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GALILEO.
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Mathematical-experimental method of the Italian scientist/astronomer.... More...
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Paper Abstract:
Mathematical-experimental method of the Italian scientist/astronomer. Its use to test the relationship between velocity and time for a falling body. Galileo's employment of the hypothetical-deductive method to study the science of motion. His observations through the telescope. Galileo's challenge to Aristotelian theory. His proving the correctness of Copernicus' heliocentric theory.
Paper Introduction:
Galileo’s mathematical-experimental method was used to test the relationship between velocity and time for a falling body:
V ? T (Cohen, 1985). Since V could not be measured, he used a combination of mathematics and experimentation to verify this relationship: if V ? T, then D ? T2 by deduction, and this is a relationship which can be tested experimentally. By confirming this relationship experimentally, he could be confident that V ? T is valid. Because D ? T2 is derived from V ? T by mathematics, and then tested experimentally, this method was named the mathematical-experimental method. This method has also been called the hypothetico-deductive method because it is used to test a hypothesis which can’t be tested directly by experimentation. Essentially, the hypothetico-deductive method allows for the experimenter to test a theory by proxy.
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For instance, heobserved the moons circling Jupiter and likened them to the planetscircling the Sun. Galileo's mathematical-experimental method was used to test therelationship between velocity and time for a falling body:V % T (Cohen, 1985). The four moons orbiting Jupiter, each with their own orbits andorbit times, served as a model of the whole Copernican system of theplanets moving around the Sun (Cohen, 1985). In this sense he used the hypothetico-deductivemethod to prove Copernicus was right. Because Galileo knew that if V.T was true then itwould follow that D.Tsquared, he resolved to test D.Tsquared in order tovalidate the V.T supposition. 85, 2 7).Galileo also studied the Moon, and determined that it shone by reflectedlight from the Sun, and showed this was true of other planets (Cohen,1985). (2 2).http://www.physics.gmu.edu/classinfo/astr1 3/CourseNotes Again, because velocity wasdifficult to assign from the outset of the experiment, Galileo employed themathematical-experimental method to test time and distance over and overagain in order to best determine the velocity of falling bodies (Cohen,1985, p. Galileo's observations on falling bodies, while they did not provethe movement of the Earth, showed that they would hold true whether theEarth was still or moving (Cohen, 1985). L. Aristotle believed thatwhen this point is reached, the velocity would be zero. (1996). Galileo Galilei.http://www.lucidcafe.com/library/96feb/galileo.html Spradley, J. Essentially, the hypothetico-deductive method allows for the experimenter to test a theory by proxy. This method has also been called thehypothetico-deductive method because it is used to test a hypothesis whichcan't be tested directly by experimentation. The mathematical-experimental method was useful to Galileo as heendeavored to study the science of motion. In other words, by studying the behavior of the Moon and otherplanets, Galileo was able to deduce the behavior of the Earth. It also showed that theEarth was not unique in the solar system in having orbiting moons. Lucidcafe. The other major Aristotlian belief was thatearthly things were composed of four elements - earth, wind, fire, andwater - whereas those in the heavens were composed of an entirely differentsubstance, named aether, and were unchanging. He proved that there were heavenly bodies which did notorbit the Earth. Terrestrial and celestial motion. (1991). Inother words, because Galileo was unable to test V.T (there was no way forhim to by experiment make a direct correlation between times and velocitiesbecause velocity was unknown), he instead tested the hypothetical deductionthat followed from V.T. It countered one of the mainarguments to the Copernican heliocentric system - it proved that the Earthcould move through space without losing its Moon. He hypothesized what he thought theEarth and other planets did in terms of motion, and his observationalexperiments were used to prove his hypotheses. Because Distance and Time were knownentities, this was possible to do. New York, NY:Norton. Aristotlian philosophy proposed that the Earth did not move becauseit was not natural for it to do so, and it was unnatural for it to have acircular orbit around the Sun, or a daily rotation around its own axis(Cohen, 1985). Although many of Galileo's method's were not strictly scientific, andsome of his theories, such as the planets orbiting in circular paths, wouldlater be proven wrong, his work on falling bodies and his observationsthrough the telescope made significant contributions to modern science, andfinally put to rest the idea that the Earth was the center of the Universeand all planets orbited around it, and proved Copernicus's heliocentrictheory to be correct. When he later became interested in telescopes, he wasable to substantiate Copernicus's theories on the basis of directobservation (Terrestrial and Celestial Motion, 2 2). Theselaws were used as proof that the Earth does not move because if the Earthwas moving, when things were dropped and moving downwards, the Earth wouldalso be moving downwards, and because it has much greater mass, it wouldmove at a much greater speed and so the objects dropped would never catchup with it (Cohen, 1985). He observed that if a body falls long enough, the air resistance willequal the body's weight being pulled to Earth, and a terminal velocity willbe reached, but the body will continue to move. He also showed that the dark spots seen on the Moon with the nakedeye were due to mountains and craters and the light of the Sun shining onthem, just as mountains and valleys on Earth light up at different times ofthe day, depending on the position of the Sun. The mathematical-experimental method, (in whichrepeated, scientific testing was utilized), and the hypothetico-deductivemethod (in which unknown variables were figured through the testing ofknown variables) were the backbone of Galileo's remarkable findings. Galileo asserted that the speedof a falling body depends on the length of time during which it falls, noton its weight or the force moving it, which was what Aristotle hadproposed. He also showed that if Jupiter could keep its satelliteswhile moving, then by analogy, the Earth could move around the Sun withoutlosing its satellite - the Moon. Thus, thehypothetico-deductive method was again a key factor in determiningGalileo's theories. Galileo's repeated experiments in which he dropped items of varyingsizes and weights from a tower allowed him to formulate and test histheories on velocity. Cohen reminds us that because "B" is derived from "A" by mathematics andthen tested by experiments, then the method is also mathematico-deductive(or mathematical-experimental) (1985, p. All these observations toldGalileo that if the Earth was not unique in the Universe, then there was noreason it should be stationary, and it could revolve around its axis aswell as orbiting the Sun. B. (1985). The natural motion of a terrestrial object would bestraight upwards if it was light in weight and straight downwards if it washeavy, calculated on a straight line from the center of the Earth. 2 7). Galileo'sobservations through the telescope confirmed Copernican theory that theEarth orbited the Sun, dispelling the first Aristotlian belief that theEarth was stationary at the center of the Universe and all the planets werein orbit around it. By confirming this relationship experimentally, he couldbe confident that V % T is valid. By working backward in this fashion,Galileo was employing the hypothetico-deductive method (Cohen, 1985, p.2 7). The Birth of a New Physics. His observations of imperfections in the heavens, suchas lunar craters and sunspots, disproved the second Aristotlian belief ofthe perfection of heavenly bodies and their immutability (Spradley, 1991).His showing that the surface of the Moon resembled some places on Earthdispelled the Aristotlian belief that all heavenly bodies were smooth andspherical, and of a different composition than the Earth. When he held a professorship in astronomy at the University of Pisa,Galileo was forced to teach the Aristotlian theory at the time that the Sunand all the planets revolve around the Earth (Lucidcafe, 2 2). Since V could not be measured, he used a combinationof mathematics and experimentation to verify this relationship: if V % T,then D % T2 by deduction, and this is a relationship which can be testedexperimentally. This disproved the Aristotlian theorythat if the Earth moved, it would leave the Moon behind. Where the Earth cannot be explicitly tested andobserved other, comparable celestial bodies are tested and observed in itsplace, which allows the astronomer to divine overarching truths andprinciples that can be applied to the Earth by deductive logic (Cohen,1985, p. References Cohen, I. Tradition and faith in the Copernicanrevolution. Bernard Cohen in TheBirth of a New Physics, it is clear that rather than testing "A", Galileodeduced "B" from "A" and tested it, and then concluded that "A" would hold. 85). Heavenly bodies were smoothspheres, totally different in composition than the Earth, and all werealike. Perspectives on Science and Christian Faith, 43, 36-42. Aristotlian laws of natural and unnatural motion showedthat the two major factors in motion were the motive force and theresistance, and the motive force must be greater than the resistance formotion to occur. Galileo's first challenge to Aristotlian theory was his discovery ofa new star in the Serpentarius constellation in 16 4, proving that theheavens could change: they were not immutable (Cohen, 1985). Because D % T2 is derived from V % T bymathematics, and then tested experimentally, this method was named themathematical-experimental method. Borrowing the symbolic terms proffered by I. Later, atthe University of Padua, he learned of the theories of Nicolas Copernicusthat the Earth and all the other planets revolve around the Sun - theheliocentric theory. Although this was not a new observation, Galileo's discovery ofthe laws of falling bodies using his mathematical-experimental method wasnew.
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