“To the scientists of 1850, Hamilton's principle was the realization of a dream. …from the time of Galileo scientists had been striving to deduce as many phenomena of nature as possible from a few fundamental physical principles. …they made striking progress …But even before these successes were achieved Descartes had already expressed the hope and expectation that all the laws of science would be derivable from a single basic law of the universe. This hope became a driving force in the late eighteenth century after Maupertuis's and Euler's work showed that optics and mechanics could very likely be unified under one principle. Hamilton's achievement in encompassing the most developed and largest branches of physical science, mechanics, optics, electricity, and magnetism under one principle was therefore regarded as the pinnacle of mathematical physics.”

— Morris Kline

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 441.

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "To the scientists of 1850, Hamilton's principle was the realization of a dream. …from the time of Galileo scientists ha…" by Morris Kline?

Morris Kline 42

American mathematician 1908–1992

Morris Kline (1908–1992) American mathematician

Source: Mathematics and the Physical World (1959), pp. 224-225

“The minimum principle that unified the knowledge of light, gravitation, and electricity of Hamilton's time no longer suffices to relate these fundamental branches of physics. Within fifty years of its creation, the belief that Hamilton's principle would outlive all other physical laws of physics was shattered. Minimum principles have since been created for separate branches of physics… but these are not only restricted… but seem to be contrived…
A single minimum principle, a universal law governing all processes in nature, is still the direction in which the search for simplicity is headed, with the price of simplicity now raised from a mastery of differential equations to a mastery of the calculus of variations.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 442.

“The goal of deriving all the phenomena of nature from a few basic physical laws and the axioms of mathematics had been set by Galileo…
In studying curvilinear motions on the earth Galileo had found the parabola to be the basic curve. In the heavens… Kepler… had found the ellipse to be the basic curve. Why this difference? …since parabola and ellipse are both conic sections there was the provocative suggestion that perhaps some physical law unified these related paths of motion. …
It has often happened in the history of mathematics and science that major problems remained outstanding… great minds… succeeded only in revealing the true difficulties… and in generating an atmosphere of dispair… Then a genius appeared… with ideas that seemed remarkably simple once propounded, clarified the entire situation, dispelled the confusion, restored order, and produced a new synthesis that embraced far more even than the phenomena under consideration. The genius who… picked up the torch of science dropped by Galileo, was Isaac Newton.”

Morris Kline (1908–1992) American mathematician

Source: Mathematics and the Physical World (1959), p. 225

“An essential distinction exists between two stages in the process of advancing our knowledge of the laws of physical phenomena; the first stage consists in observing the relations of phenomena, whether of such as occur in the ordinary course of nature, or of such as are artificially produced in experimental investigations, and in expressing the relations so observed by propositions called formal laws. The second stage consists in reducing the formal laws of an entire class of phenomena to the form of a science; that is to say, in discovering the most simple system of principles, from which all the formal laws of the class of phenomena can be deduced as consequences.”

William John Macquorn Rankine (1820–1872) civil engineer

Source: "Outlines of the Science of Energetics," (1855), p. 121; Lead paragraph: Section "What Constitutes A Physical Theory"

“We can deduce, often, from one part of physics like the law of gravitation, a principle which turns out to be much more valid than the derivation.”

Richard Feynman book The Character of Physical Law

Source: The Character of Physical Law (1965), chapter 2, “ The Relation of Mathematics to Physics http://www.youtube.com/watch?v=M9ZYEb0Vf8U” referring to the law of conservation of angular momentum
Context: Now we have a problem. We can deduce, often, from one part of physics like the law of gravitation, a principle which turns out to be much more valid than the derivation. This doesn't happen in mathematics, that the theorems come out in places where they're not supposed to be!

“The aim of the scientist is to express, in as simple a statement as possible, the principles underlying the order and arrangement of phenomena.”

Herbert Dingle (1890–1978) British astronomer

page 39 https://books.google.com/books?id=hwpKAAAAIAAJ&pg=PA39
Relativity for All, London, 1922

“These principles [in art], forgotten over time, were rediscovered by a few geniuses such as Rembrandt, Vélazquez, Délacroix, Corot and Manet. These principles can be deduced from innate principles within us, ideas of harmony, common to all unspoiled men.... these are the laws of harmony and color.”

Paul Sérusier (1864–1927) French painter

Source: from: 'A letter to Maurice Denis, p. 237

“Before the quantum theory appeared, the principle of the uniformity of nature - that like causes produce like effects - had been accepted as a universal and indisputable fact of science. As soon as the atomicity of radiation became established, this principle had to be discarded.”

James Jeans (1877–1946) British mathematician and astronomer

Physics and Philosophy (1942)

“A physical theory, like an abstract science, consists of definitions and axioms as first principles, and of propositions, their consequences; but with these differences:—first, That in an abstract science, a definition assigns a name to a class of notions derived originally from observation, but not necessarily corresponding to any existing objects of real phenomena, and an axiom states a mutual relation amongst such notions, or the names denoting them; while in a physical science, a definition states properties common to a class of existing objects, or real phenomena, and a physical axiom states a general law as to the relations of phenomena; and, secondly,—That in an abstract science, the propositions first discovered are the most simple; whilst in a physical theory, the propositions first discovered are in general numerous and complex, being formal laws, the immediate results of observation and experiment, from which the definitions and axioms are subsequently arrived at by a process of reasoning differing from that whereby one proposition is deduced from another in an abstract science, partly in being more complex and difficult, and partly in being to a certain extent tentative, that is to say, involving the trial of conjectural principles, and their acceptance or rejection according as their consequences are found to agree or disagree with the formal laws deduced immediately from observation and experiment.”

William John Macquorn Rankine (1820–1872) civil engineer

Source: "Outlines of the Science of Energetics," (1855), p. 121; Second paragraph

“He had doubted the correctness of the law of refraction of light but when he found in 1661 that he could deduce it from his Principle, he not only resolved his doubts about the law but felt all the more certain that his Principle was correct.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 580
Context: Fermat knew that under reflection light takes the path requiring least time and, convinced that nature does indeed act simply and economically, affirmed in letters of 1657 and 1662 his Principle of Least Time, which states that light always takes the path requiring least time. He had doubted the correctness of the law of refraction of light but when he found in 1661 that he could deduce it from his Principle, he not only resolved his doubts about the law but felt all the more certain that his Principle was correct.... Huygens, who had at first objected to Fermat's Principle, showed that it does hold for the propagation of light in media with variable indices of refraction. Even Newton's first law of motion, which states that the straight line or shortest distance is the natural motion of a body, showed nature's desire to economize. These examples suggested that there might be a more general principle. The search for such a principle was undertaken by Maupertuis.

Help us to complete the source, original and additional information

Morris Kline 42

Related quotes

Related topics