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.
William Rowan HamiltonRelated topics
calculus differential direction fifty fundamental gravitation knowledge law light longer nature now search single universal years LawsRelated quotes
Serious debates are taking place about how law enforcement personnel relate to the communities they serve, about the appropriate use of force, and about real and perceived biases, both within and outside of law enforcement. These are important debates. Every American should feel free to express an informed opinion-to protest peacefully, to convey frustration and even anger in a constructive way. That's what makes our democracy great. Those conversations-as bumpy and uncomfortable as they can be-help us understand different perspectives, and better serve our communities. Of course, these are only conversations in the true sense of that word if we are willing not only to talk, but to listen, too.
James Comey
I am a skeptic about everything, including God and atheism. I am not certain about issues of cosmology.... I am more certain that the miraculous stories that form the basis of most religious beliefs are myths. Yet I respect the Bible and enjoy reading and teaching it. Indeed, I find it even more fascinating as a human creation than as a divine revelation. I consider myself a committed Jew, but I do not believe that being a Jew requires belief in the supernatural.... Indeed, it is while praying that I experience my greatest doubts about God, and it is while looking at the stars that I make the leap of faith.... If there is a governing force, He (or She or It) is certainly not in touch with those who purport to be speaking on His behalf.
Alan Dershowitz
The concepts which now prove to be fundamental to our understanding of nature-a space which is finite; a space which is empty, so that one point [of our 'material' world] differs from another solely in the properties of space itself; four-dimensional, seven- and more dimensional spaces; a space which for ever expands; a sequence of events which follows the laws of probability instead of the law of causation-or alternatively, a sequence of events which can only be fully and consistently described by going outside of space and time-all these concepts seem to my mind to be structures of pure thought, incapable of realisation in any sense which would properly be described as material.
James Jeans
This education, therefore, results at the very outset in knowledge which transcends all experience, which is abstract, absolute, and strictly universal, and which includes within itself beforehand all subsequently possible experience. On the other hand, the old education was concerned, as a rule, only with the actual qualities of things as they are and as they should be believed and rioted, without anyone being able to assign a reason for them. It aimed, therefore, at purely passive reception by means of the power of memory, which was completely at the service of things. It was, therefore, impossible to have any idea of the mind as an independent original principle of things themselves.
Johann Gottlieb Fichte
Having discovered the true principle, I then derived all the laws that govern the motion of light, those concerning its direct propagation, its reflection and its refraction. I reserve for particular members of our Assembly the geometrical demonstration of my theory.
I know the distaste that many mathematicians have for final causes applied to physics, a distaste that I share up to some point. I admit, it is risky to introduce such elements; their use is dangerous, as shown by the errors made by Fermat and Leibniz in following them. Nevertheless, it is perhaps not the principle that is dangerous, but rather the hastiness in taking as a basic principle that which is merely a consequence of a basic principle.
Pierre Louis Maupertuis