This is Langton’s ant. He lives on a plain sheet of paper, preferably white, with squares on it.

His name is possibly Cyril. But, it could be Rodney. It’s difficult to tell.

•           Cyril, or possibly Rodney, likes an uncomplicated life. He lives by just two rules.

•           And two pots of paint.

THE RULES OF ANTLORE

1.         If he is standing on a white square, he paints

it black, turns right and steps on to the next square.

2.         If he is standing on a black square, he paints it white, turns left and steps on to the next square.

3.         There is no rule three

I mean it just does not get any easier than that.

Just remember l said “Easier” not “more simple”

Ecce ant in his habitat:-

I have no idea when he gets lunch and, since ants don’t seem to have pockets, how he carries the paint

Maybe he has a tiny little wheelbarrow

Maybe his mum brings sandwiches at lunchtime

Following the first rule of Antlore, Cyril swiftly
paints the square he is on black, turns right and steps forward one square:

I think you can see where we’re going with this:

Leaping swiftly ahead, look what happens after:

In fact, it’s a bit of a mess, isn’t it? Staggering around like a —, well an ant on the p

It just looks almost like a random stagger, there is no discernible pattern.

Let’s go for a big number of steps

Well, this is silly, isn’t it? Cyril is wandering around, crossing and recrossing his own path. Obviously, he is getting nowhere. If you can see a pattern in this, you are the first.

But, how is this? Because we know it isn’t random at all. There are rules, strict rules, and only two of them. So why the drunken stagger?

Where will it end? Will poor Cyril stagger on for ever? How long will the paint last?

OK, we’ll give Cyril a little longer. Say, 10,000 steps

Still rubbish.

Last go – 12,000 steps?

Now, ain’t that something? Cyril has suddenly drawn an anteater, or is very pleased to see us!

Where did that come from? How did he do that? Who told him to do that? What’s in his sandwiches? Is it the fumes from all that paint?

What’s it all got to do with the price of fish and chips, anyway?

Welcome to ant country.

Before we go on to the really neat stuff, let’s deal with some of the basics: The whole thing was developed by Chris Langton in 1986

Nobody knows why Cyril does this. Well, that’s not quite true. We know Cyril is an ant of impeccable rectitude. We know he would never disobey rules. We know there are only two rules and we know neither of them is about building a super highway and going off to find The Wicked Witch Of The West.

Nobody knows which combination of the rules gives rise to this highway.

Nobody knows why it takes ten thousand and fempty poo steps precisely to start building the highway.

We know it ain’t random, ‘cos there is nothing random in the rules and he always does it exactly the same.

And here comes the first big thought:

SINCE we don’t know why he should start building a highway, NOBODY can be sure that he will go on forever

All we know is that, in all the runs done on all the computers in all the gin joints in all the world, Humphrey Bogart has never found a run where he stops. Which is almost more baffling than the fact that he starts.

Think about it. It took ONLY ten thousand and change steps to get started, so why doesn’t it ever occur to him to stop? ‘cos he’s locked in, that’s why. It took ten thousand steps to work through some tiny misfit and get to a state where every 104 steps (I think that’s the figure) he repeats himself – but one step further along the highway. So it took that long to “get rid of something”.

But, since we have no idea what it was he got rid of , we can’t be certain that something else, something that is also hidden in the rules, won’t appear after blankety blank million and three moves to start him on something else.

Here’s the next biggy:

It is impossible to predict that Cyril will build his highway.

Get this exactly straight: “predict”.          He does it every time, so he will do it next time.

Prediction? No, just confirmation of what he has done in the past and extrapolation to the future. To make a prediction, you would need to paint a square black and then declare before the run, what difference it would make to the outcome.

The only way to do that is to paint the square, run the ant and then declare that he will do the same thing again. Which is confirmation again, not prediction. All that a computer does is build an ant programme and run it.

There is no way to the outcome without following Cyril THROUGH ANT COUNTRY.

This is so important, it’s worth stating again. There is no way of predicting the outcome.

Put that another way which might be of more practical use. There is no way of going to a square and stating whether it is going to be black or white before Cyril gets there. Put yet another way and you may begin to see the problem: It might be possible to put together a theory that would predict what will happen, but it looks likely that it will always be simpler and faster to run the ant that to run the theory to make a true prediction, given only that both prediction and run must be done on the same type and standard  of computer.

So, what has a mind bogglingly simple computer game got to do with Life, the Universe and Everything?

Here’s a thought:

You may know all the rules governing a process. That does not mean you know what is going to happen. Even if you knew absolutely all the rules governing, say weather forecasting, it doesn’t mean you can forecast the weather. Unless you look at what happened in the past and extrapolate to the future.

This whole group of things is known as “Emergent Phenomena” They aren’t random, they are subject to the rules. But they are the unforeseen product of aspects of the known rules which are hidden before the action.

The bit before the highway, the bit before the emergent phenomenon manifests itself? That’s Ant Country. There is no way through it except on an ant. Even the best, most comprehensive theory will not get through faster than the ant.

The trouble is, there is nobody to tell us whether, for example, economics is ant country or whether we can find out how to make genuine predictions.

And now we come to two more thoughts, before you fall asleep.

Even if we find an underlying complete theory of everything in the Universe, the Universe may turn out to be ant country all the way.

This would mean that in order to predict something happening now from “first principles” using the super theory, it would be necessary to build a universe, set off a big bang and run it right up until now to see what happens as the fastest way to get an answer.

Which would take rather a long time. Which leads to the second thought.

You have a problem You find a solution.

You use the solution to solve the problem.

If the solution gets too complicated, you might end up using the problem to solve the solution.

I’m not kidding.

Night night

And night night from Cyril

And one last little nightcap.

When you look at the neat order of the highway compared to the preceding complicated stagger, you begin to look for the start of the highway. Exactly when, at which step precisely does Cyril start this final odyssey?

Easy.

Step 1.

He was always building the highway.

You could say that, as with much road building, the foundations and preliminaries take a long time.

But, if you are a little ant starting on a journey that will last forever, maybe you need to take some time.