Paradoxes of the Unexpected
When fixing the system makes it worse, and breaking it makes it better—you’ve entered the paradox zone.
“Today’s problem comes from yesterday’s solution.”
Peter Senge, The Fifth Discipline: The Art and Practice of the Learning Organization (1990)
“Starship experienced a rapid unscheduled disassembly during its ascent burn.” SpaceX, Jan 16, 2025 https://x.com/SpaceX/status/1880033318936199643?lang=en
An unexpected meteor shower caused by the rapid unscheduled disassembly of a
SpaceX launch vehicle over Texas.
(Jan 16, 2025)
Sometimes things go wrong in spectacularly unexpected ways. While much of this blog deals with failures that could be anticipated, there truly are times and effects that you really can’t anticipate.
This post is about failure modes that you can’t be blamed for not expecting. Or, if you’re looking for a theological rationale, these disasters are caused by acts of God, or at least by a universe that has more going on that we’ve expected. These are the kinds of things that happen when you add 2 + 2 and find the answer is “navel oranges,” something so different that you never would have expected it. Something so strikingly counterintuitive that it seems to come from outer space.
And of course, once you learn about the effects stemming from unexpected events, future consequences shouldn’t be quite so unexpected. We will have learned something new about the world. One of the things we should know the truly unexpected is that the world is full of paradoxes—things that go exactly the opposite of what you might expect. Here are a few design paradoxes that should teach to be cautious in our planning.
The Unexpected Paradoxes Design Problem
Braess's paradox is the counterintuitive effect where adding capacity to a network (e.g., building more roads in a city network) can actually increase congestion and slow down traffic flow. This seems to make no sense (that’s why it’s a paradox)—how can adding a road slow things down? This happens because drivers, acting selfishly to minimize travel time, may choose routes that, when adopted by many, end up everything more congested than before, clogging up the whole system.
This has happened many times before. In Seoul, South Korea, traffic throughout the city sped up when the heavily traveled Cheonggye Expressway was removed as part of the Cheonggyecheon stream restoration project. Remove a road to fix a stream and get improved traffic flow as a result. [Easley]
Likewise, things got worse when Stuttgart made investments to their road network by adding new segments in 1969. Again, paradoxically, the overall traffic situation did not improve until a section of newly built road was closed for traffic. By closing a road section to all traffic, the overall traffic pattern improved. [Knödel]
Even the infamous New York City traffic isn’t immune to Braess’s paradox. In 1990, oddly and ironically, the temporary closing of 42nd Street for Earth Day ended up reducing the amount of congestion in the area. [Kolata]
So it shouldn’t have been a surprise (but it was) when a few years later, in 2009, New York experimented with closures of Broadway at Times Square and Herald Square, resulting in improved traffic flow and permanent pedestrian plazas. While the road closure did improve overall traffic flow, the project didn’t quite hit their original targets—flow increased by only 5 percent—but the closure also vastly improved safety in the area, with a 35 percent decline in pedestrian injuries and a 63 percent reduction in injuries to drivers and passengers, according to city data. As a consequence, foot traffic grew by 11 percent in Times Square and by 6 percent in Herald Square. [Grynbaum]
Obviously, wanton removal of roads doesn’t always improve traffic flows, but sometimes it does. And counterintuitively, adding roads sometimes makes things worse because of Braess's paradox. Better traffic modeling methods (developed in the past few years) can help with planning and reduce the unanticipated results, but be aware of the paradoxes that could lead to a worse outcome than planned.
This effect isn’t limited just to cars on roads, but also applies to every kind of network traffice, even internet routing. In studying the effects of adding new internet cables to the existing networks in Africa, it turned out that (just as with cars, roads, and physical traffic) sometimes adding internet network capacity actually decreases the overall performance. In this case, adding another cable slows everything down. [Fanou]
What’s more, improvements in road networks often lead to no alleviation of congestion, but often create additional traffic: this is often called induced demand. Improvements to the road network may even make congestion worse if the improvements make public transport less convenient to use, or if they shift investment away from supporting the systems as it exists, causing disinvestment in the public transport system.
Braess’s paradox also shows up in the most unlikely of places.
If you think about a basketball game as a network of passes between players, changing the individual players is a lot like adding (or subtracting) a road. Some players send the ball to others on the court with style, and grace, making the whole team work better. The Ewing Paradox (named after star NBA player Patrick Ewing) is cited as a non-traffic example of Braess's Paradox. It appears in situations where a team performs better when its star player is absent or playing fewer minutes than normal. The notion is that when a dominant star player (such as Ewing) is on the court, teammates might become over-reliant on them, leading to less balanced play and a less efficient offensive flow. When the star is out, the team is forced to distribute responsibilities more evenly, leading to a more cohesive and effective overall performance—effectively improving the overall traffic flow by changing the structure of the network. [Skinner]
So what’s the moral here? Sometimes fixing the world means closing roads, benching your MVP, or just stepping away from the internet cables. The unexpected isn’t just a fluke—it’s the universe’s way of reminding us that linear thinking in a nonlinear world is a great way to end up with traffic jams, losing streaks, and internet outages. Paradoxes like Braess’s aren’t bugs in the system—they are the system, quietly laughing behind your back. Plan accordingly… and maybe leave a few oranges in the glove compartment, just in case 2 + 2 equals fruit again.
REFERENCES
Easley, D.; Kleinberg, J. (2008). Networks. Cornell Store Press. p. 71.
Fanou, R., Huffaker, B., Mok, R., & Claffy, K. C. (2020, March). Unintended consequences: Effects of submarine cable deployment on Internet routing. International Conference on Passive and Active Network Measurement (pp. 211-227). https://par.nsf.gov/servlets/purl/10186684
Grynbaum, M. “New York Traffic Experiment Gets Permanent Run” New York Times, (February 11, 2010) https://www.nytimes.com/2010/02/12/nyregion/12broadway.html
Knödel, W. (31 January 1969). Graphentheoretische Methoden Und Ihre Anwendungen. Springer-Verlag. pp. 57–59. ISBN 978-3-540-04668-4.
Kolata, Gina "What if They Closed 42d Street and Nobody Noticed?" New York Times. (25 December 1990). https://www.nytimes.com/1990/12/25/health/what-if-they-closed-42d-street-and-nobody-noticed.html
Skinner, Brian. "The price of anarchy in basketball." Journal of Quantitative Analysis in Sports 6.1 (2010). https://www.degruyter.com/document/doi/10.2202/1559-0410.1217/