Case study: Cities, Collaboratively Designed
How many hundreds or millions of questions must be considered when deciding how a city should update its transportation system? More buses? A fleet of autonomous vehicles? Questions of cost to the city, cost to the commuters, fuel efficiency, ease of use, pollution, travel time, underground digging projects, traffic accidents, transfer waiting times, parking availability, etc.—the complexity is staggering.
Whether one is designing anything, whether it be a transportation network or a robot or a chair, there will always be multiple different parts that need to interact and share work to form the unified whole. The bus-route team can’t be constantly consulting the train-schedule team, and yet their decisions affect each other. An electric car needs a battery to power it, but a bigger battery isn’t always better because it gets heavier and bulkier and so harder to move around. The optimal solution to one part of the system may be catastrophic to the workings of another.
How can designers of these various facets of a system work independently enough to make progress on their own part, while still working collaboratively enough that the parts fit together into a coherent whole? Luckily there’s math for that.
Topos researchers and their colleagues have developed “Mathematical co-design”, a mathematical theory and attendant open-source software tool, which facilitates multiple different design teams working independently and yet sharing their results. Each sub-team inputs information about the feasibility of various design choices for their own piece of the puzzle, and the coordinator inputs how the functionalities and requirements of each piece affect the other pieces. No matter how much feedback affects cascade through the system, the software automatically calculates the best solution.
This is not just abstract. Our colleagues at ETH Zurich, Stanford, and start-up Zupermind produced a case study for the transportation network of the Washington DC metro area. For a variety of different costs, they used the tool to determine how many autonomous vehicles, trains, etc. should be purchased for optimal results in terms of traffic, parking, travel times, etc.
At Topos, we direct our sights at the challenges of the day, extract their essence, and develop rigorous mathematical solutions that are abstract enough to be reused repeatedly in multiple contexts, and yet concrete enough to actually be deployed in this real world we live in. Like a good teammate, we work independently enough to take responsibility for our own contribution, and yet collaboratively enough that the results of our work make sense in the larger whole.
Our world is increasingly enmeshed in and dependent on technologies of connection, and with new natural language and artificial intelligence capabilities on the horizon, this will only continue. It is imperative that we get it right. To do so, scientists, technologists, and policy makers must work together to construct informed, value-driven technologies and policies that build systems that work for us all.