Construct · 4 fields · 5 citations
One name. Different field. Different construct. One map.
● jingle · one word, four constructs Nearest construct by meaninginvariancecompare the meaningsEvery construct on the map is compared with every other by the meaning of its definitions, and the closest one is surfaced here. The nearest construct to symmetry is invariance.
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In physics a symmetry is an invariance: a system looks the same, or its equations keep their form, after some transformation such as a shift in space, a rotation, or a change of phase. Gross, in The role of symmetry in fundamental physics (1996), treats these invariances as the deepest organizing principle of modern physics, the structure from which the known forces and their gauge fields follow. The referent is a physical law or system, and the transformation is a concrete operation on it. By Noether's theorem (Invariante Variationsprobleme, 1918) every continuous symmetry of the action carries a conserved quantity, so invariance under time gives conservation of energy and invariance under rotation gives conservation of angular momentum. What is claimed here is a property of nature that predicts conservation laws, not a group written on paper and not a fact about a face or a picture.[1][2]
In mathematics a symmetry of an object is a structure-preserving transformation that maps the object onto itself, and the set of all such transformations forms a group under composition. Armstrong, in Groups and Symmetry (1988), builds group theory from exactly this idea: the symmetries of a square, a crystal, or an equation are its self-maps, and to study the group is to study the object's symmetry. The referent is an abstract structure together with its automorphisms, and the content is algebraic, the closure, identity, and inverses that make a group. This shares the word and the notion of a transformation with the physics meaning, but here symmetry is the group, a formal object one proves theorems about, rather than an empirical invariance of nature or a trait one measures on a body.[3]
In evolutionary psychology facial or bodily symmetry is the degree to which the two sides of a face match, studied as an observable cue that a body developed without disturbance and thus as a possible signal of mate quality. Rhodes, in The evolutionary psychology of facial beauty (2006), reviews evidence that more symmetric faces tend to be rated more attractive, while noting that the tie between symmetry and actual health is weaker and more contested than the attractiveness effect. The referent is a real individual's body, and the unit is a measured asymmetry, scored from facial landmarks or from manipulated images. Unlike the physics and mathematics meanings, symmetry here is neither exact nor a transformation one applies; it is a graded, noisy property of an organism, and the claim is about perception and fitness, not about invariance or groups.[4]
In art and design symmetry is a principle of visual balance: elements arranged so that visual weight is distributed evenly about an axis or centre, giving a composition stability and order. Arnheim, in Art and Visual Perception (1974), treats balance as a fundamental of composition and symmetry as one way, though not the only way, to reach it, since a picture can be balanced without being mirror-symmetric. The referent is a made image or object, and the standard is perceptual and normative, how an arrangement strikes a viewer, rather than exact or measurable. This meaning keeps the everyday meaning of two matched halves but drops the rigour of the other three: it is a compositional value an artist weighs, not an invariance of law, a group, or a graded bodily trait.[5]
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