Twelve Mile Circle

Many superlatives describe the border between Canada and the United States. It’s the longest non-militarized border on the planet. It touches three different Oceans (Atlantic, Pacific, Arctic) plus the Great Lakes. It extends 8,891 kilometres (5,525 miles). While impressive, this isn’t about any of that. No, I’m more interested in the extremes in the opposite direction, the tiny ones.

Look at any map of the two nations and one will notice two very long straight segments. The first one forms a vertical line between Yukon and Alaska along 141 degrees west longitude. The second one forms a horizontal line from the Strait of Georgia to the Lake of the Woods, half way across the North American continent, at 49 degrees north latitude. Or do they?

These two territorial behemoths — the second and fourth largest nations on earth — established the International Boundary Commission to maintain their peaceful boundary. This commission handles border demarcation, places and maintains the physical markers, removes underbrush to keep the border visible, and generally works to prevent territorial disagreements from occurring before they can arise. It’s a noble mission.

A Regular reader of the Twelve Mile Circle, "Greg" wrote a comment back in July 2009:

The International Boundary Commission says on their website that the two closest boundary markers between the US and Canada are 46 cm apart, IIRC. Where on Earth (well, in North America) is that?

I replied at the time with the following comment:

I started looking at the boundary coordinates at [the International Boundary Commission website] http://www.internationalboundarycommission.org/products.html#maps but I started going cross-eyed. The answer would be somewhere in those data sets. It shouldn’t be too difficult to set up a spreadsheet to figure that out, so now I have a project for a rainy day.

The rainy day arrived. More accurately, it was a snowy day. Either way I had plenty of time while I was trapped indoors the last couple of days to ponder Greg’s question further.

First, let’s dispel a misconception before I dive into the coordinates and mathematics. The border doesn’t actually include long, straight segments. 141 West and 49 North? forgetaboutit. The border is actually composed of thousands of very tiny individual segments cobbled together. On land the lines run physically between monuments. On water they run virtually between turning points. A typical segment, and I’m pulling this pseudo-randomly from the data set, runs approximately 1.8 kilometers between 48.999978 N, -109.713375 W and 49.000039 N, -109.673353 W. One would expect both of those latitudes to be 49.0 N if the border were one long line, but it is not.

That’s a typical length by the way. I loaded the Boundary Commission’s coordinates into a spreadsheet and it produced a file with 11,501 rows. That’s more than eleven thousand separate lat/long coordinates used to define an 8,891 kilometer border. Thus, Greg’s question about the 46 centimeter segment doesn’t sound so far-fetched anymore, now does it? It should only a matter of going through the spreadsheet, sorting it by length and finding that shortest segment.

Ultimately I couldn’t find it. However, I narrowed it down to several possibilities.

I had a file with every lat/long coordinate along the Canadian – American border so what was the big deal? Couldn’t I simply calculate the distance between the points on the spreadsheet and find the shortest one? Theoretically, yes. Formulas exist to determine Great Circle distances between points on a sphere but the earth isn’t a perfect sphere and the basic, least complicated formulas decrease in accuracy as the points move closer together.

One of those methods is the Haversine formula, a specialized application of spherical trigonometry used in navigation. There are more complicated variations on this theme but I don’t have the inclination to decipher them. This is math I thought I’d never need when I attended Junior High School back in the Dark Ages — very shortsighted of me at the time — so my skills are rather limited in this field today.

The BlueMM website was a godsend. The author was kind enough to translate the formula into something that could be dropped directly into an Excel spreadsheet.

=ACOS(COS(RADIANS(90-Lat1)) *COS(RADIANS(90-Lat2)) +SIN(RADIANS(90-Lat1)) *SIN(RADIANS(90-Lat2)) *COS(RADIANS(Long1-Long2))) *6371

Simply replace Lat1, Lat2, Long1 and Long2 with cell references and it’s good to go. Replace 6371 (radius of the earth in kilometers) to 3959 to calculate distances in miles. Copy the formula 11,500 times and create the distance between each of the tiny segment along the Canada – USA border. I don’t know the shortest one for certain but each of the instances displayed on the map above calculate mathematically to a distance of less than a meter. I’m going to guess the 46 centimeter distance between two monuments falls within the eastern cluster but I may never know unless someone from the International Boundary Commission happens to stumble across this page.

It wasn’t much easier finding the greatest length along the border. Most of those on land appeared to be along the Yukon – Alaska boundary but even those rarely stretched ten kilometers or more. The longest distance between two monuments on the southern border appeared to be these two straddling Missisquoi Bay, an arm of Lake Champlain near the geo-oddities known as Fort Blunder and Alburg.

I didn’t find the final answers but if I ever want to create a border map I have everything I need to generate an xml file and read it into a webpage. Maybe I’ll save that for the next rainy/snowy day.

Well, here we go again. The Washington, DC area is experience its second "epic" snowstorm this season. Our previous snow in December 2009 brought about sixteen inches by the time it finished.

We were already up to sixteen inches this morning at 8:00 am with this latest storm when I took this photograph:

You’ll notice a little stick extending above the snow on the upper-right of this image. Yesterday I cut a 28-inch length of wood and pounded it into the ground. Actually I pounded several. We have a flagstone walkway from our front portico to our driveway and it’s difficult to locate and shovel in deep snow. The sticks serve as a guide. I marked this particular stick to measure the snowfall before the storm began and that’s how I know we’re at sixteen inches.

We’re supposed to get anywhere from 5-10 more inches before this is finished and it should be high on the Top-10 list for this area in its recorded history. Check back later this afternoon and I’ll post an update and perhaps some more photographs. For any other readers in the Mid-Atlantic area of the United States (and I know there are several of you): please feel free to post your snow totals or adventures in the comments.

UPDATE: 1:30 pm.

We’re at a solid 20 inches at the moment and it’s still snowing although it seems to be slowing up a bit. I took this photo about an hour ago from a distance of less than a block away. It shows two things: the heaviness of the snowfall at its peak and the silliness of some people who think they need to drive around the neighborhood simply because they own an SUV. I watched this crowd work to free the this vehicle for about a half-hour.

We got in about two solid hours of snow shoveling done in anticipation of the plows coming by sometime in the next day or two. It was nice to simply get outdoors for awhile.

UPDATE: 9:00 pm.

Yup, topped out at 20-21 inches. I found a really neat interactive map too, showing power outages in real-time. Fortunately we haven’t had to contend with that and the big dig will hopefully commence tomorrow.

Is there an area with no time zone?

At first I dismissed the question when it landed on the Twelve Mile Circle in the form of a search engine query the other morning. I noticed it waiting in my user access logs although this random visitor never asked me personally. The algorithms of his search engine determined somehow that my obscure little portal could be his Magic 8 Ball. The mystery guest clicked a path to my doorstep.

It’s convenient to feel knowledgeable, even a little smug, and I plead guilty as charged. I need to work on my humility and try not to be so judgmental. However, I did not design the Twelve Mile Circle for the general public. If it were all about numbers I wouldn’t focus on geo-oddities and anomalies. I’m not surprised that one of my most frequently viewed articles features a monster truck photo, but that’s not my core audience and they never wander over to my other pages.

I admit somewhat sheepishly that I keep a file called "Stupid Searches" for occasions just like this. I was about to add this one to several other rather unfortunate search terms I’ve recorded in the past. Things like:

• four most visited states in Alaska
• does the east coast experience sunsets?
• video of confederate soldiers crossing Potomac river

Then the brilliance of the question struck me. Is there an area with no time zone? Could this be the visible part of a profound metaphysical inquiry? Maybe akin to a Zen Buddhist koan like the the cliché: Two hands clap and there is a sound. What is the sound of one hand?. Yes, I’m also aware of the 1970 song by Chicago, "Does Anybody Really Know What Time It Is?" so let’s put that one aside and not mention it again. And no, I’m not old enough to remember hearing that except on a Classic Rock station many years after the fact, but thanks for asking.

On second though, maybe the question wasn’t posed philosophically. I considered it literally and found some interesting results.

Today all nations follow standard time zones based on Coordinated Universal Time (UTC). Some large nations have multiple time zones. One large nation, China, has a single time zone. Some places differentiate their time from nearby zones by a half-hour or even a quarter-hour. However UTC rests at the core of each of these instances.

Nations have the power to track time however they wish. Solar time ruled the world until the last hundred and fifty years, give-or-take. Nonetheless it’s convenient and advantageous to standardize on UTC in the modern world, so logically it’s been adopted by all sovereign nations.

SOURCE: National Science Foundation

That only addresses the question partially. What about the poles where time zones converge? I can’t speak for the North Pole, but the Amundsen-Scott South Pole Station follows New Zealand time. The United States operates the station and provisions it via New Zealand. It follows New Zealand time as a matter of convenience.

What about ships at sea in international waters? They follow nautical time zones but can decide when it’s convenient to change from one zone to another aboard ship. Wikipedia’s take on this follows:

Internally on the ship, e.g. for work and meal hours, the ship may use a suitable time of its own choosing. The captain is permitted to change his ship’s clocks at a time of his choice following his ship’s entry into another time zone — he often chose midnight. Long distance going ships change time zone onboard at suitable times. Ships on short distance journeys do not change time zone at all, even if they go between different time zones, like between the UK and continental Europe. Passenger ships often use both time zones on signs.

Once again, they’re relying on UTC.

We’ve established that every nation uses UTC as a baseline, as does the South Pole station, as do ships at sea beyond international boundaries. That covers pretty much the entirety of the world where people normally congregate. Or does it?

Uncontacted people still exist in the 21^st Century. Places such as the many remote corners of Amazonia and New Guinea come to mind. The Sentinelese people of North Sentinel Island, part of India’s Andaman Archipelago, provide an excellent case in point. They totally reject outside contact and "they are likely the most socially isolated people on Earth." Almost nothing is known about them. They probably neither know nor care that they are part of India. Most assuredly they follow solar time and have no concept of UTC.

North Sentinel Island has no time zone in any practical sense.