How did Italy's culture during 1500~1650 influence Italian science or vice versa?
Italy, by accident of geography, was a center of trade in ancient times during Rome, and in modern times during the Renaissance. As shipping and trade increased in the late Middle Ages, banking and capital rose concurrently. With more money in circulation, a new and numerous class, based not on noble heredity but mercantilism arose. These became patrons of arts, since they could afford to do so; because of a rising standard of living, more tradesmen could become artists, so an artist class arose. An artisan during this time was what we would consider to be scientist and/or a manufacturer. The preeminent figure that represents that concept was Leonardo Da Vinci (1452-1519). His artistic application of science (works like Vitruvius Man and other anatomical studies) and scientific inquiry into art (employing chemical principles to develop new pigments of paint) embody the symbiosis of art and science at this time. Two generations later, Galileo Galilei (1564-1642) established the principles of inquiry into the natural world, or what we in the modern world would understand as the Scientific Process. Here was a true cultural revolution -- the workings of nature were not defined by the ancients or interpreted by the church, but were determined by observation and experiment. The Scientific Process is the greatest gift Italy gave the world. That concept lead to the revolution in physics, and established the rational principles of the Enlightenment a generation later.