird zone, what can you say?

• 14:36Speaker 01

  Yeah, the weird zone, I like that.

• 14:39Flora Lichtman?

  Emma, thank you for taking the time to talk today.

• 14:41Speaker 01

  Thank you so much.

• 14:42Flora Lichtman?

  Dr. Emma Giedela is an applied mathematician at Princeton University, and she started this fashion research while she was a PhD student at Northwestern University. This episode was produced by Dee Peterschmidt. If you think Sci-Fry is the French tuck of podcasts, I don't-- actually, is that a good thing or a bad thing now? I don't know where we are in the cycle. Anyway, the point is, if you like the show, please rate and review us wherever you listen to podcasts. It really does help. Thank you for tuning in. I'm Flora Lichtman.