The priests of the cult of Science are the result of centuries of distortion of a materialistic world-view. Their spiritual longings have resulted in the scientific knowledge passed down filling the void that religion normally occupies.
They believe in Science as a literal god, one who performs miracles through normal physical processes. The beggar in the street who lost his arm, has been healed through the grace of Science, granted a mechanical substitute. He is now better than human, his arm a symbol of the might of Science, and he proselytizes without end to all who will listen. Those who don't, are pronounced Very Unscientific, and meet the business end of his mechanical arm.
The priests and acolytes of science wear long white coats as their normal dress, with black gloves covering their hands. Their bodies are covered with tribal tattoos, and their names are tattooed prominently on their foreheads. During rituals of Science, the head priest will stand on stilts, elevating his height to 12 or more feet, hiding the stilts under a ridiculously long white lab coat. He will have his ceremonial safety goggles on as he chants the liturgies: "Dihydrogen monoxide! A squared plus b squared equals c squared! Pyridine-3-carboxylic acid!"
The Scientist, as the acolytes and priests of Science is known, has an empiricist's grasp of science. He has learned a few tricks on how to repair ancient devices, or how to create certain chemical reactions (preferably ones that go "boom!"). There is no research activity going on, or understanding of the scientific method, however. Their creed is one of sacred knowledge passed from priest to priest over the ages.
Scientists take a dim view of other gods. They consider them all subservient to Science. The occasional pronouncement by an orbital AI-god that "science is the principle governing nature", when questioned by theologians, does little to dissuade the Scientists of their world-view.
Scientists value ancient artifacts and books, and will pronounce donors of such items as performing Very Scientific actions, and may provide other sorts of assistance in return.
Well-established Temples of Science have a 10' tall black pyramidal structure within. These structures have ladders built into one side, and at the top have numbers in a red light ticking down, one per second, and a small keypad with the numbers 0-9. On a daily basis, a highly-ranked priest will climb the ladder and enter in a code known only to the most trusted Scientists, causing the numbers to reset. "This is the sole sacrifice that Science demands of us, my son. His burden is light. But his wrath if we neglect our duty is great. Not a stone in this city would stand should he believe that the people have abandoned his worship!"
Inspired by Alfred Bester's "The Stars My Destination" and the TV show Lost, of course.