In a 2000 Mathematical Intelligencer article, I speculated on what would happen if we constructed a gigantic computer model which starts with the initial conditions on Earth 4 billion years ago and tries to simulate the effects that the four known forces of physics (the gravitational and electromagnetic forces and the strong and weak nuclear forces) would have on every atom and every subatomic particle on our planet. If we ran such a simulation out to the present day, I asked, would it predict that the basic forces of Nature would reorganize the basic particles of Nature into libraries full of encyclopedias, science texts and novels, nuclear power plants, aircraft carriers with supersonic jets parked on deck, and computers connected to laser printers, CRTs and keyboards?
A friend read my article and said, computers have advanced a lot in the last seven years, I think we could actually try such a simulation on my new laptop now. So I wrote the program -- in Fortran, naturally -- and we tried it. It took several hours, and at the end of the simulation we dumped the final coordinates of all the particles into a rather large data file, then ran MATLAB to plot them. Some interesting things had happened, a few mountains and valleys and volcanos had formed, but no computers, no encyclopedias, and no cars or trucks. My friend said, let me see your program. After examining it, he exclaimed, no wonder, you treated the Earth as a closed system, order can't increase in a closed system. The Earth is an open system, you need to take into account the effect of the sun's energy. So I modified the boundary conditions to simulate the effect of the entering solar radiation, and reran it. This time some clouds and rivers had formed, but otherwise Earth still looked a lot like the other planets, and still no libraries or computers or airplanes.

My imaginary friend looked more carefully at the program, and said, good grief, you are using classical physics, you can't simulate the effects of the four forces without quantum mechanics. He explained that according to quantum mechanics, the exact effects of these forces on any particular particle are impossible to predict with certainty, the new laws only provide the probabilities. I said, you mean there is a supernatural force at work here? He said, well, technically, yes, if you define the supernatural to be that which is forever beyond the ability of science to predict or explain -- British astronomer Sir Arthur Eddington said quantum mechanics "leaves us with no clear distinction between the natural and the supernatural". But there is no reason to doubt that this so-called "supernatural" effect is completely random, you can simulate it using a random number generator. So I completely re-wrote my simulator, I used an IMSL random number generator with a user-supplied probability distribution to simulate this randomness, and computed the required probability distributions by solving the Schrodinger equations with my own partial differential equation solver, PDE2D. Still no luck -- no space ships, no TV sets, no encyclopedias, not even a cheap novel.

My friend looked at the new graphs and tried to mask his disappointment. Well, he said, of course the problem is you haven't taken into account the one natural force in the universe which can violate the second law of thermodynamics and create order out of disorder -- natural selection. You mean there is a fifth force -- why didn't you say so? Just give me the equations for this force and I will add it to my model. He said, I can't give you the equations, because it isn't actually a physical force, it doesn't actually move particles. So what does it do, I asked. He explained that one day a long time ago, by pure chance, a collection of atoms formed that was able to duplicate itself, and these complex collections of atoms were able to pass their complex structures on to their descendents generation after generation, even correcting errors. He went on to talk about how genetic accidents and survival of the fittest produced even more complex collections of atoms, and how something called "intelligence" allowed some of these collections of atoms to design computers and laser printers and the Internet. But when he finished, I still didn't know how to incorporate natural selection -- or intelligence -- into my model, so I never did get the simulation to work. I decided the model was still missing a force or two -- or a smarter random number generator.

Granville Sewell is a professor of mathematics at the University of Texas El Paso.