Thursday, May 27, 2010

The purpose of numerics

Optics is a field to which numerical simulations contribute greatly. For example, Maxwell's equations can only be solved for a very small range of geometries. Different routines such as finite-difference time-domain (FDTD), the coupled dipole approximation (CDA), and the T-matrix method have been developed to solve specific problems dealing with the propagation and scattering of electromagnetic waves.

I find that numerics such as these are used in research for a large number of purposes. Some groups publish entire journal papers about the design of a certain algorithm. Other papers deal with numerical simulations of a phenomenon, often times without carrying out a physical experiment because of limits on money, time, and practicality. Still more use numerics to check experimental data against.

Are all of these good reasons to use numerics in research, or are some better reasons than others? I ask this question because I tend to give more credit to papers that perform a physical experiment that is backed up by numerics than to a paper that contains only a study involving a simulation. In the second example in the paragraph above, I mentioned that some papers perform numerical studies because a physical experiment is not practical. If, however, the goal of science is to discern the workings of the natural world, then I think that these types of studies provide little contribution to our body of scientific knowledge, since no knowledge about the real world is gained. A simulation is, after all, subject to the bounds and constraints of a model, and models are often far from accurate representations of the world.

If, however, we (the scientific community) only assign merit to studies that use numerics to verify experimental data, then it seems to me that the role of simulations becomes greatly diminished to the point that they are unnecessary. After all, data is presumably collected by honest and accurate means. Any other reproduction of the data, numerical or otherwise, could be seen as mere redundancy. Under what context then, should numerics be used in research?

My personal opinion is that they are fantastic aids in helping one understand a problem and predict outcomes from experiments. This, I think, is a subtle but important point. A good scientific theory predicts the results of an experiment; a good simulation will do the same. Under this context I think simulations can be put to good and valid use within research.