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 KlineRelated topics
basic century dream eighteenth few force fundamental hope late law likely magnetism mechanics nature optics pinnacle possible realization science single under work Laws Descartes galileoRelated quotes
The advent of the Computer age has stimulated a rapid expansion in the use of quantitative techniques for the analysis of economic, urban, social, biological and other types of systems in which it is the animate rather than in dominant role. At present, most of the techniques employed for the analysis of humanistic, i.e., human centred systems are adaptations of the methods that have been developed over a long period of time for dealing with mechanistic systems, i.e., physical systems governed in the main by-the laws of mechanics, electromagnetism, and thermodynamics. The remarkable successes of these methods in unraveling the secrets of nature and enabling us to build better and better machines have inspired a widely held belief that the same or similar techniques can be applied with comparable effectiveness to the analysis of humanistic systems.
Lotfi A. Zadeh
I reproach myself for a gross error. But I would reproach myself more if I had persisted in an error after observations revealed it clearly to be that. I made a deal of money in the late 1940s on the bull side, ignoring Satchel Paige's advice to Lot's wife, "Never look back.” Rather I would advocate Samuelson's Law: "Always look back. You may learn something from your residuals. Usually one's forecasts are not so good as one remembers them; the difference may be instructive.” The dictum "If you must forecast, forecast often,” is neither a joke nor a confession of impotence. It is a recognition of the primacy of brute fact over pretty theory. That part of the future that cannot be related to the present's past is precisely what science cannot hope to capture. Fortunately, there is plenty of work for science to do, plenty of scientific tasks not yet done.
Paul Samuelson
[We are now] in a position to judge of the validity of the objection which has been made, that the principle of Natural Selection depends on a succession of favourable chances. The objection is more in the nature of an innuendo than of a criticism, for it depends for its force upon the ambiguity of the word chance, in its popular uses. The income derived from a Casino by its proprietor may, in one sense, be said to depend upon a succession of favourable chances, although the phrase contains a suggestion of improbability more appropriate to the hopes of the patrons of his establishment. It is easy without any very profound logical analysis to perceive the difference between a succession of favourable deviations from the laws of chance, and on the other hand, the continuous and cumulative action of these laws. It is on the latter that the principle of Natural Selection relies.
Ronald Fisher
When the dialectical method is applied to the study of economic problems, economic phenomena are not viewed separately from each other, by bits and pieces, but in their inner connection as an integrated totality, structured around, and by, a basic predominant mode of production. This totality is analysed in all its aspects and manifestations, as determined by certain given laws of motion, which relate also to its origins and its inevitable disappearance. These laws of motion of the given mode of production are discovered to be nothing but the unfolding of the inner contradictions of that structure, which define its very nature. The given economic structure is seen to be characterized at one and the same time by the unity of these contradictions and by their struggle, both of which determine the constant changes which it undergoes.
Ernest Mandel
In fact, there is something puzzling about the Higgs mass we now do observe. It is generally known as the "hierarchy problem.” Since it is the Higgs mass that sets the scale for the masses of all other known elementary particles, one might guess that it should be similar to another mass that plays a fundamental role in physics, the so-called Planck mass, which is the fundamental unit of mass in the theory of gravitation. (It is the mass of hypothetical particles whose gravitational attraction for one another would be as strong as the electric force between two electrons separated by the same distance.) But the Planck mass is about a hundred thousand trillion times larger than the Higgs mass. So, although the Higgs particle is so heavy that a giant particle collider was needed to create it, we still have to ask, why is the Higgs mass so small?
Steven Weinberg