Posts tagged ‘intersection’

Never Ask a Mathematician for Directions

I spent my formative years in a very rural county. Roads didn’t have names, or at least they didn’t have road name signs.

Natural Log Lane

In college, my urban friends used to claim that if you asked someone in my hometown for directions, they’d say:

Go about a half mile, and turn left at Old Man Johnson’s farm. Then take a right at the huckleberry tree.

That very well may be true, but it’s no worse than the directions you might be given by a mathematician:

Well, you’re facing the wrong way, so do a reflection about this cross street. Go about 0.628397154 miles, then rotate π/2 radians and travel orthogonally to your previous vector for 600 light-nanoseconds. But they’ve got radar on that road, so keep your speed between 72 and 43 miles per hour. Turn left, and you should reach your destination in 2.4 minutes ± 0.3%, if you maintain an average speed of 46.8 mph.

Now, that’s bad. But at least I could understand all of it. Which is more than I can say for the directions that Google Maps provided yesterday. Traveling through the suburbs near Washington, DC, I had just crossed MacArthur Boulevard, and I was heading southwest on Arizona Avenue. As you can see from the screenshot below, Google Maps was suggesting that I turn right on Carolina Place, right on Galena Place, right on Dorsett Place, and then left on Arizona. In essence, it suggested that I reverse direction to take a 10-mile, 45-minute route.

GPS - Before

I ignored that suggestion. Instead, I stayed on Arizona Avenue with the intention of turning right onto Canal Road in a quarter-mile. Just as I passed Carolina Place, Google Maps said that it was “Rerouting…,” and within 15 seconds, it confirmed that I had made the correct choice:

GPS - After

By ignoring Google Maps, I shaved 3.8 miles and 23 minutes from my commute.


My speculation is that Google Maps attempts to avoid my chosen route because it follows Canal Road, which parallels the C&O Canal National Historic Park; it requires me to cross Chain Bridge, which offers a beautiful view of the Potomac River; and it then winds through an affluent neighborhood, where I can feel safe on tree-lined streets with elegant homes. Honestly, who would choose that when Google Maps is offering double the travel time and an opportunity to drive on the beltway?

I once asked Google Maps which highway I should take to California. It replied…

\sqrt{1^2 + 4^2 + 7^2}

Oh, yeah. Root 66.

The logic employed by Google Maps reminds me of a college friend…

He would always accelerate when coming to an intersection, race through it, and then brake on the other side. I asked him why he went so fast through intersections. He replied, “Well, statistics show that more accidents happen at intersections, so I try to spend less time there.”


November 23, 2015 at 5:40 am Leave a comment

Points of Intersection

Intersection SignIn sixth grade, I overheard two teachers talking about a new school policy. We had just moved into an elementary school that was four stories tall, and it was decided that any time a class needed to move between floors via the staircases, students should always stay to the right — “just as your parents do when driving on a road,” we were told.

One teacher said to another, “Given our principal, I’m surprised it isn’t up on the right, down on the left!”

Nothing like a little administration-bashing to cleanse the soul, eh?

I was reminded of this over the weekend, when my sons and I participated in Bike DC, a family-friendly event in which thousands of riders were given the privilege of riding along the streets of Washington, DC, on a beautiful Sunday morning, during which the streets were closed to traffic. It was quite a thrill for Alex and Eli to ride in front of the President’s house. We turned around before the designated turn-around spot, but I was rather proud that my five-year-old sons were able to log 7.5 miles.

Unfortunately, there was a problem with the course design. See map below.

We followed a simple out-and-back course along several major roads. As shown above, we went out via the blue line and returned via the green line. And just like driving, we spent the first several miles in the right lane. But as the blue line shows, we were asked to switch to the left side of the road at one point; then on the return trip, we were asked to switch again to the right side of the road. As indicated by the two red dots, this caused a problem — when you ask 10,000 bikers to cross each others’ paths, problems are bound to ensue. (You’ll note that two blue lines merge near the bottom of the map. Some bikers doing the full ride merged with those of us doing the family ride at this point.)

Today, I received an email from the ride organizers with the following explanation:

This was by far the biggest Bike DC yet, and some of the routing that had been adequate with a smaller ride was unsatisfactory for this larger group.

That made me chuckle. Crossing paths is never a good idea, with any size group. Even people who have never been very good with coordinate geometry know that non-parallel lines intersect. Parallel lines would have been a better option, unless the course was extremely long:

If parallel lines meet at infinity, then infinity must be a noisy place with all those lines crashing together!

The way to avoid the problem, as any statistician will tell you, is to pass through these points of intersection very quickly.

A statistician would always accelerate when coming to an intersection, fly through it, and then brake on the other side. A passenger asked him why he went so fast through intersections. The statistician replied, “Well, statistics show that more accidents happen at intersections, so I try to spend less time there.”

May 18, 2012 at 3:25 pm Leave a comment

About MJ4MF

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

MJ4MF (offline version)

Math Jokes 4 Mathy Folks is available from Amazon, Borders, Barnes & Noble, NCTM, Robert D. Reed Publishers, and other purveyors of exceptional literature.

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