## Tuesday, September 7, 2010

### Distances, Part I

Distance is a familar word. It means "from here to there," right? So many feet, meters, miles, etc.

Not to mathematicians. Or geometricians. Distance is a complicated topic, because it implies guiding your movements across space and possibly over a curved surface (face of the earth, etc.). And it involves choices. Here's an image from Wikipedia illustrating the difference between distance and displacement (a related math term).

Some people are obsessed with distance. Here's a nice humorous illustration that conveys what I mean:

There are lots of ways to plan a journey from one place to another. You can select the Most convenient route (least lights or traffic), shortest route (fewest miles traveled), most scenic route (best views), route with best food along the way, route without toll roads, etc.

On my first visit to France, we traveled from Paris to Berck-sur-Mar with several French families. The discussion the evening before our trip took longer than the drive itself. I didn't catch all the debate, but it seemed that the choices had to do with the terrain, the meals, and the toll roads. Now that I check Google Maps it appears there were many more options than I imagined. Look at all those roads!

In Southern California we have Interstate 5 from San Diego to Los Angeles. Alternatively you can choose to go up Interstate 15. Or you can drive on Highway 101 (surface  streets), but that takes twice as long. Those are the main choices due to obstacles such as terrain, Camp Pendleton Marine Base, etc.

In my area of the world, we rarely give distances in miles. We use time instead. If you ask How far to Los Angeles?, I say Two Hours, or maybe Three depending on the time of day. The map people agree with me. I just looked and the directions on the map site say 2 hrs 4 minutes, or 3 hours 0 minutes with traffic. What is the distance? About 120 miles, I think.

We'll talk about distance some more this week.