Unlimited units are defined as continuous elements, such as water, air, or fire. In Philolaus’s view, for the universe to be formed, the "limiters" and "unlimited" must harmonize and be fitted together. Beginning from the middle, the universe expands outward around a central point, implying a spherical nature. In the Pythagorean view, the universe is an ordered unit. Another issue with attributing the whole of Pythagorean astronomy to Philolaus is that he may have had teachers who were associated with other schools of thought. Because of questions about the reliability of ancient non-primary documents, scholars are not absolutely certain that Philolaus developed the astronomical system based on the Central Fire, but they do believe that either he, or someone else in the late fifth century BC, created it. Most of what is known today about the Pythagorean astronomical system is derived from Philolaus's views. Philolaus has been called one of "the three most prominent figures in the Pythagorean tradition" and "the outstanding figure in the Pythagorean school", who may have been the first "to commit Pythagorean doctrine to writing". Pythagoras developed a school of philosophy that was both dominated by mathematics and "profoundly mystical". 385 BC) was a follower of the pre-Socratic Greek philosopher Pythagoras of Samos. ġ) the circular motion of the celestial bodies produces a sound 2) the loudness of the sound is proportional to their speed and magnitude (according to Achytas, the loudness and pitch of the sound depends on the force with which it is produced 3) the velocities of the celestial bodies, being proportional to their distances from the earth, have the ratios of concords 4) hence the planets and stars produce harmonious sounds 5) we cannot hear this harmonious sound. Aristotle mentions the theory in De Caelo, in which he presents the theory as a "physical doctrine" that coincides with the rest of the Pythagorean cosmology, rather than attributing it to myth. Plato presents the theory in a mythological sense by including it in the legend of Er, which concludes the Republic. One surviving theory from the Pythagoreans before Philolaus, the harmony of the spheres, is first mentioned in Plato’s Republic. However, it should not be presumed that the Pythagoreans as a unanimous group agreed on a single system before the time of Philolaus. None for the remaining astronomical contributions can be attributed to a single person and, therefore, Pythagoreans as whole take the credit. Hippasus, another early Pythagorean philosopher, did not contribute to astronomy, and no evidence of Pythagoras's work on astronomy remains. Knowledge of contributions to Pythagorean astronomy before Philolaus is limited. In retrospect, Philolaus's views are "less like scientific astronomy than like symbolical speculation." While the departure from traditional reasoning is impressive, other than the inclusion of the five visible planets, very little of the Pythagorean system is based on genuine observation. How much of the system was intended to explain observed phenomena and how much was based on myth, mysticism, and religion is disputed. Although its concepts of a Central Fire distinct from the Sun, and a nonexistent " Counter-Earth" were erroneous, the system contained the insight that "the apparent motion of the heavenly bodies" was (in large part) due to "the real motion of the observer". The system has been called "the first coherent system in which celestial bodies move in circles", anticipating Copernicus in moving "the earth from the center of the cosmos making it a planet". An astronomical system positing that the Earth, Moon, Sun, and planets revolve around an unseen " Central Fire" was developed in the fifth century BC and has been attributed to the Pythagorean philosopher Philolaus.
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