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PART TYPE DRAIN. "In other words, in hierarchical transitions, there is a drain on numbers of part types at the lower level." http://www.bioone.org/doi/abs/10.1554/0014-3820(2002)056%5B0441:ACDOCI%5D2.0.CO%3B2 View in LinkedIn

LOWER-LEVEL COMPLEXITY LOSS. "A hypothesis has been advanced recently predicting that, in evolution, as higher-level entities arise from associations of lower-level organisms, and as these entities acquire the ability to feed, reproduce, defend themselves, and so on, the lower-level organisms will tend to lose much of their internal complexity." http://www.bioone.org/doi/abs/10.1554/0014-3820(2002)056%5B0441:ACDOCI%5D2.0.CO%3B2 View in LinkedIn

GENETIC COMPLEXITY. "Further examination of the DNA record suggests that these increases in gene complexity are the product of evolutionary innovation, tinkering, and expansion of genetic material." http://www.annualreviews.org/doi/abs/10.1146/annurev.genet.42.110807.091513 View in LinkedIn

ELABORATED ANIMALIA. "Escher exploited these basic patterns in his tessellations, applying what geometers would call reflections, glide reflections, translations, and rotations to obtain a greater variety of patterns. He also elaborated these patterns by distorting the basic shapes to render them into animals, birds, and other figures." https://lnkd.in/d_HZ4K8 View in LinkedIn

TRANSITIONS AND GENE NUMBER. "Comparisons of several independently evolved pairs of multicellular and unicellular relatives indicate that transitions to multicellularity are typically associated with increases in the numbers of genes involved in cell differentiation, cell-cell communication, and adhesion." https://lnkd.in/d7ecRYi View in LinkedIn

GARDEN OF DELIGHTS. "In mathematical quarters, the regular division of the plane has been considered theoretically…Does this mean that it is an exclusively mathematical question? In my opinion, it does not. [Mathematicians] have opened the gate leading to an extensive domain, but they have not entered this domain themselves. By their very nature they are more interested in the way in which the gate is opened than in the garden lying behind it." (MCE). https://lnkd.in/d_HZ4K8 View in LinkedIn

ENFORCING COOPERATION. "If the rhizobia in a root nodule do not provide nitrogen to their leguminous host plant, the plant reduces the growth rate of the bacteria by decreasing oxygen supply. In this case, each rhizobium cell is selected to fix nitrogen to avoid both itself and its relatives within the nodule being sanctioned." http://www.sciencedirect.com/science/article/pii/S0960982207014996 View in LinkedIn

EXPERIMENTAL TRANSITION. "Here we describe an evolutionary transition that occurs in experimental populations of Pseudomonas fluorescens propagated in a spatially heterogeneous environment. Cooperating groups are formed by over-production of an adhesive polymer, which causes the interests of individuals to align with those of the group." http://www.nature.com/nature/journal/v425/n6953/abs/nature01906.html View in LinkedIn

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