Tuesday, June 10, 2008

A Geeky Thought

Something I think about while waiting at intersections -- if two people try to go through an intersection (one going north and one going west, perhaps) then they are both going to have to go through the same point, the center of the intersection. They are both going to have the same "x" and "y" coordinates there.

Now if you don't want them to collide, there are a couple of things you could do. One option is to build an overpass, as people do on highways. Then the two cars can have the same "x" and "y" coordinates, but different "z" coordinates, different heights, and there is no collision. The bridge artificially increases one car's "z" coordinate.

Or, you can put in a traffic light. What does that do? It means that they will both arrive at the center of the intersection, with both have the same "x" and "y," but at different times. I picture their paths plotted on my old graphing calculator from high school -- the paths cross, but in "parametric" mode, you could run a little cursor along the two paths, and show that the "t" value at the center the intersection is different for the two different paths. Same "x" and "y," but by making one car wait, you are artificially increasing the "t" coordinate it has when it reaches the center of the intersection.

Sort of like how the bridge increases one car's "z" coordinate.

Bridge: same "x" and "y," but one car has been raised to a higher "z." Traffic light, same "x" and "y," but one car has been raised to a higher "t".

A traffic light is sort of like a bridge though time!

1 comment:

Yottabyte said...

And to think I always thought it was science fiction...