I am afraid you are equating the mystical experience with superstition and quackery via the stereotypes you have been taught by the mainstream society. In short, mysticism is not 'mind over matter'. It is spiritual union with the divine source found within oneself. It is via this spiritual union that one's ordinary view of life becomes completely transformed, allowing one to see into the true nature of reality directly. In short, it is to see things as they actually are, rather than to see them as our conditioned (ie; 'rational/conceptual') mind tells us they are, summed up in the following observation:
"The universe is the Absolute as seen through the glass of Time, Space, and Causation"
You see. That is the problem with modern science. It is out of balance with the view afforded by nature. It attempts to make nature an object of clinical analysis via logic and reason. It has failed, and that is why Kaku said what he did, that 'nature is smarter than we are'. Science fails to understand the intelligent nature of the universe. When the conceptual filters of Time, Space, and Causation are removed from the mind, we can then see things as they are, and when we can see things as they are, we will have the right view. Until that occurs, we are only nibbling around the edges with our probes and instruments, gathering data and knowledge, but failing to attain any understanding at all.