Let me illustrate with an example. Are you familiar with with the Collatz conjecture? It's an example of a system with only one variable, and two simple rules. Are you certain that there exists a computer program that in finite time can compute where any given integer ends up?

Now consider throwing a ball in the air. Can you even write down the rules that each of the ball's subatomic particles obeys? How can you be certain there exists a computer program that in finite time can predict where any of the particles, for any ball, ends up?

> the chemistry of the brain is very well modeled

There are models, but the fact of those models is that they do not apply to "any degree of accuracy", as you claim.

Consider the ball thrown in the air again. Is the ball affected by what happened 100 years ago, inside of a black hole 100 light years away? Why would it not be affected by that? Or if you grant that it is affected by that, do we then need a model to predict those effects before we can "evaluate" them?

EDIT regarding the below linked blog post: Did you read the rest of my comment? Did you even read the blog post you linked to?

> We certainly don’t have anything close to a complete understanding of how the basic laws actually play out in the real world — we don’t understand high-temperature superconductivity, or for that matter human consciousness

Can you try to consider my central point before replying: Are the rules governing physical reality simpler or more complex than the Collatz conjecture? Does there exist a (theoretical) computer that can "evaluate the Collatz conjecture to any degree of accuracy"?

EDIT 2: I'm not the one moving goalposts. On what grounds are you classifying the question whether a given number ends at 1 or not for the Collaz conjecture as an "inifite" computation? It's a simple boolean question, yes or no. All you have to do is build a computer that can answer yes or no for each integer. Isn't that simpler than answering the position of each atom in the ball after the throw? Each is just a function, what makes one more infinite than the other?

Also, regarding determinism, just read this article by the same guy you linked: https://preposterousuniverse.com/blog/2011/12/05/on-determin...

> For everyday-life purposes, we can’t get around the fact that quantum mechanics makes it impossible to predict the future robustly.