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The Meditations of Marcus Aurelius: Selections Annotated and Explained Russell McNeil, PhD Editor, Malaspina Great Books In 1862 the English literary critic and poet Matthew Arnold described Marcus Aurelius as "the most beautiful figure in history." The Stoicism of Aurelius is grounded in rationality and rests solidly on an ethical approach rooted in nature. Stoicism promises real happiness and joy in this life and a serenity that can never be soured by personal misfortune. This philosophy has universal appeal with practical implications on problems ranging from climate change and terrorism to the personal management of sickness, aging, depression and addiction. I truly believe that the Meditations of Marcus Aurelius has much to offer us now...(Click on book cover for more)

Category:	Baroque Science Baroque Literature
Name:	Isaac Newton - Physics, Math, Philosophy
Birth Year:	1642
Death Year:	1727
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Biography, Lectures, and Research Links:	Brief Biography - Physics Series, Math Series, World Philosophy Series Blog Isaac Newton SEARCH NOW: by title by author Sir Isaac Newton, (December 25, 1642 - March 20, 1727), was an English philosopher, mathematician, and physician who published the Philosophiae Naturalis Principia Mathematica, more commonly referred to as the Principia, where he described the laws of gravity and, via his laws of motion, laid the ground work for the field of Classical Mechanics. He investigated the refraction of light, demonstrating that a prism could break up white light into a spectrum of colours: from his work he concluded that any refractive telescope would suffer from the dispersion of light into colours, and devised the reflecting telescope to bypass this whole problem (later, when glasses with a variety of refractive properties became available, achromatic lenses became possible). Tradition has it that Newton was sitting under an apple tree when an apple fell on his head, and this made him understand that earthly and celestial gravitation are the same. He is also credited, along with Gottfried Wilhelm Leibniz, with the development of Calculus. Both developed the method independently in similar time-frame and used a different notation. Even though he belongs to the brightest scientists of his era, the last 25 years of Newton's life were marred by a bitter dispute with Leibniz who he accused of plagiarism of his fluxions method. Ultimately, Leibnitz's notation in calculus was adopted. Newton was also a member of Parliament, but his only recorded comments were to complain about a cold draft in the chamber. Newton was buried in Westminster Abbey. The Principia The Philosophiae naturalis principia mathematica (The Mathematical Principles of Natural Philosophy), also referred to as the Principia Mathematica or Principia, is a three-volume work on the foundations of classical mechanics, written by Isaac Newton and published in 1687. In it, Newton states his laws of motion, which form the postulates of classical mechanics. Furthermore, he formulates Newton's law of gravity, and derives Kepler's laws for the motion of the planets (which were first obtained empirically.) In formulating his physical theories, Newton had developed a field of mathematics known as calculus. However, the language of calculus was largely left out of the Principia. Instead, Newton recast the majority of his proofs as geometric arguments. Newton's laws of motion Newton's laws of motion are the three basic scientific laws of Isaac Newton concerning the motion of bodies. From these Classical Mechanics is derived. Newton's First Law, also called Law of inertia: "Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed on it." Newton's Second Law: "The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed." This is often summarized in the equation: F = ma where F is force, m is mass, and a is acceleration. Newton's Third Law: "To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts." or more commonly "For every action force, there is an equal and opposite reaction force". Using Newton's laws Much of classical mechanics is derived from Newton's second law, particularly calculations involving momentum and acceleration. When solving problems, a useful way restate the third law is, "Forces always come in equal pairs." It is important to realise that the reaction force always acts on a different body to the initial force. If body A exerts a force on body B, then body B exerts an equal force on body A. The reaction force has the same line of action, and is of the same type and magnitude as the original force. Newton first gave his laws in the first volume of his Philosophiae Naturalis Principia Mathematica in 1687 and, using the mathematical tools of his newly developed calculus, proved many results concerning the motion of idealised particles. In the third volume, he showed how, combined with his law of universal gravitation, his laws of motion explained the motion of the planets and the Laws of Kepler. Not until 1916 and Albert Einstein's theory of relativity did anyone improve upon Newton's model of the motions of the planets. Newton's Law of Gravitation Newton eventually published his still famous law of universal gravitation in his Principia Mathematica as follows: F = G m1m2/r2 Where F is the force mass one and mass two exert on each other, m1 and m2 are their respective masses, r is the distance between their centers of mass, and G is the constant of proportionality that is called the Gravitational Constant. Nobody knows for sure if the story about Newton sitting under an apple tree is true, but Newton's insight is the same nevertheless. Philosophers had thought since the Greeks that the "natural" movement of stars, planets, the Sun and the Moon was circular, Kepler established that orbits are actually elliptical, but still thought that the movements of the planets was dictated by some "divine force" emanated from the sun, but Newton realized that the same force that causes a thrown rock to fall back to the Earth keeps the planets in orbit of the Sun, and the Moon in orbit of the Earth. Newton wasn't alone in making significant contributions to the understanding of gravity. Before Newton, Galileo Galilei corrected a common misconception, started by Aristotle, that objects with different mass fall at different rates. To Aristotle, it simply made sense that objects of different mass would fall at different rates, and that was enough for him. Galileo, however, actually tried dropping objects of different mass at the same time. Aside from minor differences due to friction from the air, Galileo observed that all masses accelerate the same. Using Newton's equation, F = ma, it is plain to us why: F = G m1m2/r2 = m1a1 The above equation says that mass m1 will accelerate at acceleration a1 under the force of gravity, but divide both sides of the equation by m1 and: a1 = G m2/r2 Nowhere in the above equation does the mass of the falling body appear. When dealing with objects near the surface of a planet, the change in r divided by the initial r is so small that the acceleration due to gravity appears to be perfectly constant. The acceleration due to gravity here on earth is usually called g, and its value is about 9.8 m/s2 (or 32 ft/s2). Galileo didn't have Newton's equations, though, so his insight into gravity's proportionality to mass was invaluable, and possibly even affected Newton's formulation on how gravity works. However, across a large body, variations in r can create a significant tidal force. [This article is licensed under the GNU Free Documentation License and uses material adapted in whole or in part from the Wikipedia article on Isaac Newton.] The Great Books: Isaac Newton Please browse our Amazon list of titles about Isaac Newton. For rare and hard to find works we recommend our Alibris list of titles about Isaac Newton. Post Comments, Questions or Suggestions! 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This web page is part of a biographical database on Great Ideas. These are living ideas that have shaped, defined and directed world culture for over 2,500 years. By definition the Great Ideas are radical. As such they are sometimes misread, or distorted by popular simplifications. Understanding a Great Idea demands personal engagement. Our selection of Great Ideas is drawn from literature and philosophy, science, art, music, theatre, and cinema. We also include biographies of pivotal historical and religious figures, as well as contributions from women and other historically under-represented minorities. The result is an integrated multi-cultural and multi-disciplinary database built upon the framework of the always controversial Great Books Core List published in 1940 by the late Great Books Pioneer Mortimer Adler (1902-2001). Most of the works on that list are available in the 60 volume Great Books of the Western World.