The nature of these experiences is such that we cannot test them, run experiments or replicate them, yet enough people have enough things happen that they cannot explain that we owe it to ourselves to consider that there might be something to them. My position is not in defense of a particular belief system or even in defense of affirmative belief of any sort, but that atheism discounts evidence solely because it cannot, at the present day and with our present understanding of the universe, be scientifically tested, replicated in experiments or used consistently to achieve results. At the same time, we know that many things that we now know about could not be tested or measured in antiquity because our ancestors lacked the understanding necessary to even be looking in the right place.

Perhaps some day my odd dreams can be explained with science, and the blurred line between life and death can be measured as some sort of energetic residue, but until that time, we should remain curious and open-minded.

By the way, you're quite wrong about physics saying that bumblebees can't fly. That statement is a myth, which has been discredited and which you can see if you look on the wikipedia page for bumblebee.

People used to say the same thing about ball lightning - it couldn't possibly exist and was the result of hysteria, delusion, etc. However, now scientists are able to create it in laboratory settings, even though we don't understand it very well.