What does all this have to do with Galileo and the advances he made in the art of physics, the mechanics of motion, in support of the Copernican universe and the "new science" of the early 1600's?
It is no coincidence, I think, that the artistic renaissance and the scientific renaissance should have both developed at first largely in Italy. Scientists like Galileo were doing exactly what renaissance artists had been doing all along, with growing skill and increasingly sophisticated techniques, in their depictions of nature in realistic terms since the late 15th century.
The veracity of their mathematical vision was well-established by the time Galileo began thinking about the mathematics -- the geometry -- of space -- nearly a century later. What Renaissance artists had discovered was that in addition to careful observation and attention to underlying physical structure -- often this meant anatomical structure -- mathematics was an expecially useful tool for translating the physical reality of 3-dimensional objects in 3-dimensional space into realistic illusions of that same reality on only 2-dimensional, flat surfaces.
Galileo, like Renaissance artists of the 15th century, was interested in form, in the underlying reality of the natural world. He, too, was interested in the sort of physical reality that he felt his mathematics and the telescope were making clear for the first time. Light, optics, mathematics -- all were as important keys for Galileo as they had been for Brunelleschi, Alberti and Piero della Francesca. But there is no grander, more impressive example of all this than Raphael's magnificent "School of Athens."
Here Plato, on the left, holds a copy of his Timaeus, and gestures upward to the aetherial realm of his eternal forms; in contrast, Aristotle's hand is outstretched -- he holds a copy of his Nichomachean Ethics -- and he indicates with his gesture the worldliness, the concreteness, of his contributions to philosophy.
On the right are the geometers and astronomers;
just off from center, wearing the clothes of a 16th century stonecutter is Michelangelo.
Throughout the School of Athens there is an emphasis on mathematics, number, ratio, harmony. Pythagoras is represented by his theory of mathematical harmony on the left, Euclid by the perfection of Geometry on the right -- and the elaborate perspective design of the architectural setting seems to embody both.
It is now time to ask how this emphasis upon mathematics, number, ratio -- indeed a mathematical theory of structure and space -- is related to Galileo's impressive studies of motion and his similarly architectonic view of space -- one that also emphasized the importance of mathematics, number and ratio -- especially in Galileo's analysis of accelerated and projectile motion.
Go on to the next section: Galileo and the Mathematics of Motion
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