I wonder if I similarly spent my startup how much science I could get done…

Also, it is amazing what $500 buys these days!

Think how many problems we could solve if we dangled a few prizes for other knotty problems.

So what made this work?

• The problem itself was well-framed and finite:  ”We need a time-reversible random number generator.”  It was something that a lot of people in the field could agree was interesting when framed to them properly.
• The group offering the prize was widely-respected for previous work on related problems.
• The prize and the solution were both posted on a highly visible physics site (arXiv).
• The reward was about fame and recognition by the community more than it was about money.

I’m now wondering if all of  the attempts to get a kickstarter or crowdsourced funding model for science (e.g. sciflies, petridish, scifundchallenge, fundageek) are just a bit misguided.  Science is darned expensive, and for better or worse, we’re going to be wedded to federal and foundation funding for science for a long time.  All funding models have an aspect of salesmanship to them – a scientist must convince the funder that the problem itself is interesting enough to need solving, and that their lab is the one to solve it.   In the NSF-style funding model, scientific communities do have significant input into what the “good problems” are, but the necessary delays in funding and the scarcity of funds means that we’re not very agile.

Perhaps we need a clearinghouse where scientific communities can agree on a tough challenge, pool some minimal award money (like $500 or $1000) and let their young colleagues have a go at winning fame by solving them.

William G. Hoover (of the Nosé-Hoover Thermostat) and Carol G. Hoover issued a $500 challenge on arXiv to generate a time-reversible random number generator.  The challenge itself would be quite remarkable news.  What’s even better is that the challenge (including the source code for an implementation) was solved in 6 days by Frederico Ricci-Tersenghi.

Why is this a big deal?  Most of the equations in physics that govern time evolution of particles obey time-reversal symmetry; the same differential equations that govern molecular or planetary motion will take you back to your starting point if you suddenly reverse the time variable.  This is a usually a fantastic way to check to see if you are doing the physics correctly in your simulations, and also means that collections of  starting points that are related to each other behave in certain predictable ways when they evolve.

Stochastic approaches to physical motion introduce an aspect of randomness to mimic the behavior of complex phenomena like the motion of solvent surrounding the molecule we’re interested in, or to mimic the transitions between different electronic states of a molecule.   The introduction of random numbers has meant we had to give up time-reversibility, and we’ve been willing to live with that for a long time because we can study more complicated phenomena.

If we have access to a time-reversible pseudo-random number generator, however, we get that very powerful tool back in our toolbox.

Now, the Langevin equation,

\(m \frac{d^2 x}{dt^2} = F – \gamma(t) \frac{dx}{dt} + R(t)\)

has two things that prevent it from being time-reversible.  Besides the stochastic or random force, \(R(t)\), there’s also a drag or friction force, \(-\gamma(t) \frac{dx}{dt}\), that depends on the velocities of the particles.  There’s no solution yet to time reversibility for this piece (and I have my doubts that there ever will be a way to reverse this).  I suppose if we offer up another $500 prize for time-reversible drag, we’d make some traction on this problem…

(The comic above courtesy of xkcd).

relax is designed for the study of molecular dynamics of organic molecules, proteins, RNA, DNA, sugars, and other biomolecules through the analysis of experimental NMR data. It supports exponential curve fitting for the calculation of the R1 and R2 relaxation rates, calculation of the NOE, reduced spectral density mapping, the Lipari and Szabo model-free analysis, study of domain motions via the N-state model or ensemble analysis and frame order dynamics theories using anisotropic NMR parameters such as RDCs and PCSs, and the investigation of stereochemistry.

Memorization of long digit strings is not an exercise that teaches a love of mathematics (or anything else useful about the natural world).  This is solely an exercise in recall, which is perhaps valuable for remembering phone numbers, but not for understanding transcendental constants. For all practical purposes, only the first few digits of \(\pi\) are really necessary - the first 40 digits of \(\pi\) is enough to compute the circumference of the Milky Way galaxy with an error less than the size of an atomic nucleus.

So, because \(\pi\) is a such an accessible entry to mathematics and science, I thought I’d come up with a list of other cool \(\pi\) things that could replace these pointless memory contests:

• The earliest written approximations of \(\pi\) are found in Egypt and Babylon, and both are within 1 percent of the true value. In Babylon, a clay tablet dated 1900–1600 BC has a geometrical statement that, by implication, treats \(\pi\) as 25/8 = 3.1250. In Egypt, the Rhind Papyrus, dated around 1650 BC, but copied from a document dated to 1850 BC has a formula for the area of a circle that treats \(\pi = \left(\frac{16}{9}\right)^2 \approx 3.1605\).
• In 220 BC, Archimedes proved that \( \frac{223}{71} < \pi < \frac{22}{7}\).  The mid-point of these fractions is 3.1418.
• Around 500 AD, the Chinese mathematician Zu Chongzhi  was using a rational approximation for \(\pi \approx 355/113 = 3.14159292\), which is astonishingly accurate.  For most day-to-day uses of \(\pi\) this particular approximation is still sufficient.
• By 800 AD, the great Persian mathematician, Al-Khwarizmi, was estimating \(\pi \approx 3.1416\)
• A good mnemonic for the decimal expansion of \(\pi\) is given by the letter count in the words of the sentences: “How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics. All of thy geometry, Herr Planck, is fairly hard…”
• Georges-Louis Leclerc, The Comte de Buffon came up with one of the first “Monte Carlo” methods for computing the value of \(\pi\) in 1777.  This method involves dropping a short needle of length \(\ell\) onto lined paper where the lines are spaced a distance \(d\) apart.  The probability that the needle crosses one of the lines is given by:  \(P = \frac{2 \ell}{\pi d}\).
• In 1901, the Italian mathematician Mario Lazzarini attempted to compute \(\pi\) using Buffon’s Needle.  Lazzarini spun around and dropped a 2.5 cm needle 3,408 times on a grid of lines spaced 3 cm apart. He got 1,808 crossings and estimated \(\pi = 3.14159292\). This is a remarkably accurate result!   There is now a fair bit of skepticism about Lazzarini’s result, because his estimate reduces to Zu Chongzhi’s rational approximation.  This controversy is covered in great detail in Mathematics Magazine 67, 83 (1994).
• Another way to estimate \(\pi\) would be to use continued fractions.  Although there are simple continued fractions for \(\pi\), none of them show any obvious patters.  There’s a beautiful (but non-simple) continued fraction for \(\frac{4}{\pi}\):
  \(\frac{4}{\pi} = 1 + \frac{1^2}{2 + \frac{3^2}{2 + \frac{5^2}{2 + \frac{7^2}{2 + …}}}}\)

  Can you spot the pattern?

• Vi Hart, the wonderful mathemusician, has a persuasive argument that we should instead be celebrating \(\tau\) day on June 28th.   Actually, all of her videos are wonderful.  If my kids spent all day doing nothing but playing with snakes  it would be better than memorizing digits of \(\pi\).
• Another wonderful way to compute \(\pi\) is to use nested round and square baking dishes (of the correct size) and drop marbles into them randomly from a distance.  Simply count up the number of marbles that land in the circular dish and keep track of the total number of marbles that landed in either the circle or the square. Since the area formulae for squares and circles are related, the value of \(\pi = 4 \frac{N_{circle}}{N_{total}}\).

There are probably 7000 better things to do with \(\pi\) day than digit memory contests. There are lots of creative teachers out there — how are all of you going to celebrate \(\pi\)-day?

Do.abl.es

Do you want to know how to measure DNA contour lengths using ImageJ?  Perhaps you want to stain a C. Elegans embryo for imaging?  Or possibly, you might want to test whether or not you have gotten an immune response using ELISA?

Martin Fitzpatrick sends word of a cool collection of open access scientific protocols called Do.abl.es.  For the uninitiated, protocols are the recipes that scientists use to carry out experiments in a reproducible way.  The list of protocols posted to Do.abl.es to date has a number of interesting and important biochemistry and biology experiments.

There’s also a neat companion site called Install.abl.es which concentrates on many of the same things we do – the use of open source software in the sciences.

And here’s my attempt:

The things we use every day are made of very tiny bits. When we put lots of those bits together we get matter. Matter changes how it acts when it gets hot or cold, or when you press on it. We want to know what happens when you get some of the matter hot. Do the bits of hot matter move to where the cold matter is? Does the hot matter touch the cold matter and make the cold matter hot? We use a computer to make pretend bits of matter. We use the computer to study how the hot matter makes cold matter hot.

The task is much harder than you think.   Here’s a collection curated by Patrick Donohue (a PhD candidate in lunar petrology right here at Notre Dame):  Common words, uncommon jobs

“Bridge” or “glue” software increases the functionality of other software by making the data formats from one package usable as input to another.  In SASSIE’s case, the molecular dynamics package being used is NAMD (from the Theoretical and Computational Biophysics Group at UIUC), along with scattering calculators Cryson and Crysol.  The Hydropro package is used for calculating hydrodynamic properties.  (Note that Cryson, Crysol, and Hydropro are not open source programs.  Boo.)

SASSIE isn’t quite a full-bore open source project yet.  I was able to download the source here (159 MB download), but there’s a registration barrier in the way on the SASSIE trac site.  I’m not sure why the small-angle scattering community locks up their code like this.  It discourages re-use, and doesn’t provide any extra benefit to the authors of the code or the home institution.  Likewise, Cryson and Crysol both appear to have an academic and research license (again, not open source).

SASSIE looks interesting.  I’m not in the small-angle scattering community, but I really like the bridge between atomistic simulation and experiment, and the code looks like it has some very useful pieces that could be reused in interesting ways.

The problem with Java applets is that many new tablet and phone web browsers don’t support them (and it looks like Java applets are being slowly disabled on Mac browsers as well).  Java has always been an elegant but relatively heavy-weight solution to dynamic content, but I think its time as a widely-used language for web content is coming to a close.

So, how do you interact with chemical structures without Java or Flash?

The Jmol team has been hard at work converting the Jmol source so that the same source code that produces the Jmol applet can also be run through Java2Script to create the entire Jmol applet in JavaScript.   The new beast is called JSmol and has almost all of the functionality of Jmol itself (file IO, scripting, etc.)    Bob Hanson’s demo pages give a taste of this work.

This is amazing work.  The same Java code is compiled to create the Jmol applet, a WebGL version of JSmol, and the HTML5 version of JSmol that can run on my phone. Almost all of Jmol is there – the ability to display orbitals, crystals, and van der Waals surfaces.  Some menu interaction is still missing, but if the goal is to display and interact with a chemically meaningful structure on a web page,  JSmol looks like a great solution.

The credit for this work largely goes to a number of people:  The GLmol interface was written by Takanori Nakane.  Java2Script was written by Zhou Renjian.  The Jmol code conversion to JavaScript was done by the current Doctor Who,  Bob Hanson.