This months blog theme is something along the lines of the first and/or most influential paper in our scientific careers. I had to think long and hard about this. Not about the paper in question - I knew immediately which paper was the first big influence in my career. More about what this reveals about me. I have no illusions about the thin veil of pseudonymity. Anyone who really wanted to figure out whom I am could likely do so with a little internet sleuthing. Telling everyone which paper was the first big influence on me might make that process a lot easier. Also, there is some slim chance that someone reading this who knows me in real life but not as a blogger will put two and two together. If you do figure it out I'd appreciate it if you didn't let everyone else know.

Despite the above caveat, this is the paper that had a big influence on me very early on:

Yes, I have a background in computational chemistry, although that's not what I do now. And yes, that is the Edward Teller. And no, I'm not that old. This was considered a very old paper when I first read it. It predates my birth. By quite a lot.

This paper was the first description of the Monte Carlo integration method applied to the simulation of molecular systems. In this case two-dimensional hard discs representing atoms. The "fast computing machines" referred to in the title were glacial in comparison to even the laptop on which I am typing this, so calculations in three dimensions weren't feasible at the time.

What is Monte Carlo integration? It's a way of using random numbers to sample from (or approximate) a distribution that can be described by an equation (e.g. the Boltzmann distribution for molecules). Here's an easy Monte Carlo experiment to help you understand: imagine a square where each side is of length one (units don't matter in this example) and corners at the origin, (0,1), (1,0) and (1,1). The area of that square will be one. Inscribe within that square a circle of diameter one - i.e. the largest circle that fits inside the square. The area of the circle will be πr^2 = π/4 since r = 1/2. Got it so far? Now start generating pairs of random numbers between zero and one. Each pair describes a point within the square. Some points will also fall inside the circle. Now, generate lots of random number pairs and start plotting inside the square. If you generate enough points, the ratio of the number of points inside the circle to the total number of points inside the square (which includes those inside the circle) will approximate the ratio of the area of the circle to the area of the square. That is:

Rearranging we get:

i.e. By generating enough pairs of random numbers we can approximate π.* Pretty cool huh? You can find a Java applet demonstrating this here.

The application of this to molecular simulations is fairly straightforward. You sample from the Boltzmann distribution using random numbers. The idea is to approximate the ensemble of states for a molecular system in this way. Once you've generated enough such states to be a reasonable approximation**, you can then calculate all kinds of interesting properties of the system.

So why was this such an influential paper for me? Two reasons.

1) I first read this as an advanced undergraduate. And I understood it. First time through. This is a well written paper. Even back then I recognized this is how papers should be written. But usually aren't. Even now I think about this paper when working on a manuscript. In this way Metropolis et al. have had a lasting impression on me.

2) This paper opened my eyes to the power of computers in chemistry and in particular in simulating molecular systems. This led me to pursue a PhD using computer simulations, which gave me just the right the expertise to land a very productive postdoc position in the lab of a well-known scientist, which in turn helped me land a tenure-track position. Basically Metropolis et al. are responsible in part for who and where I now am.

* I once heard this story about an officer injured in the American Civil War. According to this tale he was confined to bed in hospital. To pass the time he threw darts at a square piece of paper in which he had inscribed a circle. The circle was presumably far enough away that it was difficult to hit, let alone aim at the circle. He is said to have estimated π to two decimal places in this manner. Frankly I find this hard to swallow. It would take many, many thousands of dart throws to get this level of accuracy and someone had to count the points plus retrieve the darts for the bedridden officer. No one has that much patience. More likely the officer died of many mysterious small puncture wounds...

** This is in and of itself something of a science. One that is sadly often not understood.