So according to Pythagoras, a chaotic combination of sounds could not be expected to result in a pleasing melody. The important thing is that underlying harmony in musical composition is governed by simple numerical relationships. Criteria or arguments that led to this discovery by Pytagoras are not known. If the lengths are in the ratio of 3:2, the difference of tone corresponds to a fifth, and if they are in the ratio 4:3 the interval corresponds to a fourth. For example, if the lengths of two strings of identical material are in a ratio of 1:2, the sounds that they produce after being made to vibrate have the relationship of an octave. Pythagoras associated these intervals with simple numeric relationships. These three intervals are the octave, fourth and fifth. The music that Pythagoras was familiar with was constructed from three basic intervals that serve as elements of every composition. ![]() The Pythagorean paradigm for harmony comes from music. Second point: Knowledge searches for harmony present in the world and this harmony arises from establishing a limit to the unlimited For the Greeks harmony implies the pairing between two dissimilar elements. This principle combines a maxim shared by almost all the pre-Socratic thinkers. Thanks to this similarity the soul can know the world. They considered the human soul is similar to the soul of the living universe. The Pythagoreans, it is believed, aspired to resemble God. Pythagorean elements in the methodology of Keplerįirst point: sameness is made known by sameness. Finally, I will try to trace the presence of these principles in the two particular following cases of the Kepler research program. I will show how these principles are present in Pythagorean cosmology. As a hypothesis, I will propose a general outline that identifies four corresponding elements that are present in Keplerian methodology. I intend to show that Kepler´s methodology is inspired primarily on two principles of Pythagorean origin. ![]() This comment, which profoundly influenced Kepler, could be considered ‒in the strictest sense‒ as the first book of philosophy of mathematics. Kepler had read and greatly appreciated the work of Proclus, a philosopher who lived in fifth-century Alexandria and wrote, among other works, a famous commentary on the first book of Euclid's Elements of Geometry. ![]() Kepler was familiar with the works of both ristotle and Plato. The knowledge that Kepler could have ascribed ideas from the Pythagoreans comes mainly from three sources. ![]() The most important source to characterize the ideas of Pythagoras is, unquestionably, Aristotle. Moreover, we don't count with primary documents with an outline of the main ideas of the members of the school. In literature, there are plenty of anecdotes and stories with questionable evidence. It is not easy to establish precise information in relation to Py66thagoras and his school. However, the presence of Pythagoras in the work of this scientist and philosopher of the 17th century can be traced more deeply on the methodological aspects. The importance given to geometry, regular solid fixation, obsession with harmony and the fact to consider that music and astronomy as sister sciences are just some features of the Pythagorean influence protruding on the surface of the work of Johannes Kepler.
0 Comments
Leave a Reply. |