> If I smashed your hand with a hammer, do you think I could reliably predict you will feel pain? Of course you will.

In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer. The halting problem is an example: it can be proven that there is no algorithm that correctly determines whether arbitrary programs eventually halt when run. [1]

You are predicting my state in advance of it having been achieved. I'm fully capable of intentionally disrupting your prediction, for example, by drugging the nerves in my arms such that they cannot send signals to my brain. Your claim of knowledge is a false claim and I deny it.

This is not a pedantic point. It relates directly to the concept of computationally irreducible systems [2][3][4]. These processes create the condition for non-deterministic outcomes as a consequence of deterministic systems. We then have to ask: since it is possible, should it actually be that way? Which leads to research on optimal solving of games under imperfect information. Nash has shown optimal mixed/impure strategies [5][6][7][8].

> If everything can be explained by a physical processes, then it seems like if you had perfect knowledge about the current state, then you could predict the next, and if you can predict one state...

This is false. Even if you know the deterministic rules of a system it is not the case that you can predict the state of that system [1][2][3][4][5][6][7][8].

> I feel like freewill is a made up idea entirely and while we might have the experience of free will, the reality is different.

Humans seem to struggle with thinking about this for several reasons, but two important ones are that logic breaks down under self-reference and humans are cooperative with each other [9]. The first is a problem because most of our tradition of debate descends from argumentative traditions descending from Aristotle which is logical tradition of debate [10]. The second is a problem because cooperative agents tend to make themselves predictable. They make themselves stand out from "the world" rather than appearing as if "of the world". This is not actually generally the case, but because we have exceptionally capable senses we don't always realize what the actual decision problems really look like and how nice we have it due to our cooperative tendencies. For a more representative example try to spot the predators in the two cited images which pursue the "of the world" competitive equilibrium [11][12].

[1]: https://en.wikipedia.org/wiki/Undecidable_problem

[2]: https://mathworld.wolfram.com/ComputationalIrreducibility.ht...

[3]: https://www.reddit.com/r/philosophy/comments/4lbck4/computat...

[4]: https://www.wolframscience.com/nks/p750--the-phenomenon-of-f...

[5]: https://en.wikipedia.org/wiki/Strategy_(game_theory)

[6]: https://en.wikipedia.org/wiki/John_Forbes_Nash_Jr.

[7]: https://en.wikipedia.org/wiki/Nash_equilibrium

[8]: https://en.wikipedia.org/wiki/Strategy_(game_theory)#Mixed_s...

[9]: https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...

[10]: https://plato.stanford.edu/entries/aristotle-logic/

[11]: https://www.boredpanda.com/blog/wp-content/uploads/2017/04/s...

[12]: https://www.researchgate.net/profile/Michael-Kuba-2/publicat...