Diego Rivera
Michael Polanyi College
Semester Three Allopoïesis – Mechanics Essay
December 10th, 2013
Michael Polanyi College
Semester Three Allopoïesis – Mechanics Essay
December 10th, 2013
A New World
In the history of mankind, only few have achieved what Newton did with his theory of universal gravitation. His theory has revolutionized in some way all the areas of human life; from science to navigating to philosophy and religion. It has changed our conception of the universe and the relation between the earthly and the celestial bodies. He stopped the dichotomy that things on Earth were ruled by different laws than the ones from the sky, and in the process unified the rules governing both areas. Newton’s theory is one of the main foundations of modern science, an incredible creation that symbolized the capacity of human beings to create meaning to understand the world, and truly a work of art that’s worth many hours of dedicated study and admiration.
The Law of Universal Gravitation states that all particles with mass gravitate towards each other proportionately to the mass of each particle, and inversely as the square of the distances between the particles. One of the main uses of this law is to demonstrate the elliptical orbits of the planets. Newton, in order to arrive at this conclusion, followed a method that allowed him to first state the foundations of his theory, and then build an argument based on those foundations. Even though Newton had already developed his version of calculus in algebraic form, he decided to use classic geometry to express his proofs. His aim here was to use a deductive method that was more general and that allowed the continuity and precision that geometry gives. Thus, Newton’s mathematical propositions are done using ratios and proportions. In the Preface of the reader, Newton says, “And on that account we present these (writings) of ours as the mathematical principles of philosophy. For the whole difficulty of philosophy appears to turn upon this: that from the phenomena of motion we investigate the forces of nature, and then from these forces we demonstrate the rest of the phenomena.” Here, we can anticipate his method of observation and then deduction through mathematical demonstrations.
His argument is exposed in three books. In the first two, we’ll find the mathematical foundations and on the third one we’ll see his discoveries about gravitation in the world like the elliptical orbits of the planets. The core sequence of his argument starts with the mathematical foundations. These are set in definitions, laws of motion, and hypothetical mathematical propositions. In the definitions, he defines what he means by quantity of matter and motion, inherent and impressed force, and absolute, accelerative, and motive centripetal force. Then, he states that the axioms or laws of motion are three. The first one states that things will remain in their state of rest or movement if there’s no impressed force on them. The second states that a change of motion is proportional to the motive force impressed and would take place in a straight line with that force. And third, that every action has a contrary and equal reaction. Now that he has the givens, he proceeds to develop mathematical propositions. In all this process, we can see a clear parallelism in the use of method between Newton and Euclid. After stating these foundations, he gives four rules of philosophizing. These are principles he believes any philosopher uses to understand the natural things around them. The first two are the main ones, and state that Nature is simple in the sense that one must admit only the true and sufficient causes needed to explain a phenomena, and that if natural effects are of the same kind, one can assign the same causes. With these in mind, Newton derives some conclusions about our world in the Phenomena of Book III. Then, from the same book he makes propositions of the applications to our universe and it’s here that he finally derives the law of universal gravitation.
Another important point in his theory is the use of evidence. Because of the method Newton is using, he only needs some experimental data. Most of the evidence he uses is based on observations and theory generally accepted, taking into account the great observers that were before him, like Kepler and Brahe. Using these minimal data, he is able to deduce, through mathematical demonstrations, the underlying laws governing our world.
There’s no doubt that Newton’s great discovery has opened the door of a new world in which we are meant to be explorers. The many areas affected by this theory have contributed in our conception of man and the universe. Nevertheless, there are some questions that remain unanswered. In the General Scholium, Newton constantly refers to an eternal and infinite God, and it appears that he believes that even though God exists, he doesn’t intervene with the bodies on Earth. This is seen when he writes, “He (God) governs everything, not as the soul of the world, but as the lord of all things.” Moreover, he says, “God is one and the same God always and everywhere. He is omnipresent not in power alone, but also in substance. For power cannot subsist without substance. In him all things are contained and moved, but without mutual effects. God is not affected by the motions of bodies, and these do not experience any resistance from God’s omnipresence. It is universally acknowledged that the highest God exists necessarily, and by the same necessity he is always and everywhere.” This leaves the question of the role of God in our universe and whether he is capable of intervening. Also, whether God set universal laws that we can understand or not. One final question is about the exploration of the final cause of things. In the last pages, Newton says, “Hitherto I have set forth the phenomena of the heavens and of our sea through the force of gravity, but I have not yet assigned the cause of gravity.” This cause of gravity seems to be out of the reach of our capacity, and thus, Newton leaves this final cause only to be understood by God. Then, is the only aim of the natural philosopher to focus on the study of the motor causes? Would we be able to understand and determine the final cause of the world around us? This last question seems to remain unanswered. Nevertheless, it’s the responsibility of the explorer to discover new ways to understand the universe and work upon the theories that the great minds have developed throughout history, and so be able, as Newton once said, “To see further by standing on the shoulders of giants.”
The Law of Universal Gravitation states that all particles with mass gravitate towards each other proportionately to the mass of each particle, and inversely as the square of the distances between the particles. One of the main uses of this law is to demonstrate the elliptical orbits of the planets. Newton, in order to arrive at this conclusion, followed a method that allowed him to first state the foundations of his theory, and then build an argument based on those foundations. Even though Newton had already developed his version of calculus in algebraic form, he decided to use classic geometry to express his proofs. His aim here was to use a deductive method that was more general and that allowed the continuity and precision that geometry gives. Thus, Newton’s mathematical propositions are done using ratios and proportions. In the Preface of the reader, Newton says, “And on that account we present these (writings) of ours as the mathematical principles of philosophy. For the whole difficulty of philosophy appears to turn upon this: that from the phenomena of motion we investigate the forces of nature, and then from these forces we demonstrate the rest of the phenomena.” Here, we can anticipate his method of observation and then deduction through mathematical demonstrations.
His argument is exposed in three books. In the first two, we’ll find the mathematical foundations and on the third one we’ll see his discoveries about gravitation in the world like the elliptical orbits of the planets. The core sequence of his argument starts with the mathematical foundations. These are set in definitions, laws of motion, and hypothetical mathematical propositions. In the definitions, he defines what he means by quantity of matter and motion, inherent and impressed force, and absolute, accelerative, and motive centripetal force. Then, he states that the axioms or laws of motion are three. The first one states that things will remain in their state of rest or movement if there’s no impressed force on them. The second states that a change of motion is proportional to the motive force impressed and would take place in a straight line with that force. And third, that every action has a contrary and equal reaction. Now that he has the givens, he proceeds to develop mathematical propositions. In all this process, we can see a clear parallelism in the use of method between Newton and Euclid. After stating these foundations, he gives four rules of philosophizing. These are principles he believes any philosopher uses to understand the natural things around them. The first two are the main ones, and state that Nature is simple in the sense that one must admit only the true and sufficient causes needed to explain a phenomena, and that if natural effects are of the same kind, one can assign the same causes. With these in mind, Newton derives some conclusions about our world in the Phenomena of Book III. Then, from the same book he makes propositions of the applications to our universe and it’s here that he finally derives the law of universal gravitation.
Another important point in his theory is the use of evidence. Because of the method Newton is using, he only needs some experimental data. Most of the evidence he uses is based on observations and theory generally accepted, taking into account the great observers that were before him, like Kepler and Brahe. Using these minimal data, he is able to deduce, through mathematical demonstrations, the underlying laws governing our world.
There’s no doubt that Newton’s great discovery has opened the door of a new world in which we are meant to be explorers. The many areas affected by this theory have contributed in our conception of man and the universe. Nevertheless, there are some questions that remain unanswered. In the General Scholium, Newton constantly refers to an eternal and infinite God, and it appears that he believes that even though God exists, he doesn’t intervene with the bodies on Earth. This is seen when he writes, “He (God) governs everything, not as the soul of the world, but as the lord of all things.” Moreover, he says, “God is one and the same God always and everywhere. He is omnipresent not in power alone, but also in substance. For power cannot subsist without substance. In him all things are contained and moved, but without mutual effects. God is not affected by the motions of bodies, and these do not experience any resistance from God’s omnipresence. It is universally acknowledged that the highest God exists necessarily, and by the same necessity he is always and everywhere.” This leaves the question of the role of God in our universe and whether he is capable of intervening. Also, whether God set universal laws that we can understand or not. One final question is about the exploration of the final cause of things. In the last pages, Newton says, “Hitherto I have set forth the phenomena of the heavens and of our sea through the force of gravity, but I have not yet assigned the cause of gravity.” This cause of gravity seems to be out of the reach of our capacity, and thus, Newton leaves this final cause only to be understood by God. Then, is the only aim of the natural philosopher to focus on the study of the motor causes? Would we be able to understand and determine the final cause of the world around us? This last question seems to remain unanswered. Nevertheless, it’s the responsibility of the explorer to discover new ways to understand the universe and work upon the theories that the great minds have developed throughout history, and so be able, as Newton once said, “To see further by standing on the shoulders of giants.”