How Do We Find Interesting Things in Very Large Simulations?

It’s a growing problem in computational astrophysics.  Hydrodynamic simulations (say of giant molecular clouds and star forming regions) are getting very large.  When we want to analyse them and find interesting features to compare to the physical Universe, simply searching them “by eye” is becoming an enormous task.

One simple solution to this is to farm out the problem to citizen scientists, essentially doing the “by eye” hundreds of thousands of times in a few days.  This technique is great if you can break up the simulation into easily viewable chunks for each citizen scientist to look at.  But what if you can’t do this, or you don’t have access to millions of enthusiastic people?

We must rely on algorithms to solve this problem.  Luckily cosmologists came across similar issues in N-Body simulations of dark matter.  These simulations have slightly less physics inside, and hence grew to large sizes much quicker, which was essential to modelling the growth of structure on cosmic scales.  They used something called tensor classification to analyse the mass distribution.

This is a technique which relies on computing a rank 2 tensor, a matrix, which contains information about how the simulation changes with position over all 3 dimensions.

For example, we can compute a tidal tensor, which is two derivatives of the gravitational potential.  This measures how the gravitational force changes as a function of position.  Manipulation of the tensor (finding its eigenvalues and eigenvectors) allows us to say what shapes and geometries the gravitational force is trying to build.  Is it making pancake-like sheets? Rope-like filaments? Or is it squeezing everything into a sphere? Or, is it doing none of this, creating a void?

This technique gives cosmologists useful information about the filamentary structure of dark matter on very large scales.  In a recent paper, I investigated how these N-Body methods (where the only force active is gravity) could be ported into hydrodynamic calculations (where pressure forces, radiation and perhaps magnetic fields also play a role).

As we work with smoothed particle hydrodynamics (SPH), which also simulates a fluid using particles, these methods are easy to apply, with the advantage that there are less free parameters in the calculation.

And it has some stunning uses.  Want to find the spiral arms in a self-gravitating disc? Presto:

Want to trace the blast wave of a supernova as it travels through interstellar gas? Sure:

It is also quite good at detecting filaments in molecular clouds, but the results aren’t quite as impressive – yet.  Most recently, we’ve been using the technique on simulations of entire galaxies, and we’re starting to see how material flows in and out of spiral arms, which helps to produce molecular clouds.

We’ve really only just begun using tensor classification for problems like this, and there are some great possibilities for analysing magnetic field structures in a similar way.

I have some very exciting plans for this technique, so stay tuned for further updates!

If aliens exist, they’ll find political union as tough as we do

I’ve thought a great deal about the so called Zoo solution to Fermi’s Paradox over the last five years. This is the idea that intelligent aliens have decided not to reveal themselves to us, and this is why we see no signs of intelligent life.

It’s quite an unscientific solution, as we cannot gather evidence in favour of it.  If we could, then we would have proof of intelligent life, and that would be the end of it!

The question now is: can we prove (or disprove) this solution while still having no evidence for aliens? The best we can do at this stage is challenge the assumptions that we must make to support it.

This is what I did in my latest paper.  The critical assumption about solutions that forbid contact with us (the Zoo Solution, the Prime Directive, the Interdict Hypothesis) is that this requires some form of law or moral tradition. Laws require agreement between multiple parties – in this case, most likely multiple species of intelligent life, from a variety of different backgrounds with very different belief systems.  To use Carl Sagan’s line, these solutions need a “Galactic Club” – underwritten by a host of treaties – to work.

So how can we test if a “uniformity of motive” can be established? I ran some computer simulations that were in effect an experiment in uniformity. In each experiment, I assumed that there N civilisations would appear in the Galaxy over its lifetime.   I placed them at given locations at a given time. I then tested whether a signal from civilisation a) would reach civilisation b) before b) became advanced enough to receive it. In other words, I wanted to measure how much civilisation a) can influence civilisation b).

This is a strict condition for universal interstellar law to emerge. It’s true that we can relax this condition by allowing civilisations to evolve after they make contact, but I wanted to see whether a universal legal system is a natural consequence in a populated Galaxy.

And, surprise surprise, it isn’t. In previous work, I was able to show that Galactic Clubs were very unlikely. In my latest research, I was able to quantify what the Club would be replaced with. More often than not, my simulations showed a large number of small civilisation groupings, which I call “Galactic cliques”.  It’s quite likely that these cliques do not share much in common culturally (at least initially).

So we can conclude that Galactic Clubs are far from guaranteed. In fact, to obtain a single Club the distribution of civilisations in space and time must be quite odd (you can read the paper to find out more), or one clique must dominate the others well after the fact (via political or military means).

This work hardly destroys these solutions to Fermi’s Paradox. What it does show us is the weaknesses in the assumptions we make to propose these solutions.  The Galaxy is big enough that it would be pretty tough for every civilisation to come to an agreement about how to conduct themselves.

This is a consequence of the laws of physics, and it holds true whether there are ten or ten thousand civilisations out there.

It’s certainly true even if there’s only one, as our own civilisation can attest to.