If universe is deterministic and computable, then it is possible to create a simulation of a part of the universe that would be complex enough to contain humans and would be simple enough to pause computation, make changes to the state, copy the state, etc. So for simplicity i will talk about this simulated universe.

Separable here roughly means that to compute further states of a human you need to follow only particles in that human and not deal with variables describing the whole universe.

You can recompute exact same universe with exact same human, but it will give you the same result. Recomputing with different human shows that different choice was possible in principle.

In the simulation we can perfectly predict what the human will do, but if computational irreducibility conjecture is true there is only one algorithm to make that prediction, which is running the simulation itself. And because running the simulation is equivalent to letting the simulated human to live that means we do not predict, but merely observe the choice.

This is not exactly what everyone thinks when talking about free will, but this is a close enough equivalent that can exist in a computable universe, because multiple choices are available, and the choice is made by the part of the universe representing the human.

> If universe is deterministic and computable, then it is possible to create a simulation of a part of the universe that would be complex enough to contain humans and would be simple enough to pause computation, make changes to the state, copy the state, etc. So for simplicity i will talk about this simulated universe.

I don't see how the 'computable' part is relevant in regards to free will. You can write a program that outputs random numbers that it reads from some source, and you can simulate it by writing another program that outputs random numbers from the same source. The two equivalent programs will generate different numbers, but that doesn't mean they had any choice over the numbers they printed.

> Recomputing with different human shows that different choice was possible in principle.

Recomputing with different human is equivalent to creating an impossible universe. It's impossible to have two different people in the exact same situation at the same point in time in the same deterministic universe. The very action of pausing or modifying the universe from without would make the universe non-deterministic.

> And because running the simulation is equivalent to letting the simulated human to live that means we do not predict, but merely observe the choice.

Who's choice? If the algorithm is making the choice then the humans simulated by such an algorithm would not have any more free will than a video game NPC.

Using random numbers affects the condition about determinism not computability. If universe is not deterministic then the choice made does not depend only on the human making choice but also on the state of generator that creates random numbers. Of course even here it is possible that the state of human is organized in such a way to change probability distribution to not depend on randomness, but that becomes equivalent to deterministic universe with additional complications.

The computability is relevant to the argument because it allows us to create simulation, and to observe a universe from outside. If it was not computable, say required real numbers with infinite precision, and the finite approximations were not able to describe complex things such as humans, then we would not be able to complete our thought experiment.

> The very action of pausing or modifying the universe from without would make the universe non-deterministic.

There are two parts, the starting state and the evolution rule. Here the evolution rule is still deterministic, and the requirement is for it to be able to continue from different starting states.

> Who's choice? If the algorithm is making the choice then the humans simulated by such an algorithm would not have any more free will than a video game NPC.

If human is a part of universe, and does not have a soul, then he is equivalent to its starting state plus the algorithm. If the computation cannot be reduced to a simpler algorithm then no matter how you compute the future state you get that human thinking, feeling and making a choice. The difference with game NPC is that the algorithm doesn't have a hardcoded set of inputs and outcomes but can accept any inputs and produce outcomes that can't be predicted by anything other than that algorithm with that starting state.

> If the computation cannot be reduced to a simpler algorithm then no matter how you compute the future state you get that human thinking, feeling and making a choice.

What's the difference between the human thinking, feeling, making a choice and a trained neural network making a 'choice'? I would not say a neural network has free will.

> The difference with game NPC is that the algorithm doesn't have a hardcoded set of inputs and outcomes but can accept any inputs and produce outcomes that can't be predicted by anything other than that algorithm with that starting state.

You can have a program that could accept any inputs (say any binary sequence) and produce output based on that.

I think that if the universe is deterministic and computable then that implies no free will, since humans are part of the universe and therefore also deterministic and computable.

The difference is most likely the organization and the complexity of a network. Neural network doesn't have free will because it is too simple and can't even pass turing test.

> I think that if the universe is deterministic and computable then that implies no free will, since humans are part of the universe and therefore also deterministic and computable.

I agree that universe being deterministic and computable means that humans are deterministic and computable.

But what is the evidence for "deterministic and computable" implying "no free will"?

I think that computational irreducibility allows the exact opposite interpretation. Humans are deterministic and computable but the process of computation is equivalent to humans living, no matter what is used to perform the computation (moving atoms in the original universe, a computer program, or even many people with pen and paper).

So even if you can compute what the human will do, you can't predict, because the act of computing is the same as human doing. This provides the "will" part of the free will.

And if you do not stop the algorithm, and change the state to get a different outcome, then it is also free.

As a side-note, this interpretation is surprisingly consistent with the original formulation of the question of free will in religious setting, where some being outside the universe knows everything about the universe, can arbitrarily manipulate the state of the universe, but can't predict what the creatures in the universe are going to do and claims that they are free to chose.

> The difference is most likely the organization and the complexity of a network. Neural network doesn't have free will because it is too simple and can't even pass turing test.

I don't see what the Turing test has to do with free will, but it has been beaten multiple times already.

> But what is the evidence for "deterministic and computable" implying "no free will"?

Deterministic and computable universe would mean the entire existence of a human would be deterministically determined by the point in space and time he was born. If you re-ran the simulation from before the person was born to their death, the universe would progress through the exact same states.

> So even if you can compute what the human will do, you can't predict, because the act of computing is the same as human doing.

That's like saying if you ran a random program without knowing it's source code you could not predict what it would do until you actually ran it. I don't see what that has to do with free will. In a simulation free will would be the ability to change your choices between runs of the exact same universe.

>>> What's the difference between the human thinking, feeling, making a choice and a trained neural network making a 'choice'? I would not say a neural network has free will.

>> The difference is most likely the organization and the complexity of a network. Neural network doesn't have free will because it is too simple and can't even pass turing test.

> I don't see what the Turing test has to do with free will, but it has been beaten multiple times already.

my point was that neural network doesn't have free will, because it is too simple and cannot be regarded as a person, Turing test is one objective way to check if a program is capable of thinking. The wikipedia page on Turing test https://en.wikipedia.org/wiki/Turing_test is not aware of any of the times when it was beaten.

> If you re-ran the simulation from before the person was born to their death, the universe would progress through the exact same states.

sure, it would be like a time machine.

> In a simulation free will would be the ability to change your choices between runs of the exact same universe.

that would not be a free will, that would be an absence of will, because if nothing changes why would person's reaction change?