"Left-minded" or "left-brained" is referring to that part of human though the operates in the realm of the concept of the physical universe. If it can me measured, if it can be weighed, if it can labeled that portion of human thinking accepts it. Left-brained thinking also tends to be dismissive of right-brained thinking.
Right-brained thinking is that which we recognize, but cannot put into words of put our finger on whether literally or figuratively. It is also the realm of intuition. That is why persons who have certain experiences of a divine nature have trouble putting that experience in words.
As far as the Failed Hypothesis, I totally agree -
Stenger believes we have more than enough evidence of absence of the Judeo-Christian God. He adds that many arguments for God that were once compelling are now weak or irrelevant in light of modern scientific understanding. Stenger does not think we should be dogmatic about disbelief in God, but says the evidence is overwhelmingly against the belief.
Any evidence/experience one can obtain about God will not line up with the concepts of the Bible.