Fractals and Scaling: Interview: Christa Brelsford

Dr. Feldman: So, our guest today is Christa Brelsford. She is a post-doc at the Santa Fe Institute. She has a B.S. in Civil Engineering from Columbia University and also a master’s in Climate and Society. She recently completed her Ph.D. in the School of Sustainability at Arizona State, and then came to join us at Santa Fe. So, welcome. Dr. Brelsford: Thank you. It’s fun to be here. Dr. Feldman: Great. Thanks for taking the time. So, I was wondering if maybe you could start by telling us a little bit about what you’re working on now at Santa Fe. Dr. Brelsford: Yeah, the big project that I’ve been working on is thinking about the topology of cities. Rather than the scaling ideas of cities, what I think about is that the problem that cities exist to solve is the circulation of people, goods, and ideas. This is a connectivity problem, then, not a geometry problem. If you’re connected, it doesn’t exactly matter how far away you are. And the mathematical language of topology is exactly what we use to talk about connectivity. So, because cities are about a connectivity problem, we think the mathematical language of topology is a natural way to describe cities. Dr. Feldman: Nice. And what drew you to this work? What interests you about the sorts of questions you’re working on? Dr. Brelsford: So, I’m lucky enough to get to have access to some of the best education in the world. And I’ve always thought that the purpose of this is to do good in the world. So, as an undergraduate civil engineer, I thought I was going to build bridges and build roads in the developing world and that would solve problems. Dr. Feldman: Yep. Dr. Brelsford: It didn’t take very long of engineering school to realize that just better engineering skills isn’t how we solve problems for people in cities. In my Ph.D., when I was studying sustainability, again, I was looking at drivers of decision making around urban infrastructure systems. This was specifically applied to water systems. But again, what I was trying to do is figure out, okay, just knowing how to build the infrastructure isn’t enough. Maybe if we know how people make decisions about how infrastructure is built that will give us a better understanding of how to build better cities in the future. As a Ph.D., again, I felt like that wasn’t enough. We need a broader theory of the local scale processes within cities in order to figure out how to build better cities. I mean, the urban population in going to double over the next– pick your number, but 40 to 50 years. And that means we need almost as much infrastructure as we built in the entire history of our species to house and feed all of those people. [That’s the] problem, and so we should get it right. Dr. Feldman: Yep, so, to what extent has some of the theory of scaling around cities, some of the work that Luís Bettencourt, Geoffrey West and that group has done. How has that informed or motivated your work? In what ways? Dr. Brelsford: Yeah, so I think that’s some of the best empirical theory we have about cities right now. And these are all aggregate answers, right. They’re looking at the average relationships between population and area, or population and whichever variable you’re talking about at the city-wide level. And that’s important, and it’s a really good step in figuring out how to understand cities from a broader perspective. But we also need to think about the local and heterogeneous processes within cities, which is what I’m really interested in. Dr. Feldman: So I guess maybe this is a very coarse paraphrase of what you just said, and this is a little bit how I tend to think of the scaling work. As you said, it’s very empirical so it’s describing a certain pattern or regularity and there’s some ideas about where those patterns might come from, but to a large part it sort of begs the question of how local processes and different processes give rise to these sorts of things. I think of it as intriguing empirical work that then requires some more mechanistic detailed work. Is that a fair assessment, you think? Dr. Brelsford: The mechanistic and detailed part of it is the part that I’m interested in. Yeah, that the empirical relationships are robust given the literature so far. And there’s some theories for why those empirical relationships exist that are based on local processes which are the things that I’m really interested in investigating. Dr. Feldman: Do you think there are any, maybe, limitations to the urban scaling approach or–danger is too strong a word, but– anything to be cautious about when thinking about that work? Dr. Brelsford: I mean, sure, if you’re being critical, it’s just bean counting. It’s a robustly observed empirical relationship. That is absolutely true. And that’s–that could be the end of it. It could be that all the theories about why this empirical relationship exists are wrong. Dr. Feldman: I wonder also… I mean, you’re interested in, I think, not just how–to put it broadly– how cities are built, but how to build them better, where better could mean more sustainable, fairer, more justly. And so, I sometimes wonder if these power laws–yes, it’s a nice, robust relationship, but maybe that’s actually a sort of bad relationship and there’s some way we could do better. In other words, that a city is doing it right if it’s on the line maybe isn’t necessarily true. You know what I mean? Dr. Brelsford: Yeah. I mean, you could talk about not whether it’s on the line or off the line, but its distance from the line, the residuals in these regressions. Again, that might be something that’s interesting to think about. Is it possible to shift that, to change the relationship between crime and population? Or, for a city that’s above the line to get closer to the line and think about what local scale processes are driving it to be an outlier and have more crime per population than our theories think it should. Dr. Feldman: Yep. Is there a–either in terms of your own work or some of the more aggregate-level scaling work– is there some recent developments or directions that you’re particularly excited about? Things that you think hold great promise? Dr. Brelsford: I’m an empiricist, and the data set that I’m currently really excited about working with is looking at census [track] level data in Brazil. There’s been a lot of work on this kind of stuff, especially in the developed world, in the U.S. and Europe. And starting to use the census style and real small-scale demographic information in the developing world, and also in slums, which is a big part of the work that Luís and I have been working on for a while, I think is really important. Dr. Feldman: And what are you hoping to learn or figure out from all that? Dr. Brelsford: I think you can’t understand cities if you don’t understand slums. Dr. Feldman: Can you say how you’re using the word “slum” just in case people aren’t familiar with that term? Dr. Brelsford: Okay. When I’m being more precise with my language I say “informal settlement.” Dr. Feldman: Right. Dr. Brelsford: In the way that I look at it, a slum is any place where lots of people don’t have access to formal urban infrastructure systems. So, there may not be– within a city, so there may be running water in the city, but people who live in this particular neighborhood don’t have access to that. Or power systems, or whatever. Dr. Feldman: Yep. So, sorry, so you were saying that this data set– you’re optimistic or excited that it’s going to shed new light on the dynamics of slums and informal settlements? Dr. Brelsford: Yeah. I think that we can use what we can learn about slums and informal setttlements to inform a broader understanding of cities. Thus far, more or less all we’ve measured is the formal parts of cities, which by 2050 might be only half of the world’s urban population. So, by getting some empirical handle on what’s going on in slums, we’ll start to know more about how cities function. Dr. Feldman: So, do you think –this may be an unfair question to ask you to predict the future, but do you think when you look at –if you try to look at various aggregate or empirical statistics, would slums look the same as cities or would they look– have sort of different signatures? Dr. Brelsford: That’s a really interesting question.>From a topological perspective, which is what I spent a long time looking at. I can tell you that slums are qualitatively different, not just quantitatively different, but they’re topologically qualitatively different, which is really interesting. And we think those topological differences, which, again, are about connectivity, mean that there are likely to be very big differences in how people who live in slums interact with the rest of the city than people who are able to live in formal neighborhoods. Dr. Feldman: Yep, great. Dr. Brelsford: But we haven’t tested that yet. Dr. Feldman: Well, we look– I look forward to hearing about that. That definitely sounds like exciting work. Are there any other thoughts on urban scaling or science of cities that you want to leave us with? Any bits of advice for the students in the course? Dr. Brelsford: I think that understanding cities is the way to solve problems in the world over the next century. I think that we can’t solve the big problems we face without a good understanding of cities. So that’s why I do what I do. Dr. Feldman: Great. Sounds good. Well, thanks so much for your time and sharing some thoughts with us. Dr. Brelsford: Yeah, thanks for having me. Dr. Feldman: Take care.

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