# Science after the Zombie Apocalypse

It is generally assumed that, once the zombie apocalypse hits, our societies will crumble into anarchy; and that those who survive the initial panic will be reduced to fighting for their bare necessities. We will be scavenging for food and supplies, and fending off the undead hordes and the darkest excesses of human nature, which will bubble to the surface in such inhuman circumstances. The edifice of science will be largely lost, and surely making any new scientific contributions will be impossible.

Who needs science when your neighbours are rising from the grave to eat your brains and you’re spending every last calorie of your energy to live to see another day, right? But what if science could find a solution, a cure? Wouldn’t we need science more than ever, to be a bright beacon of hope in humanity’s hour of darkness? To deliver us from the dark forces of entropy into a renaissance of reason?

Ah, but how do we continue the grand effort that is science when our laboratories are overrun by the hungry hordes, when the power grids no longer provide the electricity to charge our laptops, and when the referees who determine the fates of our grant proposals, having become the walking dead, no longer condescend to read our painstakingly drafted pleas?

Luckily scientists are now preparing for this eventuality. Dumoulin and Thouin, researchers at the University of Montréal, recently put out a paper that lays the first groundwork for this new field of interest. Their work provides hope that we may still be able to science in the post-apocalyptic wasteland.

#### Pi

One of the most important numbers known to science is π. Most of us know that its value is about 3.14. Some know a few more digits by heart, Google will tell you the value to 11 decimals and of course the number has been recorded to nauseating precision in many digital and analogue forms.

But what if you don’t have access to any of that any more? What if you’re out in the woods, trapping rabbits for food and stealthily avoiding the packs of zombies that occasionally wander by? Whether you’re trying your luck at basic geometry, or painstakingly calculating a Fourier transform by hand, chances are you’re going to need the value of π to a higher precision than you can remember. So what’s a scientist to do? It turns out you can turn to your trusty old shotgun (if you made it this far in a zombie apocalypse, you probably have one of those) for help!

The number π is the ratio between a circle’s surface area and the square of its radius,

$A = \pi r^2.$

This formula gives us a method of estimating π using statistical means. Let’s draw a square with sides of length 1, and inside of it a quarter of a circle with radius 1. The area of the square is 1 and the area of the quarter circle is $\frac{\pi}{4}$. If we now randomly choose a point inside the square, there’s a chance of $\frac{\pi}{4}$ that this point will fall within the circle. If we keep choosing points randomly, over and over again, we can count the fraction of them that lie in the circle, which will then give us an estimate of the number $\frac{\pi}{4}$ and thus of π. The procedure is illustrated in Fig. 1.

Estimating π by throwing random points on a 1×1 square, divided in two by a quarter circle. The more points we use, the better our estimate of π becomes. (Credit: Wikipedia user CaitlinJo. Source.)

#### Weapon of Choice

So how does a shotgun help us put this method into practice? As it turns out, the shot fired from your shotgun provides an effective method of choosing random points on a surface. You just take a square surface, draw a quarter circle on it, and fire your shotgun at it until you have enough samples.

Plot of the probability density for hailshot fired at a square surface from a shotgun. The distribution is clearly peaked in the center. Data extracted from [1].

There’s a catch, though. Besides the obvious problem of attracting zombies with the noise of your shots, a shotgun doesn’t produce a uniform spread of pellets, which you need for the basic method described above to work. Instead, the shot is slightly focused towards the central point you aim at. The authors measured this distribution and the result is shown in Fig. 2.

Luckily, the statistical framework allows one to take this non-uniform distribution into account, as long as one knows what it is. This is then exactly what the authors did. Taking Fig. 2 into account, they fired 200 shots from a shotgun to produce around 30,000 random points. Counting how many of those fell inside the circle, they found an approximate value for π of 3.131, which is within 1% of the correct answer! A more elaborate experiment, with more samples, should yield even more accurate results.

By giving a proof-of-principle for a post-apocalyptic determination of the most important number in science, the authors have made the first pioneering step into this new field. No doubt many researchers will follow to build upon and extend our preparation for science after the zombie apocalypse, and it is comforting to know that the end of civilization does not necessarily entail the end of that most noble endeavor we call science.

#### Sources:

[1] Vincent Dumoulin and Félix Thouin. “A Ballistic Monte Carlo Approximation of π.” arXiv:1404.1499 [physics.pop-ph]

Marco is a theoretical (bio)physicist, currently engaged in unraveling the sequence-dependent dynamics of DNA molecules to earn his PhD at Leiden University. Other passions include literature and history.

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