If mind was random, people would miscalculate 1+1 with 50% probability. So earth might be flat, but it's unlikely.

There's a difference between making and testing hypothesis, and desperately scrambling to find proof to justify a conclusion made in advance in the face of mounting evidence that said conclusion is false, which is what Penrose is doing regarding quantum consciousness.

Grossly simplifying: he is a dualist, he wants to reconcile his belief in the soul and his physicist's materialist view of biology, so he resorts to putting the source of consciousness in quantum phenomenas, and seeks to prove that they occur in the brain. I disagree that there's an immaterial soul, I disagree that it puppets the material universe through quantum phenomenas, and I disagree that there are important quantum phenomenas in the brain. Most physicists are with me on these.