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The composition of the braids σ and τ is written as στ.. The set of all braids on four strands is denoted by .The above composition of braids is indeed a group operation. . The identity element is the braid consisting of four parallel horizontal strands, and the inverse of a braid consists of that braid which "undoes" whatever the first braid did, which is obtained by flipping a diagram ...
James Braid in the nineteenth century saw fixing the eyes on a bright object as the key to hypnotic induction. [3]A century later, Sigmund Freud saw fixing the eyes, or listening to a monotonous sound as indirect methods of induction, as opposed to “the direct methods of influence by way of staring or stroking” [4] —all leading however to the same result, the subject's unconscious ...
Braid, therefore, adopted the term "ideo-dynamic", meaning "by the power of an idea", to explain a broad range of "psycho-physiological" (mind–body) phenomena. Braid coined the term "mono-ideodynamic" to refer to the theory that hypnotism operates by concentrating attention on a single idea in order to amplify the ideo-dynamic reflex response.
Loop braid group; M. Matsumoto's theorem (group theory) S. Spherical braid group
Braid soon adopted Carpenter's ideo-motor terminology, to facilitate the transmission of his most fundamental views, based upon those of his teacher, the philosopher Thomas Brown, [9] that the efficacy of hypnotic suggestion was contingent upon the subject's concentration upon a single (thus, "dominant") idea.
They are closely related with Coxeter groups. Examples are free groups, free abelian groups, braid groups, and right-angled Artin–Tits groups, among others. The groups are named after Emil Artin, due to his early work on braid groups in the 1920s to 1940s, [1] and Jacques Tits who developed the theory of a more general class of groups in the ...
Categorization is a type of cognition involving conceptual differentiation between characteristics of conscious experience, such as objects, events, or ideas.It involves the abstraction and differentiation of aspects of experience by sorting and distinguishing between groupings, through classification or typification [1] [2] on the basis of traits, features, similarities or other criteria that ...
In the mathematical area of braid theory, the Dehornoy order is a left-invariant total order on the braid group, found by Patrick Dehornoy. [1] [2] Dehornoy's original discovery of the order on the braid group used huge cardinals, but there are now several more elementary constructions of it. [3]