Supernatural Occurances

Is there any scientific or mathematical evidence of clairvoyant or "supernatural" occurrences or phenomena? I know that asking this is trampling the definition of supernatural, but I'm curious if there are any cases like this. If you do answer, please cite a source.

I'm sorry I was snarky in my last post. 

Report you?  Science abhors a rat.  It's why we experiment on them.

I agree entirely, though I would add the word (yet) after "...cannot account for everything that is real" 
We run into things that turn our understanding up side down from time to time, and even have to deal with internal dogmatism and irrational resistance from supposedly unbiased practitioners.  The beauty of the system is that in the end, the data will force the restructuring.
Your assertion that something may exist that is exempt from "the mechanistic logic of science that governs much of the universe" is valid.  It's just a well worn and slippery slope that, as yet, has always led into the darkness of superstition. It's become scientifically uninteresting; the arguments little more than masturbatory exercises in indoctrination for both sides.  It's not really even philosophically interesting anymore.  We've done it to death and have had enough.  Not that we don't pay attention.  And continue to study the observable characteristics of religions and spirituality.
 
I'm a Taoist and have found no inconsistencies with Science yet. I have also personally been to fundamentalist christian churches, spiritualists, fortunetellers, witches, alleged haunted houses, Synagogues, Mosques, the Aga Sophia in Istanbul, the Vatican, Eastern Orthodox churches in, get this, Transylvania, the pyramids, Hindu temples in India, Buddhist temples all over Asia, Taoist temples in China, I even stepped inside a Mormon temple once.  I study Chi Gong.  I could continue, but I think I've made my point.  Our investigations into our spiritual aspect must remain divorced from our intellectual pursuits.  History insists upon it.  Science requires it.  I have faith in it.

Peace