The Banana Peel Project

What is the resolution of the real world? How small are the smallest things in the Universe? Thousands of years ago, philosophers reasoned that there was a limit to how many times you could cut a given object in half; they called this smallest unit of matter an atom. Now, it has become common knowledge that an atom is far from the smallest thing out there. Atoms themselves are composed of subatomic particles, those particles are composed of even smaller particles, and even those particles appear to be breakable into units so small that they straddle the line between energy and matter. The question has become, How far does it go?

This becomes an extraordinarily important question when we start thinking about simulation and modeling technology. The goal of simulation is to allow us to experience phenomena that can and do happen in the real world, and the way it accomplishes this is by generating virtual phenomena so rich in information that they are–for all practical purposes–identical to real phenomena.

What does “for all practical purposes” mean? It depends. In video games, the simulated environment doesn’t have to be all that rich because the human brain does so much”filling-in” of sensory information. (High-definition, computationally intense video games are, of course, more convincing.) But when scientists use simulation to model and predict complex systems like nuclear bombs and earthquakes, it is vitally important both experimentally and theoretically to create a simulation that is as faithful to real world systems as possible.

So doesn’t it make sense that more data points you include in a given simulation, the more accurate your model will be? If (hypothetically) the movement of hurricanes across the open ocean is determined by ten million variables, each of which is determined by a specific equation, then a supercomputer programmed to process all of those equations should be able to predict the behavior of a given hurricane with 100% accuracy.

But are there ten million variables that determine the path of a hurricane? Are there ten billion? Or are there as many variables as there are individual particles in the hurricane system? If the latter is true, then the prognosis for our ability to predict the movement of hurricanes is exceedingly dire.

Thankfully, it seems that simulation is not about the 1-to-1 representation of real-world phenomena. In Image and Logic: A Material Culture of Microphysics, Peter Galison has described the process by which simulation became the primary mode of experimentation and theory of atomic physicists during and after WWII. The true power of simulation is not in its ability to calculate the hell out of the real world and thus provide control. Instead, simulation in the nuclear weapons labs of the Cold War depended on the accurate–but heavily simulated–representation of real world phenomena. In essence, by combining powerful computers with simplified equations, scientists were able to watch a nuclear bomb explode without leveling their labs, annihilating islands in the South Pacific, or committing genocide.

So simulation doesn’t necessarily depend on how many numbers a computer can throw out in a given clock cycle. It also relies heavily on the theoretical approximations that are made before the simulation is even run. One mathematician from Virginia Tech seems to believe that he has the tools to simplify the equations that “govern” complex systems. Despite the epistemological issues I have with the underlying notion that the real world is governed by mathematical equations, it seems that Gugercin has a bead on the link between simulation and control:

You wouldn’t want to design a mechanism to control a process that is based on 80,000 equations. It would be too complex and would not be able to act quickly and accurately. So you design your controller based on a simple model so it can act quickly.

True. And I think that to the extent that complex systems can be approximated for all practical purposes, simulation has a bright future.