grains of corn - chess and "cereology"

Nice post there, Jan. The geometry of crop circles often hints at or makes direct reference to cosmographic templates that relate directly to the construction of game boards. As a collection, they also draw attention to a "naos" or "apex" - an omphalos or a zenith suggestive of a reward structure. Holography and holism are deeply implied as are Godelian ideas of a self-contained, self-referential, recombinating system of closed and open loops. References to octaves and octonion math - ie. "Clifford Algebra" - represent a foundational theme in chess as does the 8x8 astapada inference of lawful albeit randomized (dice chess) pursuits of an entirely sacred nature. Researches who see something closely resembling Vedic ideas in ancient Egyptian texts are not mistaken. An additional concept relating Egyptian music to geometry captures the lawful sense of ratio and proportion and redirects it from visual media to auditory parallelisms. Over at this site, the auditory phemonema that accompanies the formation of legitimate crop circles comes alive. http://www.mysterious-america.net/soundcropcircles.html If we are looking for modern parallelisms in science, the term "sonoluminescence" is a nice approximation. Otherwise, geometric sand patterns formed on the shaman's drum head suggest that recognition of a similar phenomena is very ancient and culturally stimulating. African drums and those of other native peoples speak directly to the combined harmonies and rythms of life, the cosmos and everything. Chess fits neatly into this matrix and replicates the basic "life rythms" of the seasons and their primordial passage, a concept that melds crop circles, chess, vegetative and agricultural cycles into a single seed. From the one - the many... an axiomatic view that allows us to see the chess-oriented "grains of corn" problem of geometrical increments in a mathematical context one might also refer to as "concentric hierarchy" or, more correctly, the eternal "process" of hierarchal "self accumulation". In their own write, the Ancient Egyptians understood the rythmic basis of social reconsolidation and the result furnished increasingly sophisticated views of "the self-created - self creating ONE". THe entire matter of self-generative insights and improvements flows directly into the personification of Ptah and the cavalcade of pharaohs who were the beneficiaries of Ptah's creationist paradigm. One would suppose that this venerable trail of facts has led the Dutch Crop Circle investigators to offer a Ptah Award for excellence in the field of crop circle research. As for Sopdet and Sothis, I think they make an excellent statement about female Brilliancy... ;-) So, the circle of this post completes itself and fits nicely inside or outside any square... proving once again that there is more to heaven, earth and chess than ever was dreamed of in H.J.R. Murray's reductionist, materialist, rationalist point of view.