I heard the words, "In the Name of the Father" many times in my Lutheran upbringing in Indiana. While not of any religious orientation, I have had experiences that would be considered mystical or spiritual or 'experiences with God' by those who follow a monotheistic tradition. These first-person experiences are difficult to describe because in naming them, one becomes removed from them. Lao-tzu spoke of this challenge in the classic Tao Te Ching, in the line "The Tao that can be told is not the eternal Tao." Investigation into the nature of such experiences are being described through neuroscience today, with 'God experiences' brought upon through hallucinogenic drugs, neurosurgical procedures, meditation, or brain anomalies such as temporal lobe seizures.
The brain is a window into the self-transcendent states described by mystics (for example, see William James book, The Varieties of Religious Experience). Self-transcendent experiences are correlated with activity of the right hemisphere of the brain, the sort of parallel (non-linear, non-verbal) processor of experience when not under the control of the left hemisphere, the serial (linear, verbal) processor of experience. Leonard Shlain wrote in The Alphabet Versus the Goddess: The Conflict Between Word and Image how cultures emphasizing more right hemisphere (art, nature) than left hemisphere (writing, reading) activities correspond with religious orientation shifting from more paternal/hierarchical to maternal/holistic. While certainly not that simple, it is an intriguing thought that the spiritual (and non-religious) shift in parts of the world today may be coinciding with the onset of the Internet, computers and visual media that place a greater emphasis on right hemisphere processing than print media of the past.
What would the world be like if we all had more mystical or spiritual experiences and did not work to label them and create doctrine around them? It is likely that we would fight less for religious reasons as that arises when we label, define, contrast and compare. It is likely that we would be kinder and more peaceful, as mystical experiences generally increase a sense of interconnectedness and dependent nature. Spiritual experiences arise naturally but may also be nudged through meditation practices, yoga, contemplative practices, breathing meditation, TM, Tai Chi, mindfulness, or brought on without request as in the case of life-altering events such as near death experiences, tragedy, or life-threatening illness.
As science moves closer to understanding the brain and body and how our world views are shaped, we will begin to understand the differences between the spiritual experiences we have and the names we give them. As science continues to measure and define spirituality from biology, we need remember that the Experience and its Description are very different things. A scientific description doesn't alter the experience of communing with God, the Oneness of the Universe, or seeing our Dependent Nature, it merely provides a new Description of it. The Taoist saying may need to be reworded in the 21st century of science and technology age as "The Tao that can be Weighed is not the constant Way." It may be the greatest challenge in human evolution to enhance spirituality, experience it, but not attempt to control it by Name.