IllusionAn illusion is a distortion of the senses, which can reveal how the mind normally organizes and interprets sensory stimulation. Although illusions distort the human perception of reality, they are generally shared by most people. Illusions may occur with any of the human senses, but visual illusions (optical illusions) are the best-known and understood. The emphasis on visual illusions occurs because vision often dominates the other senses.
Low-dimensional topologyIn mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot theory, and braid groups. This can be regarded as a part of geometric topology. It may also be used to refer to the study of topological spaces of dimension 1, though this is more typically considered part of continuum theory.
Direct and indirect realismIn the philosophy of perception and philosophy of mind, direct or naïve realism, as opposed to indirect or representational realism, are differing models that describe the nature of conscious experiences; out of the metaphysical question of whether the world we see around us is the real world itself or merely an internal perceptual copy of that world generated by our conscious experience. Indirect realism is broadly equivalent to the scientific view of perception that subjects do not experience the external world as it really is, but perceive it through the lens of a conceptual framework.
Roman surfaceIn mathematics, the Roman surface or Steiner surface is a self-intersecting mapping of the real projective plane into three-dimensional space, with an unusually high degree of symmetry. This mapping is not an immersion of the projective plane; however, the figure resulting from removing six singular points is one. Its name arises because it was discovered by Jakob Steiner when he was in Rome in 1844.
HypersurfaceIn geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface. A hypersurface is a manifold or an algebraic variety of dimension n − 1, which is embedded in an ambient space of dimension n, generally a Euclidean space, an affine space or a projective space. Hypersurfaces share, with surfaces in a three-dimensional space, the property of being defined by a single implicit equation, at least locally (near every point), and sometimes globally.
