Saturday, January 29, 2005

The Genome of Chess

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The following reflections are my guiding inspiration: "Nothing is more characteristic of the classical works of the great geometers of Greece.… than the absence of any indication of the steps by which they worked their ways to the discovery of their great theorems. As they have come down to us, these theorems are finished masterpieces which leave no traces of any rough--hewn stage, no hint of the method by which they were evolved.” as T.Heath explains in A History of Greek Mathematics along with Einstein's 1916 reflection: "Concepts which have proved useful for ordering things easily assume so great an authority over us, that we forget their terrestrial origin and accept them as unalterable facts. They then become labeled as 'conceptual necessities', 'a priori situations', etc. The road of scientific progress is frequently blocked for long periods by such errors. It is therefore not an idle game to exercise our ability to analyze familiar concepts, and to demonstrate the conditions upon which their justification and usefulness depend, and the way in which these developed, little by little.”

In 1982, after an insight into the probable origin of the geometric concept which was critical to the creation of Chess, I began to re-create from the tabula rasa of the “collective unconscious” [Jung] – an ancient archetypal a priori pre-Euclidean geometric model. Subsequently I began to understand that I had entered a universal domain not unlike that described by Tons Brunes in his unusual book The Secrets of Ancient Geometry. What is striking about my initial quasi-mystical experience is that I independently developed the fundamental graphical gestalt of ORIGINSZ © prior to doing any formal research. The model’s key principles and features could well have been Pythagoras's course material by which "the Euclidean consortium'" proceeded from the empirical to the axiomatic deductive system and in so doing, one might perhaps suggest, quite unintentionally perpetrated somewhat of a fraud in the realm of human intellectual endeavor. Unfortunately there is a long history in the esoteric schools of NOT revealing the ‘secret teachings’ other than through art or arcane puzzle-like writings. Over the years in my attempts to demonstrate certain clear cut elements from the geometry, which I believe necessarily led to the creation of essential chess concepts, I’ve met with various responses running the gamut from ‘duh what?’ to ‘Aha’! in turn colored by the permutations of ‘where is your proof?’, ‘what makes you an authority?’, and my favorite one, a tenet from the sciences: “an empiricist cannot hypothesize” - because one is selectively fitting data or facts to fit a pre-determined bias. Mea culpa – but to which I can only answer, that in the absence of anything which reveals a substantially contradictory resolution as to how chess suddenly ‘appears’, isn’t it preferable to identify and consider as many of the features of the forensic evidence which provides for the most inclusive synthesis? Since I am neither a formally accredited mathematician nor historian, my focus has been upon practical applications aimed at the commercialization of a gaming system having potential educational applications which attempts to bridge the gap between informal and formal explorations. I am currently in the process of negociating the terms whereby I can begin to publish on-line with an inter-active format, as I continue my search for kindred spirits which might lead to the formation of new school based upon my pioneering work to date.

In the meantime I’ve been inspired to prevail against the odds by de-bunking some of the quasi-historical myths surrounding the origins of Chess. When historians traced its beginnings to Chaturanga (meaning quadripartite, i.e. the division into four), they were on the right track, but unfortunately confused substance with form. Yes, the Indian army had four divisions and the idea that these may have became the basis for the pieces, is acceptable but only if we don’t overlook that their form represents their substance: the geometry of the piece displacement, which in turn must be related to the arithmetical characteristics of a more ancient game: Pachisi, meaning twenty-five. This I believe occurred at a critical phase in the history of mathematics concurrent with the discovery of zero. The Chinese who were mathematically far advanced, (having found Pi = 355/113), may have made a major contribution, perhaps by converting it from its 4-fold schema to the 2 armies (separated by a river – representing the immutable values in a tabular distribution) Later appearing as Ashtapada, as an 8x8 board, (which used to be played using dice) it can be directly traced to Chatranj which adopted by the Arabs became Shahtranj the indisputable forerunner of modern chess. Due to the creation of a notation system (stemming out of their mastery of pre-Cartesian concepts) the game of Kings was assured its survival, since it could easily have fallen into obscurity, as did Rhythmomacia, a complex game of mean proportionals played by the intelligentsia. Chess clearly owes its survival to its figurines with their projected cultural characteristics – given that the obvious ‘royal’ court symbolism had a broader appeal for the less educated.

There has been a tendency to include writings about the popular history of Chess with the search for its origins. Finally 20th Century research uncovered its roots in Sacred Geometry as a ‘divinatory’ mathematics extending far beneath “The Silk Road”. Clearly the concepts necessary to formulate Chess as a game had antecedents which date well before its unexplained sudden ‘appearance’ in the 7th Century, which certainly at least in principle vindicates the assessment (by Forbes and others) that its beginnings lay in antiquity. Plausibly, since several cultures developed similar notions of gaming stemming from mathematical notions it is reasonable to assume that a melting pot of influences led to the creation of Chess. But at times it seems that certain historians tend to have difficulty in seeing the ‘board’[grid] for the ‘squares’, as they simply reproduce material without even understanding it. Of course self-discipline is required not to simply yield to every whim and conjecture. Speculation is easy, its like tactical play in Chess. Methodical, rigorous research is more like diligent strategical play. But both are essential to the ‘game’, each has its time. I wish to contribute a perspective to provide some new insights within this relatively unexplored domain by employing retrograde analysis from Chess as we know it. I may go out on a limb from time to time: but is just to get a better view of the forest.

The 8x8 Ashtapada board is the projection of four 5x5 grids sharing a 2x2 central grid should stand as indisputable proof. A careful scrutiny of the Pachisi board’s ‘cardinal cross’ also features distinct X’s (“cross-cut” squares) which through recomposition relate back to the 5x5 board where the elements of Chaturanga critical to the concept of piece movements finds its foundation. The direct clue is the Knight positions at g8 (h7), b8 (a7) and b1( a2), g1(h2) and their “development” to f6,c6, and c3, f3 which shows their “control” of the central 4 squares: this being the first strategic notion in chess. Placing of the Bishops and Rooks can similarly be shown to be in keeping with their ancestry from the 5x5 board. The requisite element applied in the creation of chess relates to the early demonstration of the square root of two ‘proportional’, the recursive principle (45 degree rotation of half and double area tiles) which was an early attempt to reconcile “irrational” values. This permits the transition from the odd 5x5 grid to the even 8x8 grid such that the ‘harmonic’ values in the ‘knight’ square monarch positions on the 5x5 ( in turn as determinants of 2x2 matrix of a Nasik magic square ) simultaneously are found in their analogous positions projected onto the 8x8 board. There is a corresponding projection to a 9x9 grid, establishing the critical connection between geometry and its arithmetic shorthand (*) presaging the development of algebra. Intuitively, artistically, the knights figuratively ‘carry’ each monarch into position: all the ‘King’s horses’ - matched by all the ‘Queen’s steeds’. This study is in turn related to what I call ' the parallel projection proof ' which addresses the initial Chess array. It is one of dozens which I hope to publish in the hopes of broadening the field of inquiry so as to fill in the gaps of the historical record.

Evidence for my hypothesis can be found in certain designs published by the most often recognized authority Chess historian H.Murray, although he records them in terms of their supposed appearance, hence often out of time and context of their true origins. He also engages in highly subjective editorializing with respect to critical documentation. His dismissal of the significance of the 4 kings, which establishes that the precursors of chess were 4-handed games – or at least employed four cardinal viewpoints is a type of surprisingly rather undisciplined reflection which plagues attempts at reconstruction and hypothesis formulation. Modern theories fortunately share a common thread, whether it be Joseph Needham’s discovery of an ancient Chinese precursor which is related to the discovery of magnetism, paralleled by Pavle Bidev’s initial astrological theory or Tartakover’s reference to Isaieff’s analysis of Magic Squares. The latter corresponds directly to this writer’s explorations of the link between arithmetic and geometry as a compelling overview as to ‘how’ chess necessarily came into being. This Blog serves only as a journal pending the development of my web site.

The challenge before us now is not to quibble about ‘when’ and ‘where’ but rather to understand the ‘what’, as we carefully explore the logic of the probable ‘how’. The true value of this timeless knowledge is not as a nebulous exercise in esoteric contemplation, but the realization of this legacy from the mathematics of ‘order in space’ (K.Critchlow). Given the myriad of chess-like games, the exploration of its ‘re-creational’ elements is essential to draw a clearer distinction as to what legitimately constitutes the area of inquiry which may be deemed to be the origin(s) of Chess as being separate from a study of its so called History. The latter permits the study and acceptance of a great number of seemingly at times conflicting viewpoints or theories as is the present case. However the former requires a far more comprehensive exploration of materials which would be contingent to the History of Mathematics, the true cradle of primordial Chess concepts. The Pythagoreans were surely the originators of what may have for centuries been an esoteric pursuit whose secrets were well guarded in that there was “power” in the knowledge how to practically treat incommensurable values which was not uncovered until the Renaissance. However In the multi-dimensional geometric garden of math concepts, Chess is a hybrid plant, an intriguing curiosity at best, whereas the environment of its origins provides a nearly unlimited opportunity to open “the doors of perception” and thereby explore both the creative and analytical nature of the human spirit and mind.

As a game its abstraction it was but a single gateway of potential concept formation, even somewhat limited. However there was a certain unforeseeable synergy which produced fascinating outcomes. The common view that Chess facilitates the development of problem-solving skills is like claiming that the of learning high school algebra enables one to have original insights into quantum physics. It is a closed environment with little real-world learning transfer value. By returning to the source we should perhaps envision applying contemporary mathematical pursuits and technologies to lift Chess it to a higher level of creative development through expanding its playing parameters so as to reflect its intrinsic values in a manner which transcends the notion of battle it sadly embodies. Ironically the interest in Chess variants establishes that there is a need and desire for creativity and imagination, whether expressed as an art or science: this is the true legacy of human intelligence binding cultures and time. Expanding its design parameters to both even and odd grids, with the resulting hybrid grid(s) as being neutral zones, or permitting lateral movement and imagining point-to-point lines to enclose space, or a four viewpoints game with the playing board expanded to its square root of two recursive proportional, could lead to its evolution: a return to its source, as the game of the future. The creation of ‘simultaneous’ play alternatives, the objective being the formulation of potential rules analogous to the laws of physics, permitting a mind’s-eye glimpse of the Divine Synergy, at the interface of the micro and macro universes: these are the themes explored within the gaming system of ORIGINZ ©1982-2006 rt .

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