The shortest distance connecting two points is always a straight line — one of the most basic rules of geometry. However, it’s not always applicable when you’re navigating the landscape around you. When walking through a busy city street, for example, avoiding oncoming traffic and crowds of people, following a straight line can often be impossible. So how do you set your course and not lose your way?
A recent MIT study proposes that the human brain may not be optimized for determining the shortest path to get to our destination whenever we travel on foot. After poring over the data sets from more than 14,000 different people as they walked about day by day, the researchers discovered that rather than take the path that’s quickest, pedestrians have a tendency to select paths that offer the most direct route to wherever they happen to be going, even in cases where these routes take longer. The researchers refer to this as the “pointiest” path.
This strategy, a pattern known as vector-based navigation, has already been observed in other studies of animals, going up the evolutionary ladder from insects all the way to primates. In their new paper, the MIT researchers also argue that vector-based navigation may have also evolved in the animal kingdom to let the brain devote more energy to other tasks, as it uses less brain power than letting the brain determine the quickest route.
“There appears to be a trade-off that allows computational power in our brain to be used for other things — 30,000 years ago, to avoid a lion, or now, to avoid a perilous SUV,” says Dr. Carlo Ratti, who is a professor of urban technologies at MIT’s Department of Urban Studies and Planning and the director of MIT’s Senseable City Laboratory. “Vector-based navigation does not produce the shortest path, but it’s close enough to the shortest path, and it’s very simple to compute it.”
The study appeared in Nature Computational Science. Ratti was the study’s senior author, working in collaboration with Dr. Christian Bongiorno, who is an associate professor at Université Paris-Saclay and also a member of Senseable City Laboratory, and also the study’s lead author.
Using A Vector-Based Navigation System
Back when he was a graduate student at Cambridge University just over 20 years ago, Ratti routinely commuted on foot from his residential college to the location of his departmental office five days a week. Then one day, he had an epiphany. He suddenly noticed that when he walked this distance, he always took two slightly different routes — one for traveling to the office and a slightly modified route that he took back to the campus apartment.
“Surely one route was more efficient than the other, but I had drifted into adapting two, one for each direction,” Ratti recalls. “I was consistently inconsistent, a small but frustrating realization for a student devoting his life to rational thinking.”
Today, the Senseable City Laboratory is analyzing large data sets acquired from mobile devices to understand how people navigate and move about in an urban environment. Just a few years ago, the lab looked at a data set of anonymous GPS signals sent from nearby cellphones as their owners walked between the streets of Boston and Cambridge, Massachusetts, captured over the span of one year.
Ratti believed that this data, which consisted of over 550,000 pathways taken by more than 14,000 different people, were the puzzle pieces he needed to further explore the way in which people choose their route as they navigate a city on foot — which paths to take, which sides of the street and sometimes even just knowing which subway to jump onto to get to the next leg of their journey.
The analysis of the data carried out by Ratti’s research team showed them something interesting. While you might intuitively assume that an individual would pick the shortest route to get to their destination, the pedestrians did something a little bit different. They selected routes that were just a bit longer on average, but minimized the angular distances from their destination. For example, someone who works on the opposite end of the Fine Arts Museum might be more likely to select a trail that allows them to view their destination from a particular side as they begin, even if their phone’s GPS allows them a more direct route that is slightly to the left or right of their starting point.
“Instead of calculating minimal distances, we found that the most predictive model was not one that found the shortest path, but instead one that tried to minimize angular displacement — pointing directly toward the destination as much as possible, even if traveling at larger angles would actually be more efficient,” says Dr. Paolo Santi, one of the principal research scientists at the Senseable City Lab and also for the Italian National Research Council, who co-authored the paper. “We have proposed to call this the pointiest path.”
This was found to be true for pedestrians moving between Boston and Cambridge, which share a fairly intricate network of streets, and also for those in San Francisco, which uses a grid-style layout for its streets. In both of these cities, the research team also found that the same people often tended to choose different routes whenever they made a round trip between two different destinations, just like Ratti did when he was a graduate student.
“When we make decisions based on angle to destination, the street network will lead you to an asymmetrical path,” Ratti concludes. “Based on thousands of walkers, it is very clear that I am not the only one: Human beings are not optimal navigators.”
Moving On Up In The World
Recent studies on animal behavior and their brain activity, particularly those studies focused on the hippocampus, have led neuroscientists to suspect that calculating vectors are responsible for the brain’s navigation strategies. This kind of navigation is quite different from any of the computer algorithms that your smartphone or car’s GPS uses — which are programmed to compute and leave a set of options for the closest distance between any two given points, drawing from their large memory bank of maps.
Since the average animal — be they a cabdriver or an aardvark — doesn’t have internal access to an array of three-dimensional maps, the animal brain therefore must be able to improvise with an alternate strategy for navigating between different locations. “You can’t have a detailed, distance-based map downloaded into the brain, so how else are you going to do it? The more natural thing might be to use information that’s more available to us from our experience,” says Dr. Joshua Tenenbaum, a professor of computational cognitive science at MIT and also an author of the study.
It’s likely that our senses of direction therefore came from primitive habits like looking for food, traveling to the watering hole, or migrating when the seasons changed — going in one direction and building a map on the way. Tenenbaum continues, “Thinking in terms of points of reference, landmarks, and angles is a very natural way to build algorithms for mapping and navigating space based on what you learn from your own experience moving around in the world.”
“As smartphone and portable electronics increasingly couple human and artificial intelligence, it is becoming increasingly important to better understand the computational mechanisms used by our brain and how they relate to those used by machines,” states Ratti.
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