Navigating the Yard in the time of COVID
Our on-campus Prediction course for Harvard undergraduates (known as GenEd 1112), includes an exercise that asks students to "navigate" to a particular location in Harvard Yard. The goal of the exercise is to understand how uncertainty determines the predictive accuracy of navigational systems, by demonstrating how small errors at each step in a "dead-reckoning" system can lead to very large errors after many steps. Students are given no navigational aids--only a set of instructions directing them to walk a certain distance with a certain heading from their "Start Point" to "Point A," then another, different, distance in a different direction to "Point B," and then, finally, in a third distance in a third direction to their final "End Point."
In a non-pandemic year, students carry out the assignment in five color-coded groups, all walking around in-person in Harvard Yard, during class time. Each colored group is assigned a different path, which unbeknownst to the students, should end at the same place near the middle of Harvard Yard.
During the COVID-19 pandemic Spring of 2021, when about half of Harvard's undergraduates were on-campus, and half attended class remotely, the navigation exercise was re-designed, pairing each on-campus student with an off-campus one, as navigational team. The on-campus student walked through the Yard, as the off-campus student on video chat followed along and helped in deciding on direction and distance for each leg of the pair's assigned path. The on-campus student recorded latitude and longitude using their smart phone at the end of each leg of their assigned path. Each pair carried out the assignment, as homework, at their convenience, and they reported their results using an online survey that fed data to a common spreadsheet for the full class.
In addition to uploading GPS coordinates, each pair of students took a photo of the Harvard building nearest to their End point. Of course, if all Navigation was perfect, every photo would have shown the same building...but that's surely NOT what happened!
All the students' reported coordinates fed into a Google Spreadsheet that Prof. Goodman loaded into her favorite exploratory data visualization environment, glue, which includes a WorldWide Telescope module where data can be overlain on satellite images. The colorful dots on the image below show the many DIFFERENT "End" positions reported by students. The dots' colors indicate which of the five different possible paths pairs were assigned to, but, all paths would lead to the same END point if followed exactly.
Looking at the fun assortment of Harvard buildings photographed, it's clear that not every path was followed exactly! Given that students could only estimate distance based on human intuition, or literally measuring feet with their feet, and direction based on their knowledge of Harvard Yard's layout, or the position of the Sun, it's not at all surprising that a wide range of End positions were reached. What surprised students most was just how FAR off from where they thought they were they actually were.
In a key element of the assignment, students were asked to estimate how far off, in feet, they were likely to be from where they actually ended up: in other words, they were asked to estimate the UNCERTAINTY associated with the navigational system they'd used to reach their endpoint.
Harvard students turn out to be largely very overconfident about their dead-reckoning abilities. In the graph here, the dashed colored lines show the five different color-coded paths on which the students were sent, all of which end at the (0,0) point in the middle--the common End point of all the paths. The translucent white discs show the students' individual estimates of uncertainty (of how many feet they thought they were likely to be off from the End point). Notice how far off the students were from the true End point--typically MUCH farther than they thought they were! Most of the uncertainty discs are not even close to overlapping with the true End point.
The closest pair's position is highlighted with a purple circle. Not only was this pair closest--they were among the very few students to estimate their uncertainty correctly!
For their great navigational skills, the closest pair's members were each rewarded with a colorful print showing an historical map of Harvard Yard.
Learn more about Navigation in "Lost without Longitude"