Measuring Boston coastlines with increasingly tiny measuring sticks…

OSH_in_BostonAs I toured Boston this past week, I seemed to be drawn inexorably towards the Old State House.  Historically the Old State House was built at the center of civic activity. The Old State House “was prominently sited at the juncture of King Street, Boston’s primary commercial thoroughfare, and Orange Street, the peninsula’s sole overland route to Roxbury and interior settlements,” says the Boston Landmarks Commission. What this means is that if you stood in front of the Old State House in 1700, you could see the bay only a few blocks away. Now, the bay is a ½ mile down the road and nowhere in sight.

Here’s two maps of Boston. Notice how the map on the left of Old Boston is almost an island (you can click on it to make it bigger)- Present-day Boston, on the right, does not look like that anymore. But in both cases, the Old State House is basically in the middle.


A lot has changed since 1630. Crazy!  Humans leveled the hills that existed in Boston to expand the shoreline. They did this without construction vehicles or steam engines. This blows my mind! Then, much later, Bostonians used landfill to fill more space in.  Here is a map of how things have changed over time.


This map is from who referenced which is amazing, but doesn’t seem to have the image on their site any longer.

Boston is a maritime city with lots of boat traffic. Because of this I would love to know how the length shoreline has changed over time. Can we fit more or less boats in Boston harbor than we used to? Did we get more shoreline out of this land expansion? Or less? Since we have a map of Boston, this should be an easy task right?

Shorelines are notoriously hard to measure. This is because shorelines are fractal-like. This is a mathematical feature which (loosely) means that at each level of zooming in there are lots of bumps and rough edges. You can zoom into a coast line over and over again and not know how close to the coast you are! How does this manifest itself when you try to measure the coast?

The length of your measuring stick directly affects the length of the coastline. This is called the Coastline Paradox. Here is an amazingly awesome video about measuring a coastline from science presenter Steve Mould.

But if you don’t have 8 minutes, that’s okay. The long and the short of it is


Thus we can get a shoreline of infinite length for any point over the history of Boston. If we picked a specific measuring stick length, we could compare the shoreline from one time to another. But we can never truly know the length of the shoreline of Boston at any time.

Despite the disappointing state of affairs of the shoreline, there does seem to be a link between the shoreline of Boston and the placement of the Old State House.  Somehow, I believe, it has continued to be the centroid of the peninsula. That is to say it is the center in some way. It is (approximately) the location of the weighted mean of all the points in the peninsula. Which seems pretty cool to me.

I believe this because of my limited experience in Boston. As I traveled back and forth across the peninsula, my trajectory through the city always included the Old State House. It was though the historic placement of the building drew me to it just as it drew travelers towards it 300 years ago. For travelers then and now, the Old State House holds a place of prominence even though Boston isn’t really an island and the shoreline is way further away. Not to mention that there is now a T-stop in the basement…

About Samantha from SocialMath

Applied Mathematician and writer of
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