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

[Pontiuth Pilate]

So according to your vote God exists

Yes, I believe God exists.

No, I don't necessarily turn left, I actually turn left. That I turn left is contingent on my free will. "God" knows what choice I'm going to make - that doesn't mean I don't have a choice to begin with.

If there is no way you can change an outcome then there is only the illusion of decisionmaking. If I know the future then it doesn't matter in the slightest what you think you're being influenced by.

You say that a computer program or an ant "necessarily" turns left but you "actually" turn left. There's no difference here, just the desire to keep the rules we all agree apply to the ant from applying to the human. As you can see from the poll results, a lot of people are in denial

Erik: as usual you are making the best points, will reply to you when I get back from class

 

[Pontiuth Pilate]

'kay.

As far as I can tell (I forget if you're the Christian/mystic/hacker poster ) you are proposing a quantum defense of free will.

OK, so first we should be clear that a quantum defense is a tacit admission that determinism up to quantum is reliable i.e. I assume you are not going to question my example with the coin. This gives us a perspective on the argument, because if we are deriving free will from quantum randomness or unpredictability, then what we are really saying is that free will / quantum renders an outcome theoretically uncalculable one in a trillion times. I then am forced to wonder what's the big deal

The other thing about the quantum defense is that it's possible to create a hypothesis about a being that exists outside of our universe's physical constraints and is superpotent, e.g. "god". Heisenbergian uncertainty etc would mean nothing to such a being, and he would be able to predict us as easily as the ant.

I should stress that even if one does not believe in a god this counterargument to the quantum defense does not lose its relevance. God can be treated as a theoretical being, just as Deep Blue & other chess supercomputers were until recently theoretical machines. Nothing about chess says that it is fundamentally unsolvable, only that it is very difficult and arduous to solve. Nothing about the universe says that quantum is fundamentally unknowable, only that it is fundamentally unmeasurable using physical means.

The possibility of the existence of a god (which I hope everyone acknowledges) is thus as sure a proof that the universe is deterministic as the possibility of a computer someday solving chess (universally acknowledged) is a sure proof that chess is a puzzle masquerading as a game.

We have not discovered anything that is fundamentally unknowable yet, only lots of things that we can't measure. I expect the moment someone writes an equation and then proves that it is mathematically impossible to solve it, the universe will explode in a puff of pure antilogic.

What this adds up to imo is that it is impossible to introduce theoretical uncalculability into the universe and the notion that the universe is anything BUT deterministic is DOA.

 

[mdwh]

That is not "unpredictable". Since all the ant movements are deterministic, it is by definition predictable. Mathematics (when it comes to results) disregards all that run-time analysis stuff.

Nope, that's not true - predictability, at least in the context of chaos theory, is defined as I gave earlier. Determinisim doesn't imply predictiability.

This is nothing to do with limits of our computation ability, it is a fundamental property - e.g., simple deterministic iterative equations are unpredictable, that is, as small changes to the input will completely change the output after a certain number of steps.

I'm not aware of any other mathematical meaning of "predictable".

 

[mdwh]

Right. and in our case we have full control over the inputs as well as perfect data on the state of the experiment.. thus making the whole thing 100% predictable.

The definition of predictability is nothing to do with whether we have control over the inputs, it's about what happens when those inputs change (either through our control or not).

It may be predictable in the vague layman's usage of the word - but I think it's better not to confuse the issue, and talk about it being deterministic.

The point is that the OP's usage of the word predictable (which related to chaos theory - whether he knew that or not) is not the same as your usage of the word predictable (which is a synonym for determinism). It's by conflating these different meanings that he manages to suggest that Langton's Ant has free will.

So rather than arguing word definitions, we should just say that being predictable is irrelevant, and that the fact that the Ant is deterministic is all that matters, and therefore it doesn't have free will.

 

[warpus]

So rather than arguing word definitions, we should just say that being predictable is irrelevant, and that the fact that the Ant is deterministic is all that matters, and therefore it doesn't have free will.

With this I agree fully.

 

[Fugitive Sisyphus]

I find it amusing that the same number of people who voted that Humans are deterministic voted for the "------------------------------" option.

 

[nihilistic]

Nope, that's not true - predictability, at least in the context of chaos theory, is defined as I gave earlier. Determinisim doesn't imply predictiability.

This is nothing to do with limits of our computation ability, it is a fundamental property - e.g., simple deterministic iterative equations are unpredictable, that is, as small changes to the input will completely change the output after a certain number of steps.

I'm not aware of any other mathematical meaning of "predictable".

The mathematical meaning of "predictable", or at least the classic one, is "provable". If an answer to the question can potentially be found by any means, it is "predictable". The 10^10^10^10th prime number? Predictable.

Your definition of "predictability" arguably more a scientific rather than mathematical term, as it pertains more to analog systems than discrete. "Analog", not "continuous", as continuous does imply somewhat that you have perfect knowledge. Also, what do you mean by a "small change"? Anyway, let's bring up your previous quote and examine why:

Although at first it seems that any deterministic event should be predictable, predictability is to do with how the outcome changes based on a small change in the inputs. So given that usually we can only measure things with finite accuracy, if a small error in the inputs means our results end up completely wrong, we call it "unpredictable". The classic example is weather - even if this is an entirely deterministic process, it's very hard to predict.

Read that quote again, and compare it to the scenario, and you will see that while the scenario describes a discrete situation while you presented a analog one. Specifically, the part that states "we can only measure things with finite accuracy" is kind of misleading, though true. Because, finite accuracy in a discrete (and finite) system could be infinitely accurate. 3 is an infinitely accurate representation of 3. Which means there is no "small error" in the input if we simply define "small" to be smaller than one pixel.

You have to realize that this is not predicting weather, where there are floating point representations of analog events. We have here a digital (integral) representation of finitely discrete events. The input is given in exact form and the function given explicitly.

If you claim these conditions to satisfy "unpredictability", then you must also accept that 34563567458657 * 9236402663 is is also "unpredictable" for the exact same reason.

 

[The Last Conformist]

Langton's ant i obviously deterministic. Human beings are not - QM ensures that. As for free will, I'm with Perf - I don't really grok the concept.

 

[The Last Conformist]

Your definition of "predictability" arguably more a scientific rather than mathematical term, as it pertains more to analog systems than discrete.

Well, in my experience it is how "predictability" is used in chaos theory. Applied mathematicians have to make certain concessions to pragmaticism, and if you (or your computer) can't predict something it makes pragmatic sense to call it unpredictable.

 

[nihilistic]

Well, in my experience it is how "predictability" is used in chaos theory. Applied mathematicians have to make certain concessions to pragmaticism, and if you (or your computer) can't predict something it makes pragmatic sense to call it unpredictable.

All I am saying is that with regard to this problem, there are no "concessions" to be made because we can actually model the situation exactly. Therefore, instead of chaos theory, we have dynamic programming and runtime analysis. You might want to re-read my comments above on how this is not an analog problem.

 

[mdwh]

Your definition of "predictability" arguably more a scientific rather than mathematical term

Chaos theory is a branch of mathematics.

Anyhow, my point is that there's no point in conflating word definitions - the OP appealed to one definition of predictability, and then switched to the definition of predictability being synonymous with deterministic.

You have to realize that this is not predicting weather, where there are floating point representations of analog events.

Unpredictability in chaos theory is nothing to do with limited floating point representations.

If you claim these conditions to satisfy "unpredictability", then you must also accept that 34563567458657 * 9236402663 is is also "unpredictable" for the exact same reason.

I don't see why?

The classic example is the iteration x(n+1) = a * x(n) * (1-x(n)) which exhibits chaotic behaviour for some values of a (see http://en.wikipedia.org/wiki/Logistic_map ).

 

[nihilistic]

Chaos theory is a branch of mathematics.

A different subfield thereof from computation complexity.

Unpredictability in chaos theory is nothing to do with limited floating point representations.

Yes it does. The whole point of chaos theory is to model a complex phenomenon without knowing its basic unit (or even assuming that it has a basic unit). That's why terms like "precision" have meaning in chaos theory. But this problem is not the case. In this problem we CAN actually afford to be infinitely precise about everything

I don't see why?

The classic example is the iteration x(n+1) = a * x(n) * (1-x(n)) which exhibits chaotic behaviour for some values of a (see http://en.wikipedia.org/wiki/Logistic_map ).

See, I'm not claiming that your physicist approach won't work. I agree that you can pretend you are only given limited precision and try to "approximate" with whatever you have. However, I want you to see that this problem can be modeled with infinite precision at O(n log n) time.

 

[The Last Conformist]

All I am saying is that with regard to this problem, there are no "concessions" to be made because we can actually model the situation exactly. Therefore, instead of chaos theory, we have dynamic programming and runtime analysis. You might want to re-read my comments above on how this is not an analog problem.

I didn't say chaos theory is applicable to the ant. I was just pointing out that mdwh's usage of "predictability" is conventional in that branch of maths.

Yes it does. The whole point of chaos theory is to model a complex phenomenon without knowing its basic unit (or even assuming that it has a basic unit). That's why terms like "precision" have meaning in chaos theory.

Not really - in practical applications, the limiting factor is the precision of measurements, not the number of bits in your computer representations.


Oh, and suggesting that abstract automata like Langton's ant have free will is heretical.

 

[Perfection]

Not really - in practical applications, the limiting factor is the precision of measurements, not the number of bits in your computer representations.

Well, it's often both. There's a reason you get digital camera pictures in .jpg form.

 

[nihilistic]

Not really - in practical applications, the limiting factor is the precision of measurements, not the number of bits in your computer representations.

Except here that the limiting factor you speak of does not exist. The topology is discrete. The precision is infinite.

Oh, and suggesting that abstract automata like Langton's ant have free will is heretical.

Is 'heretical' supposed to mean 'bad'? How does it have 'relevance' to the topic at hand?

 

[The Last Conformist]

Except here that the limiting factor you speak of does not exist. The topology is discrete. The precision is infinite.

Well, duh. Langton's ant is neither practical nor an application of chaos theory.

Is 'heretical' supposed to mean 'bad'?

It's supposed to mean it violates Catholic dogma.

 

[mdwh]

A different subfield thereof from computation complexity.

I don't recall the OP specifying any particular fields - the problem was, he just conflated two meanings.

See, I'm not claiming that your physicist approach won't work.

This is not a physicist approach. I thought I would try to enlighten people on how predictability is defined in chaos theory, thus shedding light on what the OP may have meant by saying it's unpredictable, and how that is different from saying it's synonymous with being deterministic.

If predictability doesn't apply to Langton's Ant, then that's all the more reason why we shouldn't be talking about the term, and instead restrict ourselves to determinism.

 

[nihilistic]

This is not a physicist approach. I thought I would try to enlighten people on how predictability is defined in chaos theory, thus shedding light on what the OP may have meant by saying it's unpredictable, and how that is different from saying it's synonymous with being deterministic.

If predictability doesn't apply to Langton's Ant, then that's all the more reason why we shouldn't be talking about the term, and instead restrict ourselves to determinism.

I'm not saying that you cannot analyze it in terms of chaos theory. What I am saying is that since it can be modeled exactly, the amount of chaos is 0. It is then therefore perfectly "predictable", which if you look up, is my original claim.

And your approach is most definitely the physicist's approach, as it is an attempt to analyze a system which is most likely deterministic at a level in which we cannot measure (yet). However, Langton's Ant is deterministic at a level where we can distinguish every detail. That's the main difference. Precision.

 

[cyxrulz]

Found a way to predict why and when the ant builds the highway !!! so its definitely deterministic

 

[cyxrulz]

Found a way to predict why and when the ant builds the highway !!! so its definitely deterministic

I want to know by proving it how is it useful that part i don't understand