What is beyond the reach of science?

Yes, "true believer" is often used in a non-theistic sense. It is used to refer to people who seem absolutely committed to a particular view, and seem completely immune to any evidence to the contrary. For example, it is used to refer to some people who believe that the Twin Towers of the trade center were actually taken down by explosives set up on the inside, presumably by the US government. Such people are usually called "conspiracy theorists" because they see massive conspiracies everywhere. But when their arguing style shows that they will ignore all evidence that disagrees with them, they are called "true believers".You can google "true believer" (with the quotes) for more information. These sorts of incidents do occur. I think most psychologists would say that it is your mind playing tricks on you. That is, the events evoked some old memories.I'm inclined to think that might well be the explanation. However, such events are rare and sporadic, so hard to investigate. You should not be depending on faith here. The scientific method works mainly because it is based on skeptical observation, rather than faith. There are certainly questions that science has not yet settled, and perhaps may never settle. The mandate for science is to investigate what it can, and follow the evidence. There's no requirement that it answer everything.Should I eat steak or chicken tonight? Now there's a simple question which is outside the province of science.

No, we are not on that road. I'm inclined to think that the idea of omniscience is merely a myth, anyway. We know that the ratio is a quantity, but we also know that we cannot find the exact decimal expansion by scientific or mathematical means. This does not seem to pose any problem for science or for mathematics.(I'm not sure if latex support is broken. Preview is not working for this post. I'll try submitting as a post and see what happens.)This is what happened on submission: I am disabling the latex, to try again. Latex is working now - the text and background colors are incorrect, but that will have to wait. --AdminEdited by Admin, : Correction.Edited by Admin, : Rerender after latex fix.