That is irrelevant. Landton’s Ant is based on a board with random white and black squares. I gave you the most stripped example derived from it: all squares are white (or black, same result). It doesn’t matter what the landing position is since they’re all the same. And with all known rules, including your starting position, since all starting positions are the same, you can’t predict what will happen.
See? This is why you’re not getting it. All of these problems are solvable. None of these problems are predictable. Chaos theory isn’t about unsolvable systems. It’s about unpredictable ones.
So, to further the point:
With the previously stripped down Ant problem, which, I remind you, we could never predict from the start but which we already know the outcome of, let’s introduce a single new rule change:
1-Squares still turn black and white
2-Instead of turning left and right you now go forward on a black square and back on a white square.
Can you predict the outcome? After all, you know all the variables, you know the initial position (which, I remind you again, since they’re all white, means any square is the same) and you even know the outcome of the previous system.
You can make a computer to simulate the outcome, but you have no way of knowing what the end result will be.
So, to circle back to the original point: if a system as simple and barebones as this is unpredictable, what do you think the result is of introducing a single unique item to a system like LE or PoE? Can you predict all the outcome? Or are you only able to predict some of the outcomes and several others are unpredictable?
Which means that, in order to fully make sure that there are no surprises, you have to test for every single one.
Or you just accept that that is an impossible task and simply test for the expected outcomes and know that a lot of unpexpected ones will come up that you will have to deal with.
Not for mathematics. You can’t prove P/NP, but you can prove that the Polya conjecture is false (thus doesn’t exist) and that the Poincare conjecture is true (thus exists). And since Chaos Theory is a mathematical field, your logic doesn’t apply here.
That is irrelevant, though. The whole point of it is that a 2 body problem, mathematically, is completely predictable when you know all the variables. It always has been. Whereas a 3 body problem, mathematically, is an unpredictable one.
It doesn’t matter if you can never find those exact conditions in the world. The whole point of the field is to study the emergence of complexity out of deterministic systems and try to identify underlying patterns in it.