Thank you.
We don't. God knows exactly what we will do in every circumstance, without fail. This does not change the fact that we were designed with the capacity to choose according to our own tattered will, within our constraints (personality, sinfulness, circumstances). That was what I was trying to get across with the analogy.
Ultimately, all our thinking fails to fully fathom the dichotomy of God's sovereignty and man's freedom to choose. But we do our best to understand as much as we can.
Maybe I should have stated the analogy differently. Perhaps this will clear what I was trying to say up:
Let us say that the line has a purpose in moving through the 3 dimensional space... say it is trying to reach a certain point in that space. Instead of changing directions randomly, let us say that he designed the line to be an AI, so it can choose the best route to reach that point, only under the constraint that it must change directions to some degree at each point. Let us further state that the line is able to select for itself which point it wants to get to (even if the programmer wants it to reach another point), and how best to get there. So even though the programmer knows what the line will do, it does not change the fact that he designed the line with the capacity to select it's own course.
We could add layers of complexity into the analogy (such as opposing forces, other lines, the programmer interacting with the lines, etc.), in order to make it more accurately reflect reality... but I'm trying to keep the analogy as concise as possible in order to reveal a simple reality: God designing us with the capacity to choose. The programmer represents God, who designed the universe and everything (and everyone) in it, and knows the actions each being will take from the foundation of the universe. Yet God designed us, like the line, with the ability to set our own goals, and reach those goals in a way which seems best to us. Of course God can and does intervene in His universe in order to achieve His purposes (Pharaoh, Paul, etc.), but for the most part He achieves His purposes through and around our choices. This is the genius of God, designing beings who can act contrary to His will, yet still accomplishing His will around and through the choices of broken, sinful creatures.
Thank you for taking the time to read it. God bless you as well!