As a certified armchair researcher, I settled into my armchair in a dark room, watching distant flashes of lightning over the desert landscape surrounding me. The scattered storms brought to mind the problem of weather forecasting, or rather, the common failings of accurate forecasts beyond the next several days.
Like other High Performance Computing (HPC) problems, weather forecasting requires enormous computational resources. The world is a big place, after all, and the weather is notoriously fickle. Other HPC problems, such as protein folding and fluid dynamics, suffer from similar issues; duplicating nature with a set of processors is an approximation, at best.
And to make matters worse, the approximations we have today must be performed on von Neumann machines.