It was the habit of medieval scientists who worked in the Aristotelian rhetorical tradition of philosophical speculation to propose theories for the ways in which the world worked based on how well they agreed with the claims of the most respected philosophers, or with how well one could marshal explanations to support one's theory. The sixteenth and seventeenth centuries saw a serious challenge to this way of learning about the world in the new methods of experimental science undergirded by mathematical justification which were pioneered by Galileo Galilei (1564 - 1642).
The new methods approached reality as knowable through rational argumentation based on mathematical principles and agreement of theory with experimentation, what is now identified as the scientific method. Instead of speculation as to why phenomena occurred as they did, the new scientist described precisely what the phenomena were and measured their effects on other phenomena quantitatively in an effort to isolate the essential ingredients that composed the observables. Once these underlying components were identified, then rational deduction was employed, as in mathematics, to formulate theories about the phenomena. Galileo formulated these new principles in The Assayer (1610):
[Natural] philosophy is written in that great book which ever lies before our eyes--I mean the universe--but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in the mathematical language, and the symbols are triangles, circles, and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.Galileo, born into a family of nobility, had at first planned on a career of medicine, but became enamored of mathematics after attending the lectures of Ostilio Ricci, a student of Tartaglia's, on Euclid's Elements at the University of Pisa. At age 25, he obtained a lectureship at the university, and it is said that he gave public demonstrations at the campanille (the famous Leaning Tower) on how bodies of different weights fall in equal times, in contrast to the claims of Aristotle. Rather than convincing the Aristotelian philosphers, he was accused of sorcery, and was forced to give up his position at Pisa after only three years. He later moved to the University of Padua where he taught as professor of mathematics for 18 years. While at Padua, he learned of the manufacture of a telescope in 1609 by Hans Lipperhey and built one for himself. He spent the next years observing the night sky, discovering the Galilean moons of Jupiter (which he named the Medicean moons after his patrons, the wealthy Medici family), mountains on the Earth's Moon, and the makeup of the Milky Way as millions of individual stars. These discoveries, and a defense of the Copernican theory of heliocentrism (that the Earth and the planets revolved about the Sun) were published in The Starry Messenger (Sidereus Nuncius) in 1610, bringing him instant notoriety. His controversial stances forced him to leave his position at Padua under a barage of criticism to return to the University of Pisa and the patronage of the Grand Duke of Tuscany, Cosimo de Medici.
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