The setup is as follows: if we have N objects in space, with N masses, initial positions, and speeds, where and how fast will each of those N objects be moving if they are subject only to each other’s gravity (and the laws of classical physics – e.g. Newton’s Laws of Motion, etc)?

For a situation with 2 objects (N=2) and some of the cases with 3 objects (N=3), the problem has been well-discussed (the former leads to elliptical orbits, the latter results in the dynamics of the moon orbiting around the earth while subject to the sun’s gravity). But for problems more complex, the solution is anything but pretty. Behavior can emerge which may seem regular and predictable but degenerate into pure chaos. In fact, Poincare’s study of the N=3 problem eventually served as the foundation for the study of chaos theory, or the rise of chaotic, seemingly random behavior (like turbulence) out of “orderly” equations and behavior.

But, the challenge of studying these problems and formulating/testing hypotheses becomes increasingly more challenging as N increases. After all, how do you test an idea for how the N body problem plays out when the problem is that its so difficult to figure out how the N body problem plays out?

Enter the age of the computer simulation. Mathematicians/physicists/astronomers now have the tools to test their ideas (or just pass the time watching simulations) using computers to simulate the behavior of complex systems of N bodies.

But, the fun doesn’t stop with just a handful, or even hundreds, of particles. For an N-body simulation to be sufficient for as astronomer trying to study the structure of the universe, it would have to be scaled up to model billions of particles over distances in the billions of light years.

These super simulations are staggering to comprehend. The Millennium Simulation, run in 2005 to test our understanding of quasars and dark matter, simulated ~10 billion particles (with each “particle” representing a mass about a billion times larger than our sun) across a mind-boggling 8 trillion quadrillion cubic light years expanse of space containing over 20 million galaxies.

But even the Millennium simulation is mere child’s play compared to Project Horizon, which aimed to model “half the observable universe with enough resolution to describe a Milky Way-like galaxy with more than 100 dark matter particles”.

And, probably, this is merely the tip of the iceberg for what such super simulations may be capable of. How the future of this will shape out, I believe, is dependent on the following N=3 (pun intended) questions:

1. It is relatively simple (although computationally challenging) to create a toy simulation to validate or disprove one’s theory. It is much more challenging to build a simulation which can reveal testable/actionable (e.g. not simply if one’s theory is right or wrong) conclusions to further our understanding of the system of interest. For example, will future models of the human metabolome reveal genes or regulatory pathways of interest, or are they simply to validate existing models (something which may bias the model design away from revealing more interesting behavior)? Answering this question in the affirmative is essential, or else these simulations becomes vanity toys – something to use up research funds on without driving real value for the underlying science.
2. Will Moore’s Law/alternative processors/computer science keep up with demands for greater precision and computational power? Otherwise, these super simulations will hit constraints like energy consumption or the introduction of calculation error.
3. Will scientists become more adept at communicating the value of these models? This is potentially the most important question as the investment necessary to run these simulations are significant, not only in terms of cost, but in terms of manpower and energy consumption. With the current financial crisis and a potential future energy crisis, demonstrating value to the public and to more “traditional” scientists/doctors/engineers who rely on non-computational techniques will become more and more important for these future simulations to survive.

For now, I’ll leave you with a video summarizing the gorgeous results of the Millennium simulation: