linkedin post 2016-12-18 07:37:14

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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
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linkedin post 2016-12-18 07:33:53

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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
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linkedin post 2016-12-18 07:31:05

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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
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linkedin post 2016-12-18 07:22:21

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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
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linkedin post 2016-12-22 06:16:51

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LARGE DOWNSTREAM IMPACTS. "Although each change on an evolutionary path has some causal relation to the circumstances in which it arose, outcomes must eventually depend on the details of long chains of antecedent states, small changes in which may have enormous long-term repercussions." http://www.pnas.org/content/105/23/7899.full View in LinkedIn
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linkedin post 2016-12-20 05:52:35

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TEST POPULATION. "Twelve initially identical populations of Escherichia coli were founded in 1988 to investigate this issue. They have since evolved in a glucose-limited medium that also contains citrate, which E. coli cannot use as a carbon source under oxic conditions. No population evolved the capacity to exploit citrate for >30,000 generations, although each population tested billions of mutations." http://www.pnas.org/content/105/23/7899.full View in LinkedIn
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linkedin post 2016-12-22 06:12:16

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ACCIDENTS OF HISTORY. "For example, multiple beneficial mutations will arise in some unpredictable order, and those that are substituted first may differ from others in their pleiotropic effects and epistatic interactions, thus constraining some evolutionary paths while potentiating other outcomes. These accidents of history may even determine the survival or extinction of entire lineages, given the capricious and sudden nature of some environmental changes." http://www.pnas.org/content/105/23/7899.full View in LinkedIn
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