Decomposition is a lethal method in analysis. The idea is to break up the object in question into well-known elements through a logical process. It is a powerful tool for a wide range of problems.
Take programming for an example. For a beginner, the binary world of coding is daunting. Even picking a universal language is not an easy task: Java, C, C++, C#, Python, FORTRAN, all have their fans and haters. Then there are different programming paradigms (procedural or object-oriented), and specific applications (Mathematica and MAPLE for mathematicians, MATLAB for engineers, SAS and R for statisticians, EXCEL and VBA for business folks). The variety is mind-bogging.
But through the lens of decomposition, you can see they all share the same logical core, i.e., they all break down to two fundamental operations: IF condition and loop. All programs, be your WINDOWS OS or iPhone Apps, large or small, are all constructed with these two bricks.
The second example is how the analytical papers in economics and business are written. Like any other papers, they all tell a story. What set them apart—or give them an authoritative tone—is the use of math models. Here, again, decomposition is the key: all analytical models boil down to either optimization or game (equilibrium).
Indeed, game thinking is so pervasive that people use it without knowing it consciously. Here is an urban legend.
People like to play with little Bill Harrison, a seemingly dumb kid. They offer him a penny and a nickel to choose and keep. Bill always picks penny, making everybody laugh. People love to play this game with him; never get tired .
One day, an old lady asks little Bill: “don’t you know a nickel worth more than a penny?”
“I know”, Bill smiles, “but if I pick the nickel, no one is going to play that game with me again.”
[Atlanta aquarium, June, 2006]