Psi powers -- ESP, precognition, psychokinesis and the like -- is one of those topics that seem to polarize human opinions (I'm referring to the modern era, not to prior periods when their reality was taken for granted by essentially everyone).
Some folks, largely on the strength of their own personal experiences, take their existence as an obvious truth.
Others reject them without much consideration -- because current scientific theories fail to indicate any clear mechanism for their operation, and because so many charlatans have falsely claimed various psychic powers and then been debunked.
I encourage everyone to read Damien Broderick's fantastic book "Outside the Gates of Science," which carefully reviews some of the scientific evidence that psi exists, and also analyzes its apparent limitations. Before reading his book and exploring the scientific literature it cites, I was basically 50-50 regarding the reality of psi; but after reading it I've shifted to 90-10 in favor.
I strongly suspect that during the next half-century a scientific model of psi will be created, which will tell us something about how psi works and under what conditions it has what capabilities.
The implications of psi for future technology and Cosmism in general are not particularly clear at the moment, because psi is so poorly understood.
But at a broad level one message comes through clearly from the data Broderick reviews: the universe is more tightly and intricately interconnected than the modern Western world-view admits. Patterns in parts of the world that appear to be separated and uncorrelated, are actually tightly tied together. We don't know much about how this works but the implications are potentially quite broad ... certainly this meme resonates with the notion of the "mind of the universe" that was mentioned earlier in this Manifesto. Psi could potentially reflect processes, as yet largely opaque to humans, by which the universal mind carries out its coordinated intelligent dynamics.