Seed Salon: Steven Strogatz + Carlo Ratti

Steven Strogatz mathematically describes how natural and sociocultural complexity resolves into vast webs of order. Carlo Ratti uses technology as a tool to create interactive urban environments. Strogatz holds that we have a poor understanding of the complexity underlying such networked systems. Ratti suggests that building them may actually further our understanding. Seed invited them to consider: Are there laws that govern urban behavior? How do feedback loops behave in dynamic systems? What will cities of the future look like?

STEVEN STROGATZ: Tell me about the New York Talk Exchange -what were you trying to do with that project?

CARLO RATTI: Well, let me first tell you about the framework we’re trying to develop in the SENSEable City Lab at MIT. We think there’s a big change underway related to our physical space, our environment. We know how cities of the past were built with concrete, brick, glass, and steel. But cities of the future will also be made of silicon. So, how to marry concrete and silicon? This is what we’re looking at.

In the case of the New York Talk Exchange we were trying to see how people’s use of technology can allow us to better understand the city. So, using AT&T data, we looked at how New York connects in real time with the rest of the world, which gives you the effect of time zones, the effect of the specific neighborhood, for example, the rich parts of the city talk to the rich parts of the globe and so on. We wanted to know how the city could be seen differently by looking at all these connections.

SS: What kind of resolution did you use in the case of New York? Did you have it by borough or by street or…?

CR: Actually, we had maps of different scales. On one, New York was just one point. But then zooming in, we could go to the 200×200-meter resolution. So, quite fine-grained. For example, looking at Flushing, Queens we could see that we had a huge number of calls to Guyana. And we said, well what’s going on, maybe we didn’t properly analyze the data from AT&T. And then, we went on site and found out that it’s actually one of the main Guyanese communities outside Guyana. A lot of interesting things like this came out of the data.

SS: That’s actually something I wanted to get into a little bit. This process of visualizing the connections between different communities -in this case worldwide- gives us a different feel for the world we’re living in. There’s something kind of mystifying about complex networks and globalization in general. So many of the things that we face today, whether in ecosystems or in global climate change or economics, involve these vast networks that we really have trouble thinking about, partly because we can’t see them. I wonder if these studies might give us some kind of new intuition.

CR: I think the interesting thing is that the amount of information we can visualize is actually increasing. We keep overlaying more and more previously invisible information onto our physical space. And by making it visible, by analyzing it, you can actually have an effect on people’s perception of it. By looking at cell phone networks we can see a city as a living organism, a pulsating entity.

SS: Yeah, it’s very provocative to me, this idea of looking at cities this way. We tend to think of them as geographical regions filled with people, but we don’t have a very clear dynamic sense of what’s happening, of the pulse, as you say.

In a lot of your work it seems to me as if there’s an inherent optimism that human beings interacting with each other in new ways, and with their surroundings, will generally be a good thing. Do you ever worry about this?

CR: The fact that we have the potential to communicate with more people in a variety of ways seems to me to be very, very good. It’s like a democracy of opportunities. Also, from an evolutionary point of view, it’s the opposite of inbreeding, being able to reach out to anybody else on the planet.

SS: Yes, that’s clearly good. What I’m a bit worried about though is when people interact with their environment and the environment can act back. I don’t know anything about architecture or urban planning, but I get the impression that the old view is that structures exist and then people move around them or use them, but they don’t actually alter the space, by and large. But in some of your work it’s clear that the structures are responding to the people.

CR: You’re right. Traditionally, there was very little interaction. Architects have big egos, so they felt that the interaction would go mostly from the built environment to the people. For instance, 50 years ago, Buckminster Fuller said, “Reform the environment, stop trying to reform the people. They will reform themselves if the environment is right.” What’s happening today, I think, is that we’re able to create a full feedback loop. The two things can have an interplay, thanks to the new technology. For example, we created the Digital Water Pavilion for the Expo 2008 in Spain. The Expo’s theme was water so the idea was make a building completely out of water. Bill Mitchell at MIT had the idea to treat water like little valves you could open and close, creating pixels made of water. So it was like a living building. When you approach it, it opens to let you in, it reacts to your presence. It becomes a fully engaging experience between the human and the building. So, we’re able to actuate the city in different ways than we could in the past. Why do you see this as troubling?

SS: What I’m worried about is exactly what you put your finger on, feedback loops. In the world of dynamical systems, from a mathematical standpoint, feedback loops, especially in complex systems, can be really scary. Because of their unintended consequences. They can create all the beauty and richness in the world around us as well as unforeseen horrors. Just to take a super simple example of what I’m thinking of here, look at the Millennium Bridge in London: one of the world’s thinnest foot bridges and a very elegant structure. All the architects agreed that it was gorgeous, but it looked like it wanted to vibrate, like it was practically a guitar string strung across the Thames River. And on opening day when people walked across the bridge it wobbled a little bit. Which then fed to the people, and made them tend to synchronize their footfalls with the bridge’s motion, which made the bridge’s motion worse. None of this was supposed to happen. This was not built in.

CR: It was very funny -I was in London that day, at the opening.

SS: Oh, so you should tell me!

CR: Yeah, for a couple of days before they closed it, it actually became the thing to do in London, to walk on the wobbly bridge. But, if I get your point correctly, I think you’re saying feedback loops can create instability and resonance or some type of divergence in the equation.

SS: That’s one possible unforeseen consequence, yes. And, true, those would probably be easy enough to engineer against. So I’m not losing sleep over it, but I have this general concern about entering this networked era, which we’re clearly already in. For example, the power grid used to not be a grid. It was just a lot of isolated power stations. When there was trouble people would just close down the power plants and repair whatever the problem was. But now that there’s a grid, when something bad happens at one point in the grid, and you use the defense strategy of just shutting down that plant, it can have propagating effects. It can put too much load on other plants, which may cause them to shut down. And this is exactly what we saw here in the northeast when we had the 2003 blackout. Or think about what is happening right now in the market, where there are all kinds of propagating, cascading failures in our market and financial systems. So, I’m just thinking that you may be opening a Pandora’s Box for architecture when you let people feedback on the built environment. There will possibly be a lot of wonderful, emergent things, but there may be some very disturbing things.

CR: I like your example of the power grid. But isn’t part of the problem that we’re treating new distributed systems with old, centralized controllers? What if the intelligence were spread into the system? Then the system would regulate itself in a different way.

SS: Right. That’s actually the solution that nature tries to use. So, the thing is if you’re going to create these big, complex networks, you better be prepared to control them in a decentralized way also. The two should go hand-in-hand. In the case of the financial system, we don’t have anything like that really. We use the language that comes from the power-grid scenario. We talk about pulling the circuit breaker when the market has a problem. It’s a very crude kind of response.

CR: I see your point. My view is that the two will actually develop more or less at the same time. You cannot really develop the architecture and the control system until you have a network with which you can experiment. The two would likely develop in tandem. The other good thing about cities is that they’re under so much concrete. They’re very stable.

SS: Good point.

CR: Also, the city has such inertia. It’s not as if when you have a traffic jam you can just make the street double the width and let it go. You can do a little bit, you can change the traffic lights, synchronize them, but you can’t do much. If you get this information back to the humans, though, the humans can become the system actuators. The beautiful thing about that is if humans contribute to the intelligence of the system then it is, as a result, decentralized, intelligent control.

SS: You are optimistic!

THE LAW OF KEVIN BACON?

SS: In science, we try to discover natural laws within biological or physical phenomena. With all that we’re discussing, it seems like there’s waiting to be discovered all kinds of laws for urban phenomena.

CR: Absolutely. One of the most fascinating questions to me is the law of the scale of the city. Cities evolved for a large number of reasons. We didn’t have cities 8,000 years ago and that’s a pretty short time ago. They evolved for commerce, trading, defense, the industrial revolution, and so on. Today it seems that cities are mostly for helping us connect with each other, to meet and physically connect and to exchange and trade information. It’s what makes cities exciting. Ten or 15 years ago, at the beginning of the internet revolution, people were writing about the death of cities. The fact that we had a big, horizontal network and could connect every place in the world meant that cities would disappear. You can find a lot of literature in the mid ’90s about this. Ironically, the past 15 years have actually seen the most extreme urbanization process in history. This year, for the first time, over half of the world’s population is living in cities. This has something to do with a fundamental law that hasn’t yet been found. This is where we would need help.

SS: You want to take a guess? What’s your guess at what this law looks like?

CR: It’s related to the way we communicate as humans. From an evolutionary point of view, it seems advantageous to have a higher chance of meeting, and potentially mating, with more people, of being more connected with the world physically and digitally through networks. So what next? We’ve seen cities in the past decades reaching 20 million. Are we soon going to see a city reach 100 million? Why don’t we then live on the planet in a way that resembles New York and Central Park: a city of 6 billion surrounded by green space? These are important questions that are deeply connected to the way we communicate with each other and structure ourselves in society.

But, the thing is, it looks like technology is changing the way we communicate and because of these new connection patterns, we need a new type of physical structure for cities. Let me tell you something interesting that we found. We haven’t solved it yet, but we are working on it.

We were looking at the data generated by the New York Talk Exchange project and how New York City communicates with all the cities in the US. Now, if you take all the calls from New York City to all these other cities, you get a very surprising power law. If you look at a city of 100,000 and a city of 1 million, the city of 1 million will have a hundred times more connections with New York than the city of 100,000. If you think about the uniform system, you would expect a simple linear or gravitational model. You have two populations, and connections should be proportional to population. What we find instead is that connections are proportional to population squared.

SS: That’s interesting. Did you happen to know, offhand, how far that extended? Was it down to cities of size 100 or 1,000 or 10,000?

CR: It’s consistent between 1,000 and several million. It looks like an extremely consistent pattern. We’re still working on the data, but one interesting finding it suggests is that if you’re in a big city you’re much more connected to the rest of the population. The old experiment of six degrees of separation, which was very interesting, but quite approximate, could be validated today on a very large scale. People have started to do it with MSN actually.

SS: Oh yes, I heard about that -Jure Leskovec’s work. Interesting stuff.

CR: Yeah, they published a paper last summer. The problem is that they don’t have the precise location of the people. If you did the same thing on a telephone network, then you’d know the location of the network nodes. For instance, I think it would be incredible to find out that in New York City people have two fewer degrees of separation from the world than in Iowa City!

EVOLUTION BY ARCHITECTURE

SS: I study nonlinear systems where the causes are not just proportional to the effects that they produce, or the sum of the parts doesn’t necessarily equal the whole. In these kinds of systems, which have been studied now for about 100 years, we know that all kinds of weird things can happen that are hard to predict. Chaos is probably the most famous phenomenon -a little disturbance gives rise to the proverbial butterfly flapping it’s wings that starts a hurricane in Brazil. Even Chaos Theory, which was developed and came to full flower in the 1980s, has only really helped us understand nonlinear systems with very few parts, only two or three degrees of freedom. So, when I hear about all the good things that are going to happen when populations of 10 million interact with their built environment, I worry because we’re nowhere close to understanding these kind of phenomena from a theoretical point of view. This is why we have so much trouble in genomics, for example, where we still don’t understand why a person is more complicated than a pea, or why its organization is immensely less complicated than that of a person.

CR: I’m playing the optimist now. But the fact that we’re not able to model a system into solving the equations behind it doesn’t mean that the system itself is dangerous. In a sense, what’s exciting about the world is that many systems seem to have been engineered with a huge safety factor built in.

SS: Those systems that have already evolved, you mean?

CR: Yes.

SS: Well, those may have evolved to be robust and have safety factors, but as we create new ones, meanwhile, we’re still using our old linear thinking; that is we didn’t evolve in the world of the web, and a world where we can affect the ecosystem or the climate. We’ve only been doing this for the past 50 or 100 years, and we don’t have the cortex to know what the hell we’re doing. It’s not even clear that we have the cortex to ever know what we’re doing because these problems are so high-dimensional, and have so many parts, that even if the answer were known I’m not sure we’d understand it. So, yes, at the level of professional people working in this field, there’s a lot for us to do and we’ll be employed. But, we can really screw things up by introducing nonlinear feedbacks into these complex networks that we’re creating.

CR: But, in the end, aren’t most of the systems that nature evolved also nonlinear systems? We sometimes pretend they’re linear, because we know how to cope with them and they’re easier to study. But, aren’t all of them very complex, nonlinear systems?

SS: Absolutely. The linear world would be very gray, boring, terrible. The miracle of life and the richness of the world around us are due to its nonlinear and interconnected nature. I totally take that point, but it’s taken many millions of years to get like this.

Einstein said something like, “Everything has changed except our ways of thinking.” I hope that we, as a species, will get to be as fully capable of dealing with interconnectedness as the interconnected things we are creating. Can we keep up with our own creations?

CR: But, isn’t that how evolution works? By introducing something entirely new into the evolutionary chain?

SS: Right. And a lot of things go extinct. Most things that have ever been born on Earth, most species are done, they had their evolutionary experiments and they lost, right?

CR: Well, they mutated into something else. I mean, we are the living legacy of that.

SS: Right, they may have had survivors that were better adapted. And so, yes, if that is some consolation for us, that it will give rise to something else that will survive us, then okay.

CR: But I think some of the things we are experimenting with are really following some evolutionary principles and, I think, making us more diverse. There are a number of studies on species that went extinct and most of them seem to refer to the fact that those who had become too specialized disappeared. A small change in the environment killed them. And aren’t the things that we’re discussing making us less specialized? Isn’t it all going in the direction of making us evolutionarily more effective?

SS: Maybe. I hope so. Generally that would be a good strategy to be more diversified in uncertain times. But, I think, our best way of coping with it is to try to develop new ways of having intuition about the world. With the rise of the World Wide Web, I think a lot of us started to have an understanding of what a network is, in a way that we didn’t have 20 years ago. And even the language -when people speak about surfing the web, that’s a very physical metaphor. To me that shows progress in our way of thinking, in our understanding of this gigantic, seemingly endless web of connections.

CR: Speaking from that point of view, what are the key challenges from a mathematical point of view in this field?

SS: The challenges are enormous. We can’t solve the equations of any of these systems that we are talking about in the traditional sense that we could solve Newton’s Laws for mechanical systems, for example. So, the math that we all grew up on, calculus and differential equations, is still very valuable, but it’s not clear that it will really suffice because we can’t solve the equations. Not in the sense of getting explicit formulas for the answers. We need some other kind of insight.

CR: Right.

SS: At least in chaos and traditional nonlinear dynamics we had pictures. We could understand what was happening by visualizing these pictures in two or three, and sometimes four or five, dimensions. But now that we’re dealing with network systems with millions of nodes, we can’t use geometry either. We need something else. We have graph theory, that’s something. We have simulation but the simulations are often as hard to understand as the reality. So I think we have a real psychological question here as to whether we will ever be able to develop what’s needed to understand this modern world. And it may be, speaking of evolution, that we’re not the ones who will understand it. The artificially intelligent devices that we create will understand it and they will report back to us. I think that’s probably the most likely scenario. If we survive this networked world it will be because entities much more intelligent than us will figure out the laws. Who knows? The history of science has always kept moving forward, but, on the other hand, that doesn’t mean it always will.

CR: Okay, so the topological instruments we have are not sufficient to analyze these huge networks. But some networks do end up in physical space, like, for example, the network of people talking cell phone to cell phone. And when you go back to the physical space, we have a huge number of traditional tools that we can use. And so I wonder if, for some networks, going back to the Euclidean space can actually help us to better analyze what’s going on. We’re really not sure how to structure the network, but we have already structured the physical Euclidean space that is imposing on it.

SS: Right. That’s a very interesting point. Very little in network theory has been done, believe it or not, on networks in geographical Euclidean space. But yeah, on top of the pure topology of who is connected to whom, is the structure of actual distances. So, people have started to think about spatial networks and I think that could be a really important area for the development of network theory in the next few years.

CR: So, do you think architecture could save mathematics?

SS: Yeah, sure. Lead the way! Autor: Edit Staff
Fuente: sem