The world now has almost 30 megacities — urban areas where the population is 10 million or more. This urban sprawl also applies to the transportation infrastructure, which usually combines subway systems and other modes of travel, such as bus systems. Wondering whether navigating very large cities has become too difficult, a team of physicists and mathematicians arrived at a not so surprising conclusion. Big city transportation networks have reached a level of complexity that exceeds our processing capability, say the researchers led by Dr. Mason Porter, a mathematics professor at the University of Oxford.

Sadly, even the app on your phone won't help, says co-author and physicist Marc Barthelemy.

"When networks are very large and systems very interconnected (such as subway and buses) it won't be possible (in a reasonable time and for untrained persons) to check actually that the app is giving you the right or best answer," Barthelemy wrote Medical Daily in an email.

TMI, Citystyle

Humans, the researchers explain, have intrinsic cognitive limits for processing information. For example, in the 1990s Anthropologist Robin Dunbar first suggested that an individual can maintain relationships only on the order of 150 stable relationships. Though the “Dunbar number” is controversial, the researchers wonder if we may be similarly limited when steering our way through a new city. Is there a navigation equivalent for the Dunbar number?

To explore this question, Barthelemy, Porter and their colleague Dr. Ricardo Gallotti imagined the case where you see a map for the first time and you try to find your way from one point to another.

"In this context, visual memory is important and we know from previous studies that we can essentially remember four objects," Barthelemy said. Yet other factors beside memory also come into play when you are looking at a new map. In the blur of a busy subway station with time passing, the “pattern of eye fixations” change “to a random scattering of eye focus all over the map,” the researchers wrote.

Based on all these reasons, they considered the most complex trip possible for an untrained person to be paths with just four nodes — origin and destination and at maximum two connection stations — and they quantified this as 8 bits of information.

Plotting A Path

Next, the researchers analyzed the world's 15 largest metropolitan transport networks, including New York, Paris, and Tokyo. Using both mathematics and physics, the team designed journeys requiring exactly two connections in each of the megacities. Here, they determined that, for a map to be easily readable, it should not consist of more than 250 connection points yet the transport networks they examined exceeded average cognitive powers. However, when other modes of transport, such as buses or trams, were added into the mix, the complexity of transportation infrastructure rose well above the 8-bit threshold.

In fact, they find more than 80 percent of the analyzed treks across large cities are above human cognitive limits due to transportation system complexities.

When too many interconnections and too many modes of transportation exist, Barthelemy, Porter and Gallotti conclude the search for the simplest path through a city becomes inefficient. Unfortunately, the number of distractions contained on a typical map turn a fun excursion in a fascinating megacity into a not very amusing game of Where's Waldo.

Source: Gallotti R, Porter MA, Barthelemy M. Lost in transportation: Information measures and cognitive limits in multilayer navigation. Sciences Advances. 2016.