Well, you need to be able to simulate what happens in the problem domain in order to arrive at a conclusion. There isn't really any other feasible option. Thi

Well, you need to be able to simulate what happens in the problem domain in order to arrive at a conclusion. There isn't really any other feasible option. This is what humans do, we visualize and predict the outcome of actions within a system. And if our imagination is not enough, we can outsource the reasoning to the outside world, by doing experiments or using tools like geometry etc. (drawing in the sand, drawing on paper). It is impossible to arrive at a conclusion without "doing the work", unless you've seen the result before and can recite it. Therefore, you need to be able to model the problem domain in order to solve the problem.