Bob said : it seems unlikely we would be able to mathematically predict behavior.
I agree, to an extent. Don't forget, research on hardwired brain function is still in its infancy. But as Stuart Hameroff demonstrated we can certainly induce specific behavior mathematically (electronically) and Anil Seth demonstrates how easy it is to fool the brain into believing something that isn't there and vice versa allowing the brain to "learn" an obscured mathematical sound pattern instantaneously .
Descartes “brain in a vat”. Hook up the brain to a computer and it won’t know the difference between reality and program.
The fake arm experiment clearly demonstrates how the brain can be made to believe the fake arm is part of the body. IMO, that is a remarkable phenomenon, demonstrating that the brain forms its own conscious “expectations” of reality, independent of will.
Disconnect the brain from our senses and it will create it’s own reality. A certain length of time in a sensory deprivation chamber will result in a completely abstract hallucinatory experience. (madness).