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The paper analyzes the monument of Le Menec at Carnac, in Brittany, France. It advances a number of propositions, key among them being that the strings of stones at Le Menec are not linear parallel alignments but converging arcs. These stones and strings performed a variety of cultural functions. Arcs acted as a Theme Park for celestial objects and their orbits. It is suggested that Le Grand Menec, Kermario, Kerlescan, and Le Petit Menec represented the four seasons. The paper also suggests that the stones' shadows were used as part of sundials. Each stone was used as a computing device, and collectively they constituted a proto Neolithic supercomputer.

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All content in this area was uploaded by Dimitrios S. Dendrinos on Dec 11, 2017

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... A central feature of this paper, the role of shadows in Archeology and Neolithic Architecture, has been first recognized and elaborated by the author in two previous papers. One was on Carnac's Le Grand Menec monument, cited in [1]; the second was on Gobekli Tepe's structures C and D (Layer III) cited in [2]. These two papers constituted a dual effort: first, to analyze the role that shadows apparently played in the design of Neolithic monuments and demonstrate that shadows of standing stones in specific and structures in general were an integral part of the monuments' architectonic design; and second, to bring the subject to the forefront of archeological research and make it a branch of the studies in Neolithic Architecture. ...

... The reader is directed to the references in [5] for more information on certain isolated efforts to deal with shadows in monumental Architecture. In so far as how the expected shadows cast by monoliths have directly affected the architectural design of the monuments themselves during the Neolithic (and beyond, down to the design of monuments in Classical Greece) the reader is referred to the papers in [1] and [2] written by this author. It is an extension of these two specific papers that this paper is written. ...

... In two specific cases examined in some detail by this author, it was found that the positioning of monoliths (orthostats and pillars in the case of Gobekli Tepe's structures, see [2], and strings of free standing stones in the case of Carnac' Le Menec and its allied monuments, see [1]) the architect wanted to convey information to the relevant public at the time, i.e., pass on cultural messages associated with the various social functions performed by these monuments. Moreover, due to these shadows, the architect designed the monument to accommodate the shadows' movements, their daily as well as the annual dynamics. ...

The paper presents both an introduction to the theory of shadows and their mathematics, with a concentration in the cast-off shadows from megalithic Neolithic monuments. It is addressing lengths of shadows' dynamics above the Tropic of Cancer at the Northern Hemisphere. A companion paper presents the length of shadows' dynamics at and below the Tropic of Cancer here: https://www.academia.edu/32426535/The_Dynamics_of_Shadows_at_and_below_the_Tropic_of_Cancer_in_the_Northern_Hemisphere

... That search could be in part responsible for the shape of the major 2-d arcs of the monument (also manifested in 3-d, by utilizing the ground's slopes) in Le Menec's form. See [1] on the formation of arcs in 2-d and 3-d and the implications this design has for the monuments at Carnac. A number of the triangles involved are probably different ways of approximating (and possibly deriving) both Pythagorean triples and primitive Pythagorean triples (PPTs), among a plethora of other triangles of a different (lesser or greater, depending on the point of view) import. ...

... Indeed, by any standard, Le Menec is a striking case of a monument employing built capital stock and amount of land of that magnitude. Addressing the question why would these Neolithic people go to such extreme lengths of utilizing land and resources to construct a monument of this scale is an issue extensively elaborated in [1]. Observing the Moon for a few minutes at the tip of Le Grand Menhir Brize from a few miles away simply isn't a good enough justification in terms of social and economic benefits to lead a social group towards incurring such extraordinary costs of constructing a monument of that size. ...

... The setup of the stones in the form seen today (in spite of their numerous possible dislocations by many agents and agencies during the intervening millennia) may still provide enough clues to demonstrate that they have been set up by their original architect as an attempt to systematically study specific triangles, their angles, edges' lengths and their associated circles. This paper must be read in conjunction with a companion paper by the author, see [1]. Without employing any jargon from Archeology or technical terms from Mathematics, it is written neither for archeologists nor mathematicians, but for the general public with a College level Mathematics background. ...

A conjecture is advanced in this paper, which is a sequence to the paper by the author "In the shadows of Carnac's Le Menec Stones: a Neolithic proto supercomputer". It states that on the strings of stones at Le Menec, there are primitive Pythagorean triples embedded in them, measured in modular lengths. These triples may have determined the size of the monument. The modulus is estimated to be 3.60 meters.

... A central feature of this paper, the role of shadows in Archeology and Neolithic Architecture, has been first recognized and elaborated by the author in two previous papers. One was on Carnac's Le Grand Menec monument, cited in [1]; the second was on Gobekli Tepe's structures C and D (Layer III) cited in [2]. These two papers constituted a dual effort: first, to analyze the role that shadows apparently played in the design of Neolithic monuments and demonstrate that shadows of standing stones in specific and structures in general were an integral part of the monuments' architectonic design; and second, to bring the subject to the forefront of archeological research and make it a branch of the studies in Neolithic Architecture. ...

... The reader is directed to the references in [5] for more information on certain isolated efforts to deal with shadows in monumental Architecture. In so far as how the expected shadows cast by monoliths have directly affected the architectural design of the monuments themselves during the Neolithic (and beyond, down to the design of monuments in Classical Greece) the reader is referred to the papers in [1] and [2] written by this author. It is an extension of these two specific papers that this paper is written. ...

... In two specific cases examined in some detail by this author, it was found that the positioning of monoliths (orthostats and pillars in the case of Gobekli Tepe's structures, see [2], and strings of free standing stones in the case of Carnac' Le Menec and its allied monuments, see [1]) the architect wanted to convey information to the relevant public at the time, i.e., pass on cultural messages associated with the various social functions performed by these monuments. Moreover, due to these shadows, the architect designed the monument to accommodate the shadows' movements, their daily as well as the annual dynamics. ...

The paper presents both an introduction to the theory of shadows and their mathematics, with a concentration in the cast-off shadows from megalithic Neolithic monuments. It is addressing lengths of shadows' dynamics above the Tropic of Cancer at the Northern Hemisphere. A companion paper presents the length of shadows' dynamics at and below the Tropic of Cancer here: https://www.academia.edu/32426535/The_Dynamics_of_Shadows_at_and_below_the_Tropic_of_Cancer_in_the_Northern_Hemisphere_update_1

... However, it is quite likely that the various almost perfect natural geometric forms, that may also be found in geological formations, have endowed observers with the ability to conceive abstract mathematical ideas and do Geometry (Euclidean or otherwise). The author has expanded on this view in a number of his papers on archeological subjects, see for example, ref. [16], [17]. For more on this see also Note 1 at the end of the paper. ...

His contributions to Symbolic Logic, and by extension to Epistemology, are only comparable to those by Aristotle. In the photo, Gödel is shown in his "Incompleteness Theorems" days. Source of photograph: reference [A] Nature is in an incessant process of adjusting, self-correcting imperfections of its own making. "Most often things go well, but at times they go awry", reflected the observer. The paper is dedicated to my wife Catherine and to our two daughters Daphne and Alexia 3 Abstract Preface

... [1. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. ...

The Mathematics and embedded Astronomy are explored of the almost elliptical in shape Minoan 5-priestess gold signet ring of the c 1450 BC Mycenaean “Griffin Warrior” tomb at Pylos found during the 2015 archeological excavation there. It is documented that the shape of the ring is extremely close, albeit not exactly identical, to the true ellipse of an identical major and minor axes. The likely knowledge of ellipses possessed by the ring’s maker is identified. In the paper, a detailed description of the ring’s iconography is also offered, which to an extent differs from the current archeologists’ based description. The iconography’s Astronomy, is found to be associated with a ceremony dedicated to the fertility of Mother Earth, that quite likely was taking place around the Winter Solstice. An estimate of the ceremony’s duration, eighteen days, is also obtained, as having been engraved onto the ring’s iconography.

The paper elaborates on points raised on a previous paper by this author titled “Carbon-14 evidence and Neolithic sites: dating the Architectures of Boncuklu Tarla and Gobekli Tepe”. It also discusses and analyzes some more recent carbon-14 related evidence from Gobekli Tepe published by a team of archeologists associated with the excavation there.

This is the first paper of a two-paper series, dealing with ancient artifacts and their movement in space-time. It provides the background to the theoretical mathematical model supplied in the second paper.

This is an update of the paper under the same title by the author. It contains editorial corrections and the formal permission by the University of Cincinnati Dept. of Classics to use the image of the ring.

The paper is an updated version of the December 2, 2017 paper under an identical title by this author. It incorporates in it exact measurements of the ring (received by the author on December 3, 2017). The paper strengthens and expands on the findings of the previous paper, as well as it amends and extends the prior analysis. Editorial corrections are also carried out.

The paper addresses the fuzzy nature of shadows cast by Neolithic monuments. It presents a mathematical theory of fuzzy shadows, and extends a previous paper by the author of a General Dynamical Theory of Shadows.
That original paper is found at the site academia.edu here:
https://www.academia.edu/31671102/ON_THE_FUZZY_NATURE_OF_SHADOWS
and also here at researchgate.net here:
https://www.researchgate.net/publication/317506046_On_the_Monoliths'_Shadows

The paper presents an early work by the author, regarding the Tomb at Kasta Hill, Amphipolis, MAKEDONIA, Greece. It was based on three hypotheses: that the tomb was completed at the last quarter of the 4th Century BC, and that the architect was Deinokratis are both assumptions attributed to Katerina Peristeri, the archeologist in charge of the excavation; the third assumption was based on Professor Theodoros Mavrojannis hypothesis that HFAISTION was the (single) person buried there. Further, the paper was based on information prior to a November 29th, 2014 conference given by K. Peristeri, where new evidence was presented (having to do with Roman coins and pottery fragments found in chambers 1 and 2 - although no 3-d specific location for these items was disclosed). As a result of these new revelations, and subsequent announcements about the skeletal bones from a number of individuals found in the funerary chamber, major revisions are needed. thus, this paper serves purely as a means in archiving and recording on-going research by this author.

This is the Final Version of the paper by the author "On Certain Key Architectural Elements of Kasta Tumulus" first published on 8/12/2015 and had four updates. A new paper is its successor, which incorporates new findings, titled: "On the Tumulus at Amphipolis".

The study is an attempt to formulate and trace the complex dynamics of Alexander's cities of the period 340 BC to 323 BC. Concepts in dynamical analysis from Urban and Transportation Planning as well as Economic Geography are utilized to place the evolution of the cities founded by Alexander III in their proper context. The author supplies at the end a more elaborate list of cities established by and directly linked with Alexander III.

This is an updated version of an earlier paper titled "Stonehenge, Durrington Walls, Newgrange: Monuments to the Egyptian Bull and Cow Cults and Origins of Innovation" by the same author. However, in this paper new material has been included. Thus, this paper marginally amends (in view of the summer 2016 retraction of the summer 2015 announcement regarding Durrington Walls) and considerably extends the previous paper.
On September 19th, 2016 I revised the view presented in this paper regarding the date of Gobekli Tepe's oldest layer's construction with this paper:
https://www.academia.edu/28603175/Dating_Gobekli_Tepe
A new version of this paper is forthcoming to account for this update.

A conjecture is advanced in this paper, which is a sequence to the paper by the author "In the shadows of Carnac's Le Menec Stones: a Neolithic proto supercomputer". It states that on the strings of stones at Le Menec, there are primitive Pythagorean triples embedded in them, measured in modular lengths. These triples may have determined the size of the monument. The modulus is estimated to be 3.60 meters.

The paper analyzes the evidence regarding the dating of the Gobekli Tepe complex. First, it examines the C14 dating information supplied by the archeologist in charge of the Gobekli Tepe excavation, Klaus Schmidt, and a number of others. This is claimed as evidence that Gobekli Tepe is of the at least PPNB period. The evidence they analyzed was obtained from both the fill, as well as from the plaster at the surface of certain Gobekli Tepe structures. The paper also examines the lithic based evidence regarding the fill at the site. Clear evidence that counters these claims is presented is presented in this paper. Although the Gobekli Tepe site can be shown to be of much later construction date than PPPNB, the paper sets as a modest aim to show that the structures at GT so far analyzed are of a later than PPNB date. Evidence covering both C14 dating, as well as architectural, urban design, urban planning, demography and art evidence is offered to back this argument. Extensive use is made of architectural elements from PPNA Natufian settlements, as well as PPNA/B settlements Hallan Cemi and Jerf el-Ahmar.

The paper documents the date for the initial construction phases of Layer III of structures D (middle 6th millennium BC) and structure C (end of 6th millennium BC - beginning of 5th millennium BC) at Gobekli Tepe. It is a sequel to the author's September 19, 2016 paper "Dating Gobekli Tepe". It uses comparative Architecture and Design analysis from Catalhoyuk and Nevali Cori as well as Jerf El Ahmar for the dating process. It also employs Alexander Thom's schema of classifying stone enclosures, by appropriately expanding it and applying it to Gobekli Tepe. The paper also traces linkages between Gobekli Tepe, Carnac, Malta, Stonhenge and Menorca.

This book develops a theory of inter- and intra-urban evolution as a branch of mathematical ecology and population dynamics. In recent years profound changes have been taking place in the methodology of dynamical analysis. These new ideas are encompassed by catastrophe and bifurcation theory, and nonlinear differential equations. The authors of this book show how one can attain an understanding of urban evolution by using these new methods. The topics which are covered include: the relative population and income levels of metropolitan areas, slum formation, gentrification, and suburbanization. Senior students at first-degree level and above taking courses in urban geography, planning, economics, demography, sociology, urban affairs, and public administration.