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The Crime Of Galileo Galilei - Biography

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Bianca
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« Reply #15 on: April 02, 2008, 04:26:58 pm »









Scientific methods



Galileo Galilei pioneered the use of quantitative experiments whose results could be analyzed with mathematical precision (More typical of science at the time were the qualitative studies of William Gilbert, on magnetism and electricity). Galileo's father, Vincenzo Galilei, a lutenist and music theorist, had performed experiments establishing perhaps the oldest known non-linear relation in physics: for a stretched string, the pitch varies as the square root of the tension. These observations lay within the framework of the Pythagorean tradition of music, well-known to instrument makers, which included the fact that subdividing a string by a whole number produces a harmonious scale.

Thus, a limited amount of mathematics had long related music and physical science, and young Galileo could see his own father's observations expand on that tradition. Galileo is perhaps the first to clearly state that the laws of nature are mathematical.



In The Assayer he wrote

"Philosophy is written in this grand book, the universe ... It is written in the language of mathematics,

and its characters are triangles, circles, and other geometric figures; ...".



His mathematical analyses are a further development of a tradition employed by late scholastic natural philosophers, which Galileo learned when he studied philosophy.

Although he tried to remain loyal to the Catholic Church, his adherence to experimental results, and their most honest interpretation, led to a rejection of blind allegiance to authority, both philosophical and religious, in matters of science. In broader terms, this aided to separate science from both philosophy and religion;

                                      a major development in human thought.


By the standards of his time, Galileo was often willing to change his views in accordance with observation.

Philosopher of science Paul Feyerabend also noted the supposedly improper aspects of Galileo's methodology, but he argued that Galileo's methods could be justified retroactively by their results.
The bulk of Feyerabend's major work, Against Method (1975), was devoted to an analysis of Galileo, using his astronomical research as a case study to support Feyerabend's own anarchistic theory of scientific method. As he put it:

"Aristotelians ... demanded strong empirical support while the Galileans were content with far-reaching, unsupported and partially refuted theories. I do not criticize them for that; on the contrary, I favour Niels Bohr's "this is not crazy enough.   In order to perform his experiments, Galileo had to set up standards of length and time, so that measurements made on different days and in different laboratories could be compared in a reproducible fashion.

Galileo showed a remarkably modern appreciation for the proper relationship between mathematics, theoretical physics, and experimental physics.

He understood the parabola, both in terms of conic sections and in terms of the ordinate (y) varying as the square of the abscissa (x). Galilei further asserted that the parabola was the theoretically-ideal trajectory for uniformly accelerated motion, in the absence of friction and other disturbances. He also noted that there are limits to the validity of this theory, stating that it was appropriate only for laboratory-scale and battlefield-scale trajectories, and noting on theoretical grounds that the parabola could not possibly apply to a trajectory so large as to be comparable to the size of the planet.

Thirdly, Galilei recognized that his experimental data would never agree exactly with any theoretical or mathematical form, because of the imprecision of measurement, irreducible friction, and other factors."



According to Stephen Hawking, Galileo probably bears more of the responsibility for the birth of
Modern Science than anybody else, and Albert Einstein called him the father of Modern Science.
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