Often times, when we hear the term "mindfulness," or "meditation" it conjures up images of religious ritual, requiring robes, holy bells or beads, weird mantras like "ohm," or "ho-hum," or whatever. We assume that meditation is inherently a religious or covertly spiritual practice, but nothing could be further from the truth.
I am a life-long humanist, and have had a daily meditation practice for nearly 15 years...in that time, I have come to discover what so many have discovered about meditation, who have applied themselves to it with discipline....at it's core....it's science or perhaps, more specifically, neuroscience: http://www.samharris.org/blog/item/how-to-meditate. Even secular celebrity Sam Harris has written about the topic, extensively.
Meditation is less about "getting somewhere," or "transcending," or "awakening" or any other number of esoteric notions that are difficult to wrap the mind around, and more about simply "being" very much awake and aware in th