Simulation: Whatever Is It Good For?

To simulate is to shift your perspective.

We tend to look at data and ask, given that we've observed X, is Y true?

But it's more fun to ask, if Y were true, what should we observe? That's what we do when we create models and run simulations. These simulations are virtual experiments that illuminate, surprise, and help us better understand how things work.

Simulation complements data analysis. It can be a fertile source of ideas for what to look for in a data set (big or small). It can also be a way to cross-check the results of data analysis.

Simulation can be useful for many reasons:
  • Even simple problems get complicated very quickly; simulation is a way to explore how things will turn out
  • It's hard for most of us to intuitively grasp the full meaning and implications of systems described by mathematical equations; being able to simulate is a way to get a deeper understanding of these systems
  • Manipulating equations is hard and often thankless; simulation is a way to manipulate them without using heavy mathematical machinery
  • It's often hard to get something you're interested in into equation form, so simulation is the only choice for making headway
  • Even when something is in equation form, it might not have a closed form solution (e.g. the Navier-Stokes equation in fluid dynamics) and simulation (or computation in general) becomes essential
  • Some problems are riddled with uncertainty and simulations are a great way to get a handle on these problems
My favorite reason is the unexpected twists and turns of discovery that accompany these investigations. These pages contain a number of examples of simulation at work.