The use of mathematics in the beginning was used as something was not used for accuracy, but rather as something that could exercise the mind into rationalizing perspectives in a more logical way. The celestial heavens were considered more flawless and predictable compared to the ever changing and the visible deterioration on Earth. However to Plato, the importance of mathematics and unchanging patterns was to exercise the mind instead of explaining physical phenomena; basically, Earth is always changing, so the use of mathematical patterns will never be accurate enough because, in order to be accurate, Earth would need to stay consistent and unchanging, which Plato and others believed the heavens is such (P1, pg. 17).
The approach of mathematics and physical explanations was also considered not to be related to each other mainly because of the accomplishments made by Aristotle. Aristotle also shares the idea that the application
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Galileo believed that any physical objects, even the cosmos, heavens, and earth are all mathematically applicable, unlike Aristotle, who strictly did not believe in applied mathematics. Instead of using algebraic reasoning to derive his law of freefall, he used geometrical reasoning (P1 pg. 99). Something unique about Galileo’s mathematical reasoning fro freefall was that he demonstrated his findings experimentally, such as his inclined plane experiment. The only thing that could have made him not as credible was that he did not have an explanation as to why things happened in his experiments and findings. Not only was he steering physical science to a new direction, but he was also diminishing the line segregating astronomical and celestial phenomenon, forcing the traditional thought into reconsideration. His work would push western science that will lead into Newton and only then will there be an explanation for the motion of earth (P1 pg.