I find the intuitive ideas in the paper very stimulating, but they may be false. The paper use a concept "conditional independence" as a way to measure how information flow when applying an algorithm. Visually, you can think any step of your algorithm is a move in a certain graph. You can not visit all solutions, since there are a exponential number of them and they are not related. So is a lovely intuition, but maybe false. If if turns out to be true, I will devote more time to read the paper. In particular, I would like to believe that there exists such a visual representation of any algorithm, as a trajectory in a graph. The comments in that page are stimulating since they open many ideas to explore. Perhaps someone with a lot of time and energy can introduce the appropriate concepts, as we all know, first step seems easy but then all get very complex, so I imagine there is a lot of work for the author in the future.