In networks, links and nodes are duals. In two-dimensional projective geometry, points and lines are duals. In three-dimensional projective geometry, planes and points are duals. In three-dimensional space, lines bound surfaces, and surfaces bound lines, so mathematical theorems about lines have corresponding mathematical theorems about surfaces. On n-manifolds, p-forms and (n-p)-forms are duals, so 1-form (covariant tensor, linear function of coordinates, or manifold gradient) and vector field (contravariant tensor, function, or manifold) are duals, and they interact to make scalar products. For vectors, tangent vectors have covector duals. Perhaps, mind and brain are duals, and phenomena and manifolds are duals {duals and sensations}.
Consciousness>Consciousness>Speculations>Sensation>Mathematics
1-Consciousness-Speculations-Sensation-Mathematics
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Date Modified: 2022.0224