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You know, the one really interesting dynamic domain is chaotic, which is a subdomain of the deterministic! I figure free will is a chaotic phenomenon.

Groundhog day is your intuition pump here. Go back in time and most assume that the day will go mostly the same, except for the butterfly effect if you change something. Given exactly the same conditions (we went back in time, so that's pretty exact), people will make the same decisions.

Most people don't assume that the day will be completely different the next time loop. The town won't suddenly spontaneously all start breakdancing or standing on their heads.

(Edit: The murderer is the one who -given the same/similar conditions- will murder again. I'd politely suggest maybe we put them behind bars as a precaution against that; until/unless they learn to act differently. )

(Edit 2: Throw in stochasticity and this actually tends to smooth out chaotic systems. This is counter-intuitive! People's brains break on Evolution in the same way. Meanwhile somehow folks intuit birdshot without difficulty; which is weird!)

To extend on your edit #1: And, when you go back in time, delete all punishment for murder and see whether you get the same number of murderers.

If you get more than before, the punishment might make some sense in a deterministic world so reinstate it.

And it probably does, right? Punishment adds a negative bias to the payoff matrix. Funny side note: increasing punishment severity past a certain point actually saturates and doesn't alter the dynamics further. (which is why modern judicial punishment schedules sometimes seem so mild)

Eh, sorry chaos theory doesn't work this way.

It's just as likely you go back and perform whatever magic you need to to delete punishment for murder, then zip back to 'now' and see the world is a global panopticon making sure people don't murder each other.

Some of this may be a failure of people to realize what P !=NP is about, especially in non-linear systems.

Small perturbations in an early state of the system can lead to wildly different outcomes in the final measured state of the system. You can't determine what that will be in non-polynomial time. The only thing you can do is make probabilistic models by running a full simulation in real time (or reality with a time machine I guess).

If you look at chaos in dynamical systems, you can often find some equilibria (like attractors, spirals, saddle points etc ) at least, even if the details might vary. This is how people still manage to predict the weather somewhat, for instance. Oddly orbital mechanics is chaotic too, but it sort of rhymes over the millennia.

Your correct. You'd have to run the universe simulation a bunch and pick the most probable outcomes (which makes you the most brutal serial killer in existence). The probability graph would represent the state stability of the underlying structures that guide what you're trying to measure.

In weather you have things that are chaotic, but follow rules and don't create them. Things can surprise you, but you'll mostly center around particular solutions.

With humans this gets a lot more complicated because you are messing with systems that follow fixed rulesets (chemistry) and things that follow self modifying rulesets (social conventions). A very unstable system on top of a semi-chaotic probability state.

A good example of this would be if I deleted the concept of rain from the human mind and all of human history and knowledge. Humanity would be very surprised on the thunderstorms that popped up, but they'd continue on just as they did before.

Now lets imagine I delete the concept of all gods. Would the idea of gods come back, for sure. Would they look like our gods now. Very questionable indeed. We wouldn't be getting jesus back. And the new set of religions could have wildly large effects on how the people act.

I think this debate is rooted in our instinctual beliefs about fairness. An organism in a social group needs to decide how to react to the brutish behavior of its peers. And so Mother Nature has encoded a good strategy in our brains. (For example, dogs seem to understand fairness.)

But this only means the strategy is practical - it doesn't mean it's consistent. I think "responsibility" falls into this category. So we have strong intuitions about it that don't quite logically work. And this is where free will and determinism and choice and punishment all crash together.

>you can't hold the person responsible

The act of holding them responsible is supposed to determine them not do it. If stochastic behavior is impeding them in being a functional member of society then it still makes sense to remove them from society, why would you choose to live amongst people who are not behaving rationally? Or allow them to hurt other people? At the end of the day the why matters less to removing them or not from society. And sentences are clearly used as a determining factor.

The holding responsible part deals with politics and more primitive aspects of our societies and biologies. Getting tangled up in holding them responsible or not is hardly something you should give much attention to. Rather to make sure they do not cause any more harm and also make sure such things are not created in the first place. Which opens up another can of worms for which society and politicians are ready for.