as an aside:
Both the circle and the square are purely imaginary constructs as they do not exist in reality as with any human geometry that fails to take in the "organic" nature of reality.
Straight lines do not exist either except in our imaginations.
Perhaps
Sarkus, your fascination with circles and squares needs to be upgraded somewhat?
No, it doesn't, QQ. The "square circle" is simply an analogy to your assertion that the indeterministic system can exist within the deterministic universe. It is sufficient for them (the square and the circle) to be mere imaginary constructs for them to hold up as the analogy.
So trying to rebut the analogy because those things don't match anything in reality isn't going to work. You have to rebut the principle of the analogy, not claim an irrelevancy about it.
Strict determinism requires "straight lines" of causality to effect and these "straight lines" do not exist in reality. (Even space is curved)
Equivocation, QQ. You are mixing (deliberately or otherwise) the geometric notion of "straight line" with one step following another.
Theoretically there is no mechanism demonstrated or even explained to support the idea of strict determinism.
Except mathematics, perhaps?
Except the computer system you are using, perhaps?
The determinism acting upon the thrower in the "1000 dice" solution is unable to be even rudimentarilly explained in the immediate time frame, let alone in a way that accommodates 14 billion years of evolution.
Irrelevant. The notion of determinism doesn't require actual practical knowledge of the initial state, nor actual calculation of subsequent states. You are confusing the notions with what is practically possible.
Essentially you have an infinite variable ( cause) throwing an infinite variable (effect) therefore infinitely unpredictable. (thus indeterminate)
In a system that adds one to the initial number to arrive at the output, for example, then there are an infinite numbers we can choose from... but if we know what the initial number is then we know what the output number is. That is the point of a deterministic system: if we know the input, and know the system, we know the output. We don't need know it on a practical level but it is enough that
if we know the inputs and
if we know the nature of the system (i.e. how things interact)
then we know the output, not just the immediate output but every subsequent output.