Scientific Awakening--Newton

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[ Enlightenment ]


Nature and nature's laws lay hid in night;
God said, "let Newton be," and all was light--
Alexander Pope

Check out Youtube documentary on Newton and the apple with some historical context,
and recapitulation of Scientific Awakening; excellent wrap up and review!
< > Go on to Part 2 if you're interested;
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Newton's and Leibniz's predecessors made possible their invention of calculus. Réné Descartes (left--1596-1650 ) invented analytic geometry, showing that "geometric lines, surfaces, and shapes can be reduced to algegraic equations" that can be graphed geometrically (Bardi 8). He, like Newton also studied optics. Blaise Pascal (right--1623-1662,) proved himself a mathematical genius by completing studies of Euclid and Descartes by the time he was 13. He is credited with inventing the first mechanical calculator. Like Fermat, he investigated and developed theories on probability.

Descartes (left) < >
Pascal (right) < >


Sir Isaac Newton (1642-1727) occupies a paramount space in the history of mathematics and science; like Kepler and Tycho Brahe before him, he remained fascinated by different aspects of the occult, notably alchemy. Like Galileo he was devout. He continued his experiments in alchemy hoping to find the elixer of life and/or how to transform base metals into gold. In fact, the famous British economist of the 20th century, John Maynard Keynes, said of Newton, "He was the last of the magicians..., looking on the world as a mystical secret" (McKay, et al. 470). That said, Newton was a mathematical genius, invented calculus,* investigated the composition of light, and--as his greatest achievement--articulated the Universal Law of Gravitation in his monumental work, Mathematical Principles of Natural Philosophy, more popularly known as the Prinicipia (McKay, et al. 470-1). He completed the work of Copernicus, Kepler, and Galileo, demonstrating "that the universe was one huge, regulated, and uniform machine operating according to natural laws" (McKay, et al. 471).
Every high school physics student knows his three laws:
1. every object continues in a state of rest or uniform motion in a straight line unless deflected by an outside force;
2. the rate of change of motion of an object is proportional to the force acting upon it;
3. for every action there is an equal and opposite reaction
(McKay, et al. 471).

(Newton portrait by Godfrey Kneller, 1689? 1702?--check)
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5 minute Cloud biography of Newton < >


Newton's synthesis of Kepler's laws of planetary/celestial motion and Galileo's laws of terrestrial/earthly motion linked the heavens and the earth: Newton created "a new cosmology in which the world was seen largely in mechanistic terms" (McKay, et al. 471). Kepler's elliptical orbits and Galileo's rolling balls were different aspects of one majestic system (Spielvogel 600). To put it another way, natural laws functioned in absolute time, space, and motion, and they could be investigated, demonstrated, explained, proved mathematically.

The key element of the Newtonian synthesis was the Universal Law of Gravitation: "...[E]very body in the universe attracts every other body in the universe in a precise mathematical relationship, whereby the force of attraction is proportional to the quantity of the matter of the objects and inversely proportional to the square of the distance between them" (Spielvogel 600).

(Newton portrait, 1726 by Enoch Seeman)
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Students of the history of science and mathematics cannot leave a discussion of Newton without considering the work of his great rival, Gottfried Wilhelm Leibniz (1646-1716.) Each of these towering giants "defended his...right to claim intellectual ownership of calculus..."* (Bardi v). They waged a bitter letter and pamphlet war against one another to the end of their respective lives. The 21st century verdict on the two seems to be that Newton invented calculus first but withheld publication for personal reasons; Leibniz developed his theories independently of Newton and published them before his great rival. Leibniz "had two great strengths seldom found together: he was a scholar of such range that he seemed to have swallowed a library, and he was a creative thinker who poured forth ideas and inventions in half a dozen fields so new they had not yet been named" (Dolnick 45). Diderot--no slouch himelf--quailed in the face of Leibniz's awesome intellect. "Frederick the Great declared him "'a whole academy in himself'" (45). An historian of science said, "In the century of Kepler, Galileo, Decartes, Pascal, and Newton, the most versatile genius of all was...Leibniz" (237).

image source < >

The conceptual breakthrough, calculus, was "the key that opened the way to the modern age, and it made possible countless advances throughout science.... [T]he world we live in is made of ideas and inventions as much as it is made of steel and concrete. Calculus is one of the most vital of those ideas. In an era that gave birth to the telescope and the was calculus that one distinguished historian proclaimed, 'by all odds the most truly revolutionary intellectual achievement of the 17th century'" (Dolnick 44).


*calculus--a type of mathematical analysis that can be used to study bodies in motion, i.e. the position, speed, and trajectory of an object in motion. (Bardi 6).
"Calculus" is the Latin word for "pebble," a reference to "the heaps of stone once used as a calculating aid in addition and multiplication" (Dolnick 223).

Unfortunately, many of these sites have flown away or been taken down by their authors/webmasters (alas)

Bardi, Jason Socrates. The Calculus Wars. New York: Thunder's Mouth Press, 2006.

"Blaise Pascal." The History of Computing. Online Available.
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Dolnick, Edward. The Clockwork Universe. New York, et al.: Harper Perennial, 2011.

Hauck, D. W. Isaac Newton. Online Available.
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Henry, Matthew. "Isaac Newton." A History of Science. Online Available.--gone?
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McKay, John, et al. A History of Western Society, 6th ed. Boston and New York: Houghton Mifflin Co., 1999.

McNab, Andrew. "Isaac." Newtonia. Online Available
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O'Connor, John and Edmund Robertson."Sir Isaac Newton." The MacTutor History of Mathematics Archive.
Online Available < >

Palmer, R. R., et al. A History of the Modern World, 9th ed. Boston, et al.: McGraw-Hill, 2002.

Sobel, Dava. Galileo's Daughter. New York: Penguin Books, 2000.

Spielvogel, Jackson. Western Civilization, 4th ed. Belmont, et al.: Wadsworth/Thomson Learning, 2000.

Stephenson, Neal. "Isaac Newton." Quicksilver Metaweb. Online Available
< >--gone



McKee, Peggy. "Newton." The Scientific Awakening. Updated. January 13, 2015 . Online Available.
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(McKee. "Newton")