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Example problem based on Shepard & Metzlar's "Mental Rotation Task": are these two three-dimensional shapes identical when rotated? Mental rotation is the ability to rotate mental representations of two-dimensional and three-dimensional objects as it is related to the visual representation of such rotation within the human mind. [1]
Attribution theory is the original parent theory with Harold Kelley's covariation model and Bernard Weiner's three-dimensional model branching from Attribution theory. Attribution theory also influenced several other theories as well such as Heider's Perceived Locus of Causality which eventually led to Deci and Ryan's Theory of Self-determination.
The Gestalt theory was founded in the 20th century in Austria and Germany as a reaction against the associationist and structural schools' atomistic orientation. [2] In 1912, the Gestalt school was formed by Max Wertheimer, Wolfgang Köhler, and Kurt Koffka. The word "gestalt" is a German word translated to English as "pattern" or "configuration."
For example, as stated above, a rectangle swept along a straight axis would define a "brick" and the cross section would be straight. Axis: straight vs. curved. Size of cross-section as it is swept along an axis: constant vs. expanding (or contracting) vs. expanding then contracting vs. contracting then expanding.
Visual object recognition refers to the ability to identify the objects in view based on visual input. One important signature of visual object recognition is "object invariance", or the ability to identify objects across changes in the detailed context in which objects are viewed, including changes in illumination, object pose, and background context.
For example, if part of a shape's border is missing people still tend to see the shape as completely enclosed by the border and ignore the gaps. This reaction stems from the mind's natural tendency to recognize patterns that are familiar and thus fill in any information that may be missing.
For example, the verbal measure of identity fusion taps feelings of reciprocal strength between the individual and the group (e.g., "I am strong because of my group"; "I would do more for my group than any other group members would do") as well as feelings of oneness with the group (e.g., "I am one with my group"; "My group is me"). [3]
For example, in 2-space n = 2, a rotation by angle θ has eigenvalues λ = e iθ and λ = e −iθ, so there is no axis of rotation except when θ = 0, the case of the null rotation. In 3-space n = 3, the axis of a non-null proper rotation is always a unique line, and a rotation around this axis by angle θ has eigenvalues λ = 1, e iθ, e −iθ.