October 13, 2011

The Geometry Behind Serendipitous Meetings

In dramas, we often encounter scenes where one half is looking for the other half. And usually, three things happen. Either they find each other across the street, they find each other on the other end of a bridge, or they don't find each other at all.

Finding each other across the street adds an element of surprise and defies the laws of nature. The first time you see it, it's like "Wow, that won't happen in real life". The second time, it's =/. The third time, it becomes a clique. It defies the laws of nature (or mathematics). Since when do points on parallel lines ever meet? The answer is never.

Imagine that the streets were parallel lines and people on the streets are points on the lines. Then the most that point a on Line A and point b on Line B can do, is wave at each other, because parallel lines will never intersect. So geometrically, finding each other across the street and then running towards each other is impossible. 

Finding each other across a bridge is very romantic, especially in Asian cultures, where bridges are connected to the story of the cow herder and silk weaver. Meeting across a bridge sends a very powerful message about the two people's relationship. Again, three things can happen. First, when both parties' backs are turned towards the direction they came from, then they are meeting each other at the center like the cow herder and the silk weaver.

Second, if both parties' backs are turned towards the same direction, then one party is leaving while the other is looking on with tears in thy tears or they are walking together hand in hand. If both parties' backs are opposite each other, then they have separated and are walking their own paths.

Geometrically speaking, the direction matters the most here since they are both on the same line. If they're going in opposite directions, they're done. One is going to go to negative infinity, the other to positive infinity.

Apparently there is a fourth outcome. Episode 4 of "In Time With You" broke the norm and went for something even better.

Ariel and Bo Lin have their first phone conversation after a particularly awkward period in their friendship. Ariel yells joyfully into the phone and Bo Lin looks up from his phone. They turn their heads and make eye contact. At first, it looks like they are on opposite sides of the street. But then the camera pans out...and OH MY GOD, they are on a circular fountain path! They spotted each other on a circle! I know I'm making a big deal out of this, but it IS a big deal! They're on a circle! Director, you are so brilliant!

Why am I so excited that they met on a circle and not a line? Because geometrically speaking, a circle is round which means every starting point is also an ending point. Take two points to be anywhere on the circle. Those two points will always see each other, no matter where they are located. Also, it doesn't matter which direction either point travels, they will always meet because they are on a circle.

You must must watch In Love With You. It's a cleverly directed drama that has extremely insightful views on love and friendship. 


  1. I don't know why I love this so much, but I do. You're right! I didn't think of the significance of them meeting on a circle, but it fits perfectly with ITWY. That is so amazing :D Thanks for sharing!

  2. damn I never realised this, but now that I have I'm gonna keep an eye out for things like this.