What Math Can Tell Us About Technology's Spread Through Cities
Sociologists have been studying social networks for some 50 years, trying to understand how groups of people connect to each other and how new ideas and tools travel between them. Our understanding of these networks is rapidly evolving, though. "Now," says Nick McCullen, a researcher based in the U.K., "physicists and mathematicians have been getting in on the game with their computer models." And the potential implications for some of our largest physical networks of people – cities – are pretty intriguing.
McCullen and a team of colleagues have been trying to mathematically model how energy-efficient technology is diffused through a community, in the hopes that city policy-makers might one day be able to use this sophisticated math to figure out how to get you (and your friends, and your friends’ friends) to install solar panels on your roof or to retrofit that drafty attic.
Globally, cities are responsible for 70 percent of all carbon emissions. And in many urban areas, about 30 percent of that comes from the residential sector. If mathematical models could help cities understand how energy technology catches on – a slightly different question from how iPads proliferate – it would be a victory both for the environment and the emerging field of complexity science.
“At the moment,” says McCullen, a lecturer in the Department of Architecture and Civil Engineering at the University of Bath, “we’re at a stage of proof of concept with these models, trying to show that they can show something useful about the real world, that they can provide useful decision-making tools.”
The model that McCullen and his colleagues have constructed, outlined in a paper recently published in the journal SIAM Journal on Applied Dynamical Systems, is based in part on our understanding of how other ideas like health innovations spread through social contact.
“Some of these ideas come from health, where to catch a disease, you only need a single contact,” McCullen says. “With technology, sometimes you take a bit of convincing. It may take several of your friends – half of your friends – to have a certain technology before you’re convinced that it’s useful to you.”
In the model the researchers have constructed, each individual is represented as a node in the network. And people are motivated to adopt the new technology based on three factors: personal preference (will this weatherization save me money or reinforce my environmental views?), peer influences (do a lot of my friends use this technology, too?) and social norms (does everyone seem to be using it?).
“For example,” says collaborator Catherine Bale of this last effect, “if everybody in your neighborhood suddenly had solar panels, and you could see that they did, it’s like a ‘keeping up with the Jones’ effect.’”
Plenty of environmental technology isn’t visible to others, though (smart phones are visibly ubiquitous, but efficient water heaters are not). And people aren’t likely to gab about their energy use (or lack thereof) on Twitter in the same way they might share information through social media about laptops or cell phones. “People don’t go online and start raving about their loft insulation,” McCullen says, “because it just doesn’t sound cool.”
This means that the spread of this kind of technology may be particularly dependent on face-to-face interactions (and there are a lot fewer nodes in your face-to-face network than your online one). For more visible technology like those solar panels, online social networks would also likely be less influential than the people you know (and whose houses you see) on your block. Other research released last year reinforces this idea: It turns out the higher the adoption of solar panels in a zip code, the more likely other people living there are to adopt them, too.
“One thing we have fund is that it’s really some of the local connections that matter,” Bale says. “If you’re a friend of a friend, and there’s clustering going on, that helps.”
The point of this whole mathematical exercise isn’t to predict what any individual household might decide to do about a new technology, but rather to simulate how entire complex networks of people behave. With more real-world data about how people talk about energy use (there is, unsurprisingly, not a lot of that out there) these models could become even more accurate. And with their help, city officials could test policy interventions – a recommend-a-friend scheme, a rebate, a particular marketing campaign – for the strategies that would most effectively encourage the spread of technology.
“Local authorities don’t normally use mathematical computational modeling at all to look into decision-making,” McCullen says. “It was a first time for us to interact with them.” But we like the sound of this odd partnership: mathematicians and physicists working with City Hall to leverage the science of how technology spreads.