Lost in transportation: when public transport maps are too complex for our brain

Cities and their transportation systems become increasingly complex as they grow, and it is natural to wonder if navigating in these systems can be a task that is too difficult for humans. In other words, can we quantitatively characterize our difficulty to navigate in cities and does it exceed our cognitive limit?

To answering this question, we quantify the difficulty of navigating in an urban transportation network from an information perspective. By studying in the 15 world's largest metro systems, we find that this limits is of the order of 8 bits or 250 connections between routes in a map. When the total number of connections of a transportation system exceeds a critical value of about 250, the system becomes then too complicated for humans.

The Paris metro map is close to this threshold, but when one also includes all transportation modes and intermodal connections (bus, trams and light rail), the information needed increases dramatically. We find that more than 80% of origin-destination pairs in the multimodal network of Paris, New York and Tokyo necessitate navigation whose complexity exceeds humans' natural cognitive limit: the network is therefore so complicated that information-technology services are necessary for navigating in the system.