The author makes statements with qualification of "almost all" even though "almost all" physically allowed systems (that is, solutions to the PDEs under question) are not physically relevant or beneficial. I can only see this applying to chaotic systems like the weather, which is a valid point. The key argument that finite volume contains finite information seems potentially true but suspect. Case in point, take a unit square, it will have a diagonal who's digits have a long "infinite" string of digits but sqrt(2) isn't "infinite information", it's very finite (ie., one number!)
This desperately needs to be peer reviewed by people who study the foundations of physics.
This desperately needs to be peer reviewed by people who study the foundations of physics.