Mathematical study is often thought of as ‘purer’ than scientific research- instead of labs full of chemicals, fruit flies or lasers, our work could in theory proceed with nothing more than a chalkboard; rather than believing theories through weight of evidence and an absence of counterexamples, we prove theorems as undeniable consequences of our base assumptions.
But theorems rarely spring into our minds fully formed, simply awaiting proof. Instead mathematical research can often mimic the scientific method- experimenting with ideas, following promising leads, looking for tests that would break or support hunches, until they look convincing enough to attempt a proof.
This has very much been the nature of my work over the past few months- and although the actual proofs have mostly been worked out by pen and paper, with supporting calculations on a MacBook laptop, the exploratory phase requires something rather more powerful. One of the perks of being a University of Edinburgh researcher is access to the ECDF – a cluster of over 1400 processors, as illustrated above. Provided a problem can be split up into many independent sub-problems, such a resource can offer staggering reductions in computation time, by farming them out to multiple machines and running them in parallel.
For instance, I usually wish to generate very, very long lists of matrices and test them for a certain property, keeping only the much smaller subset of those with the property. A typical calculation of this type might take five days on my little Mac, assuming it doesn’t simply run out of memory in the process. But by splitting it into ten smaller calculations (each exploring a subset of the matrices), I can have the answer from the grid in 12 hours- or, splitting to 20 jobs, I can load it up overnight, and collect the answer the next morning just in time for a supervisor meeting!
Of course, a twenty-fold reduction in calculation time only hints at the power of the cluster; another 70 users could also get such a job done that night. Running all-out on a single task, ECDF could complete four years worth of calculation in a day!
Not all researchers have access to systems like Eddie, but there is one network almost everyone has access to- the internet. The idea of harnessing the power of idle home computers is nothing new: over ten years ago, I was contributing spare cycles of my (then powerful) Pentium 200 to a distributed.net project that succeeded in demonstrating the insecurity of 56-bit encryption keys, which at the time was the maximum allowed by the US government in software exports. Other famous distributed efforts include the alien-seeking SETI and the biological research project folding@home.
The potential for highly parallelised computing has surged as processor counts have grown and always-on internet connectivity becomes increasingly ubiquitous. Modern PCs often have multiple processor cores (and many homes have multiple PCs), and there has been work on exploiting highly powerful (yet specialised) graphics card technology for general purpose computation too: you can even contribute to folding@home with a PlayStation3!
However, except for a few long-range ‘big ticket’ schemes such as the ones I’ve mentioned, setting up, managing and publicising your own distributed computing project might be more daunting than solving your original problem! Fortunately, there is an increasing range of ways to connect researchers to resources. At ANTS (in connection with another cryptographic challenge) I learnt of BOINC, a general platform that has grown out of SETI: you can submit a project to the volunteer community, or manage a grid within your own organisation. All modern Apple computers include the Xgrid feature, allowing again for local grid computing with your own machines or harnessing donated cycles through the openmacgrid project. Recently, Fedora Nightlife was announced, to create a community grid from machines running the popular linux distribution.
There are limitations, of course. Not all calculations fall in to the ‘embarassingly parallel’ category that lends itself so well to distributed computing. There are also concerns about the other costs of such schemes – home PCs are not necessarily cut out for 24/7 running, and those that are will probably add a bit to their owner’s power bill. However, Bryan’s blog makes a good case for the environmental merits of distributed computing over data centres, assuming that the calculations are worthwhile and thus going to be done somewhere anyway – a claim that is perhaps easier to defend for cancer studies than the search for alien signals. Or you can think of it as a very direct form of charity in support of science- donating some electricity, processing power and wear-and-tear rather than cash. So, if like me your home features more computers than people, why not devote some of their time to volunteer computing?