Reciprocity Theorem

In electromagnetism, reciprocity states that if the current densities (sources) are exchanged, their respective fields can be switched too. In terms of electrostatics, if the voltage source in one branch of the circuit produces a current in the other, the same current will be produced in the first branch if the source is moved to the second. Reciprocity has applications in politics (Canadian free trade with the US) and photography as well. In simple English, source and destination are interchangeable.

This is a mighty, powerful theorem for it simplifies computation, eases understanding and supplements the modeling of many complex systems. But as usual, I wonder if this scientific concept can be translated into real life. Can we exchange sources and destinations without changing certain results?

When it comes to traveling, this is true. The distance from point a to point b is the same as the distance from point b to a. However, can we elevate this concept into something even less objective?

I just watched My sister's Keeper. I am not one to get sensitive during movies, but this one certainly captured my emotions. It's a story about a teenager, Kate, who suffers from cancer. Her younger sister, Anna, has been donating her marrow since birth. During an incredibly crucial moment, she refuses to allow her parents to make any more medical decisions on her behalf. When Kate was three, she was diagnosed with cancer. Since they could not find a marrow match for her, the parents had to conceive another child. This child was Anna. To me, this is a brilliant case of irony. There is ambiguity in who is the source and who is the destination. Is Anna the source since she has been donating her marrow to Kate her entire life? Or is Kate the source as her sickness is the very reason for Anna's existence? The truth is, no matter who the source is, the result is still that of sisterhood. Reciprocity exists.

It is difficult to justify reciprocal relationships in our subjective lives. However, we can analyze this concept for a single instant. At a particular time point and in a certain relationship, there must exist a source (someone who is giving) and a sink (someone who is receiving). At a later time point, the relationship may be reversed. One such example is that of parents and kids. Until a certain age, parents are the care-givers. However, at some point, it becomes the child's responsibility to care for the parents. I suppose reciprocity exists for romantic relationships in an oscillatory fashion.

However, today is a day to discuss the reciprocity between a prankster and his victim. If you are the prankster, make sure you devised an intelligent trick. If you are the victim, have a sense of humor and make sure you reverse your role next time ;). Either way, the result is to have fun.

Happy April Fool's Day!

ps: Add me on Draw something. It's the technological epitome of reciprocity. You can switch off between being the draw-er and the guess-er oh so frequently! ;)