Greek science was born around 600 B.C. as a way to find explanations of the world. The first theories, based on few observations, tried to explain the unknown not appealing to divinities or myths, but using rational arguments (even if they would often prove themselves wrong). It this is attitude that characterizes science.
Plato (429-348 B.C.), one of the greatest philosophers of ancient Greece, lived in Athens he where he founded a school of thought, his Academy. During his life he travelled to southern Italy (at that time a Greek colony) where he met the Pitagoric school, that later influenced his thought. A great influence on his development was also given by Socrates.
His attitude toward nature was similar to that of many other Greek thinkers: he tried to explain Nature in a way that would fit the preconceptions of reason instead of adapting reason to the information he could get from Nature. No wonder that he considered geometry as the model of true science. The legend tells us that on the entrance of his Academy was a writing that warned anyone who did not know mathematics not to enter; whether it is truth or not, this shows that mathematics has an important role in his philosophy.
In fact, geometry, as well as mathematics in general, devotes itself to the study of an eternal and immutable subject, not everchanging and corruptible as are things in the real world: geometry studies Ideas. Ideas are at the base of Plato conception of the world: he said that true Nature consists of Ideas, which are eternal Essence, unchangeable Spirit, perfect Model of all the things we see in the
world, that are subject to mutation and deterioration, and cannot therefore be perfect. His theory implies a peculiar attitude towards the knowledge one can derive from observing Nature (meant here as the world we see around): in fact if everything we can see is subject to change and transformation, how can we get any real, durable knowledge from it? Instead, true knowledge is the knowledge of Ideas, of the immutable Model: so visible things cannot be object of study if not insofar as they participate to the true immutable Being.
So we can say that geometry studies Ideas because it studies shapes as triangles and circles, which are ideal and perfect, and the knowledge we derive is valid for all the shapes of the same kind (say circles) and not only for the particular one that was object of our study (the circle we draw to explain a certain property). However, this rational attitude, this effort to trace everything back to a perfect underlying model lead him (and in later time his disciples) to develop theories that departed largely from observations. His cosmology is an example.
According to Plato, it was necessary that our world, as well as the celestial bodies that are the most immutable things, have a spherical shape. All of them move with constant velocity on perfectly circular orbits that had no beginning and will have no end. The visible movements of the planets are not important, since they pertain to the unstable material world, that is nothing more than a shadow of the world of the Ideas. A further alteration was made by Plato's friend Eudocio (408-355 B.C.) who imagined a system of concentrical spheres rotating with different (but constant) velocities around axes oriented in different directions: seen from the Earth this would look like a very irregular and complex movement, that is, somewhat closer to observations.
A similar model was adopted by Aristotle and inherited in the Medieval Times, creating some problems, as the difficulty to fit observational data: for example the variation of the apparent diameter of the Moon could not be explained. But such flaws in his model would have not worried Plato, because true Nature cannot be found perfectly reflected in the visible world. In fact, for him this model is an hypothesis on the true character of Ideas, it does not have to fit perfectly to the real world, while Aristotle used it as a model to describe the world, a calculation tool (depriving it of its original meaning).
In a conception in which knowledge only comes from the study of Ideas done with
Reason, experiments are despised: the phenomena one should study are not the ones we see with our eyes but the ones recognized by our spirit. Therefore Plato disregarded applied science; the reason is not only philosophical, as he came from an aristocratic family and at the time manual work was considered something
that deprived man from his freedom. Applied science was considered unworthy of a free man: pure science should be studied for its own sake, not for its material application. So Plato recommended the study of mathematics to cultivate the spirit, not for its application in business.
This preconception against experimental science is not exclusive of Plato: also Aristoteles and many other early thinkers shared the same opinion. So the lack of a development of experimental science can be traced back not to a technical or intellectual incapacity, but to social conventions and philosophical ideas.