Paris metro map (

The complexity of a transit map isn't defined by the number of stations on it.

"The number of stations is totally irrelevant," says Marc Barthelemy, a researcher at the Institut de Physique Theorique in France, where he studies complex networks like, well, the Paris subway system. "Imagine that you have the simplest case: one super-long, straight subway line with many, many stops on it," he says. "Its complexity is absolutely zero. There’s no complexity there at all."

What trips us up — and what might interest a physicist — is a subway system with many connections, those points where you transfer from the 4 to the 7, from the red line to the green. The more connections a transit system has, the harder our brains must work when we're figuring out how to navigate it.

"What makes it messy is the presence of different possibilities," Barthelemy says. "When you arrive at a specific point, you have many choices."

The Paris system has 78 such choice points. The New York subway, the most complex in the world, has 161. New York's system is so sprawling and interconnected, Barthelemy and colleagues Riccardo Gallotti and Mason Porter concluded in a recent analysis, that it approaches the maximum complexity our human minds can handle, the equivalent of about 8 bits of information.

"But then if you add the bus," Barthelemy warns, "the 8-bit limit is exploded."

Big-city transit systems — especially when they require riders to combine the train with the bus with the ferry with the streetcar — entail mental overload. "Human cognitive capacity is limited," the researchers write in the new paper in Science Advances, "and cities and their transportation networks have grown to a point that they have reached a level of complexity that is beyond humans’ processing capability to navigate in them."

This doesn't mean that New Yorkers, paralyzed by their transit maps, can never go anywhere, because obviously commuters find a way to navigate the bus and subway there every day. But if you drop a person who's never been to New York or Paris into either city and hand them a pair of bus and subway maps to find their way from point A to B, it's unlikely they'll be able to handily figure out the optimal route (whether that means the route with the shortest time or the fewest connections).

Just as researchers have theorized that there's a cognitive limit to how many relationships we can maintain — Dunbar's number — Barthelemy and his colleagues suggest that there's a limit (Dunbar's number for transportation?) to how complex a transit network can be before it becomes gibberish to us.

That's partly because, when you're looking at a map, you have to eliminate all the excess information of those other connections that aren't relevant to your trip. "All the possible choices are acting as distractors," Barthelemy says.

Past research on visual memory has suggested that we can only retain information about four objects at one time. Translate that into a transit commute, and we're talking about an origin and a destination, and two connection points in between. Once your commute requires three connections — and this part may feel like common sense — we start to get overwhelmed.

Even in the big, chaotic New York subway, every trip between two pairs of points can still be made with no more than two connections. So that means that even the most complex subway system in the world still demands less than the 8 bits of information that the authors argue is our cognitive limit.

But for many commuters, simply riding the train isn't an option. Instead, they take a bikeshare to the subway, or the train to a bus, or several buses. And many bus maps are even more complex than the New York subway. "Honestly, the bus maps in Paris are completely useless," Barthelemy says. "They’re far too complex."

So this leaves us, more than ever, needing apps that can do this work for us, that can take a complex system and edit out all the other distracting choices for us. Without apps, it's nearly impossible for us to take advantage of all the transit options — and all the places transit might take us — that exist.

This dilemma has particular implications for the poor. Not only are they among the most reliant on transit, but they also must often take long and complicated commutes, because living near work is a luxury. And their lives are already mentally taxed in many ways by poverty. They're also less likely to have the smartphone you'd need to use a route-planning app.