The first principles of Astronomy, are based on the topological study of the site, conducted in the broard light of day, using a gnomic indicator (a gnomon is any technological device that is either naturally occurring, or man made, that enables the indication of a signature record). From this primary study, the records of the sun's shadow, traced through space over time, provide the visual mapping of the othographic projection of actual daily and annular cycles.

Vitruvian orthographic projection

Tracing the signature record of the Sun's shadow on the ground plane results in the marking of continuous "lines of time" on the spatial field of the ground plane, from dawn to dusk, which inform the mapping of the ratios of day to night. thumb From the longest day to the day of equal night which exhibits zero curvature, to the shortest day of the year, the limits of the patterns recorded over the course of around 183 days are realised as a cyclic process shifting backwards and forwards over the same information, informing the projection the annular cycle, resulting a complex set of hyperbolic arcs with postivie negative and zero curvature. From the days of equal night, know as the Equinoxes, our orientation in space, and the latitudinal directions West East is determined. From the Crests of the hyperbolic arcs that define the longest and shortest days of the year, known in temperate regions as the summer and winter solstices, and defined as the registration of the "Zenith" and point at which the Sun is directly above (boreas) the gnomic indicator Noontime, our orientation North South is defined.

Confirmation of this complex cycle is registered in the observation of the gradual shift in the location of the Sun, observed from the gnomic indicator, to the circle of the horizon. As such the figure of the chevron /\ is equal to the full cycle of the year, and run of chevrons which inform the ancient Egyptian heiroglyph for wave or water: /\/\/\/\/\/\, transliterated as "n" and infers a 6 year period. Additionally, this heiroglyph has a direct relation to the construction of the complex isometric matrix, constructed from the rulings of three lattices, from the basic 2 circle topological model: "( ( ) )" which in being turned 90 degrees, informs the heiroglyph of the "eye" transliterated as "r". Together, the "eye" and the "wave" informs the combinatory heiroglyph that transliterates as Rn, and holds the meaning Name. This heiroglyph has spuriously been regarded as inferring a space ship hovering over the waters, and singularly represents the dire neccessity to bring to light, the very thing that has been -by neccessity- concealed, for the purpose of separating the theoretical facts from the applications, as without this non disclosure, the potential to progress precise knowledge bases is compromised by those who run with inferrences without interrogating the full body of information inherent in the study. Ironically, the considered neccessity for non disclosure has led to numerous speculations regarding the Pythagorean Cube, as if this is the final product constructed from the 2D image of the complex isometric matrix, which flourished throughout the middle ages, and specifically since the intentionally obscurationist work of John Dee, as embodied in his Monas Heiroglyphicus, which brought the Pythagorean Cube, the Pythagorean Quaternary, and the Pythagorean Tetrakys, to the fore as an occult study.

Its non disclosure has also led to the dire issue of all manner of arbitrary models being claimed as the false foundation to Quantum Phenomena, as instantiated by Sophus Lie's intuitive notions pertaining to the 2Dimensional model, and its "string thing" studies.

Additionally this was returned to by Lissi, which presupposes the lesser object known as the "seed" and "flower of life", which refers to a template employed by neccessity, by the Ancient Egyptians, for the purpose of supporting the more precise ruling of lines in the outer regions of the matrix construction, as it was applied in the act of "rope stretching", for the purpose of underpinning precise foundations for architectural constructions.

Exploitation of this necessary diversion from the original structure, informed the common descent towards corruption, and extreme superstitions held in the social sphere of the greater number, demanding continuous "restorations", that is, returning to the foundational "teachings" informed by the heiroglyph which transliterates as SBA, indicated by the five spoked wheel, which, with a circle circumscribing this structure, transliterated as DUAT, meant underground, or pertaining the utility of this structure as a system of mensuration required for the study of the "night time hours"- duat. From this heroglyph, the spurious notion that the Ancient Egyptians wished to the return to the "stars", is seeded, as the generalised meaning of the five spoked wheel is "star". Alternatively, as indicated by earlier (predynasitc to the first of the dynastic kingdoms) neccessities for restoration, at the time of S-NFR-U, informed by the reponse to the concerns raised by this Pharoah, as recorded in the "prophecy of Nfr-ti", the "return to the foundations of "re", and hence to the primary model of the two circles, and its rulings, pushed to the degree of complexity shown below, and in turn, to the point of informing the construction of 12 hexagon shells, where the horizontal diameter line is divided into 24 equal parts, indicating the measure of 3/24 and 1/8 = 0.125, was enacted. This enactment resulted in the consruction of the first pyramids in Ancient Egypt. the heirglyph for pyramid indicates the 24 degrees, and this structure informs the inner corbelled arch of the body of the construction. The true pyramid inferred the complete reckoning of the complex isometric matrix, as one that resulted in the Rhombic Dodecohedron, whereby the primary structure realised in the 3D construction from the 2D image, was the octahedron, not the cube nor cube cage.

In its direct relation to the complex ruling of the "double" isometric matrix that results, the matrix constructed to the point of informing 6 hexagon shells, the significant relation bewteen the 5th and 6th of 6 hexagon shells, and the 10th and 12th of 12 hexagon shells, informs the relation between the circle of the meridean and the Vitruvian "dial" whereby the description of the circle of the meridean, divided into 15 equal parts, provides intelligible access to the closest aproximation of the Earth's Axial Tilt.

Between the two extremes of the longest and shortest days of the year, and the means -being the two days of equal night, the complete annular cycle is quadrated by these four days. As the Earth is a sphere, rotating on a tilted axis, the experience of seasonal change is determined by the location of the observer. In temperate regions, the longest, equal and shortest days of the year, define the midpoints of the four seasons. In regions closer in proximity to the equator, it is common to experience three phases of the year, as with Ancient Egypt who acknowledge 3 primary seasons, according to the times of planting, harvesting and inundation of the waters of the Nile River.

From this set of hyperbolic arcs, the topologically coherent model of these relations is constructed which enables the shift from that which is visible and intuitively experienced, hence infering that the Sun appears to rise at dawn and set at dusk, in a recuring pattern of hyperbolic arcs, all that is intelligible transcends the intuitive notion, and exposes the counter-intuitive facts of the planets relation to the Sun, which exhibits two complementary standpoints of the one and same system.

As the Ancient Egyptian linguistic code included immaterial phenomena, largely based on the system of mensuration which underpins the relation between the sexigesimal system and the decimal system, informed by the elementary principles of astronomy, and the topological model of the analemma, and "dial", it is considered to be a far more complete foundation than that which is speculated as emergent from Mesopotamia, or Babylon and Chaldea, and inturn related to the Indo-Aryan root, which in turn informs the flourishing of mysticism consolidated in many pagan belief systems including the Slavic nationalistic belief systems, that some consider to indicate a superior culture, rather than finding common ground with the many world religions all of which can be shown to have foundations in primary astronomical information.

Hence the return to mysticism at the end of the 19th century, through the work of Gurdieff, Ospensky, Blavatsky, Bailey, Leadbeater and Crowley, inspired largely by the work of Frederick Neitzsche and the failure to comprehend the true meaning of the reference to Hyperboreans, from Herotodus and others, regarding the ancient greek term Boreas as meaning from above, being the Zenith of the Sun and the Nootime of the hyperbolic arc, from which the Septentrio, or Septentrionalis which indicates the compass point to the direction of the North, and Meridional South, oriental east and occidental west, informs the orientation determined by the one and same ancient system anchored to the elementary study of Astronomy. From whence the North wind blows, is the common interpretation that has led to spurious notions and the rise of both negative theology, and a host of spurious notions flourished by "sceptics" who appear to retrofit ancient narratives and "scholas" to servie the interests of a paradigm based largely on speculations on Alchemy, leading to forced evolution, transhumanism, and totalitarian control systems.

In extending this study to other regions outside of the constraints of the Ancient Egyptian political system which is based on the one and same geometrical model and its rulings, we find the monumental architecture of Stone Henge, and preceding this, of all 12 spoked wheels and henges of a more simple design, hold the same foundational structure, to which Stone Henge, represents the most complex computer able to be utilised as the means of predicting an annular eclipse.

It appears to me, that we are faced with the issue of either saving mysticism, or saving natural science, and the true foundations of computational systems which extend well beyond Plato, and well beyond the construction of Stone Henge, whilst Stone Henge indicates a higher degree of complexity, and instantiation of a relatively transparent system that remains obscure only in the failure to support the greater numbers induction into the primary attributes of astronomy and foundational systems of mensuration.

Regarding the relation between the preceding work and the single chirality Klein Bottle

There are a number of permutations of the Kleinbottle. The most common, or classic figure of the Kleinbottle is discussed in various volumes of Carl Gustave Jung's work on Alchemy, and as Jung described, is a reiteration of both the Pelican Flask of the Ancient Alchemists, and its resonance with the iconic and mystical symbol known as the Pelican Christus. Another, far less known, is related to an altogether different, yet mystical structure known as the "Purse of Futunatus".

After writing a Masters of Fine Arts Thesis on Alchemy and the Creative Process, called "A Point in Time As We Create The Future.", I was vexxed by the issue of antithetical relations, dialectics, and the potential to reconcile apparent extreme opositions which tend towards a point of similarity. Indicating antithetical relations in a manner that presupposes a common center, appeared to me constitute a far too simplistic structure. Whilst I had a significant knowledge regarding Alchemical structures, narratives, signs and symbols, I did not have have the means of comprehending the underlying relations between the two dominant structure figures, commonly known as the Pelican Christus and Oroborean Ring, or snake eating its tail.

The common models which flourished in the Middle ages and beyond, employed by both Raymond Llull and Leibniz, exploited the classic division of the circle, primarily into 12 parts, and variations on this theme, leading to divisions of numerous equally proportioned segments, which included various combinations of such wheels, as in the work of Llull. This is not unlike a classic cololur wheel, which is also related to the 12 half tones of the musical octave. The primary motivation for the use of these models by both Llul and Leibniz, was to create some form of rigorous proof for the concept of God.

Additionally the means through which an astrological wheel is constructed, preserved the integrity of the geometrical method which can be seen in the two circle model used by Copernicus; discussed in Plato's Timaeus from the standpoint of a process of reverse engineering what the "artificer" had done; discussed in Vitruvius with regards to the construction of a sun dial, whose model is directly employed by Ptolemy

even though both he and Copernicus preferred to underpin their astronomical studies with the technological tool of the Astrolabe, is reconstructed in the image below, through the inclusion of the method of rulings pertaining to the complex isometric matrix.

With regards to astrology, the presumption that the apparent forward and backward motion of a planet, as it traces its epicyclic spyrographic pattern, as viewed from the planet looking outwards, inferred positive and negative attributes, constitutes a man made imposition, based on appearances which are transcended in the understanding of the higher degree of information that constitutes counter intuitive intellgiible information.

With this vexation regarding the need for a more complex structural analysis of antithetical relations in mind, I decided to engage with the Philosophy Department at Newcastle University, with the intention to work on a PhD, whilst lecturing on issues in PostModern philosophy and a short course on the compartive structural relations underpinning Architecture and town planning from the ancient world. It is here that I first met Shiela Morgan, a retired science teacher and weaving enthusiast, engaged in exploring the structural relations of the Moebius strip and Kleinbottle, from the standpoint of a diagonally woven single joind thread.

It was the end of 1993, and I had twin boys aged about 6 months old. I was so deeply affected- moved- enthused and excited by Shiela's demonstration of the motion inherent in her models, that I rang my partner to say I was not coming home, at least for some time as I had to stay and speak with this exceptional woman.

After waiting for the majority of people from the audience to leave, I went up to Shiela, and tried to hold back my tears as I gushed out these words: "Shiela, you have created the Mercurious. It unifies the Pelican Christus and the Oroborus. Its extraordinary." This would be the beginning of an wonderful decade, and both of us consider each of our work to be likened to two sides of the one coin. Hers, continuing with the formal lineage of explorations in apparently "higher dimensional" spacetime structures, which began with her study of the 1976 publication of Australian Philosopher and humanist Graham Nerllich's "The Shape of Space". Coming from a Fine Arts background, and having studied Alchemy from the work of Carl Jung, Robert Hargraves, Silbere, Kircher, and more, as well as being fully cognisant of Theosophical, Anthroposophical, Rosecrucian, Platonic, Neo Platonic, Neo Pythagorean and mystical works that flourished throughout the middle ages, and from the anals of speculative philosophy, all of which underpinned my research interest since 1978, which continued with the American school of Popular New Physics publications, my world view was, at the time, leaning heavily towards an antirealist standpoint. It is the rejection of this specific standpoint that occurred to me after I persisted in seeking to comprehend whether or not there were any real geometrical foundations that could underpin the natural sciences, as I finally began to understood that many including myself, generally mistook the Veil of Mysticism, for the things that this veil concealed. This was a somewhat terrifying realisation.

My side of the coin so to speak, investigated the shape form and function of the largely unknown Kleinbottle commonly referred to as the "Purse of Fortunatus", the history of which is echoed throughout the history of knowledge. It is this work, and the championing of Shiela Morgans research, and that of Australian scientist Chris Illert, that informed by Phd Thesis, Titled "Towards a New E.R.A.: Epistemological Resolution Analysis, by and through the Kleinbottle and Transdisciplinary Education. This thesis was completed in 2006, and was examined by Eric Trell from Swedon, Stein Eric Johansen from Trondheim University of Technology Norway, and philosopher to the Institute of Basic Research Florida, USA., and Steven M Rosen from SUNY, USA.

It was now 2008. Siela had passed away in 2006, and although I did all I could to get her work out to the world, discussing it, as well as mine at all conferences I participated in, any mention of her work in Wikipedia for example wa constantly shouted down, and any mention of the various elements from my research, also was met with a constant rejection. This in itself began to speak rheims. As all of the speculative works didnt simply hint at a general unification of geometry, they- largely English philsophers such as Roger Bacon for example, were in fact quite explicit, and named reasons for the separation of the disciplines. I became familiar with how non disclosure of the elementary facts that underpinned everything from basic Astronomical studies to Ludwig Wittgenstein's Logic, from the "Laws of Form", by  Spencer Brown, to the principles of Growth and Form by Darcy Wentworth Thompson, and the structural principles of "Art Forms in Nature" by Haeckel, to his monumental works on Histology and speculations on Quasi liquid crystals in his "soul in matter" to the studies in Conchology by Australian scientist and friend Chris Illert, and my investigations on Ultrastructure reseach from the 1960's, leading to my study of Crystallography, all of which informed an awareness of how nondisclosure not only burnt people from the antipodean sphere, who became marginalised, even after the fact of having serious interest expressed from outside of this nation, it show how non disclosure functioned as a binary tool, and how it was so easily exploited by socio-political and religious forces. Behind this research, was my thorough knowledge of the many voices of Post Modern Philosophers on the one hand, and spiritualist from the New Age sphere on the other hand, which now began to make far more sense, as I always felt that they were all intentionally failing to reveal the fact that alchemy informed most of their ideas, and their failure to identify this fact, appeared to me to infer a form of plageristic pomposity. But then, I am a female, not privy to the exclusive circle that males frequent. And this more than anything else, represented an exposure of a Pythagorean social system, where the elevation or reduction of an individual according to the merit of their work, would effectively inform a hidden hand of cultivation, that could have both positive and negative outcomes for any given society, depending on what the objective of that society was. That is, if sucess was measured by financial gain, and the accumulation of patents from the application of natural sciences towards the progression of technologies, or by the merit of one's critical interrogation of the philosophical issues that prevailed in both the sciences, the arts, and mathematics. Indeed, from this standpoint, which is obviously where my heart was at, such merit is considered not just irrelevant, it is abhorrent to those seeking to gain wealth and power beyond reasonable limits.

note to eric

To be continued tomorrow. just watched joe rogan 1945---- Diego Rappaport (recieved a 500 page book of my post doctoral geometry research in 2010, and recently began working with Steven Rosen from Suny who was one of my examiners and hence has my PhD thesis...... he contacted me in 2005 regarding my research hence becoming my examiner. Eric Trell translated sophus lie into English in 1996 another examiner. Stein work with Santilli - Hadron sciences...and Chris illert (6D spacetime conchology research) is assocated with Santilli.....and Peter Rowlands with his universal rewrite system was in attendance in conference with british computer society.... the gemoetry worked out by them and Vanessa Hill, who I dont hear anything about since then, is not fully worked out...... .. Diego has written me out of his work on torsion physics- all of his studies on the kleinbottle came from my research. ...... As I have lost my library, it will take some time to write this all out off the top of head. I apologise for the numerous spelling mistakes, as there appears to be no spell check here. Here in the antipodeans, Google is the dominant force, which has concealed so much and all of your sites. I have now found them, and am studying as much a I can. Very much enjoyed your discussion with Lissi, but have numerous points that vex me, from both sides of the discourse. It is such a pleasure to listen to such intellects. I hope you dont mind me writing to you in this way, Eric. If so, you now have an email address. Thankyou for your brilliant mind and inspiring work.