Year: 2022

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

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

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

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

MIRAGE. "A third type of “impossible drawing” relies on the brain’s insistence upon using visual clues to construct a three-dimensional object from a two-dimensional representation, and Escher created many works which address this type of anomaly." https://lnkd.in/d_HZ4K8 View in LinkedIn

THE IMPOSSIBLE. "One of the most intriguing is based on an idea of the mathematician Roger Penrose’s—the impossible triangle. In this lithograph, Waterfall, two Penrose triangles have been combined into one impossible figure." https://lnkd.in/d_HZ4K8 View in LinkedIn

ARTIFICIAL INTELLIGENCE. "A central concept Escher captured is that of self-reference, which many believe lies near the heart of the enigma of consciousness—and the brain’s ability to process information in a way that no computer has yet mimicked successfully." https://lnkd.in/d_HZ4K8 View in LinkedIn

SELF REFERENCE. "On a deeper level, self-reference is found in the way our worlds of perception reflect and intersect one another. We are each like a character in a book who is reading his or her own story, or like a picture of a mirror reflecting its own landscape. Many of Escher’s works exhibit this theme of intersecting worlds." https://lnkd.in/d_HZ4K8 View in LinkedIn

SO ENDS this journey into the work of MC Escher. He was deeply inspired by the remarkable Moorish art from the ancient Great Mosque of Córdoba in Andalucía Spain: "In the Great Mosque of Córdoba strong geometric principles based on the harmonic subdivisions of a squared circle in which the alternate sides relate in 1:2 and the consecutive relate in 1:√2 proportions appear to underline its architectural planning." Penrose and others expanded on this with the mathematics of tiling. But only MCE went through that mathematical door into the scented garden beyond. https://lnkd.in/dVZh_Zu View in LinkedIn

TRANSITION FROM SINGLE CELLS. "Although there is much theory, there are few empirical studies." https://lnkd.in/dM8VCEC View in LinkedIn