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The earth is a cylindrical column, surrounded by air; it floats uprigh — Symmetry

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"The earth is a cylindrical column, surrounded by air; it floats upright in the centre of the universe without support or anything to stand on, yet it does not fall because, being in the centre, it has no preferred direction towards which to lean; if it did, this would disturb the symmetry and balance of the whole. The spherical heavens enclose the atmosphere like the bark of a tree, and there are several layers of this enclosure to accommodate the various stellar objects."
Symmetry
Symmetry
Symmetry
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Symmetry in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations, such as translation, reflection, rotation, or scaling. Although these two meanings of the word can sometimes be told apart, they are intricately related, and hen

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"For every symmetry there comes a constraint. ...If physics is to look the same when the origin of time is shifted... [o]nly those processes that conserve energy are allowed. ...If physical law is to be immune to the arbitrary displacement of our spatial axes, then nature requires the conservation of . ...If the laws are to be unaffected by the arbitrary rotation of a coordinate system, then must be conserved. ...If the laws are to be the same for all inertial observers, then the space-time interval must be invariant. ...[A]nother constraint ...so beautiful as to make one jaw drop in wonder ...symmetry creates force. ...[T]he symmetry of identical particles forces matter ...to be enrolled as either or ...Bosons, typified by the photon, carry the fundamental forces that cause fermions to attract and repel. Fermions, led by electrons and quarks, become constituents of ordinary matter. ...Gravity. Electromagnetism. The strong force. The weak force. Each is called into being by the requirements of a particular local symmetry."
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"Men achieve tranquillity through moderation in pleasure and through the symmetry of life. Want and superfluity are apt to upset them and to cause great perturbations in the soul. The souls that are rent by violent conflicts are neither stable nor tranquil. ...one ought not to desire other mens blessings, and one ought not to envy those who have more, but rather, comparing his life with that of those who fare worse, and laying to heart their sufferings, deem himself blest of fortune in that he lives and fares so much better than they. Holding fast to this saying you will pass your life in greater tranquillity and will avert not a few of the plagues of life—envy and jealousy and bitterness of mind."
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"One overarching lesson... during the past hundred years is that the known laws of physics are associated with principles of symmetry. Special relativity is based on the symmetry embodied in the —the symmetry between all constant-velocity vantage points. The gravitational force, as embodied in the general theory of relativity, is based on the equivalence principle—the extension of the principle of relativity to embrace all vantage points regardless of the complexity of their states of motion. And the strong, weak, and electromagnetic forces are based on the... gauge symmetry principles. ...String theory takes us down another notch on the scale of explanatory depth because all of these symmetry principles, as well as another——emerge from its structure."
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"... the plays an important role deducing the consequences of symmetry in quantum mechanics. With the tools of group theory many consequences of symmetry are revealed. For example, the s that govern are simply the consequences of rotational symmetry. Quantum mechanics also revealed a new kind of symmetry, that of exchange of identical particles. This lead to a classification of all elementary particles as either s, whose wave function is invariant under interchange of two identical particles, or s, whose wave function changes sign when two identical particles are interchanged. The of such particles is different, with profound implications for their behavior in aggregate."
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