Is Langton's Ant deterministic? Does Langton's Ant have free will?

[Erik Mesoy]

http://www.fortunecity.com/emachines/e11/86/langton.html

http://en.wikipedia.org/wiki/Langton's_ant

The original:

Langton's ant is a two-dimensional Turing machine with a very simple set of rules, invented by Chris Langton.

Squares on a plane are colored variously either black or white. We arbitrarily identify one square as the "ant". The ant can travel in any of the four cardinal directions at each step it takes. The ant moves according to the rules below:

* At a black square, turn 90° right, flip the color of the square, move forward one unit
* At a white square, turn 90° left, flip the color of the square, move forward one unit

Now...

E.G.D. Cohen and X. P. Kong of the Rockefeller University proved that the ant's trajectory is necessarily unbounded. It escapes from any finite region.

If I am offered an otherwise neutral choice between a chocolate ice-cream and having dog feces smeared in my face, I will choose the chocolate ice-cream. This is predictable in advance if you have watched me for some time, or even if you generalize from other people like me. If time is somehow "rewound", I will choose the same again. If I am given the same choice later, I will make the same choice.

Langton's Ant, however, is arguably less predictable. You cannot predict what it will do except by letting it run and then looking at it afterwards. If given a huge board with random distributions of black and white squares, the ant will move according to a very clear set of rules - but you can't really predict what it will do. You can work out its moves, but this is like reading a history book and declaring that the people described there don't have free will because we know what they did, since all you've done is to let the ant move on another board. We cannot, as with mathematics, simplify the calculations and "predict" in advance. We can add 2¹²°° + 2¹²°° and get 2¹²°¹ in less time than 2¹²°° planck times (ca 8*10³¹° seconds). We cannot skip Langton's ant ahead in the same way without losing precision, while the previous calculation is arbitrarily precise. (A planck time is the shortest known time in which something can happen.)

So. I submit that Langton's ant is deterministic in that it can be simulated, and has free will in that we cannot predict its behavior - only watch it behave.

I do not submit any conclusions with regard to humans as yet, but I think that we may need to throw out both concepts of "determinism" and "free will".


Well, there are my ideas from this evening, mashed into postable form. Feedback welcome, since I'm thinking a good deal about this, and it's likely that someone else will think of and post something that I won't yet have thought of. I hope someone else finds the debate interesting. I'm sure there will be clarifications forthcoming, but I wanted to post this now and start communicating with people rather than spend a week polishing my post.

 

[Masquerouge]

Well from the Wiki:
'These simple rules lead to surprisingly complex behavior: after an initial period of apparently chaotic behavior, the ant appears invariably to start building a road of 104 steps that repeat indefinitely - regardless of the pattern you start off with. This suggests that the "highway" configuration is an attractor of Langton's ant.'

So it seems that the ant is a bit more deterministic, and has less free will, than a human.

I did not vote on the human part because I think that humans are partly deterministic.

 

[ArneHD]

Irregardless of our ability to predict how it will move, it is a fact that it will move in a set pattern according to set rules. It has no free will since it MUST follow certain rules on how to move, and thus it cannot have free will.

 

[Masquerouge]

Irregardless of our ability to predict how it will move, it is a fact that it will move in a set pattern according to set rules. It has no free will since it MUST follow certain rules on how to move, and thus it cannot have free will.

While we can also argue that humans have "rules", like for instance they'd rather have an ice cream than have their faces rubbed in dog's poo (Mesoy's theorem I agree with you in that a human can, but usually won't, decide to have his face rubbed in the poo instead of having the ice cream.

In other words, most of mankind's rules are not binding, while the ant's are.

 

[Mise]

The difference is, the ant's actions are mathematically defined, whereas humans' aren't.

It's possible that our actions are predetermined, but our free will isn't. Both the ant's actions and its "will" are mathematically determinable.

For the poll I voted:
-Langton's Ant is deterministic.
-Langton's Ant does not have free will.
-Humans have free will.

I don't know whether or not humans are deterministic.

 

[warpus]

So. I submit that Langton's ant is deterministic in that it can be simulated, and has free will in that we cannot predict its behavior - only watch it behave.

Of course you could predict its behaviour.

It would be simple to write a computer program that would be able to forsee any of the ant's move in the future.

Thus it does not have free will.

 

[MobBoss]

If I am offered an otherwise neutral choice between a chocolate ice-cream and having dog feces smeared in my face, I will choose the chocolate ice-cream. This is predictable in advance if you have watched me for some time, or even if you generalize from other people like me. If time is somehow "rewound", I will choose the same again. If I am given the same choice later, I will make the same choice.

You might, however, there are assuredly people out there that would choose the dog feces just on a whim. Not only that....they would take a photo of them doing it, frame it and call it art.

So. I submit that Langton's ant is deterministic in that it can be simulated, and has free will in that we cannot predict its behavior - only watch it behave.

How can it have free will when you know exactly how it will react given its instruction set? Humans are not like that. Humans break rules via their free will. I humbly submit that if Langdons ant cannot change its instructions then it does not have free will.

 

[Mise]

You can work out its moves, but this is like reading a history book and declaring that the people described there don't have free will because we know what they did, since all you've done is to let the ant move on another board.

But that's exactly what prediction means!

It's like saying, "you can't predict that the ball will have velocity v at time t -- you can work out it's velocity at whatever time you want, but you're just letting the ball move on another board."

It's an absurd statement.

 

[Erik Mesoy]

Well from the Wiki:
'These simple rules lead to surprisingly complex behavior: after an initial period of apparently chaotic behavior, the ant appears invariably to start building a road of 104 steps that repeat indefinitely - regardless of the pattern you start off with. This suggests that the "highway" configuration is an attractor of Langton's ant.'

So it seems that the ant is a bit more deterministic, and has less free will, than a human.

That's like saying "humans die, regardless of what conditions you start them off with". Still hard to predict what they'll do underway except by letting it happen.

Of course you could predict its behaviour.

It would be simple to write a computer program that would be able to forsee any of the ant's move in the future.

Thus it does not have free will.

And that computer program would do what... simulate the ant? How would this be different from letting the ant, which is a program/ruleset to begin with, run its course?

You might, however, there are assuredly people out there that would choose the dog feces just on a whim. Not only that....they would take a photo of them doing it, frame it and call it art.

Yes, but they have different rule sets, and I bet I could identify them ahead of time. I could also rewrite Langton's Ant to suddenly dash three squares forward "on a whim" every 74593 moves.

How can it have free will when you know exactly how it will react given its instruction set? Humans are not like that. Humans break rules via their free will. I humbly submit that if Langdons ant cannot change its instructions then it does not have free will.

I submit that if I knew the full instruction set of a human, I could predict exactly how it would react. I predict, for example, that you will choose ice-cream over dog feces in an otherwise neutral choice. (My posting this makes it no longer neutral, unfortunately, as I have known several people who would at this point choose the dog feces in an attempt to prove me wrong. Hence the "otherwise neutral" clause.)

 

[Erik Mesoy]

But that's exactly what prediction means!

It's like saying, "you can't predict that the ball will have velocity v at time t -- you can work out it's velocity at whatever time you want, but you're just letting the ball move on another board."

It's an absurd statement.

No no no! The distinction is that predicting a ball's velocity is a computation that can be done symbolically and without a ball. You can't do that with the Ant! You have to do it step-by-step, with the Ant or a copy of it!

 

[ArneHD]

While we can also argue that humans have "rules", like for instance they'd rather have an ice cream than have their faces rubbed in dog's poo (Mesoy's theorem I agree with you in that a human can, but usually won't, decide to have his face rubbed in the poo instead of having the ice cream.

In other words, most of mankind's rules are not binding, while the ant's are.

Actually, I don't belive in free will (at least not the total one) for humans on a psychological basis. A Skinnerian basis to be precise.

 

[Masquerouge]

(My posting this makes it no longer neutral, unfortunately, as I have known several people who would at this point choose the dog feces in an attempt to prove me wrong. Hence the "otherwise neutral" clause.)

Forget the whole philosophy debate. You have a golden opportunity to make a lot of money right there!

 

[warpus]

And that computer program would do what... simulate the ant? How would this be different from letting the ant, which is a program/ruleset to begin with, run its course?

Yes, it would simulate the ant and predict what it's going to do. If you compared the predictions with the actual results, they would match up. You would not be able to predict the movements of the ant like this if it had free will.

Your ant is a deterministic computer program. Deterministic computer programs cannot have free will.

No no no! The distinction is that predicting a ball's velocity is a computation that can be done symbolically and without a ball. You can't do that with the Ant! You have to do it step-by-step, with the Ant or a copy of it!

So? It doesn't matter how you predict what the ant is going to do.. if you can make such a prediction every single time, then the ant can't possibly have free will.

If you could construct a being that duplicated everything I did and felt - and it aaaalways matched up to what i was doing.. then i can't possibly have free will.

I submit that if I knew the full instruction set of a human, I could predict exactly how it would react. I predict, for example, that you will choose ice-cream over dog feces in an otherwise neutral choice. (My posting this makes it no longer neutral, unfortunately, as I have known several people who would at this point choose the dog feces in an attempt to prove me wrong. Hence the "otherwise neutral" clause.)

You are forgetting about quantum tunneling and the heisenberg uncertaintly principle. You would not be able to make a perfectly accurate prediction.

 

[Mise]

No no no! The distinction is that predicting a ball's velocity is a computation that can be done symbolically and without a ball. You can't do that with the Ant! You have to do it step-by-step, with the Ant or a copy of it!

You do it with an "abstract ball", in the same way that you do it with an "abstract ant".

 

[Erik Mesoy]

Yes, it would simulate the ant and predict what it's going to do.

So on the left we have an ant, and on the right we have an ant, and since they're identical, they'll do the same things...

If you compared the predictions with the actual results, they would match up. You would not be able to predict the movements of the ant like this if it had free will.

If I were superpotent (not quite omnipotent, to avoid certain logical contradictions, nor omniscient), I could "copy" the universe, "freeze" the original in time relative to me, and watch the copy for a while. Once I unfroze the original, I would know what would happen there, since I've "already seen it happen". Do the inhabitants of the "original" universe then lose their free will and regain it once they reach the point at which I stopped running the copy?

 

[Masquerouge]

You do it with an "abstract ball", in the same way that you do it with an "abstract ant".

Actually Erik's right.

With the right formulas, you can predict the position and velocity of a ball at any instant T, regardless of where it was at t-1.

You can not do that with this Ant. There is no formula that tells you, at a time T it will be here. You have to go through all of the n-1 moves in order to get the nth move.

 

[warpus]

So on the left we have an ant, and on the right we have an ant, and since they're identical, they'll do the same things...

Yes, and if these ants had free will, they would not be doing the same things.

Since they are, every single move, no free will.

 

[warpus]

Actually Erik's right.

With the right formulas, you can predict the position and velocity of a ball at any instant T, regardless of where it was at t-1.

You can not do that with this Ant. There is no formula that tells you, at a time T it will be here. You have to go through all of the n-1 moves in order to get the nth move.

So? It doesn't matter how you compute where it's going to be at time T. The important part is that you are able to sit down and work out where it's going to be.

Since you can do this at all = no free will.

 

[warpus]

If I were superpotent (not quite omnipotent, to avoid certain logical contradictions, nor omniscient), I could "copy" the universe, "freeze" the original in time relative to me, and watch the copy for a while. Once I unfroze the original, I would know what would happen there, since I've "already seen it happen". Do the inhabitants of the "original" universe then lose their free will and regain it once they reach the point at which I stopped running the copy?

No, because due to the nature of the Universe and principles of quantum physics, your two universes would behave differently.

 

[Erik Mesoy]

Yes, and if these ants had free will, they would not be doing the same things.

Since they are, every single move, no free will.
<...>
No, because due to the nature of the Universe and principles of quantum physics, your two universes would behave differently.

Second Godwin's Law: The first person to invoke quantum mechanics to justify his argument loses.

More seriously, are you arguing that free will is dependent on quantum uncertainty? Are you suggesting that I must act differently in identical circumstances to have free will? Must I act "unpredictably" to have free will? If this is necessary, is it not then predictable? Are humans unpredictable?