Ask HN: Is Freewill a Requirement of Consciousness?

Another attempt at dumbing it down:

We sometimes don't know what will happen until it does. The best we can do is to make a guess. Sometimes this guess will be very often good, but it is still a guess and we need to be open to the idea that our guess was wrong in some aspects.

Suppose we could have a perfect guess though.

We can use the guess to figure out what would happen and it would always work. Okay, lets use it to determine what happens in the future in which we use it to determine what happens. Do you see the issue here? The guess references itself. So it can't predict the future in advance of it. There comes a point where it is looping and giving you the leading edge of what is knowable given the amount of time that has passed so far.

So we don't have the perfect guess, even when we have the perfect guess. We don't know what will happen before it happens, even if we know the rules that tell us what happens before they happen.

There are a bunch of wierd things that get implied by the math that is consequent to this, especially when you get into transpositional structures, but it isn't silly so much as it is non-sensory.

I mean, it does sound laughable. When Feynman said we guess when we do science and then validate the guesses with experiments people did laugh. Yet this is not because it is silly. It is because the non-sensory cases we can't differentiate from can only be differentiated from the sensory cases via the experiment.

What often happens though is that directly after the moment people pretend that it was all known before hand. It is a tricky moment, the present.

For some calculations you can make them simpler and do them faster, but for other calculations you can't. When two things that try to predict things by making things simpler apply themselves to predicting each other... well.

In order to think about this sensibly you have to think through the consequences of the infinite self-reference. Logic fails here. So does evidence. For example if you observe that your opponent is playing badly, modeling them as a bad player doesn't work, because if you choose to do this, they could exploit the bad model by playing better than that model would predict. So even though the evidence suggests that they are a bad player, the self-reference considerations forces you away from acting as if they actually are.

So lets say you play rock? They play paper. Lets say you play scissors? They play rock. Lets say you play paper. They play scissors.

Lets say you fully determine everything they are going to do using your complete knowledge of physics and you play rock because your model told you that they would play scissors... They will play paper; obviously.

Lets say you anticipate that and you play scissors. Then they play rock. As long as you claim that you can figure everything out, it means they could figure everything out. The harder you push against this, the harder it pushes back. You have to move with the force, diverting it, not fight against it. You've got to take advantage of the inevitability of being unable to overpower, not try to overpower. You have to act as if you can do everything at once, because the undecidability allows you to do so. Not try to determine everything, because if you try to, then you can't, because others try to do the same thing.

> It sounds like your assertion is more that a system cannot be deterministic because the complete state is not knowable and without the complete state of a system, there is no way for it to be deterministic because state form outside of it will influence it?

Not quite.

The choice of perfect knowledge of state is irrelevant. Even with perfect knowledge you can't, for example, predict the thought you think next. If you did, you didn't predict it, you experienced it, because the very act of predicting it was the act of thinking it.

There are leading edges to the computation. It is a hindsight bias upon thinking them to think they were predictable.

> I definitely think there is probably a contradiction between perfect knowledge and self reference, thus it is impossible to have perfect knowledge of a system from within the system.

This is a lot closer to what I'm actually trying to say. Critically, that leading edge of information is a barrier that is very important and agents can use it to cause other agents to be unable to predict what will happen before they experience it.

> I don't think I understand why game theory is relevant

The reason it becomes relevant is because of optimal decision structure. From the math of game theory we learn that the optimal structure of an agent's decision making isn't to play rock or to play paper or to play scissors. If you choose any of these then an argument from the equilibrium considerations - which is basically an argument from the consequences of self-reference - shows the choice is exploitable. So in game theory we don't select rock and we don't select paper and we don't select scissors. Instead we select a probability vector over those choices.

Basically it turns out that when things become unknowable the appropriate response is to change the level of abstraction over which actions are taken.

Your consideration about the limits is somewhat aligned with how I think about things, but I think you need to take one further step before things will snap into clarity and the entire discussion will become dissolved.

You have a world state in your mental model of the Turing Machine state, right? That is why you talk about a specific Turing Machine as if you could look at it from outside it. What do you think you get when you pause, not from within the Turing Machine, but in the space of Turing Machines implied by your observation so far?

How many programs do you think I could write which would output "Hello" midway through the computation? One? Two? Could I suggest to you that there are an infinite number of such potential programs? The observation space corresponds with a sort of superposition of potential world states.

It is worse than that though. Your observation space? It contains more statements as more computation takes place. Eventually it has to be abstracted or it isn't computationally reducible. So there are actually more than one observation per information state. When you think about things from within the universe, even though chair is atoms, you are better off having the superposition of chair being highly variable. It corresponds to many different things.

So when you are entering decision problems you are in actuality in multiple potential universes, in multiple potential observation spaces, and you can't even tell one way or another except by expanding the computation.