Excellent question.

My answer comes from science - that which is physically observed, and from spirituality - specifically spiritual experience and reflection.

From the dictionary, 'science', predominantly physics in this context, is the study of that which is material. 'spirit' is essentially the vital animating essence of something, and spirituality the exploration of that 'vital animating essence'.

Given these simple definitions, and what I have indeed observed and experienced myself, I see no conflict between science and spirituality whatsoever. In fact, I have come to see the two as just very different perspectives of the exact same thing. Neither one is wrong, they're just two drastically different ways of seeing the very same things. In fact, in my experience, each is vastly stronger when they work together.

That is how I 'reconcile' science and spirituality.