here is one quote. I don't have his book, but have read a couple chapters of it, one of which he talks to some length on the differences between the two methods of understanding. I don't recall picking up on him dismissing science entirely, but I need to find and read the whole chapter again.
Andrei Tarkovsky wrote:
The only condition of fighting for the right to create is faith in your own vocation, readiness to serve, and refusal to compromise. Artistic creation demands of the artist that he 'perish utterly', in the full, tragic sense of those words. And so, if art carries within it a hieroglyphic of absolute truth, this will always be an image of the world, made manifest in the work once and for all time. And if cold, positivistic, scientific cognition of the world is like the ascent of an unending staircase, its artistic counterpoint suggests an endless system of spheres, each one perfect and contained within itself. One may complement or contradict another, but in no circumstances can they cancel each other out; on the contrary, they enrich one another, and accumulate to form an all-embracing sphere that grows out into infinity...