Isaac Newton Calculus Quotes

[All phenomena] are equally susceptible of being calculated, and all that is necessary, to reduce the whole of nature to laws similar to those which Newton discovered with the aid of the calculus, is to have a sufficient number of observations and a mathematics that is complex enough.

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method—more daring than anything that the history of philosophy records—of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.

Foreshadowings of the principles and even of the language of [the infinitesimal] calculus can be found in the writings of Napier, Kepler, Cavalieri, Fermat, Wallis, and Barrow. It was Newton's good luck to come at a time when everything was ripe for the discovery, and his ability enabled him to construct almost at once a complete calculus.

Isaac Newton is perhaps the greatest scientist who ever lived. In a world obsessed with witchcraft and sorcery, he dared to write down the universal laws of the heavens and apply a new mathematics he invented to study forces, called the calculus. As physicist Steven Weinberg has written, 'It is with Isaac Newton that the modern dream of a final theory really begins.' In its time, it was considered to be the theory of everything-that is, the theory that described all motion. It all began when he was twenty-three years old. Cambridge University was closed because of the black plague. One day in 1666, while walking around his country estate, he saw an apple fall. Then he asked himself a question that would alter the course of human history. If an apple falls, then does the moon also fall? Before Newton, the church taught that there were two kinds of laws. The first were the laws found on Earth, which were corrupted by the sin of mortals. The second were the pure, perfect, and harmonious laws of the heavens. The essence of Newton's idea was to propose a unified theory that encompassed the heavens and the Earth. In his notebook, he drew a fateful picture (see figure 1). If a cannonball is fired from a mountaintop, it goes a certain distance before hitting the ground. But if you fire the cannonball at increasing velocities, it travels farther and farther before coming back to Earth, until it eventually completely circles the Earth and returns to the mountaintop. He concluded that the natural law that governs apples and cannonballs, gravity, also grips the moon in its orbit around the Earth. Terrestrial and heavenly physics were the same.

theory. “The development of the general theory of relativity introduced Einstein to the power of abstract mathematical formalisms, notably that of tensor calculus,” writes the astrophysicist John Barrow. “A deep physical insight orchestrated the mathematics of general relativity, but in the years that followed the balance tipped the other way. Einstein’s search for a unified theory was characterized by a fascination with the abstract formalisms themselves.”44 In his Oxford lecture, Einstein began with a nod to empiricism: “All knowledge of reality starts from experience and ends in it.” But he immediately proceeded to emphasize the role that “pure reason” and logical deductions play. He conceded, without apology, that his success using tensor calculus to come up with the equations of general relativity had converted him to a faith in a mathematical approach, one that emphasized the simplicity and elegance of equations more than the role of experience. The fact that this method paid off in general relativity, he said, “justifies us in believing that nature is the realization of the simplest conceivable mathematical ideas.”45 That is an elegant—and also astonishingly interesting—creed. It captured the essence of Einstein’s thought during the decades when mathematical “simplicity” guided him in his search for a unified field theory. And it echoed the great Isaac Newton’s declaration in book 3 of the Principia: “Nature is pleased with simplicity.” But Einstein offered no proof of this creed, one that seems belied by modern particle physics.46 Nor did he ever fully explain what, exactly, he meant by mathematical simplicity. Instead, he merely asserted his deep intuition that this is the way God would make the universe. “I am convinced that we can discover by means of purely mathematical constructions the concepts and the laws connecting them with each other,” he claimed.

Newton ruled the Royal Society like a tyrant. This led to some ugly incidents. The worst was the fight about who really invented calculus.

Now walking out onto the upper deck to find Minerva sailing steadily eastward on calm seas, Daniel is appalled that anyone ever doubted these matters. The horizon is a perfect line. The sun a red circle tracing a neat path through the sky and proceeding through an orderly series of color changes: red, yellow, white. Thus nature. Minerva, the human world, is a family of curves. There are no straight lines here. The decks are slightly arched, to shed water and supply greater strength. The masts flexed, impelled by the thrust of the sails, but restrained by webs of rigging, curved grids like Isaac’s sundial lines. Of course, wherever wind collects in a sail or water skims around the hull, it follows rules that Bernoulli has set down using the calculus, Leibniz’s version. Minerva is a congregation of Leibniz curves, navigating according to Bernoulli rules, across a vast mostly water-covered sphere whose size, precise shape, trajectory through the heavens and destiny were all laid down by Newton.

Nathaniel Bowditch… the father of American Navigation was born on March 26, 1773, in Salem, Massachusetts. At the age of ten; he left school to work in his father's cooperage, before becoming a bookkeeping apprentice, to a ship chandler. At fourteen years of age he taught himself Algebra and later Calculus. He poured over books critical to the development of Astronomy, such as those written by Sir Isaac Newton. He also corrected thousands of calculation errors in John Hamilton Moore’s book “The New Practical Navigator.” As a young man he learned Latin and French allowing him to read foreign technical books and translated Pierre Simon de Laplace’s book on mathematics and theoretical astronomy. In 1795, Bowditch went to sea on his first voyage as a ship's clerk and yeoman. By his fifth voyage at sea he was promoted to Captain and was a part owner of the vessel. Following this voyage, he returned to Salem in 1803, resuming his studies. In 1802, his book The American Practical Navigator was first published. That same year, Harvard University awarded Bowditch an honorary Master of Arts degree. His tireless academic work earned him a significant standing, including acceptance to the “American Academy of Arts and Sciences.” In 1806, Bowditch was offered the “Chair of Mathematics and Physics at Harvard” as well as at the “United States Military Academy and the University of Virginia.” His encyclopedia of navigation “The American Practical Navigator,” usually just referred to by his name “Bowditch,” still serves as a valuable handbook on oceanography and meteorology, and contains useful tables and a maritime glossary. Without a doubt it is the finest book on Navagation ever written.

Isaac Newton, the man who rejected the demonic Aryan theology of the Trinity and were recompensed by The Lord with CALCULUS as a reward for his fidelity.

To innovate, people need to have faith in the future. A stable currency is a vital component of a stable society. Between 1700 and 1914, to give one example, Great Britain generated an immense amount of economic progress. George Gilder pointed out that along with transforming physics and co-developing calculus, the English polymath Sir Isaac Newton (1643–1727) also served as the master of the mint. During his tenure, Great Britain moved to the gold standard, which ensured the stability of the pound sterling and provided the monetary structure of the British Empire during one of the greatest periods of economic growth ever experienced by the human race.55

The immediate catalyst for the emergence of the Enlightenment in the eighteenth century was the scientific revolution of the sixteenth and seventeenth centuries, which included three momentous discoveries in astronomy: Johannes Kepler delineated the rules that govern the movement of the planets, Galileo Galilei placed the sun at the center of the universe, and Isaac Newton discovered the force of gravity, invented calculus (Gottfried Wilhelm Leibniz independently discovered it at the same time), and used it to describe the three laws of motion. In so doing, Newton joined physics and astronomy and illustrated that even the deepest truths in the universe could be revealed by the methods of science. These contributions were celebrated in 1660 with the formation of the first scientific society in the world: the Royal Society of London for Improving Natural Knowledge, which elected Isaac Newton as its president in 1703. The founders of the Royal Society thought of God as a mathematician who had designed the universe to function according to logical and mathematical principles. The role of the scientist—the natural philosopher—was to employ the scientific method to discover the physical principles underlying the universe and thereby decipher the codebook that God had used in creating the cosmos. Success in the realm of science led eighteenth-century thinkers to assume that other aspects of human action, including political behavior, creativity, and art, could be improved by the application of reason, leading ultimately to an improved society and better conditions for all humankind. This confidence in reason and science affected all aspects of political and social life in Europe and soon spread to the North American colonies. There, the Enlightenment ideas that society can be improved through reason and that rational people have a natural right to the pursuit of happiness are thought to have contributed to the Jeffersonian democracy that we enjoy today in the United States.