Potential energy involves space configurations or distances, while kinetic energy involves motion. For example, nuclear energy involves the configuration of nuclei, chemical energy involves the configuration of electrons in atoms, and electrostatic energy involves the configuration of electrons in substances. Magnetic energy is the kinetic energy stored in moving charges, and fly wheels store mechanical kinetic energy.
Energy is best visualized in terms of force and distance. Carrying 50 pounds up a 10 foot ladder would require 500 foot-pounds of energy. If pushing a skid took 100 pounds of push, it would take 1000 foot-pounds of energy to push the skid 10 feet.
The Hamiltonian ("h") is equal to the total energy of a system. If space is isotropic ("h" does not depend on direction in space) and is homogeneous ("h" does not change with uniform translation in space), Hamilton's equations yield the laws of conservation of angular momentum and linear momentum, respectively.
Power is how fast work is done. It takes more power to do work in less time.
In 1840 James Prescott Joule (1818-1889), a brewer who could not get his theories about the conservation of energy published in a scientific journal, published a landmark paper in a newspaper where his brother worked, demonstrating that various forms of energy existed (Mechanical, electrical, and heat) and could be changed, one into another. His paper formed the basis of the law of conservation of energy, and the first law of thermodynamics.
In 1847, Hermann von Helmholtz (1821-1894) published a paper, "On the Conservation of Force", which expanded upon Joule's conservation of energy ideas.
To a large extent, Kepler, Newton, and modern physicists are like the ancient augurs, but where the ancient augurs established statistical relationships between "signs" like earthquakes, lightning strikes, the positions of the stars and floods, the modern augurs established statistical relationships between "signs" like the positions of material bodies and electrical charges. Both schools, modern physicists and ancient augurs, tended to look upon these methods as a means to understand, rather than a means to control nature.
The men who shaped the modern world were not augurs who used signs, astrology and mathematics to divine the future, but men who looked upon these methods as a means to control, rather than a means to understand nature. Men like James Watt, Thomas Edison, Goodyear, Land, and hundreds of thousands of inventors and entrepreneurs who were more interested in controlling, than understanding, nature.
I suggest that the Western World took an important step in rejecting augurism in1766 when a Presbyterian minister, Joseph Priestley (1733-1804) rejected rule by "divine right", and most of the fundamental doctrines of Christianity, including the Trinity, and predestination, embraced the French Revolution, and with a few free thinkers like James Watt, Erasmus Darwin, and Josiah Wedgwood, formed the Lunar Society which met monthly at the full moon in Birmingham, England to discuss how to shape the world (It is interesting to note that, at 61 years of age, Priestley, who was ostracized in England for rejecting rule by "divine right", immigrated to America in 1794 where he became friends with John Adams, Ben Franklin and Thomas Jefferson, and where he was offered many public offices and chairs at major universities, all of which he rejected.).
The purpose of this piece is to point out that Western Europe and the rest of the world was pretty much alike until about 1750 when, inspired by the works of that master augur Newton, a few men made the break from being playthings of Kings and Gods, to becoming independent, free will, sentient beings who had control over their own destinies. While some in Western Europe and America inherited the legacy of Priestley, Watt and the Lunar Society; most of the world continued to augur, believing they were playthings of gods and kings, believing in signs, and looking to statistical correlations to control their actions. Archimedes (287-212 BC) pioneered the rejection of augurism when he stated, "Give me a place to stand, and I will move the world.", but the overpowering central authority of Rome destroyed this embryonic idea before it took hold.
Japan, after being humiliated by a squadron of U.S. warships commanded by Commodore Matthew C. Perry in July 1853, abandoned auguring and adopted the ways of Priestley and Watt, and they now lead the world in confronting, rather than abiding nature. The Peoples Republic of China has gotten the message, and no doubt, China will become the major player in world politics in the 21st century.
Lest the point be missed, statistics and equations should be used to control, not augur. A sentient being cannot go wrong by assuming that cause and effect are real, and that his will can serve as a principle cause.
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