For 1: I didn't mean to imply anything about the work being easy or hard, by the way. I was just contrasting against the difficulty of proving BQP=BPP. (e.g. I

For 1: I didn't mean to imply anything about the work being easy or hard, by the way. I was just contrasting against the difficulty of proving BQP=BPP. (e.g. I might refer to Terence Tao's work on Navier-Stokes [1] as 'solving an easier version', but certainly no connotation about the difficulty of the work would be intended). But I do think you should avoid making such large claims based on what was actually done. It comes off as naive; unaware of how much work has gone into trying to make these things work. Of course people have tried hierarchical models! For 2: You're still confusing "I have an efficient deterministic algorithm to make predictions about X" with "X must be deterministic". The efficiency of the algorithm is totally independent of whether or not the other system is "really" random or not! Some random processes are downright trivial to make predictions about, even with really truly literally random inputs. And some are arbitrarily hard to predict, even when we replace the randomness with a cryptographic pseudo-random number generator (but don't tell you the seed). Consider that we already have deterministic algorithms that predict quantum mechanics. The fact that the algorithms take a long time to run has little bearing on the predictions they make. Finding a more efficient algorithm for quantum won't turn it into a deterministic process. You'll still be able to pass Bell tests, and the algorithm had better predict that too or its demonstrably wrong! 1: https://terrytao.wordpress.com/2014/02/04/finite-time-blowup-for-an-averaged-three-dimensional-navier-stokes-equation/ https://terrytao.wordpress.com/2014/02/04/finite-time-blowup...