Foundations of Modern Science and Mathematical Physics
The Scientific Revolution and Mathematical Physics
The Scientific Revolution, spanning the 15th to 17th centuries, was decisive for the emergence of modern thought. The appearance of mathematical physics caused the abandonment of the Aristotelian-Ptolemaic Imago Mundi. This transition from geocentrism to heliocentrism occurred through the proposals of several key figures.
Nicolaus Copernicus and the Heliocentric Model
Copernicus defended the Sun as the center of the universe. The idea of Earth's movement was not entirely new, as it had been defended previously, but the heliocentric hypothesis implied that Earth rotates on its axis and performs an annual journey around the Sun. This model presented the advantage of allowing the calculation of orbital trajectories. For Copernicus, heliocentrism was a primordial hypothesis.
Johannes Kepler: Laws of Planetary Motion
Kepler's investigations, inspired by Pythagorean thought, sought a mathematical explanation for the universe. His primary contributions were the three laws of planetary motion:
- First Law: The orbits of the planets revolving around the Sun are elliptical.
- Second Law: The radius connecting the planet to the Sun sweeps equal areas in equal times.
- Third Law: The squares of the periods of revolution of the planets are proportional to the cubes of their mean distances from the Sun.
Galileo Galilei and the Scientific Method
Galileo defended heliocentrism against the theocentrism of the Church. He intended to found the knowledge of nature on experience, arguing that one is blind without an adequate research method. He perfected a method following these steps:
- Observation: Analyze essential properties.
- Hypothesis: Formulate an explanatory hypothesis and deduce experimental consequences.
- Experimentation: Design an experiment to test the hypothesis.
- Law: If predictions are confirmed, the hypothesis reaches the category of scientific law.
Galileo’s importance lies in his formulation of laws within a mathematical structure.
Descartes and the Mathematical Structure of Truth
Regarding scientific developments, there exists a great coincidence between scientific objectives and the search of René Descartes. The Cartesian search for a method of research and discovery is closely related to the work of Copernicus and Kepler, specifically regarding the emphasis on mathematics in understanding reality.