A random walk from the origin in 2D will go back to the origin infinite time in expectation. It is not true in 3D where the expected number of returns is a constant. (Both can be proved by Markov Chains) So if we assume all objects are 100% reflective, everything will be super bright? (not sure whether it might be one of the reasons why we don't encounter aliens in a 3D world?)
A random walk from the origin in 2D will go back to the origin infinite time in expectation. It is not true in 3D where the expected number of returns is a constant. (Both can be proved by Markov Chains) So if we assume all objects are 100% reflective, everything will be super bright? (not sure whether it might be one of the reasons why we don't encounter aliens in a 3D world?)
evil cow