Just watched Normal Again --- brilliant television. It made me wonder, if I was faced with two competing realities each claiming that the other is my delusion, how could I determine which one is real?
Here's an idea. Make up a very large number and ask one's friends in each world to factorize it in a reasonably short amount of time. You can check the answers manually via simple arithmetic. The inhabitants of the real world have access to computers and will be able to give a correct answer. The inhabitants of the imaginary world will not. (I'm making some reasonable assumptions, e.g. that my mental illness does not grant superhuman cognitive abilities or force me to cheat on multiplication!)
This probably would have worked for John Nash too. Who would have suspected that cryptographic primitives would be useful for psychotherapy and metaphysics!