The basic problem with what Roger Penrose has to say in this video is that, in both of the following cases, he is talking about a moving/ evolving system:
- The Schrödinger equation represents “how a system evolves with time”; and
- The collapse of the wave function is where the system “doesn't evolve according to the Schrödinger equation”.
But in fact, equations can’t ever represent a moving/ evolving system. Physicists, including Roger Penrose, ASSUME number movement but their equations actually only represent relationships between categories.
Any set of equations, even equations with delta symbols like the equations that represent the law of nature relationships that physicists have found, can’t ever represent a moving system. A moving world, like the universe we live in, can only be represented algorithmically, i.e. using the type of logical connective symbols used in computer programs, as well as the usual equations.
What logical connective symbols can represent is:
- Using the symbols AND, OR and IS TRUE, logical connective symbols represent knowledge of the current numbers that apply to particular categories of information, i.e. they represent conscious knowledge of the current information situation;
- Using the symbols IF… and THEN… , logical connective symbols represent non-law-of-nature action taken (i.e. assigning new numbers to particular categories if information) in response to knowledge of the current information situation.
Logical connective symbols represent the aspects of the world that are necessary if you want to have a moving system. Basically, the above-described logical connective symbols represent consciousness and free will. If you didn’t have consciousness and free will, or something very much like them, you couldn’t have a moving system.