Galileo’s Mathematical-Experimental Method

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During the summer of 1609, Galileo Galilei (1564-1642) used his innovative astronomical telescope to observe the Venetian night sky. Through these observations, he made groundbreaking discoveries that revealed new aspects of the universe. These revelations ultimately transformed scientific thought at that time. In Galileo’s era, scientists and philosophers often adhered strictly to existing scientific and religious beliefs without questioning them, which hindered intellectual progress.

Galileo made significant discoveries using scientific methods, explaining important scientific laws such as the orientation of the universe, the motion of free-falling bodies, and the Galilean principle of relativity. His wide range of studies, from celestial bodies to minuscule pebbles and water droplets on a ship, demonstrate his immense scientific interest. It cannot be emphasized enough how his discoveries have been credited with founding a new rational science.

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During Galileo’s time, the study of ancient science was a fusion of religious tenets and Aristotelian philosophy, adapted to align with church teachings. Consequently, scientific progress was minimal. The prevailing scientific understanding heavily relied on the interpretations of Saint Thomas Aquinas (1225-1275), a theologian who examined Aristotle’s works and provided religious interpretations.

According to Aristotle, an essential concept in the field of astronomy was the idea that celestial bodies moved due to the influence of a divine entity that remained stationary. Aquinas interpreted Aristotle’s idea by associating the divine mover with God and attributing the planetary motions to angels. Aquinas’s astronomical theories centered around the belief that the universe was finite and shaped like a perfect sphere. He also believed that the Earth, positioned at the center, would remain stationary while the other celestial bodies orbited around it in a consistent manner.

The Church strongly affirmed convictions like these, which originated from biblical references such as Psalm 96:10 that states, “the world is firmly established, it cannot be moved.” Scientists and philosophers, referred to as Simplicio by Galileo in his dialogues, continued to support this theory even after Copernicus (1473-1543) introduced the heliocentric theory of the universe (Frova 26).

Based on two main concepts, Copernicus’s heliocentric theory posits that the Earth rotates on its axis every twenty-four hours and completes a full orbit around the Sun annually (365.25 days) (Cohen 35). Nevertheless, despite this evidence, certain scientists opted to embrace the ancient hypotheses of Eudoxes (410-355 BC), Ptolemy (90-168 AD), and the Church. They put forth significant efforts in proving that the Earth is at the center of the universe through methods involving intricate motions known as epicycles, which were designed to match their observations (Cohen 28).

Although Copernicus suggested the heliocentric theory, which dismissed the intricate movements of epicycles and equants as not reflecting actual physical reality and proposed a revolving Earth, it was only in the seventeenth century that his theory gained widespread acceptance due to Galileo’s experiments. Through his research, Galileo questioned Aristotelian physics and successfully refuted one of the main objections against the heliocentric theory.

The proponents of the geocentric model argued that if the Earth rotated, there would be observable effects. They questioned why people did not notice the Earth’s rotation when it orbits the sun at a speed of 100,000 feet per second (Cohen 10). They also wondered why a ball dropped from a tall building falls directly below instead of thousands of feet away (Frova 41), as Galileo demonstrated with the leaning tower of Pisa. Galileo’s support for Copernican’s heliocentric theory provided logical and mathematical explanations for these challenges. Through his astronomical observations, Galileo made significant discoveries that challenged old ideas and embraced a new understanding of the universe. The traditional belief in astronomy was centered around a universe that rotates spherically around the Earth while constellations and planets remain unchanged and perfectly symmetrical.

Galileo’s contemporaries held the belief that the moon possessed a shiny and polished sphere-like visage. Contrarily, Galileo’s observations unveiled the imperfections of its surface, characterized by rough mountainous regions and deep valleys which he termed as “seas.” These regions were distinguished by dark spots. It is noteworthy that the ruggedness of the moon’s surface mirrored that of Earth, implying that Earth’s surface was not singular in its characteristics. Moreover, Galileo could observe stars with enhanced clarity owing to his improved telescope.

Galileo’s groundbreaking observations challenged the prevailing notion of a timeless universe. Notably, he discovered recently formed stars and star clusters, directly contradicting Aristotelian beliefs. Additionally, he observed four of Jupiter’s largest moons orbiting the planet, which contradicted the idea that all celestial bodies revolve around Earth. Most importantly, Galileo’s study of Venus’s phases and the sun’s spots provided evidence for the theory of planetary rotation around the sun, mirroring how lunar phases indicate the moon’s rotation around Earth (Frova 179, 159).

These key astronomical observations were the basis for the laws of motion that Galileo would later introduce, confirming the Copernican model for a heliocentric solar system. Galileo’s experiments on free-falling bodies provided important and easily visible evidence of uniformly varied motion. In these experiments, Galileo demonstrated that objects of different weights, when dropped at the same time, would land simultaneously. This contradicted Aristotle’s hypothesis, which stated that objects would land directly proportionally to their weights. In reality, the timing of their falls is determined by the amount of wind resistance they experience, rather than their weights (Frova 47).

According to Galileo, if we ignore wind resistance and imagine that objects are dropped in a vacuum, the acceleration rate would be equal for all objects. Additionally, whether an object is dropped directly down or propelled horizontally with a constant speed, the outcome would be the same, with all objects landing at the same time in the absence of air resistance. Objects that are projected outward follow a parabolic trajectory during their fall, and this horizontal component does not affect the rate of descent (Frova 83).

Galileo’s experiments of free-falling bodies demonstrated that each body experiences a consistent vertical acceleration, which is equivalent to gravity. These findings directly opposed the viewpoint of “Simplicios” that argued Earth must be the center of the universe, suggesting the Earth’s constant motion and resulting gravitational force. The significance of Galileo’s experiments lies in their ability to confirm the presence of a universal gravitational pull on falling objects, which is a direct consequence of Earth’s continuous motion.

In his Dialogue Concerning the Two World System, Galileo discussed the situations of free-falling bodies to provide logical arguments supporting the Copernican theory. Both Aristotle and Galileo agree that if an object is dropped from the mast of a ship while the ship is stationary, it will land vertically below its initial position. However, their beliefs diverge when considering a moving ship. According to Aristotle, as the ship moves forward at a constant speed, the ball would fall behind the mast while moving downward.

According to Frova (68), Galileo’s experiments mentioned in “Dialogue Concerning Two Chief World Systems” demonstrate that when an object is dropped from the top of a mast, it will land directly at the foot of the mast and descend perfectly vertically. Another experiment by Galileo involves placing free-falling objects below the deck of ships. Galileo explains that if water is dripping from the roof, it will also land directly into a bowl positioned below it. This parallels the outcome observed with the falling object from the top of the mast.

Furthermore, if someone were beneath the deck of a ship that is traveling at a constant speed, they would be unable to distinguish whether the vessel is moving or stationary. On the other hand, an individual positioned in a still location who witnesses objects descending would perceive those objects as following curved trajectories resembling parabolas during their descent (Frova 74). Consequently, even though the actual movements are identical, the appearance of falling objects would vary depending on one’s perspective – either aboard the moving boat or from a fixed point observing the boat.

Galileo’s principle of relativity states that “the laws of mechanics will be the same for all observers moving at the same speed and direction with respect to one another” (Frova 248). Therefore, because the Earth is constantly rotating around the sun, which is a universal movement experienced by all locations, we cannot actively perceive this rotational motion (similar to how a viewer on a ship cannot perceive its constant motion).

Galileo’s approach to scientific discovery was influenced by the philosophies of previous thinkers, despite refuting some of their ideas. Plato believed that the laws of nature could be explained through simple math, while Aristotle emphasized knowledge gained through the senses. Galileo’s experiments incorporated both approaches to uncover laws with mathematical formulas.

Galileo used an approach that involved identifying measurable features of observable phenomena and applying a mathematical-experimental method. He formulated mathematical laws based on his conceptually mathematical measurements. Galileo then conducted observable experiments to test if situations aligned with the equations. His experimental methodology combined ancient philosophical practices and grounded experiments with observational data. This approach allowed for clear logical arguments and the formulation of mathematical laws.

The beliefs of Aristotelian philosophers, who believed in a stationary, central Earth, have been disproved by philosophical arguments, astronomical observations, and mathematical laws. These discredits support Copernicus’s heliocentric theory. Galileo, despite being marked as a heretic by the Roman Inquisition, introduced ground-breaking theories that would trigger the scientific revolution and establish modern science.

Galileo’s contributions paved the way for a new physical theory, which was further expanded by Sir Isaac Newton. Newton’s principle of relativity then became the basis for Einstein’s Special Theory of Relativity. These are merely two instances showcasing Galileo’s lasting influence on science and philosophy.

Works Cited

Cohen, L B. The Birth of a New Physics. 2nd ed. New York: W. W. Norton & Company Inc., 1985. Print. Frova, A, and M Marenzana. Thus Spoke Galileo. 2nd ed. New York: Oxford University Press, 2006. Print.

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