(This post contains some thought about gACI)


What does it mean that I have free will? If we can define free will like this: 

If in a deterministic universe, no observer B can 100% correctly predict the behavior of subject A, except when B is in the future of A, we can say that subject A has free will. 

We can prove that free will does exist in a universe where light speed is not infinite, even when we don’t consider quantum randomness. Here is the proof:

In a deterministic universe, the information of an event A (or in other words the behavior of a subject A) can be completely known, only if its prior states (or its causes) are completely known.

In a universe where light speed is not infinite, all the causes of an event A, lies on or inside its past light cone. If you don’t know all the causes of the event A, there will always be some uncertainty about A.


Light cone of event A

According to this picture, we can see that only observer B3 is able to know all the prior states of event A, because B3 is in the future of A. It’s impossible for B1 and B2 to know, for example, event C which may affect event A. Because C is not inside or on their past light cone.

For example, when you are chatting with your friend, you will never be able to anticipate that there might be a gamma ray photon hit their brain neurons from the far side of you and unpredictably change their mind.

(Some people may argue that there’s no free will in the presence of an all-knowing God. But that’s another story.)

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16 comments, sorted by Click to highlight new comments since: Today at 4:30 PM

This is fine as far as it goes, but you've redefined free will away from what most people mean by it, which is basically the same thing as saying free will doesn't exist (because libertarian free will seems very unlikely to exist), so the title seems misleading.

Sorry for the misleading, but I also believe that libertarian free will is not an illusion. I hope I can explain that in the next post on this topic.

(Maybe I should add a "(1)" behind the title?)

I agree with Gordon: I don't think that free will is unpredictability per se.

Determinism needs to be distinguished from predictability. A universe that unfolds deterministically is a universe that can be predicted by an omniscient being which can both capture a snapshot of all the causally relevant events, and have a perfect knowledge of the laws of physics.

The existence of such a predictor, known as a Laplace's demon is not a prerequisite for the actual existence of determinism, it is just a way of explaining the concept. It is not contradictory to assert that the universe is deterministic but unpredictable. But there is a relationship between determinism and predictability: predictability is the main evidence for determinism. Nonetheless, determinism itself is the crux, and predictability only features indirectly as evidence for it.


Just to clarify my position, I think that the intuitive sense of free will people feel is caused by an inability to predict future states of the world from a subjective state of limited information. My objection in the other comment is to claiming that free will exists when the content of the post is explaining why it doesn't exist in a form most people would intuitively judge to be free will rather than an explaining away of free will.

In the post I was just trying to describe the internal unpredictability in a deterministic universe, so I think I have already made a distinction between predictability and determinism. The main disagreement between us is that which one is more related to free will. Thank you for pointing out this, I will focus on this topic in the next post.

I second this. In my comment this is why I wanted to ask more about what's meant by "observer" in the definition.  An individual mind/perspective (regardless of computational power) being able to predict action is different than "predictability" by theoretical simulations of the universe. 

That said, if we do define free will as predictability by a fellow human observer, then we could absolutely have free will of that type. We don't even really need proof of that, we can just observe the plethora of evidence that people do not often perfectly predict each others actions. 

Note that according to both QM and GR you don't need to know "all causes", only the initial state on a given spatial hypersurface, in order to be able to do a Cauchy development of that hypersurface, subject to some rather technical and non-restrictive energy conditions. Whether the initial state can be known exactly depends a fair bit on what one wants to calculate (e.g. a full quantum state, or a classical state). In that sense, one can, at least in theory, predict the behavior of a physical object, including a human, to a high degree of accuracy, though of course never 100%, and the remainder is not related to light cones, just to the uncertainty of one's state, especially the quantum state. 

Still, if another human can predict your actions with high accuracy, though not 100%, how much free will do you really have? 0.1%? Would you be happy with that?

You are right, I should use "all initial state on a given spatial hypersurface" instead of "all causes", but the conclusion is the same: wherever the hypersurface is, no observer is able to know all the initial state on that hypersurface which can affect event A, except when the observer is in the future of A. 

The second question, I think that "high accuracy" is only the upper limit of a prediction, which is not that easy to reach. In oder to make high accuracy prediction, you need a large amount of resources for observations and calculations. The amount of resources can be some kind of measurement of my free will. However, if I have access to that resources, I can make myself much more difficult to predict, e.g. some optical or electric camouflage.

Seems like you are in love with your conclusion and are throwing all supporting evidence into it, which works in a court of law, but not when you are trying to construct accurate models.

Thank you for your comment, but it would be appreciated if you could prove my conclusion is wrong (e.g. either observer B1 or B2 is able to know or predict event C)

The picture is of a flat space. Weird topologies might break the proof.

You are right, this picture only works in an infinite universe.

If in a deterministic universe, no observer B can 100% correctly predict the behavior of subject A, except when B is in the future of A, we can say that subject A has free will. 

This strikes me as a very unintuitive definition of free will.

We often talk about free will experientially; defining it based on a specific external observer strikes me as odd. But before I critique that in any way, I'd love more clarification on what you mean by "observer." Is this anything capable of prediction (e.g. a faithful simulation of the universe)? 

But more importantly, I think "100% correctly" is doing the bulk of the work here. I fully agree with your claim that if we define free will in a manner similar to this, we will never reach it. But really, very little outside of statements within self-contained axiomatic systems can ever be held to the standard of 100% certainty. If your concept of free will hinges on the realistically minuscule chance that a random event will alter your decisions substantively, then I ask if this conception still resembles anything like the idea of "free will" as we tend to think of it. 

Overall, I concede your claim follows from your definition. But I question the usefulness of such a definition in the first place. I think we can all agree that we cannot have 100% predictive certainty. The question is more whether or not we want to call that shred of uncertainty "free will." Semantically, I think it's confusing to call this "free will" when that is not usually the intended meaning of the phrase, but ultimately the decision is somewhat arbitrary as our experience remains the same regardless. 

Thank you for your comment. Actually I am trying to build a practical and quantitative model of free will instead of just say free will is or is not an illusion, but I can't find a better way to define free will in a practical way. That's why I introduce an "observer" which can make prediction.

And I agree with you,  claims like "not 100% correctly" are too weak. But possibly we can define some functions like "degree of free will", representing how much one subject could be predicted or controlled. I'm not sure if this definition resembles the common meaning of "free will", but it might be somewhat useful.

I do like the idea of coming up with a good way to quantify the degree of deterministic free will. While it's not necessarily a useful concept in terms of actionability, when did that ever stop curiosity? I think we can fairly reasonably estimate that this degree of free will is very very low.

In response to defining types of free will, I'd personally propose "experiential free will" and "deterministic free will." The former refers to the more common usage. When someone says "I have free will" outside of a rigorous philosophical debate, they usually mean "I experience life in such a way that I feel I can make at least some conscious choices about what actions to take." This is pretty hard to dispute. People do tend to feel this way. This definition of free will may well be an illusion, but that illusion is very much experientially real and worth discussing. It seems like "deterministic free will" might be a better term for what you're talking about. The idea that free will is a spectrum where the higher the certainty with which your actions can be predicted, the less free will you have. 

I want to define "degree of free will" like:  for a given observer B, what is the lower limit of event A's unpredictability. This observer does not have to be human, it can be an intelligence agent with infinite computing ability. It just does not have enough information to make prediction. The degree of free will could be very low for an event very close to the observer, but unable to ignore when controlling a mars rover. I don't know if anybody has ever described this quantity (like the opposite of Markov Blanket?), if you know please tell me.

I like your distinction between "experiential free will" and "deterministic free will". As for "experiential free will", maybe we can focus more on the definition of "reality" and "illusion". (I am still working on it)