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In cognitive psychology, George Kelly developed "constructive alternativism" as a form of personal construct psychology and an alternative to what he considered "accumulative fragmentalism". For this theory, knowledge is seen as the construction of successful mental models of the exterior world, rather than the accumulation of independent ...
A mental representation (or cognitive representation), in philosophy of mind, cognitive psychology, neuroscience, and cognitive science, is a hypothetical internal cognitive symbol that represents external reality or its abstractions. [1] [2] Mental representation is the mental imagery of things that are not actually present to the senses. [3]
For n = 3 the obvious analogue of the (n − 1)-dimensional representation is reducible – the permutation representation coincides with the regular representation, and thus breaks up into the three one-dimensional representations, as A 3 ≅ C 3 is abelian; see the discrete Fourier transform for representation theory of cyclic groups.
Theories of mental representation are those that rest the cognitive abilities of the mind on the processing of content-laden vehicles, called representations. Naturalizing these theories involves an account of how a representation, initially posited as a theoretical construct, can be realized in a physical system.
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If has exactly two subrepresentations, namely the trivial subspace {0} and itself, then the representation is said to be irreducible; if has a proper nontrivial subrepresentation, the representation is said to be reducible. [19] The definition of an irreducible representation implies Schur's lemma: an equivariant map : (,) (′, ′) between ...
Irreducible representations are always indecomposable (i.e. cannot be decomposed further into a direct sum of representations), but the converse may not hold, e.g. the two-dimensional representation of the real numbers acting by upper triangular unipotent matrices is indecomposable but reducible.
Holonomic brain theory is a branch of neuroscience investigating the idea that consciousness is formed by quantum effects in or between brain cells. Holonomic refers to representations in a Hilbert phase space defined by both spectral and space-time coordinates. [1]