Spirasolaris

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SPIRA SOLARIS:Form andPhyllotaxis Assignedto the main heading SPIRASOLARIS this January 2007 essay owes itsorigins to a number of events and issues, but the subtitleitself (Form and Phyllotaxis) arises from the neglected SolarSystem researches of Americanmathematician Benjamin Peirce (1809-1880). His investigations andconclusions resurfaced in September 2006 after the elevationof the asteroid Ceres and simultaneous demotion of the planetPluto to the status of "Dwarf Planets." Essentially,withPlutothus demoted Neptune once more becomes the outermost planet, as Peircestipulated ontheoretical grounds over 150 yearsago. Firstpublished in 1850and later recorded by his friend Louis Agassiz (1807-1873) in thelatter'sfamousEssay onClassification (1857:131)Peirce theorised that "therecan beplanet exterior to Neptune, but there may be one interior to Mercury."Revisitingown attempts to come to terms with the fundamentalstructure of the Solar System in the first three sections of Spira SolarisArchytas-Mirabilissimilarities between thetwo approaches nowsuggestedthat while I hadunknowingly followed Peirce by omitting Pluto and adding aninter-Mercurial object, I had missed the point completely when itcame to the significance of Neptune. Not so Benjamin Peirce.Nevertheless, although Agassizprovided additional details in his Essayon Classificationconcerningthe latter'sSolarSystem research including "theratios of the lawsof phyllotaxis"in this same astronomical context, Peirce's major conclusion was castaside despite its potential significance. Although not stated inthese precise terms, it wasnothing less than the perception thatSolar System isPheidian in Form1andPhyllotactic2in NatureJust howright (or wrong)was Benjamin Peirceconcerningthe phyllotactic aspect of the SolarSystem? He was certainlyone of the leading scholars of his day, and there is little doubt thatwas also an influential scientist in his own right, asfollowingexcerpts from his ScientificBiblographyattest: PEIRCE,BENJAMINSalem,Mass., 1809; d. Cambridge, Mass., 1880), mathematics, astronomy. Graduated fromHarvard (1829;M.A.,1833), where he was a tutor (1831-33) and professor (1832-80). Inmathematics, he amended N.Bowditch's translation of Laplace's Mechaniqueceleste(1829-39);proved (1832) that there is no oddperfect number with fewer than four prime factors; published popularelementary textbooks; discussed possible systems of multiple algebrasin LinearAssociative Algebra ... andset forth, in ASystem of AnalyticMechanics (1855),principles and methods of that science asa branch of mathematical theory, developed from the idea of the"potential." In astronomy, he studied comets; worked on revision ofplanetary theory and was the first to compute the perturbing influenceof other planets on Neptune; and worked on the mathematics of the ringsof Saturn, deducing that they were fluid. From 1852 he worked with theU.S. Coast Survey on longitude determination, ... became head of thesurvey (1867-74) (and) superintended measurement of the arc of thethirty-ninth parallel in order to join the Atlantic and Pacific systemsof triangulation. Influential in founding the Smithsonian Institutionand the National Academy of Sciences. (ConciseDictionary ofScientific Bibliography,Charles Scribner, New York1981:540)For myown part, I intend to showin this titleessay that Benjamin Peirce's phyllotactic approach to the structure ofthe Solar system was indeed correct, allramifications and consequences notwithstanding.Inshort, thelong-delayedlegacy of Benjamin Peirceand the policies laidout in hisclosing remarks to themembersof the AmericanAssociation for the Advancement of Science concerning thefounding of the SmithsonianInstitution, and not least of all, the honest, unhindered pursuit ofknowledge:and, instructed by the wisdom of thishigh-minded son of England, learn to confide in our own rulers. Let usbe aroused to anearnest and harmonious effort to accomplish the plan proposed by ourPresident atAlbany, for the building up of an "institution for science,supplementary to existinginstitutions, to guide public action in reference to scientificmatters." With the details of theplan and the arguments in its favor you are familiar. You know howuseful it would be asa protection from the wasteful expenditure upon abortive attempts toreverse the laws ofnature. You know how much it is required to sustain the purity andindependence ofscience, even within its own proper domain. You know that in no age orcountry was thereever a more urgent call for a scientific society, in which scientificinfluence shouldpredominate, where it should not be smothered by excess of patronage,and whence itshould not be liable to banishment through any spirit or form ofostracism. If Americangenius is not fettered by the chains of necessity, and helplesslyexposed to the assaultsof envious mediocrity, but is generously nourished in the bosom ofliberty, it will joyfullyexpand its free wings, and soar with the eagle to the conquest of theskies."Concluding remarks from "TheAddress ofProfessor Benjamin Peirce, President of the AmericanAssociation forthe Year 1853, on retiring from the duties of President"revolution, etc., e.g.,Ammonitesand Shellsphyllotaxisphyllotaxynoun2. phyllotaxes, phyllotaxiesfractions were applied by BenjaminPeirce to the mean periods of revolution alone; the present dynamictreatment is morecomplex.Associatedgraphics: SolarSystem PhyllotacticResonant Triples, Neptune to MercuryBode's FlawBode's "Law" - more correctly the Titius-Bode relationship - was anad hoc scheme for approximating mean planetary distancesoriginated by Johann Titius in 1866 and later popularized by JohannBode in1871. The " law " later failed in the cases of the outermostplanets Neptune and Pluto, but it was flawed from the outset withrespect to distances of both MERCURY and EARTH, as Titius was perhapsaware.IIThe Alternative Describes an alternative approach to the structureof the Solar Systemthat employs logarithmic data, orbital velocity, synodic motion, andplanetary periods in contrast to ad hoc methodology and theof mean heliocentric distances alone. Previous version:http://www.spirasolaris.ca/sbb4b.html]IIIThe ExponentialOrder The constant of linearity for the resulting planetaryframework is theubiquitous constant Phi known since antiquity. Majordeparturesfrom the theoretical norm are the ASTEROID BELT, NEPTUNE, and EARTH ina resonant synodic position between VENUS and MARS.[ Previous version:http://www.spirasolaris.ca/sbb4c.html]THESPIRAL FORM AND UBIQUITOUS GOLDEN SECTIONIVSpira SolarisArchytas-Mirabilis Most suitably represented in terms ofexponential growth and a complexequiangular spiral, the Phi-series based planetary modelappearsto be new in one sense and yet quite ancient in another. Title graphic (91kb, best viewed at 1280 x 1024 resolution).HistoricalDigressions on theGolden SectionIVd2Spira Solaris andThe Middle Ages Ostensively the translation of Aristotle's DeCaelo from medieval latin to French, Nicole Oresme's Le Livreciel et du monde [ ca.1375 CE] was more than a translation and acommentary.The numerous references in this work to the insights of the ArabscholarIbn Rushd [Averroes,1128-1198 CE] lead back to Plato's Republic,Archimedes, Pythagoras, and the Golden Section inearlyAlchemical contexts.SPIRAL FORM AND NATURAL GROWTHIVd2b Spira Solaris andthe 3-Fold Number "The three-fold number is present in all thingswhatsoever; nor did we ourselves invent this number, but rather natureteaches it to us." HaliotisParva andthe Golden Rectangle IVd2c Spira Solaris andthe Pheidian Planorbidae Applied to Nautiloid spirals, Ammonites,Snails and Seashells. Appendix: The Matter ofLost LightHISTORICALCONSIDERATIONSIVcSpira Solaris, theFourth Planet and Fifth Element PROCLUS [ Commentary on theTimaeus of Plato ]: "For through analogy the universe iscompletelyrendered one, this having the power of making things that are dividedto be one, of congregating things that are multiplied, and connectingthings that are dissipated.Hence theologists surveying the cause of these things in the Gods,encloseVenus with Mars, and surround them with Vulcanian bonds; the differencewhich is in the world being connected through harmony and friendship.this complication and connection likewise has Vulcan for its cause, whothrough demiurgic bonds connects sameness with difference, harmony withdiscord, and communion with contrariety."VSpira Solaris.TheChaldean Oracles. Proclus, and Johannes Kepler Examines therole played by the Chaldean Oracles in influencing theNeoplatonist Proclus [410 - 485 CE] and the connection between thelatter, The Harmonies of theWorld, and the Harmonic Law "conceived on the eighth day of thethirdmonth in the year 1618" by Johannes Kepler [1571-1630 CE].VISpira Solaris andthe Universal Ouroboros Explores the historical antecedentsand the relationship between the Equiangular Period Spiral, theOuroboros, Alchemy, and theSun.VIISpira Solaris andtheThree Parts of the Wisdom of the World The spiralconfigurationis found on rock art in regions as distant as Nicaragua, Italy,Indonesia,and the United States. It is also found on the Plains of Nazca in Peru,Malta, in France, in Britain, and especially in Ireland, where acomplextriple spiral is illuminated on the winter solstice inside theNeolithicSite at Newgrange. What is the significance of this complex motif, whatmessagewas it intended to convey, and where does the inquiry lead?SPECULATIONSVII-IISpira Solaris:Where Virtue, Wisdom and Equity are Assembled [ Additional text: Tenebrosity; also in PDF. RelatedGraphics: Outof the East(77kb; in full,single-page PDF). OutoftheDark (54 kb)] BACK TO THETOPthe Greenland Vikings simply fade away, or was there more to theirstory and more to the Viking Sagas in addition? It would seem thatthere was far more. In fact sufficient evidence exists to suggest thatthe last Vikings triumphed over the Northwest Passage and that thelegendary lands of the Viking Sagas- Helluland, Markland and Vinland - are located on the West Coastof North America, not the East. Helluland extending fromEtolinIsland in Alaska south past the Bella Coola region of British Columbia;the Queen Charlotte Islands (Haida Gwai since 2010) more than meetingthe basic requirementsfor Marklandwith BritishColumbia's Cowichan Valley at Duncan in the south-east corner ofVancouver Island providingthemost logical technical fit for Vinland itself. But this is onlyof this complex matter....INTRODUCTIONPart 1. VikingPress andVikingShipsPart 2. West by NorthwestPart 3. Three Steps BackPart 4. Symbols,Markers andIndicatorsPart5. TheCopperCanoePart 6. The Warp and the WeavePart 7. Helluland, MarklandandVinlandCURACHMEN OF THE WEST Curachmen "For nearly anthe men stood waiting to launch the curach. It was blowing fresh fromthe south-west, with hard squalls of wind and rain; and the breakerscame charging in, rank after rank, in unending succession. From time totime the men would retreat before the biggest sea, afterwards shovingtheir curach well out into the water again. It looked as if thelong-awaited deibhil, orlull, would never come..." [G. J. Marcus. TheConquest of the North Atlantic, Oxford UniversityPress,New York 1981:3-4.] (PDF: 26 kb; also in HTML)A MACKENZIE SOUND CARVING MacKenzie Sound"The rock carving in this photograph was found at a remote place on thenorth end of Vancouver Island about 50 miles from Alert Bay by StephenLablosky of 12320 Old Yale Road, Surrey. The figures are about 8 incheshigh and 1/4" deep on the face of a large granite boulder. Whatinterests both he and I about this carving is that it can't be Indian,nor is it feasible that a logger would have the skill to do such work.Because of the religious symbolism and because of the skill necessaryto carve in granite, we tend to believe that early Hudson's Bayexplorers left it ... but for what reason?" [ Charles Lillard,"Notesand Queries," TheRaincoast Chronicles FIRST FIVE, Numbers 2 and 4,Edited by Howard White, 1976, 1994:91,193]. (Single-page PDF:167 kb; also in HTML)MINERBIRDS OF THEMONTANAWaterstone of theWild."All through the Peruvian and Bolivian Montanato be found asmall bird like akingfisher, which makes its nest in neat round holes in the rockyescarpments above the river. These holescan plainly be seen, but are not usually accessible, and strangelyenough they are found only where thebirds are present. I once expressed surprise that they were luckyenough to find nesting-holesconveniently placed for them, and so neatly hollowed out as though witha drill.' They makethe holes themselves.'The wordswere spoken by a man who had spent a quarter of a century in theforests. ' I've seen how they do it,many a time. I've watched, I have, and seen the birds come to the cliffwith leaves of some sort in their beaks, and clingto the rock like woodpeckers to a tree while they rubbed the leaves ina circular motion over the surface. Then theywould fly off, and come back with more leaves, and carry on with therubbing process. After three or four repetitionsthey dropped the leaves and started pecking at the place with theirsharp beaks, and here's themarvelous part, theywould soon open out a round hole in the stone. Then off they'd goagain, and go through the rubbing process withleaves several times before continuing to peck. It took several days,but finally they had opened out holes deep enoughto contain their nests. I've climbed up and taken a look at them, and,believe me, a man couldn't drill a neater hole !' " [ Brian Fawcett, ExplorationFawcett.The Companion Book Club, London, 1954:105-106 ]. HTML; alsoin PDF(88 kb). If such a birddoes exist, what might it be? A hole-makingBolivian Ovenbird perhaps? A "Common miner" (Geositta cunicularia) or a "Punaminer"(geositta punensis)?PETRIE'S CORE 7From a wider, earlier and more distant perspective there is somethingelse to be considered. Namely, whether the repeatedpouring of a "softening" liquid of this sort while drilling couldprovide an explanation for "Petrie's Core #7,"aslightly conical,cyclindrical residual core drilledfrom a solid block of stone block by ancientEgyptians that requires modern power tools to emulate. For the Record"Aspendid cast of the deeply carved face of Wi te Manewha was taken byLindauer and Sir Walter Buller. His moko was perfect, the lines cutexceptionally deeply, even to the eyelids. It was said that thetattooing was done twice to make deeper markings. The cast was madeduring the lifetime of the chief. Itis of considerable ethnological value because it is the only knowninstance of an old-time Maori permitting such a thing, since the headwas considered sacred." [ An extract from MAORIPAINTINGS: Pictures from the Partridge Collection of Paintings byGottfriedLindauer. Edited by J. C.Graham, A. H A.W. Reed,Wellington, 1956]. (HTML; also in PDF: 440 kb)COASTSALISH / SQUAMISH WELCOME FIGUREShould you wander down an increasingly urbanpathway along the westernbank ofBritishColumbia's Capilano River (the natural boundaryseparating Northand WestVancouver), you may come across a small inscription on a rockby the wayside. Carved with care, it is clearly modern, inscription andtext alike. It says sadly and simply:Strengthin your weeping,Tears thatcome seeping,Down the oldcanyons,Back to thesea.From TheRiver by Jean GowlandPassing under a bridge the path continues along the pavement of a roadthat leads around a large Mall, where (now separated from the river bya wire and split-board fence) the path curves south again into a smallwoodedarea. Finally, one eventually reaches the rivermouth andfollowing the shoreline to thewest, a small bay bounded by a pair of rocky outcroppings. Augmentedstrengthened, these too are modern, and often visited for they extendoutwards from the beach area of West Vancouver's AmblesidePark. At theend of the largest outcropping, however, there is another recentinscription, this time on a bronze bi-lingual plaque. But here the textis accompanied by something else, namely a large wooden figure lookingout over the Inlet towards the southwest with both arms outstretched.This is the Coast Salish WelcomeFigure erected by the Squamish FirstNation to commemorate the first "Gathering of OceanCanoes" inthe summer of 2001. For this is their land; this is their will,and this is their generous welcome.GEORGEWOODCOCK : PEOPLES OF THE COASTA Witnessing "Yet it was in one way the most dramatic danceof the whole night, for the drummers came down out of the bleachers tojoin those on the floor and make an avenue of sound through which theold dancer progressed, with hundreds of voices shouting out her song,and her attendants scattering handfuls of coins among the drummers andthe singers. It was obviously a farewell, for we felt no doubt thatthis was the old woman's last dance, and that she and everyoneelse knew it. But it was also the kind of assertion of continuity, forhere was a person who had been a child in the last flourishing of theold native culture, and by supporting her in her dance the rest of thepeople were not only proclaiming their continuity with the past butalso celebrating the revival of the old ways." [AWitnessing: The concluding chapter of George Woodcock's PEOPLESOF THE COAST : The Indiansof the Pacific Northwest, Hurtig Publishers, Edmonton,1977:209-214.] (HTML; also inPDF: 56kb)QUANTUMENTANGLEMENT : THE STARFISH TELEGRAPHQuantum Entanglement:"I hoisted the anchor and arrived at Barney's to find him collapsedand hemorrhaging. I took him in my boat to the nearest settlement,leaving the two starfish in a bucket of sea water in the shack. Barneylater died in the Prince Rupert hospital. When I got back toKettle Inlet, the starfish were dead. The water should have beenchanged every twenty-four hours or oftener. The years havepassed and I've never related this story for fear that I might become acandidate for the funny house. Quite recently I read an article similarin regard to plants which gave me the courage to contribute my story atthis time." (C.H. Doane [ "The StarfishTelegraph," TheRaincoast Chronicles SIX/TEN, Number 10.Edited byHoward White, 1976, 1994:237 ]. Single-page PDF:29 kb; also in HTML) The Times and Tidesof JohnDavis: Selectionsfrom The Voyages and Works of JohnDavis the Navigator (1880). [ PDF: One page Index (as below) ] original 1880 publication of TheVoyagesand Works of John Davis the Navigator, more often than notrestrictedSpecial Collections and Rare Book Departments, etc., is currentlyavailable on the Internet as a large, graphics-based GoogleDigital PDF file.Because of its sheer size, however, the various topicsin this 515-page volume may still tend to overwhelm thecasualreader, especially in this particular format. For this reason, selectedsegments from the above are provided here in smaller, searchable PDFfiles that retain the originalantiquated English texts, typesetting andpagination. The choice of material, however, doesnot center on the voyages ofJohn Davis per se, but on hisuse of theheliocentric concept and the impact of this understanding on thedevelopment ofElizabethan navigation in general. Thus, in addition to The Worlde'sHydrographical Discription (1595) and Seaman'sSecrets (1594,1607) by JohnDavis himself theselection includes the "Noteon the New Map" of A.1600 by Charles Henry Coote and an extensive BibliographicalList of Works on Navigation during the Reign of Elizabethprepared by Albert Hastings Markham. Lastly, an additional supplement: Introduction,Symbols and Abbreviations, and a Short Bibliography to Copernicus andKepler (1952) by Charles Glenn Wallis has also been included toprovide a necessary background foropposing geocentric and heliocentric planetary theories of thetime. [Sources: John Davis, Albert.Hastings Markham andCharlesHenry Coote in TheVoyages and Works of John Davis, the Navigator,The HakluytSociety, No. LIX, London, 1880.Charles Glenn Wallis in Great Booksof theWesternWorld 16, Editor-in-Chief Robert Maynard Hutchison, WilliamBenton, Chicago 1952:481-495. ]WORKSBY JOHN DAVIS:TheWorlde'sHydrographical Discription (PDF: 256 kb)Seaman'sSecrets : Book I .(Degrees, Times, and Tides, etc. PDF: 1.33 Mb)Seaman'sSecrets : Book II.(The Globe and Other Instruments. PDF: 1.49 Mb)ALBERTHASTINGS MARKHAM:John Davis the Navigator[Introduction plus Note and 3rd Voyage(1587). PDF: 664 kb]Letters of Marque andOther Matters (PDF: 61 kb)BibliographicalList ofWorks on Navigation (PDF: 215 kb) CHARLESHENRY COOTE:"Note on the New Map" ofA. D. 1600 (PDF: 113 kb)CHARLESGLENN WALLIS:"Introduction toCopernicus and Kepler, etc." (PDF: 147 kb)RELATED MATERIAL:The World Encompassed bySir Francis Drake "Collected out of the Notes of Master Francis Fletcher, Preacher in thisemployment, compared with divers others notes that went in the sameVOYAGE. Printed at Londonfor Nicholas Bourne, dwellingat thesouth entrance of the Royal Exchange, 1652." (PDF: 856 kb)CHARLESLILLARD : INTRODUCTION TO WARRIORS OF THE NORTH PACIFIC" Now that there is no longer a western frontier, we are slowlyrecognizing the American "melting pot" and the Canadian "mosaic" forwhat they are, stewpan and collage. Also, we are learning our ancestorsrode roughshod over the land with little consideration for the future.They took the land, built their towns and villages, and then, knowingthey had civilized a new world, died. What we are no longer sure of isour own place in this new world of theirs. The question asked byMargaret Atwood in Survival belongsto all of us: "what do you do for a past if you are white, relativelynew to a continent, and rootless?" Personally, I doubt anyonewill answer Atwood's question satisfactorily. The wording is tooexquisitely subjective, every answer leads to a new question. A mazethis large and confusing suggests we no longer believe in the NoblePioneer, this creature has gone the way of the Noble Democrat and theNobleSavage -oldermyths created byearlier North Americanhistorians.If this is so, is it not possible that the history we have learned fromour text books, this history we call ours, may be ambiguous? [ CharlesLillard: Introduction to WARRIORS OF THE NORTH PACIIFIC: MissionaryAccounts of the Northwest Coast, the Skeena and Stikine Rivers and theKlondike,1829–1900,Editedand Annotated by CharlesLillard,Sono Nis Press, Victoria, B.C. 1984:10. PDF: 124 Kb;also in HTML] CHARLESGLENN WALLIS:BACK TO THETOPTimes Series Analysis.The advent of modern computers permits the investigation of planetarymotionon an unprecedented scale. It is now feasible to treat single eventssequentially and apply detailed time-series analyses to the results;also in PDF.SERIES GRAPHICSTime Series GraphicsExamples of chaotic and resonant planetary relationships in the SolarSystem anda possible link with Solar Activity.TheTyrant and the BrideThe Number of the Tyrant is 9. What is the Number of the Bride?Plato's Republic is an enduring and much admired work, but the problemspresented here have still confuted hundreds, if not thousands ofinquiring minds since Plato's time [427-347 BC]. So be forewarned, thisis not a simplematter; nor is it a matter of simple arithmetic, either. Clues aboundeverywhere, but watch for phantoms and misdirections nevertheless.(HTML). March 2019 expanded version in PDF: 561 kb)PYTHAGOREANFRAGMENTSPythagorean FragmentsSelections from the Doxographers, Fragments of Philolaus, FragmentsArchytas, Metaphysical and Political Fragments. (HTML; also in PDF: 204 kb) QUINTESSENTIALJACK LINDSAYTime and EternityII(HTML; also in PDF:48 kb)"Timeis the moving image of Eternity, Plato remarked among the Stars. Eternity is the sudden wholeness of Time,Apollo answers amid the Flowers."The firstand concluding chapters from TheOrigins of Alchemy in Graeco-Roman Egypt by Jack Lindsay,Ebenezer Baylis and Son, Trinity Press, London 1970 ( PDF: 230 kb).THESTAR OF BETHLEHEM AND BABYLONTheStar of Bethlehem and Babylon From a technical viewpoint thedetection of the faint butunquestionably visible planet URANUS by Babylonian astronomers in 9 BCprovides one ofthe more logical mechanistic explanations for the phenomenon. Anon-denominational discourse for open minds. BABYLONIANMATHEMATICS ANDSEXAGESIMAL NOTATIONBabylonian Mathematicsand Sexagesimal Notation Base-60 has its advantages, e.g., the Mayarelationship of 81 synodic months = 2392 days results in a decimalvalue of 29.530864... days for the mean synodic month. In Base-60 it isexactly 29;31,51,6,40 days(the modern estimate is 29;31,50,7,30 days) as opposed to the roundedBabylonian estimate of 29;31,50,8,20 days. The latter, allied with the Babylonian mean sidereal month of 27;19,18 daysproduces an excellent value for the sidereal year (essentially the heliocentric motion of Earthin this context) of 365.25647 days(the modern estimate is 365.25636days). For more concerning this calculation and additional lunisolarcycles see the limited introduction to "Babylonian Planetary Theory andthe Heliocentric Concept" below.MATHEMATICAL ODDITIESAt present a number of oddities remain in themathematical cuneiform texts of the Old Babylonian Period (1900BCE-1650 BCE). Included here is an identical yet apparently redundantoperation inprocedures dealing with the determinaton of the cube roots of theinteger squarenumbers: 27, 64, 125 and 216 (Kazuo Muroi, "Extraction of Cube Roots inBabylonian Mathematics," Centaurus,Vol. 31,1989:181-188; see also Abraham Sachs, "Babylonian MathematicalTexts II-III," Journal of CuneiformStudies, Vol. 6, No,4, 1952:151-155; VAT 8547 and YBC 6295). Either way there is somethingto be said for repetition, especiallyconcerning squares and cubes, with not only tables of both attested forthis earlier period, but also tables of fractional exponentsand (apparently), even logarithms (MLC 2078, Neugebauer and Sachs, Mathematical Cuneiform Texts,Haven, 1945:33-34). At theother end of the scale is "Plimpton322," an exceedingly complexOld Babylonian text that "tabulates the answers to a problem containingPythagorean numbers (or Pythagorean triangles)" considered to be "the oldest preserved documentin number theory." (Neugebauer and Sachs, Mathematical Cuneiform Texts,1945:38-41). JORANFRIBERG (2005, 2006, 2007) In contrast to the limited selection mentioned above thefollowing wide-ranging collations and commentaries on Babylonian mathematics provide not only additional material, butalso a major expansion of the historical, culturaland scientific complexities that attend this matter.Friberg,Joran.Amazing Traces of a Babylonian Originin Greek Mathematics (World Scientific Publishing, Singapore,2007).Friberg,Joran. A RemarkableCollection of Babylonian Mathematical texts (Springer, New York.2006). Friberg, Joran. UnexpectedLinks between Egyptian and Babylonian Mathematics (WorldScientific Publishing, Singapore, 2005).THE OPEN UNIVERSITYBabylonianMathematics fromTheOpen University (2011) BABYLONIANPLANETARY THEORY AND THE HELIOCENTRIC CONCEPTBabylonianPlanetary Theory INTRODUCTION. Over the past century or so the parameters andmethods of Babylonian planetary theory have been gradually assembledfrom the analysis of astronomical cuneiform texts from the Seleucid Era(310 BCE-75 CE). Unfortunately, such texts do not belong to a carefullypreserved, well-organized library replete with a detailed descriptionof the underlying theory. Nevertheless the available cuneiform texts -oftendamaged and scattered - have yielded perhaps an end product inthe form of ephemerides for the Sun, Moon and the Planets and acollection of "procedure" texts that describe how the meanparameters and varying motions were determined and applied.Although not fully explained in modern terms the latter have beendescribed in considerable detail, notably in Otto Neugebauer's largelyunreadable Astronomical CuneiformTexts (Lund Humphreys, London, 1955); in related sections ofthe latter's A History of AncientMathematical Astronomy(1975); in Science Awakening II(Bartel van der Wearden, 1978); and more recently in The Babylonian Theory of the Planetsby Noel Swerdlow (1998). Still difficult to comprehend, furtherinformation has been published in variousJournals, especially The Journal ofCuneiform Studies (JCS)with additional contributions by Otto Neugebauer, Abraham J. Sachs,AsgerAaboe and others. Beyond such specialised attentionthe subject of Babylonian astronomy seems to have been of littleinterest in this modern age, largely (one might suggest) becauseresearchers have consistantlytreated the subject from a non-fictive, non-model viewpoint. Given thelimitations posed by partial recovery and lack of historical guidancethis is perhaps understandable, but whether thisnegative viewpoint should have persisted so long is another matter.Against this complaint a number of reasons can be offered to explainthe apparent stagnation, including an unduly cautious approachinfluenced in part by the terminology and the unfamiliar methodology adopted by theBabylonians themselves. And also, perhaps, a general unwillingness to apply"Occam's Razor" to the impressivesimplicity of the Babylonian methodology reinforced (consciously orunconsciously) by "TemporalRacism," i.e., premature dismissal based on the belief that "They(whomever) could not know that,or do this (whatever) in those days (whenever)." this said, it also seems likelyat least part of thecurrent stagnation arose from insufficient "prior analytics," includingfailure to consider the various complexities and attendantsidereal components inherentin the Babylonian treatment of mean and varying synodic motion.Moreover, the fundamental parameters of timeand motion applied in Babylonian planetary theory were also (it wouldseem) not fully defined in either modern or ancient contexts. Why was this material not takenseriously? Perhaps the unusualmethodology, unfamiliar terminology, and - not least of all - thesexagesimalsystemapplied well beyond modern usage. Thus not simply the "minute"and the "second," but sequentially on down through the "thirds","fourths", "fifths" and"sixths," etc., and not only for units of time and degrees of motion.The general application of base-60 is not particularly difficult, justunfamiliar territory at first acquaintance, but in the pre-computer eraof the twentieth century it was likely still somewhat difficult tohandle in this specific context. On the other hand, Babylonianuse of 360degrees for revolutions,rotations and subdivisions of the same causes no difficulty since allhave been retained to the presentday, albeit occasionally defaulting to decimal values at the lower end (e.g.,time-keeping, latitudes and longitudes, etc.)BABYLONIANMONTHS AND MEAN LUNI-SOLAR CYCLESBabylonian concerns with varyingmotion seem to have followed from the determination of accurate mean values forall four typesof month. Thus 29;31,50,8,20 days for the Mean synodic month,27;33,16,20 days for the Anomalistic month; 27;19,18 days forthe Mean sidereal month and27;12,43,56 days for the Draconicmonth. It is not thought that the Babylonians possessed avalue for the Tropical month, but nevertheless additional valuesinherent in the Babylonian material can besuggested.More generally, a year of 365.256469 days(essentially the heliocentric motion of Earth)is readily obtained from theapplication of the general synodic formula(the product of two periods divided by their difference) to theBabylonian mean synodic month (MSM) and mean sidereal month(MSID), i.e, the relation (MSM*MSID)/(MSM-MSID). In identical mannerthe Babylonian Mean synodic month and Draconic month yields an eclipsecycle of 346.616572 days(modernestimate: 346.62005 days). Finally, in the same way the BabylonianAnomalistic month produces a Babyloniananomalistic cycle of 411.78054 days (modern:411.78387 days). Although far more can be said concerning Babylonianmethodology and parameters in this context the details are at presentbest left todiscussions concerning the Babylonian Lunar texts. In short,however, in addition to the possible availability ofthe above set as well as both mean and varying values, Babylonianinterest in the various complex motions ofthe Moon and the 18.6 year "Saros" cycle is generally accepted,but perhaps still not fully understood. BABYLONIAN LONG PERIOD RELATIONSThere seems little doubtthat fundamental periodrelations played a pivotal role in Babylonian planetary theory, andalso,that these periods couldhave been determined in perhaps a century or less ofcontinued observation. It could also havetaken considereably longer, but nevertheless ample time exists from thebeginningof the Old Babylonian Period (1900 BCE-1650 BCE) down to the much laterSeleucid Era (310 BCE-75 CE). Moreover, although no comparableastronomical texts from the earlier period have been recovered, thereis nothing ofmathematical nature lackingin the Old Babylonian Period. As it is now - perhaps more afunctionpartial recovery than anything else - it is the material in theastronomical cuneiform texts from the latestera that contain the methodology and the details applied sosuccessfully in Babylonian astronomy. For the superior planets Mars,Jupiter and Saturn It isknown that Babylonian astronomers employed disarmingly simple "Long"integerperiod relations derived from pairs of near-integerperiods with corrections of opposite sign to obtain an integer periodin years to which corresponded an integer number of revolutions(sidereal periods) and corresponding numbers of synodicperiods.Thus, as stated in Section 1 of No. 813, a Babylonian procedure textfor Jupiter (Neugebauer, Astronomical Cuneiform Texts,1955:402, translation by A. Sachs)with decimal values substituted forclarity the following instructions and results for this planet: "Compute(?) forthe whole zodiac (or for each sign) the according to the day and thevelocity. in 12 years you add 4;10, in 71 (years) you subtract5, in 427 (years) longitude (returns) to its (original) longitude." provide the following fundamental relationships for thedetermination of the meansynodic arcs from the division of the total sidereal motion by the totalnumbers of synodic events (thus both the mean synodic arc and also themean synodic period):JUPITER: 427 Years, 36Sidereal Revolutions(36 x 360degrees) and 391 Mean Synodic Arcs .SATURN: 265 Years, 9 SiderealRevolutions (9 x 360 degrees) and256 Mean Synodic Arcs.MARS: 284 Years, 151 Sidereal Revolutions (151 x 360degrees) and 133 Mean Synodic Arcs.Needless to say, if required, the mean sidereal arccould just as easily be obtained from the division of the totalsidereal motion by the corresponding numbers of revolutions in allthree cases.The simplicity of these periodrelations belies their accuracy. For example, from the 284-year periodof Mars the period ofrevolution is simply284/151= 1.880794 years (modern estimate: 1.880744years), an impressive result given the speed and proximity of Mars toEarthand the eccentricity of the former in particular. Moreover, thisfavourable comparison was obtained without defining the lengthof theBabylonian year. This central parameter is, unfortunately, a furthersource ofcomplexity since it involves the motion of the moon and consequently ayear expressed in mean synodic months applied in planetary contexts.There are better estimates for the year utilizing this parameter andthere also exist superior alternative derivations. Nevertheless,although a little on the high side a year of 12;22,8 mean synodic months = 365.2606377 days was chosen for its mathematical convenience.In passing it may be noted that from the above period relation forJupiter the mean synodic period obtained from the division of the longperiod of 427 years and the total number of synodic arcs (391) yields avalue of 427/391 = 1.0920716 years. With a year of 12;22,8 months theBabylonian rounded value for this period is given as 13;30,27,46 monthsin Section 1 of Jupiter procedure text No. 812 (AstronomicalCuneiform Texts, 1955:392-393), and though not fully completed in the text,13;30,27,46,16,40 months in the second section to provide analternative approach for both the mean and varying motions of thisplanet. Similar procedures were adopted for Saturn and Mars using thesame length of year, again simplicity in a practical sense, yet on amore complex level, perhaps also resonance-related concerns embracingboth the Moon and the annual/diurnal motions of Earth itself. BABYLONIANCHARACTERISTIC SYNODIC PHENOMENAHow were the planets tracked over "the wholezodiac ... according to the day and the velocity"? As far as the abovederivation may be concerned,although unusual at first acquaintance,Babylonian astronomers employed five "characteristic (synodic)phenomena" to account for themotions of the superior planets Mars, Jupiter and Saturn as observedfrom Earth, thus the apparentsynodic motion of theplanets in thenight sky. Of the five Babylonian phenomena only "opposition" remainswith us today to any extent, whereas the other four phenomena areadditional defining intervals for synodic movements that necessarily incorporatethe lap-cyclesof swifter-moving Earth. All of which in practice become furthercomplicated by the elliptical orbits and varying orbital velocities of not only the planets inquestion, but also those of Earth itself. Nevertheless, this too wasfully addressed, again with impressive simplicity.Precisely how, when, and where theBabylonian approach to planetary motionfirst originated remains unknown, but on examination it can seentheir inquiry was both logical and supremely sensible, commencing(perhaps)with the various motions of the two major luminaries (the Sun and theMoon), the development of units of time and measure in this context,and further (likely concurrent) investigation of the five visibleplanetsknown in Antiquity.Thus over the years, after the determination of themean motions and discernment of variations in position and velocity,the establishment of the extremal synodic arcs (the maxima and minimaof Babylonian Systems A and B along with their periodic times).In short, the establishment of a comprehensive framework forfurther refinement of the synodic cycles with orbital variationsfactored in for both Earth and the superior planets. Thus the eventualability to account for variations in repetitive synodic phenomenathroughout the entire 360-degree zodiacal round apparently observed againstreference frames provided by the local horizon and some 33 "Normal"stars distributedaroundthe plane of the ecliptic. Historically correct or otherwise, on examination there can be littledoubt that the Babyloniancharacteristic phenomena soused arebest understood in terms of afictive, heliocentric planetary modelthat incorporates the dual west-to-east movements of Earth. Thus (1):the west-to-east diurnal rotationof Earth about its own axis, and (2) thelikewise orbital revolutionof Earth and the planets around the center of the Solar System withvariously defined (as done today) by seconds, minutes, hours, days,months and years.METHODOLOGYAND OBSERVATIONJust how successful was the Babylonianapproach to the motions of thePlanets, Sun and Moon? This has yet to be fully established. However,although not immediately obvious, theprecise determination of mean orbital velocities followed by accurateextremallimits and lines of apsides have sidereal equivalents that provideroom for both speculation and further expansion.In any event, there would seem to havebeen ample time available forthe development of an underlying planetary theory by the Seleucid Era (310BCE-75 CE), based perhaps on dataobtained from an extensiveBabylonian observation program known to have extended fromapproximately 700 BCEthe 1st Century of thepresentera. For details see the links immediately below.ASTRONOMICALDIARIES AND RELATEDTEXTS FROM BABYLONIAINTRODUCTION toASTRONOMICALDIARIES AND RELATEDTEXTS FROM BABYLONIA (byAbraham J. Sachs and Herman Hunger, 1984) with added notes(PDF: 720 kb)INTRODUCTIONplus VAT4956 The Introduction plus a shortastronomical diary for the year 567BCE. (PDF: 285 kb)A SELEUCID TABLEOF DAILY(?) SOLAR POSITIONSAsger Aaboe, Journal ofCuneiformStudies, Volune 18, 1964:31-34. (Single-page PDF: 575 kb)TRAPEZOID IN TWO ASTRONOMICAL CUNEIFORM TEXTS FOR JUPITERThe unexplainedtrapezoid in two Babylonian astronomical cuneiform texts forJUPITER from the Seleucid Era (310 BCE-75 CE) Partialanalysis by Otto Neugebauer (AstronomicalCuneiform Texts, 1955:405,430-31; single-page PDF, 34 kb)JANUARY 2016A modern, far-reachinganalysis of the trapezoid in ACT 817, ACT 813 and new relatedBabylonian texts by Mathieu Ossendrijver (2016). "Ancient Babylonian astronomers calculated Jupiter's position from theunder a time-velocity graph."This is a complex treatment of acomplex matter, and also, since it is a fictive approach to Jupiter'smotion, a major step forward, especially since the data used herehas an almost certain heliocentric component. PROJECTILES,PARABOLAS ANDGALILEO'S APPLICATION OF THE FOURTH LAW OF PLANETARY MOTION PROJECTILES,PARABOLAS, AND VELOCITY EXPANSIONS OF THE LAWS OF PLANETARY MOTIONBY J. N. HARRIS. Cape Parry, N. W. T. (1989). Journalof the RoyalAstronomical Society of Canada, Volume 83, No. 3,207-218,June 1989.[ABSTRACT ]"Kepler'sThird Law of planetary motion: T2= R3 (T = period in years, R =mean distancein astronomicalunits) may be extended to include the inverseof the mean speed Vi (inunitsof the inverse of the Earth's mean orbital speed) such that: R = Vi2and T2 = R3= Vi6.The first relation- found in Galileo'slast major work, the Dialogues Concerning TwoSciences (1638) - may also be restated and expanded to includerelativespeed Vr (in units ofEarth's mean orbital speed k) and absolute speed= kVr. This paper explains thecontext of Galileo's velocityexpansionsthe laws of planetarymotion and applies these relationships to theparametersof the Solar System. .. A related "percussive origins" theory ofplanetaryformation is also discussed." interrupt in order that I may point out the beautiful agreement betweenthis thought of the Author[Galileo] and theviews of Plato concerningthe origin of the various uniform speeds with which the heavenly bodiesrevolve. The latter chanced upon the idea that a body could notfrom rest to any given speed and maintain it uniformly except bypassing through all the degrees of speed intermediate between the givenspeed and rest. Plato thought that God, after having created theheavenly bodies, assigned them the proper and uniform speeds with whichthey were forever to revolve; and that He made them start from rest andmove over definite distances under a natural and rectilinearacceleration such as governs the motion of terrestrial bodies. He addedthat once these bodies had gained their proper and permanent speed,their rectilinear motion was converted into a circular one, the onlymotion capable of maintaining uniformity, a motion in which the bodyrevolves without either receding from or approaching its desired goal.This conception is truly worthy of Plato; and it is to be all the morehighly prized since its underlying principles remained hidden untildiscovered by our Author who removed from them the mask and poeticaldress and set forth the idea in correct historical perspective. In viewof the fact that astronomical science furnishes us such completeinformation concerning the size of the planetary orbits, the distancesof these bodies from their centers of revolution, and their velocities,I cannot help thinking that our Author (to whom this idea of Plato wasnot unknown) had some curiosity to discover whether or not a definite"sublimity" might be assigned to each planet, such that, if it were tostart from rest at this particular height and to fall with naturallyaccelerated motion along a straight line, and were later to change thespeed thus acquired into uniform motion, the size of its orbit and itsperiod of revolution would be those actually observed.Salviati. I thinkI remember hishaving told me that he once made the computation and found asatisfactory correspondence with observation. But he did not wish tospeak of it, lest in view of the odium which his many newdiscoveries had already brought upon him, this might be adding fuel tothe fire. Butif any one desires such information he can obtain it forhimself from the theory set forth in the present treatment."(DialoguesConcerning Two New Sciences published in 1638 (translation byHenry Crew and Alfonso de Salvio, Fourth Day,1914:261-262;emphases supplied) As indeed one can, once alerted to the primary source, the materialsand themethodology provided by Galileo in the followingcondensed paper published in 1989 in the Journal ofthe RoyalAstronomical Society of Canada reproduced here wth the permissonof the Editor VelocityExpansions oftheLaws of Planetary Motion [HTML]or PDF(475 kb).ASSOCIATEDMATERIALGalilei Galileo's DialoguesConcerning Two New Sciences (1638) translated by Henry Crew andAlfonsode Salvio (1914).INTRODUCTION TitlePage, Contents, Transcriber's Notes (added) Translator'sPreface,Introduction, Galileo'sDedication, Publisher's Remarks and Index. PDF (929 kb).FIRST DAY"Treating of the resistence which solid bodies offer tofracture." PDF (938 kb).SECOND DAY"Concerning the cause of cohesion." PDF (944 kb) .THIRD DAY"Second new science, treating of motion (movemeti locali), Uniformmotion, Naturally accelerated motion." PDF (1.2 mb).FOURTH DAYconcerning:"Violentmotions. Projectiles." (Includes the reference to PLATO in the aboveastronomical context). PDF (805 kb).ADDED ( or"FIFTH" ? ) DAYfrom the Stillman Drake translation of the Two NewSciences (1974). PDF (175 kb).APPENDIX tothe FOURTH DAY also included by StillmanDrake (1974). PDF (385 kb).May 20, 2011 Update: Withslight modification Galileo's "percussive" theory might also be appliedto the origins of recently discovered "rogueplanets" thought at present to be roaming the universe insurprising large numbers. BACK TO THETOP ALCHEMICALAlchemy is asubject of which we have all heard of, and which is yet a mystery. Insome waysit belongs to the world of mystery stories from the past. Weremember perhaps the shade and wonderful light of Rembrandt's etchingof the Alchemist, or the stories we read in Chaucer or Ben Jonson. Wasthe alchemist a philosopher, deep in a mysterious studywhere he discovered the secrets of transmutation? Was he just acharlatan involved in a particularlyfantastic kind of mumbo-jumbo? Was he simply a forerunner of thescientists of today? Or had he an occult knowledge which we cannot hopeto acquire inour materialistic environment? [Introduction to The Arts of the Alchemists, C.A.Burland, 1986-1; for more on the scope and complexity of this subjectsee: Timeline ofAlchemical Books and Various AlchemicalTexts from the extensive collection of material available at the The Alchemy Web Site]Chapter 19 "You may have heard me called an atheist, but that's not quite true.Atheismis unprovable, so uninteresting... My field of interest is thepsychopathology known as Religion .... Lucretius hit it on the nailwhen he said thatreligion was the by-product of fear - a reaction to a mysterious andoftenhostile universe. For much of human prehistory, it may have been anecessaryevil - but why was it so much more evil than necessary - and why did itsurvive when it was no longer necessary? "[ condensed from Chapter 19:Madness of Mankind," 3001: The Final Odyssey by Sir Arthur C.Clarke,1997:136-142;PDF: 27 kb ].Grave e Mesto "The time for departure came. We all agreed that delay would be bad. Itook one last look around. There was the electronic box, the thing Ihad come to think of as a piano ... I had a strong urge to play on itfor one last time. I told the others, saying I would prefer to bealone, that I would follow in a few minutes. Melea answered: ' Don't betoo long.There isn't much time.' I began to play. I realized that only in musiccould I find the answer I was seeking to the questions of the previousevening.Argument I could follow, it weighed with me, yet I could decide nothingfrom it. I did not know exactly what the music was, it was animprovisationnot so much on a musical theme as on the agony of the destiny of man. Icontinued to play on and on, aware at last that I had made mycommitment. I wasplaying the Schubert Andantino when Melea returned." [ The end of Chapter 14, Octoberthe First is Too Late by Sir Fred Hoyle, 1968:158-172; PDF: 57 kb ]Man and the Sun" In following the solar cycle of this book, I have honoured those whoworshipped the Sun God in his many forms. Yet I have also honouredthosescientists whose probing minds have dispelled the simple divinity ofstar. The members of the Holy Office were right to be fearful of theideas of Copernicus to see that they would lead to the destruction ofmany ofthe old religious forms. They were wrong as well as ridiculous tryingto turn back the tide of science, of man's efforts to comprehend thephysical universe, for that pursuit is a part of what is divine inhumanity. Wehave to honour both the King of Heaven and Prometheus. The presentperil anddespair of humanity show that we cannot live without religious meaningalthough we may do without religious institutions. (The time may comewhen eventhose few who still follow them turn against priests who ingem-encrustedcopes and mitres, serve Him who taught poverty and humility, who betrayHim who taught love of one enemy by raising no murmur against aholocaustof hate.) If we cannot find god in the world, we lose Him in ourselvesbecome contemptible in our own eyes. We become mere statistics. Forthis isthe greatest evil coming from the unbalanced Apollonian mind. Sciencewon power over the universe of matter by breaking down and down, bynumbering and measuring. So at last everything that cannot be brokendown,numbered and measured must be deemed not to exist. Science is unitingman withthe sun in a totality of energy and matter. That is communion at thelowestlevel of being. But we have always been right to seek it also at thehighest." [ Quotationfrom theconcluding chapter of Man and the Sunby Jacquetta Hawkes,1962:239-241. Also in PDF ]VOICES OF REASON MSNBC TVTHOMASCAHILL : THE HINGES OF HISTORYThe Hinges ofHistory (1995). "Aswe, thepeople of the First World, the Romans of the twentieth century, lookout across our Earth, we see some signs for hope, many more fordespair. Technology proceeds apace, delivering the marvels that knitour world together-- the conquering of diseases that plagued every agebut ours and the consequent lowering of mortality rates, revolutions incrop yields that continue to feed expanding populations, thecontemplated "information highway" that will soon enable all of us toretrieve information and communicate with one another in ways soinstant and complete that they would dazzle those who built the Romanroads, the first great information system." [ Rationale and closingparagraphs from HOW THE IRISH SAVEDCIVILIZATION: The Untold Story of Ireland’s Heroic Role from the Fallof Rome to the Rise of Medieval Europe by Thomas Cahill, 1995:216-218 ] PDF: 3pages,75 kb .over forty years Alexander Thorn, Emeritus Professor of EngineeringScience and Emeritus Fellow ofBrasenose College, Oxford, has surveyed and planned stone circles andother prehistoric settings of standingstones in Great Britain and Brittany. He was assisted by his son, Dr.Archibald Stevenson Thorn not only in thesurveying but also in the preparation of many of the subsequentlypublished papers. His standards of planninghave been far higher than those of the average archaeologist andcertainly superior to most of the 19thcenturyantiquarians whose plans of circles were often inaccurate and slipshod.It has been the misfortune of thoseinterested in megalithic rings that often only such inexact plans havebeen available. For a good plan three criteria apply. The survey itselfmust have been precisely done, using adequateequipment, measuring to several points around each stone at groundlevel; an accurate scale must be providedon the drawn plan; and True North must be shown, preferably towards thetop of the page. Alexander Thom'splans fulfil all these conditions and they must be regarded as thefinest and largest collection of stone circle plansever assembled by an individual. Yet many of them have never beenpublished. Others have been so reduced that their value has beendiminished. Consequently, all his plans of British circles have beengathered together here, nearly always one toa page with an accompanying text opposite giving information about thesite. The only omissions, at Thom'srequest, are the Callanish rings, recently surveyed by the GeographyDepartment of Glasgow University, andStenness of which a plan has been published in the Proceedings of the Society ofAntiquaries of Scotland 107,1978.The resulting collection of plans should be invaluable to anyonewishing to study stone circles.During his researches Professor Thorn concluded that the prehistoricbuilders of these rings used an almostuniversal unit of measurement, the Megalithic Yard of 2.72 ft or 0.83metres; sometimes laid out non-circularrings in flattened circles, ellipses, egg-shapes and compound figureswhose construction was based on theunderstanding and use of right-angled triangles with integral sides;and had an empirical knowledge ofastronomical phenomena. The plans usually include the geometry Thornhas deduced for the sites, and theaccompanying notes contain Thom's conclusions about the lengths of thediameters and sometimes theastronomy, if any, for each ring. Theseideas remain contentious but this book is not concerned with thecontroversy. None of it detracts fromthe excellence of the plans, over 200 of them, which will beindispensable for anyone researching the Britishstone circles." [Aubrey Burl, introduction to MegalithicRings: Plans and Data for 229 monuments, by A. A.S. Thom, collated, with archaeological notes by Aubrey Burl, BAR International Series 81,Oxford, 1980.]. Alexander Thom's statistical methodology (including Broadbent'sCriterion),background materials, analyses and far-reachingconclusions were published in Megalithic Sites inBritain(1967, 1971).Detailsfrom the latter work are provided below forthose who might wish to judge this complex matter for themselves:PART1: Introduction,Statistical, Mathematical and Astronomical Backgrounds, MegalithicYard, Conclusions. (PDF,6.4 Mb; smallerWeb-View PDF: 2.27Mb).PART2:Circles, Rings, MegalithicAstronomy. (PDF, 7.4 Mb;smaller Web-View PDF: 2.47Mb)PART3: TheCalendar, Indications ofLunar Declinations. (PDF, 3.7 Mb; smalllerWeb-View PDF: 1.15 Mb)PART4: TheOuter Hebrides, A Variety ofSites. (PDF, 5.6 Mb;Smalller Web-View PDF: 1.94Mb)APPENDIX: A Remarkable 4000 Year-Old EgyptianShip with hinged, portable A-frame mast, dual-purpose sail andother sophisticatedfeatures.Single page Graphicwith text(PDF);also in HTML.ANAWAK AND THE 1993 NUNAVUT LAND CLAIMS AGREEMENT Jack Anawak,MP for Nunatsiaq (Hansard,1993):" The history of this land claim goes back many years. It spans severalfederal governments and numerous ministers of Indian and northernaffairs. Very few people realise that prior to 1973 the Government ofCanada did not have a policy to negotiate land claims. It was thecurrent leader of the opposition, under whom I am proud to serve, who,when he was Minister of Indian Affairs and Northen Development, broughtforward the first policy to negotiate and resolve land claims. In1975 the Inuit of Nunavik achieved the James Bay and Northern QuebecAgreement. The following year, in 1976, the Inuit of the NorthwestTerritories, as represented by the Inuit Tapirisat, presented theirland claim to the federal government for negotiation. Their submissionincluded the proposal for the creation of the Nunavut Territory. Theclaim proposal was subsequently revised in 1977. In that same year, theInuvialuit of the western Arctic filed their own land claim. In 1978they signed an agreement in principle with the federal government andthe final agreement was reached in 1984. Between 1976 and 1978 theInuit of the central and eastern Arctic experienced difficulty withtheir negotations. There was an impasse over dealing with Nunavut atthe land claims table. In 1980 a breakthrough was achieved. Agreementwas reached to deal withthe Inuit proposals on Nunavut through a political development processin the Northwest Territories separate from but parallel with the landclaims negotiations. In 1982 the Tungavik Federation of Nunavut wasformed for the specific purpose of negotiating the Inuit land claims.In April 1990 an agreement was reached. Article 4 of that agreement inprinciple affirmed federal, territorial and Inuit support for thecreation of Nunavut as soon as possibler. In December 1991 negotiaitonswere finalized on outstanding items in the land claims, including thecreation of Nunavut. In November 1992 the Inuit of Nunavut voted toratify their agreement.It has been a long journeyfilled with manyrough spots and roadblocks. I want to focus now on the actualland claim and some of the obstacles the Inuit encountered in theirnegotiations with the government. From the beginning the government setout all kinds of preconditions and restrictions. In return theInuit were more than generous. Some of the comments I am about to makeI have made on other occasions over the past several years and many ofthe people listening or watching today will be familiar with them.However, I feel I must restate them for the record. First. I want totake issue with the term "land claim". It is highlyinappropriate. I wish there were a better term to use but I will try toexplain what I mean by inappropriate. When aboriginal peoples talkabout their lands, we are talking aboutour homelands. We are talking about the territories and resources uponwhich our people have survived for thousands of years. We are talkingfirst and foremost about our cultures and our way of life on theseterritories. The land, the waters, the wildlife, and we the people, areone and the same. We are not separate from our environment. We are partof it, and it is part of us. Yet non-aboriginal governments have lookedupon land claim negotiations as real-estate transactions.This is notour view. It is difficult for us to understand the non-aboriginalconcept of individual land title and ownership. We seethese negotiations primarily as the means to preserve ourrelationship with the land and ensure our survival as peoples in thelarger society surrounding us. Therefore we are also talking abouteconomic and political power. We require the economical and politicalmeans to control what happens on our lands. In claim negotiations Inuitpeoples are not seeking someting that someone else already owns. Wedispute that implication. We are not asking the government to give ussomething that does not belong to us. We are only seeking recognitionof what is rightfully ours. We are trying to take back what was takenaway from us by governments without consent in the past. We arereasonable peoples. We have always been willing to shareour lands and our resources. We recognise that all peoples and allgovernments must work together for the benefit of all. This is whyInuit and other aboriginal peoples have entered into land claimsnegotiations . . . ."PDF, 4.71 Mb. Note:Nunavut means "Our Land". Reduced Englishversion (5-page pdf) . Scholium:Newton'sclosing paragraph " And now we might add something concerning acertain most subtle spirit which pervades and lies hid inall gross bodies; by the force and action of which spirit the particlesof bodies attract oneanother at near distances, and cohere, if contiguous; and electricbodies operate to greater distances, as well repelling as attractingneighboring corpuscles; and light is emitted, reflected, refracted,inflected, and heats bodies; and all sensation is excited, and themembers of animalbodies move at the command of the will, namely, by the vibrations ofthis spirit, mutually propagated along the solid filaments of thenerves, from theoutward organs of sense to the brain, and from the brain into themuscles. But these are things that cannot be explained in few words,nor are wefurnished with that sufficiency of experiments which is required to anaccurate determination and demonstration of the laws by which thiselectric and elastic spiritoperates." (also in PDF)Why didSir Isaac Newton end his opusmagnum in this way?A simple statement of faith? Or was it something more encompassing?BACK TO THETOPINUKSHUKNUMENLUMENSELECTED TEXTUAL GRAPHICSInuitWisdom: Only One Great ThingRumi and theRising Sun +PDFGreat Solitudes+ PDFAbideWith Me+PDFSistersof Softlight+ PDFTheTen Rules of theCanoe+PDFSandburg Dream GirlEndless NightReal Being StromataThe Theory ofEverything+ PDFThe Statendam et LamerDeep ContemplationsSPIRADELANY'STIMEand ETERNITYSPIRA STARBUCKSDESIDERATA + PDF THE OATHTOINSPIRE Believe in your Heart+PDFSubject Not Thy mind+ PDFTime, Eternal,Infinite + PDFOnlyTemperate Souls + PDFVisions (Ode toScipio) + PDFSTRENGTH IN YOURWEEPING THE SQUAMISH WELCOMEFIGUREE-MAIL*Kessinger Publishing OCanada 2010Quantum entanglement andthe STARFISH TELEGRAPHDO NOT GOGENTLE INTO THAT GOODNIGHTN. Harris, M.A. Last updated August 21, 2020. Bestviewed at 1280 x 1024, 10 point latin fonts, or whatever.Incredulityis given to the world as a punishment"Source :TheCrowning of Natureweary paddler resting is still ballast "Source :"CriticismWithout Light Condemns Us All to Further Darkness"

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