Gnomonicity: Part Three. From the Building of the Isometric Matrix to the Analysis of Electromagnetic and Spacetime Phenomena.

While the process of translating the primary signature of the Earth’s diurnal motions, illuminated by the constant radiance and source of light, and accessed by the unique mind of the thoughtful human being, striving to reveal that which informs the foundations of natural law, common to all peoples, leads to the topologically considered analogue model, from which the isometric matrix is ruled, the process of confirmation of this model is able to be revealed in the basic generalization of the information gathered on the day of equal night, which indicates the quadrature of the daily of the cycle, marked as the four limits, dawn, noontime, dusk, and the inverse correlative of the noontime, the midnight point. As illustrated here, the use of the square, and the division of the daily cycle into five points, dawn, mid morning, noontime, mid afternoon, and dusk informs the division of the day and night cycle, into 8 segments. The conceptualization given by Archimedes and known as the “antiprism”, constitutes the inference of a top down perspective of a “twist” of 45 degrees, scaled down with a ratio of 1: sq rt 2.

However, if the isometric matrix is constructed in three dimensions, which corresponds directly with the two dimensional “plan” of the rulings which infer the immersion of a three dimensional construction of the “one unit square” whose measure is equal to the radii of the twin circles, and measure of the distance between their centers, the image of the square constructed from the ruling of diagonals of each of four squares informed by the presumption of the xy axes, corresponds with the square of the octahedron, as viewed from the face of the cube, the center of which constitutes the vertices of the octahedron informed by the ruling of the two sets of four lines, extended to include a further set of four lines, being the “+” of the implicit representation of the gnomon and the horizontal diameter line or horizon line, that are taken for granted, with two lines ruled which complete the structure of the first “Platonic solid”.

Hence with the inclusion of the orthogonal lattice, overlayed with the two orientations of the isometric lattice turned 90 perpendicular to each other, the three primary ‘grids’ or ‘graphs’ are formed: “<><>”; ” ^v^v ” and “|-|-|”.

Each of these graphs inform the Ancient Egyptian term “KA”, each letter of this transliteration, being self explanatory as present in the isometric lattice, while the orthogonal structure, indicates the transposition of the orthogonal lattice, as the “measure of man”, for the “cubit” and hence primary “unit” measure employed in the ancient world, which informs the first and second “letters” of the alphabet, “A” and “B”, are informed by the “forearm”, measure from the elbow to the finger tips, and the lower leg measured from the knee to the base of the foot, respectively, each having an equal measure, according to the ratios and proportions of the common human figure. As such the evolution of the term KA, already entered into the register of “characters” used to inform the proper names taken by the earliest rulers of the predynastic period, the term KA graphically portrays the measure of a “one cubit” unit square, formed by fixing the upper arms to the torso, and holding the forearms perpendicular to the ground, and parallel to each other: | _ | viewed from the head of the individual looking down upon his arms. Additionally the term KA has two further characterisations: “|_o_|” and “|_._|”.

As the measure of the cubit and forearm is equal to the measure of the upper arm, raised parallel to the ground, from the middle of the neck to the elbow, the “posture” so described, indicates the 2×1 unit rectangle, where the indication of the human head, and its absence, signifies the differentiation between the Ruler, and the Ruled, who willing “gives his head” or “crown” in service to the “ruling body”, who embodies the “completed fabric of the garment of god” as an educated noble. The structure of these terms and the evolution from the isometric to the orthogonal, associated the term KA, with the terms “Hesep”: |–|–| (hesept-ti is the name taken by the 5th ruler of the predynastic period according to the kinglists) expanded as a field divided by 3 parallel lines with 5 perpendicular rulings, and “sepat” meaning defend and protect, and informing the division of lands, graphically portrayed in the grouping of broken and unbroken lines, informing the first “hexagram”, reduced to two couplets indicating the division of the one land of Ancient Egypt, into two significant domains, Upper and Lower Egypt. From the second millenium on, some thousand years or more after the instantiation of the most complex foundation of a progressive civilisation, grappling which the harsh reality of the desert region, the Egytpian terms “KA”, HESEP and SEPAT informs the Sinaitic term h(alal), meaning “rejoice”, one assumes rejoice in the “noontime” as the time of REST from the perspective of the slave or governed body, or rejoice in the “return” of the “sun” to its dawn location, from the perspective of the conditional constraints imposed on the governed body, burdened with the fear of righteousness and superstition cultivated by the negative use of the knowledge waged against the body governed and conditioned to adulate the Rising Sun, rather than generation of the cycles underpinned by the Earth’s motions. The later utility of the predictability of the annular eclipse, which permits the belief that mere mortals held the superhuman power to command their personal god, to put out the light of the Sun, a terror that informed the ignorance of the many, led to believe that super human mortals worked tirelessly to maintain the apparent motions of the Sun, common to the “cults of the sun”, which adulated the private worship of the moon. This posture in more modern times, has evolved to signify the surrender “I give up”, of the “criminal” or potential “Savior” depending on the point of view, confronted with the potential dilemma of an impending “kill shot”. The term “h(alal)” is definitively associated with the “sacrifice” given in honor of the “hidden god” who works behind the scenes, be it for the greater good of the whole as reported of Thales of Miletus, or in service of the self, for the purpose of raising one’s power and wealth “beyond bounds“, as in the case of Bias of Prienne (Herotodus’ Histories).

The division of the hours of the period of day and night, defined by the “still point” of the Sun’s shadow and point of Rest, at Noon Time, into 24 segments, informs and is informed by the primary rulings of the isometric lattice, to the point that the 24 spoked wheel is ruled, an effort which can be realised by ruling of a number of sets of lines, numbering 22 in the most basic rendition. It is only when we make the effort to construct the matrix in three dimensions, taking care to conform to the 2 dimensional design, that we begin to see the correspondence between the solids and the rulings of sets of lines.

It is also made plain that the ratios and proportions of the rulings inform a structure built with equal measured sections, and this point is fundamental to the underpinnings of an isometric system. In furthering the examination of the means through which the hours of the day and night are divided, and the degrees of the circle informed by what can only be considered as the prototypical foundation of the geometers protractor, whose complexity is raised according to the raise in complexity informed by continuing to rule the density of the matrix itself. Furthermore the degree of information realized from the pursuit of this study, is in fact reason why it is so difficult to put into words, let alone induct another into the science of ancient astronomy, without them following the same process themselves, and initiating a hands on project that was in fact impossible to have realized without the computational tools and programs that many today, take for granted.

Indeed the most surprising discovery is that the earliest graphic artefacts, dating to the Fourth Millenium BC, indicate the most profound knowledge system for the name given to the twin beings who depict the two running speeds of the planet, located on the bottom registrar of the Narmer Palette, actually reveals the half circle and rays of the sun, located above the two radials, which a ruled from the center of the topmost side of a square, to the bottom corners, as shown in these illustrations. Suffice it to say that the apprehension of the degree of knowledge that is self generating from the topologically considered modelling of the analemma, as the twin circles which inform the “eye of god”, the figure of ISIS and the gift of culture that constitutes the figure of OSIRIS, and all who are forced “underground”, as the representatives of the Cardinal Points, signifing the “son’s of horus”, or progeny of the hours, the degrees, minutes, seconds, and divisions of the second down to 1/16th of second known as the “ant”. The underworld of the shadow hours of night, is manifest as the New Kingdom reforms submerge the facts of natural law, and their products into an ever receding codification that leads to the final undoing of the Empire itself, and the loss of the knowledge that remains in the recesses of the mind, until such time as we return with the dire necessity to discover what indeed has gone wrong in the past, and is repeating the same cycle in the present, threatening to remove all potential anchors to a truely integral science, needed now more than ever before, for it is not merely the empire that is threatened, what ever or whoever that is, it is the integrity of life on this earth that is endangered by the tyranny of ignorance, and the arrogance of those who presume that all that is necessary to support a complex world, is the blind labor of artisans,  directed by blind engineers who dream of a futuristic vision, a utopian world, that will deliver only the progressive descent into a long term nightmare of exceptional proportions. Those entities who are embodied as the canopic jars which in turn embody the  deceased’s stomach, the smaller intestines, heart and the liver, are Mestha, Hapi, Tuamautef, and Quebhsennuf, who represent the four cardinal points as mentioned above, and in a more superficial reading inducted by various commentaries of the Am Tuat, constitute the “genii of the dead“. Indeed with the act of reading of the Book of the Dead, which is variously called the book of gates, the book of shadows, the book of hours, and so on, it remains a pointless exercise, without the actual graphic representations of the Ancient Heiroglyphs, and some interest in the interpretation of the graphic forms, which have given us specific transliterations, according to none more than geometry.