Imagine a universe in which we know everything there is to know. To make it easier, we might start with a universe that is an infinite white plane. There is no up or down in this universe, just forwards and backwards, left and right. Divide the plane into a grid of small squares and place a tiny robot – an 'ant' - on one of the squares. The ant knows all the rules of the universe.
Rule One states that if the ant is on a white square it is to turn to the left and move one square forward, after which the square it has just left will turn black.
Watch the ant carefully. The ant is on a white square, it moves to the square on its left: the ant is now on a new white square. It steps to the left again and does that twice more; the squares left behind by the ant turn black in its wake. Now the ant is back on the square where it started and that square has become a black square. It is time for Rule Two.
Rule Two states that if the ant is on a black square it should turn to the right and move one square forward. The square it leaves behind will turn white.
The ant moves to the right and then, of course, to the left following Rule One (because it has moved onto a white square) and so on. We can carry on imagining this in our heads but it is easier to use a computer program to help us out1.
At first, we might think we can predict the path of the ant because such simple rules must surely result in a simple shape: a square, perhaps, or a figure eight? The ant keeps moving and the pattern becomes more complex. It will be a flower-shape, maybe, or a Fibonacci spiral. Could it be the plan view of a castle with round towers? The ant keeps going.
After a few hundred steps, order starts to break down and chaos ensues. Putting aside our early thoughts of geometrical patterns, we turn, with some relief, to the concept of entropy. Increasing disorder is the way of our universe. Perhaps this is the way of all universes, even simple ones.
We keep watching because temporary short-range patterns hold our attention. The ant repeats a series of steps creating a pattern very similar to the one on that wallpaper border we bought last year and then goes off to the other side of the growing patch of black and white squares to perform the latest dance craze with some enthusiasm. The ant has now completed just over ten thousand muddled steps.
And then, without warning or preamble, the ant breaks free of its chaotic morass of footprints. The ant suddenly starts to repeat a set of 104 steps with uncanny determination creating a broad, straight, ribbon-like trail, usually referred to as a 'highway', heading out as far as we can follow it. The ant has displayed what is known as emergent behaviour and it came as a surprise. What does this teach us?
Langton's Ant and Science
The thought experiment known as Langton’s Ant2 teaches us valuable lessons about the aims of science. It also reminds us not to be cocky.
One of the Holy Grails of science is Grand Unification Theory (GUT) — a theory of life, the universe and everything, if you will. Langton's Ant tells us something about the consequences of setting out on such a quest.
After centuries in which the ideas and vocabulary of science expanded almost without check, there arose, in the late 19th and early 20th Centuries, a view that less was more. It was felt that instead of accepting that gravity, electrostatic forces, magnetism and the weak and strong nuclear forces were independent ideas, there should be a search for just one underlying theory. Science has pursued GUT to this day.
The first lesson Langton's Ant doles out is that even if we eventually succeed in knowing everything there is to know about the rules underpinning our universe, we still will not know everything about the universe. This is good news. It means that if we achieve GUT, there will still be more to learn. Science will continue to exist and scientists will still have jobs; they will not disappear up their own fundaments in a puff of smoke.
Langton's Ant also serves as a user-friendly introduction to the mathematics of emergent behaviour and, hence, complexity theory. This branch of mathematics has many applications in science and applied science: it can be used for everything from weather forecasting to explaining the growth pattern of the Romanesco cauliflower.
Lastly, no-one — however clever they think they are — ever predicts the emergent behaviour when meeting Langton's Ant for the first time. Even when they have seen the basic version of the ant, experienced mathematicians cannot predict the results of similar systems. The fact that such a simple creature can outwit humankind is somewhat comforting.