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VIOLATED LOGIC. "By the “logic” of space we mean those spatial relations among physical objects which are necessary, and which when violated result in visual paradoxes, sometimes called optical illusions. Escher understood that the geometry of space determines its logic, and likewise the logic of space often determines its geometry." https://lnkd.in/d_HZ4K8 View in LinkedIn

THE PRINT GALLERY. "Note how the scale of the grid grows continuously in a clockwise direction. And note especially what this trick entails: A hole in the middle. A mathematician would call this a singularity, a place where the fabric of the space no longer holds together. There is just no way to knit this bizarre space into a seamless whole, and Escher, rather than try to obscure it in some way, has put his trademark initials smack in the center of it." https://lnkd.in/d_HZ4K8 View in LinkedIn

DISTORTED TOPOGRAPHY. "In addition to Euclidean and non-Euclidean geometries, Escher was very interested in visual aspects of Topology, a branch of mathematics just coming into full flower during his lifetime. Topology concerns itself with those properties of a space which are unchanged by distortions which may stretch or bend it—but which do not tear or puncture it—and topologists were busy showing the world many strange objects." https://lnkd.in/d_HZ4K8 View in LinkedIn

EXPERIMENTAL EVOLUTION experiment using a defined population of E. Coli follows. This experiment is particularly informative about difficult and sudden trait development. View in LinkedIn

FIGURATIVE SPACE. "Among the most important of Escher’s works from a mathematical point of view are those dealing with the nature of space itself. His woodcut Three Intersecting Planes is a good place to begin a review of these works, for it exemplifies the artist’s concern with the dimensionality of space, and with the mind’s ability to discern three-dimensionality in a two-dimensional representation." https://lnkd.in/d_HZ4K8 View in LinkedIn

TAPE OF LIFE. "Gould argued that contingency renders evolution fundamentally quirky and unpredictable, and he famously suggested that replaying the “tape of life” from some point in the distant past would yield a living world far different from the one we see today." http://www.pnas.org/content/105/23/7899.full View in LinkedIn

STELLATIONS. "There are many interesting solids that may be obtained from the Platonic solids by intersecting them or stellating them. To stellate a solid means to replace each of its faces with a pyramid, that is, with a pointed solid having triangular faces; this transforms the polyhedron into a pointed, three-dimensional star. A beautiful example of a stellated dodecahedron may be found in Escher’s Contrast (Order and Chaos)." https://lnkd.in/d_HZ4K8 View in LinkedIn

EVOLUTION AS UNPREDICTABLE. "Accidents of history may even determine the survival or extinction of entire lineages, given the capricious and sudden nature of some environmental changes. Stephen Jay Gould maintained that these historical contingencies make evolution largely unpredictable." http://www.pnas.org/content/105/23/7899.full View in LinkedIn

PLATONIC SOLIDS. "There are only five polyhedra with exactly similar polygonal faces, and they are called the Platonic solids: the tetrahedron, with four triangular faces; the cube, with six square faces; the octahedron, with eight triangular faces; the dodecahedron, with twelve pentagonal faces; and the icosahedron, with twenty triangular faces." These were an artistic foundation for MCE. https://lnkd.in/d_HZ4K8 View in LinkedIn

LOST BETWEEN THE CRACKS. "Natural selection works systematically to adapt populations to their prevailing environments. However, selection requires heritable variation generated by random mutation, and even beneficial mutations may be lost by random drift." https://lnkd.in/dbxjmju View in LinkedIn