One thing that has always confused me since I was a bachelor: What is a power law? According to Wikipedia: “In statistics, a power law is a functional relationship between two quantities (y, x), where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another.” That is, y = c x –k, where c is a constant and k is the power-law index. Well apparently, it seems that a power law is just a mathematical definition! However, you might feel surprised when I tell you that more than a hundred power-law relationships have been identified in multiple…

When you stand on the top of a hill, and shout your name, after a short delay, you will recursively hear your bellow, although your voice is successively fainted. The returned sound is an echo. You might be curious, why cannot we hear an echo in a room? This is because the human ear cannot distinguish echo from the original sound if the delay is less than 0.1 seconds. The speed of sound through air is approximately 343 m/s, therefore, the reflector (the walls of a room) must be placed more than 17.2 m away from the sound source (a man who is also a recevier here) for the echo…