First note that how psi intervein with the seen cannot possibly be 'beyond science'. In science, we don't only exermine the seen. We are also interested with the unseen provided that they influence the seen. Since psi is just that, the influence of the seen by the unseen, there has to be scientific explanation.
The scientific theory of psi must answer some tantalizing questions. Perharps the most daunting one is why the forces associated with psi aren't seen by physicists to move the seen particles. As phenomena such as psychokinesis and telepathy influence the seen, eg our seen bodies, they must move the seen molecules, eg sodium channels in cell membranes. Ergo for that purpose, 'psi' must behave like the usual forces of nature. Yet psi must be capable of significantly eluding a physicist when he attempt to pin down the forces at work in molecules.
The purpose of psi theory is to answer this important question as to why psi can work without conflict with known physics.