SQUARING THE CIRCLE

itself, like a river issuing from an immense glacier, one droplet at a time, until ithas become a sw elling flood.If all of this w ere merely an intellectual exercise and had nothing to do w ith lifeitself or the conditions by w hich life arises, then it w ould not matter all thatmuch and our curiosity w ould be guiding us to other troughs to quench ourthirst. But the 2:1 seems to be at the root of life: the w ell-spring ofconsciousness; and that very mysterious urge for transformation – for aqualitative leap in being. How does this mysterious leap gather itself up? W hatis the means by w hich it accumulates energy and then transforms one patternor set of instructions into a new and different pattern or set of instructions?W hy does it transform instead of self-destruct? This is an important questionbecause some systems do self-destruct at points of great tension – bifurcationpoints w here the transformation cannot be contained and the w hole systembreaks dow n. In the case of a great paradigm shift, how does consciousnessact as a thread, a link that maintains continuity betw een the tw o paradigms?Something constant must underlie the pattern shift. In the Middle Ages, theGrail w as the Stone that both burned the Phoenix to ash but also containedw ithin it the capacity to restore it to its previous condition. Since the Phoenixself-immolates, the ‘Grail’, then, must be the spiritual essence of the Phoenixitself, not unlike the Egyptian notion of the “ka” or double. In this sense thedouble acts like a template, a pattern that does not die w ith the previous form.‘There is no such thing as death, only the transformation of form!’ This adage is atradition. And w hat each new generation w ants to know is w hether or not it istru e .SQUARING-THE-CIRCLE W ITH THE PRIME 2:1 and GOLDEN SECTIONCharpentier w ent on to describe how a 2:1 table possesses the root of converted by W eb2PDFConvert.com

transformation from an angular to a circular table, in other w ords the 2:1rectangle has the capacity to ‘square-the-circle’. I found its capacity to constructthe golden number infallibly w as one thing, but the ability to square the circleseemed to penetrate more deeply into the mystery of self-organization. Thenw ith time I realized that the golden section itself was the way to ‘square-the-circle’, w hich I have demonstrated below . The entire construction begins w iththe Prime 5 x 10 rectangle, ABCD. The diagonal AC is put in place. The compassstarts on A, is opened to AB and sw ung into a 10-meter diameter circle thatcrosses the diagonal at E. A is now also the center of the circle, PB, w hich is thelength of the 2:1 or 10 meters. Its circumference is31.416 meters, exactly the same as the perimeter of the King’s Chamber insidethe Great Pyramid. EC then becomes the golden section, 6.18, and is sw unginto a second circle (diameter 12.36068) that cuts BC at F, dividing BC into3.82 and 6.18, w hich relate as 1:1.618. But the arc of 6.18 also cuts theopposite side of the 2:1, AD, at G. AG can be computed by subtracting 3.6327,calculated by Pythagorean Theorem, from 10.The new length 6.367 then becomes the radius of a new circle w ith diameter,12.734 a figure that w e recognize in the Earth’s diameter. The Earth’sEquatorial Diameter is 12,756.28 km and its Polar Diameter is about 12,713.5km, so 12,734 km constitutes a reasonable mean betw een the tw o. In anycase the Square, HJLK, clearly has a perimeter of 40 and a circle w ith diameter12.734 has a circumference of about 40.0050. For the purposes of building instone or even w ood this is more than sufficient accuracy. W hat really mattershere is how the golden section serves as the means to create a circle w ith thesame perimeter as the 10 x 10 square. It is the means by w hich matter andspirit appear to unite, thereby opening a portal of some kind: a passage. Notethat the w hole operation basically occurs w ithin the 2:3 rectangle, HJCI, and w esaw in the previous post that a 2/3 rectangle frames the entire Vesica Pisciscomplex w ith its 3 double squares and tw o overlapping circles w ith a total of 3radii, w here one is shared becoming the home of the heart and lungs as well asthe womb! The Prime 2:1, ABCD, constitutes a 1/3rd part of HJCI. The Square,HJLK, is 2/3rds of it. converted by W eb2PDFConvert.com

W e can also recall that the Royal Portal at Chartres appears to be proportioned2:3 also. In one common proportional ‘frame’, w e have both operations: theVesica Piscis, w hich at Chartres frames Christ on his throne, and the ‘squaring-of-the-circle’, w hich unites above and below , spirit and matter; male and female.In some traditions outside Christianity, this is the very definition of Christ on auniversal basis. Christ is the triumph of ‘grand reunification’ after the tribulationof separation, alienation, disconnection, the profound and sometimes prolongedfeeling of having been forsaken by the entire universe including the divine itself!There is also a phase in which one can feel forsaken by the feminine. This is atransitory separation that is the prelude to the archetypal mystical marriage inw hich the male consciousness is reunited w ith the bride of the soul. I supposeone could call this the transformation of the anima w ithin.Since so many of the numbers that appear above also appear in Series E, I w illjust note again how Series E starts. The first line is 1, 5, 6, 11, 17, 28, etc. Thesecond line is 2, 10, 12, 22, 34, etc. So in effect this Series transformshorizontally via a leap from 1 to 5 and vertically by going from 1 to 2. It thenproceeds from there. The golden number, 1.618, is named on Line 2,suggesting that it is necessary for 1 to divide into 2 before the golden numberitself can be named. Here, it is Line 2, Column XIII. This Series E in fact givessquare values that seem to be arrayed around a nucleus, 1000, of Line 2,Column XII. I w ill have to explain this interesting property later.Given everything that has been said so far about this simple 2:1 rectangle, it isw orth contemplating closely how it has squared the circle here. The firstingredient is the diagonal, AC. Then a circle is draw n around point A that cutsthe diagonal at E. AE = AB w hich is Prime Unity or here, 5. This leaves 6.18 forthe rest of the diagonal, EC. EC becomes the radius of a new circle w ithdiameter 6.18 x 2 = 12.36068, centered on C. Now comes the most interestingpart. This 6.18 radius, (the golden section and navel position of BC and thelength of the Prime 5 x 10 rectangle), cuts the opposite side of the Prime 2:1,AD at G. So it has reached across the 2:1. This forms a new triangle: CGD converted by W eb2PDFConvert.com

w ith 6.18 as its hypotenuse and 5 (Unity) as its base. The short side is easy tocalculate and turns out to be 3.6327, w hich is the square root of (6.18034)² –(5)² = 38.1966 – 25 = 13.1966, the square root of w hich is 3.6327. The angleformed by CGD, incidentally is that of the pentagonal triangle, 54°. So you have54° + 90° + 36°. W hen this is doubled you have 54° + 54° + 72°. This is also aw ay to construct a pentagon, by doubling GD. The remainder of AD is naturally10 – 3.6327 = 6.36728. And it is this that becomes the radius of a circle w ithcircumference equal to 40. The creative aspect of the 2:1 is also the w ay itgenerates dynamic equilibrium through complementary opposites that start w ith1 becoming 2 and the diagonal that links opposite corners, A and C.W e have here 3 circles. The inner circle has a diameter of 10. The next circle is12.36068. They relate as 1:1.236, the same length that determines the naveland the size of the Pelvic Vesica Piscis in the female. If the Thoracic Vesica is 1,the Pelvic Vesica in the female is 1.236, contained w ithin the golden rectangle,EFGH. This golden rectangle holds more surprises ahead that I hope w e w ill beable to get some handle on, as it involves gravity. converted by W eb2PDFConvert.com

The third circle is 12.734. It relates to the inner circle as 12.734:10 or 4/π. And itrelates to the middle circle as 12.734/12.36 = 1.03007. This latter ratio happensto be one category for a common male armspan in the horizontal position. Theother most common is 1.045 w hich is probably from 1.0472. In my armspan, oneis 1.03 and the other is 1.047. If you multiply them together you get thefollow ing:1.03 x 1.0472 = 1.078689 = 1.618 ÷ 1.5 = 2/3x 1.618This 1.078689 holds the key to the male anatomy and how it differs from thefemale. Note the reciprocal of 1.078689 is .927. W ith the AU-Canon as atemplate for the meter, one can see that ‘927’ concerns the generation of thefemale Pelvic Vesica and hence the w omb. Even the number for the Pelvic Circleis a ‘lunar’ number, 29,530,000 km, the Synodical Month being 29.53 days.Through law s of harmony – the w ay spacetime is broken dow n into measures,the day and the meter find a relationship through this number 29.53.Note, too, that there are only 4 points w here the inner ‘10’ circle coincides w iththe square. At all other points, it is contained by the square. This seems toestablish the four cardinal points w hich may act as outlets. The inner circle, onthe other hand, is w holly contained w ithin the 12.734 circle. But the squareitself pushes beyond the outer circle at its diagonal points w hich are 45° to thecardinal points. In contemplating the King’s Chamber from this perspective, onecan see that it has the same diameter as the inner ’10’ circle. So it is ‘The Circle-in-the-Earth-Square” and is w holly contained w ithin the Earth Circle. Since theKing’s Chamber is located deep w ithin the Great Pyramid and w hen it w as foundby Al Mamun in 820 A.D. all the passagew ays w ere plugged w ith heavy stonesthat could not be moved. The feeling is that the King’s Chamber w as designedto be completely hermetically sealed so that it could accumulate the very energydiscussed above, by w hich the Earth’s magnetic field, electrostatic energy andgravitational ‘self-energy as it is called today, could reach a threshold capable ofinducing the coveted metamorphosis symbolized by the scarab “Khepere” (TheTransformations of Re). The harmonies locked into the paradigm of the King’sChamber appear to be such that the essence of the Stone (Grail) that ‘burnsthe Phoenix to ash’, is capable of perpetuating the link betw een body and ka inthe act of spiritual rebirth. At the same time this is w hat w as know n as theentrance to the Duat or Gate to the Netherw orld through the portal of the 2:1paradigm; the sba. converted by W eb2PDFConvert.com

In the image above I have laid out the basis of the female anatomy w ith head,thorax and pelvic vesica. There is a great deal of information in this one imagebut it w ill be too complicated for right here. The Thoracic Vesica is 1/3rd of Unity(AB) and the Pelvic Vesica is 1/3rd of 1.236 or the golden section of the height, 2and width of the golden rectangle, EFGH. I have laid 3 ‘grail tables’ over thenavel position, but w ill discuss them at a later stage. The mouth of the ThoracicVesica falls exactly on the mouth of the archetypal head marked w ith a dottedline. I put this image in to provide a sense of how the figure gathers itself upw ithin the basic geometry and even at this early stage seems to w ant to springto life. The golden section w ithin a 2:1 paradigm contributes enormously tothis w ell-spring of life.In the image below w e see the same basic paradigm applied to theAstronomical Unit. Here the golden section is playing an even deeper role. Theshort length that is around 57,338,563 km is collapsed into the abdominal circlethat w ill contain key organs including pancreas and kidneys; w hile the largersegment, 92,773,794 km collapses into a circle that is 29,530,815 km andbecomes the w omb. It is a striking coincidence that the lunar number associatedin days w ith the Synodical Month (29.53066 days) should show up in meters orkilometers in the Pelvic Vesica and Pelvic circle. A human gestates according tothe Synodical Month in exactly 266 days or 9 synodical months. One can say,provisionally, that the Synodical Month (29.53 days) has a formative influenceon human gestation. It determines ovulation. And w hen the golden section isdivided by 3 w e here have 30,922,000 km w hich is another lunar number. In 25years there are 309.2 lunations or synodical months. The w idth of theParthenon is 30.922 meters. The internal w idth of the transepts at Chartres istw ice that, or about 61.8 m, or some say a few centimeters more. One secondof arc at the Earth’s Equator is 30.922 meters. The Parthenon is also basedupon ‘squared-circle’ geometry but I w ill have to show it elsew here. converted by W eb2PDFConvert.com

SQUARED-CIRCLE ARCHETYPENow take note of the difference betw een AG and AN. It is 1.3673 = 6.3673 – 5.And w e can note an archetype here also w orthy of contemplation. 6.3673 ÷1.3673 = 4.6578 = AG ÷ NG.W e have already seen this relationship in the Great Pyramid w hich I w ill nowshow again. The number that corresponds to 1.3673 is 60 cubits or 31.416meters. This depends from the scale of 1: 43,200, proportioned to the size ofthe Earth. 432 is itself a member of an important number series I w ill call SeriesA, very familiar to the ancients. I w ill give some members right here: converted by W eb2PDFConvert.com

SERIES A27 54 108 216 432 864 1728 3456 6912 13,824 27,648 55,296 110,592Best to note here that one prime interior measure at Chartres is fromimmediately inside the Royal Portal all the w ay to the interior Round Point of theChoir is 110.76 meters. Due to the Earth’s flattening, a degree of longitudelengthens by definition as one w alks from the equator to the pole. At about 8°Lat the degree of longitude w ill be 110,591 meters (13th member of Series A).At 25° it w ill be about 110,764 meters. At Chartres itself a degree of Long isabout 111,180 meters. This measure w ould be very easy to accommodate bysimply starting from closer to the immediate door itself at the Royal Portal.Series A is amazing. In miles it gives the Moon’s diameter as 2160 miles or11404800 feet. W hen this is divided by another member of the series, 172,800you get:11404800 ÷ 172800 = 66 feetThis is the height of the Great Sphinx and tw o obelisks that disappeared fromHeliopolis near 1200 A.D. w hen the Templars w ere rebuilding Chartres. Ashadow cast by that height at Noon on the Equinox w ould be ½ the ChartresSquare: 11.5965 m.Above I have marked the proportions w here the ½-base is 1.618 = 220 cubits =115.192 meters. The height is 280 cubits or about 146.6 meters plus a 1/2 –meter platform, totaling say 147.108 meters. The difference betw een the w holeheight and the square is 60 cubits or 31.416 meters. 280/60 = 4.666… converted by W eb2PDFConvert.com

Since this is an important point I w ill also show this in a closer up version. Itallow s a better view ing of the King’s Chamber looking w est. The 31.416 metersthat can be seen at the top of the pyramid have been turned into the perimeterof the King’s Chamber. It is as if the w hole intention w as to take that 31.416meters and turn it into the sba gate, the entrance to the Netherw orld. But w hatthe Pyramid Texts tell us is that the entrance into the Netherw orld is throughand as the Eye of Horus. Therefore the King’s Chamber must be the place w herethe entire endeavor of the Egyptian Civilization reaches its apotheosis; namelythe reconstitution of the Eye of Horus. The Egyptians saw this as an example ofthe principle of Maāt, or Cosmic Equilibrium. And they view ed the Squaring-of-the-Circle as a fundamental expression of Cosmic Equilibrium or Maāt. converted by W eb2PDFConvert.com

Pi represents the horizon of a circle. Horachty meant Horus-of-the-Horizon.Sometimes Atum is referred to as “Him-of-the-Horizon”. The Berlin Papyrussuggests that the name is so mysterious that it cannot in fact be named or evenuttered. It is experienced by the spirit of any candidate as too pow erful and toomysterious or infinite to label. Encountering the horizon of Him in spirit formabsorbs w ords, language, metaphors and w as w ell-stated by the Hindu as just“that”. “That” is simply the essence of spirit that has shed the corporeal bodyand even, according to the Tibetans, the double or ka. Sages have long thoughtthat pi, 3.1416… genuinely represents or points to that mysterious “Horizon”.SQUARED-CIRCLE-MODULUS: 1.27324 ÷ .27324 = 4.659…Around 1999 I stumbled upon a few clues that turned my head and helped mesolve a number of outstanding problems w ith both female and male geometry.This occurred after I had a preliminary draw ing based upon the AU for April 16th,1998 (~ 150,108,000 km). Tw o examples are particularly important. One is amacroscopic resolution w hich nevertheless has retained considerable mystery.It involves the proportional relationship betw een the Earth and the Moon. Theother is a quantum-scale resolution that concerns the mean momentum energyassociated w ith the nucleons (protons and neutrons) that compose the bulk ofthe Earth’s atomic mass.Scientists do refer frequently now to “Mearth”, acknow ledging that the behaviorbetw een the tw o bodies is not a typical planet/moon relationship but alsopossesses aspects of a binary planetary system. For example the Moon isalw ays falling tow ard the Sun in a concave orbit and even w hen approaching converted by W eb2PDFConvert.com

the w axing square in its orbit around Earth, never goes convex to the Sun thew ay other moons do, for example around Jupiter and Saturn. Earth and Moonfall together tow ard the Sun a greater distance than ever the Moon climbsagainst the Earth in any given time frame. Now , let’s take the mean diameter ofthe Earth as about 12,732 km and the diameter of the Moon as 3476 km.Together they add up to 16,208 km w hich is close to the number of (4/π) ² or1.2732 x 1.2732 = 1.621. I have show n this above in the draw ing of the GreatPyramid. 1.621 is just a little bigger than the golden number, 1.618, butgeometers often consider w ays that these tw o great factors w ork together ordovetail. If you add the Earth and Moon together and divide by the Moon youget: 16,208 ÷ 3476 = 4.66. The Moon is behaving exactly the way the 31.416meters are behaving at the top of the Great Pyramid. It is important to emphasizethat the Egyptians appeared to follow the soli-lunar cycle religiously – literally.They w ere not only aw are of its physical influences, but w ere equally aw are ofits spiritual influences and so kept 29 altars, one for each day of the synodicalmonth w hich is also the female infradian biological clock.In the image above I used an Earth radius of 6367 to be consistent w ith theSquared-Circle illustration show n earlier. I could also have used a cut throughthe Earth according to its tilt w hich w ould be about 6370.5. But for now I w illstay closer to the mean for convenience.The difference betw een the Moon and our Squared-Circle archetype is that theMoon and Earth have become separated by about 384,401 km betw een theirrespective centers of mass. THEY ALSO SHARE A COMMON CENTER OF MASSTHAT IS LOCATED ~ 1700 KM BELOW THE EARTH’S SURFACE. This I am calling inthe human canon, the SCOM circle or ‘Shared-center-of-Mass’ circle that w ehave already seen w ithout comment. Its relative size w ithin the final canon isremarkable because it coincides with the golden section! W e have to discuss theAstronomical Unit first and how the separation betw een the Sun andEarth/Moon influenced details now incorporated into the geometry of the malein particular. Then w e can appreciate the proportional size of the SCOM circle inthe final canon. But that it coincides w ith the w idth of the golden rectangle is aremarkable example of the harmony among Earth, Moon and human anatomy. converted by W eb2PDFConvert.com

The Moon is 27.3% of the Earth’s diameter or 3476/12,732 = .273123. It isinstructive that the Sidereal Month is 27.3217 days or 27.32% of 100 days. Afterthe mean period of human gestation w hich is 9 Synodical Months (265.77 days),there are almost 100 days remaining in the year (99.48). Incredibly, thisremaining period is w here the tradition of the progressed lunation cycle derivesfrom because it show s that 1° approximately equals 1 day which approximatelybecomes 1 year. Perhaps this suggests that most of us ought to be able toreach 100 years of age if circumstances permit. It’s like an internal implicateclock that simply requires reasonable explicate expression – maintaining naturalrhythms – to make it to 100.Meanw hile the Moon during our time, has taken up a position in the sky w here ithas about the same angular diameter as the Sun w hen view ed from Earth. Mostscientists of the last few hundred years have regarded this coincidence asmeaningless. But as science begins to think more in terms of systems, w ebs ofcircumstances, patterns and phases w ithin patterns, it is possible that w e w illcome to see this coincidence as meaningful. My guess is that w e w ill see a typeof gravitational resolution in the order of a form of gravitational self-focusing. Thisis w hat an eye does. The eye does it largely in response to electromagneticradiation or light. W e w ill look at the geometry of the eye in a future post, oncew e have examined another method for squaring-the-circle. But at the level ofplanetary bodies, gravity plays a much bigger role and in fact the Earth andMoon are bound together in a very shared gravitational field. Just a planetarybody on its ow n is an eye-like resolution. It is gathering spacetime around itselfin a shared field. The Earth and Moon are completely immersed in the Sun’s fieldbut the Moon’s tidal influence on the Earth is greater than the Sun’s. The Sun’sinverse square gravity is greater on the Moon than the Earth’s is even thoughthe Earth is so much closer. The Moon’s tidal gravity is about 2.18 times greaterthan the Sun’s tidal gravity, w hile the Sun’s inverse square gravity is 2.2 timesgreater than the Earth’s is on the Moon. There is a form of decussation going onbetw een tidal gravity and inverse square gravity. Tidal gravity is approximatelyan inverse cube force that is stronger across shorter distances. It is myconviction that this sets up a tidal gravitational variation cycle around the Earththat helps set both Circadian and Infradian biological clocks located in thesuprachiasmatic nucleus just above the optic chiasma in the hypothalamus.Shifting locations suddenly induces ‘jet-lag’. Probably the cause is upsetting theentire metabolic clock that has adjusted to the tidal gravitational variation cyclethat stimulates very subtle levels of cell activity such as cytoskeletalmicrotubules w hich are involved w ith consciousness itself. So jet-lag involveseven how w e think and how our muscles w ork. It w ould take up too much spaceto theorize here how it came to be that the Moon and Earth share these crucialproportional relations. But it suggests to me a very ancient history w hen bothbodies could be shaped together by the same forces operating in the samefield. I don’t think the Moon came w andering in from outside. My guess is thatthe Moon and Earth w ere once so close together that they w ere able to beseparated in a proportional manner. Now , not only is the Moon proportioned as.2146 or 1/4.659 of the combined diameters, but it has also taken up a positionw here it appears the same size as the Sun only from the surface of Earth. Thissuggests to me a form of symmetrical gravitational self-focusing in a sharedfield. This also increased the harmonious properties of the symmetry. But I am converted by W eb2PDFConvert.com

suggesting that this ‘4.66’ factor is not merely harmonious; it is fundamental.The builders of the Great Pyramid w ere very cognizant of it since they based thedimensions of the King’s Chamber very precisely upon this factor: 280 ÷ 4.66 =60, or 146.4 ÷ 4.66 = 31.416 meters. And this w e have seen is based upon ascale model of the Earth set at 1: 43,200. At Chartres and the Great Sphinx thescale is set at 1:432,000 instead. From an engineering point of view , Chartrescould manage a 36 meter vault (118.65 feet) but not a 360 meter vault!!Terrestrial Nucleon SpeedThe next example of the involvement of squared-circle relations came as a realsurprise. I had read Fritjof Capra’s “Tao of Physics” in 1981 and had come upontw o pieces of information that w ere memorable but w hich I assumed w ereextremely ‘ballpark’ in intention. How ever, in 1999, w hen I came upon thisproportional relationship betw een Earth and Moon, I w as also checking physicsbecause of the fact that gravity w as presumed to be operating in the vacuum atthe speed of light just like electromagnetic radiation. So gravitons w eresupposedly a bit like photons: massless, spin-2, etc. And it w as thought theymight couple at some point and operate in the vacuum together. At thenanometric scale of microtubules, I thought this might be interesting especially ifquantum gravity w as a real factor and w as capable of ‘tripping’ the quantumwavefunction as it is called.One day I just intuitively checked Capra’s ‘nucleon speed’ against the speed oflight and gravity in the vacuum, believing that this had to be proportioned likeany other significant factor that has contributed to the ability for our bodies tobuild up at the Earth’s surface into w hat w e are today. Capra had given astrangely rounded figure for the ‘Heisenbergian momentum’ associated w ith themean energy of all terrestrial nucleons (protons and neutrons) w hich make upthe bulk of the mass of the Earth. W e are to picture entities that are ‘boiling’aw ay in their extreme confinement, far removed from the First Bohr Radiusw here the electrons begin to be distributed in w ave patterns around thenucleus. The nucleons can’t get too close together and can’t get too far apart.Either w ay there is a pow erful force of repulsion or attraction keeping themlocked in place in a state of extreme agitation that can be expressed in terms of‘speed’ or ‘momentum’ relative to position as calculated by Heisenberg’scomplementary Uncertainty Relation w hich makes use of Planck’s tiny littlequantum constant as its frame of reference. Capra gave about 40,000 milesper second w orth of momentum or speed. He did not make his calculation on thebasis of color theory w ith quarks and gluons as factors in how that momentumenergy w ould be distributed or shared. But I w rote him in 1999 and asked him ifI could take the figure of 64,374 km/s seriously? I basically told him w hat Iw anted to do w ith it. I also asked him about his electron speed that w as closeto 1,000 km/s compared to 2188 km/s for an electron in the First Bohr radius.Capra did not feel it w as necessary to modify or place his figure in any sort ofparenthesis. He clearly had confidence in basic rules that had allow ed him tocalculate such a figure for all the nucleons on Earth. The Earth is not verymassive so there is nothing going on here w ithin the atomic nucleus such as w esee inside our Sun or larger stars if fusion-burning is the correct explanation forthe w ay our Sun is pow ering its light.Here is w hat is so interesting about a figure of 64,374 km/s. Apparentlynothing can move through the vacuum faster than light w hich is about299,792.458 km/s. A massless photon cannot exceed “c”. If its energy isincreased it w ill increase its frequency, not its speed through the vacuum. It w illincrease its agitation w hile moving. The frequency is important because thevisible light spectrum is only a tiny segment of the great spectrum ofelectromagnetic energy. And w e humans are tuned to the visible spectrum to ahigh degree. So frequency matters to humans – among a host of things – suchas temperature, atmosphere, oxygen supply, air pressure, gravity acceleration,etc. Our Earth is quite the ally, friend, nurse and sanctuary!If gravity also moves at this rate (299,792 km/s), then it might be important toknow the proportional relationship betw een the confined momentum of our mass-carriers – the same nuclei that support the atoms found in carbon, calcium, iron,potassium, chlorine, oxygen, hydrogen and so forth. These atoms then heap uptogether into real gravitational effects w hich become significant at themacroscopic scale. In our bodies each atom does not possess much gravity.Electromagnetic forces are relatively much, much stronger. One w ay torepresent that strength is through speed. So that at the First Bohr Radius w ecan represent the energy and the strength of the electromagnetic interaction bydividing the speed of light by the very important Fine Structure Constant alsoknow n as ‘alpha’. Alpha has an effective value of 1/137 so that the speed of theelectron in hydrogen can be calculated as c x 1/137 = 299,792.458 ÷ 137 = converted by W eb2PDFConvert.com

2188.266 km/s. The relationship betw een the electron in the First Bohr Radiusand all other electrons on Earth is approximately 2.188 or ~ 2.2. W e had justsaid that the Sun exerts about 2.2 times more inverse square gravity on theMoon than Earth does and the Moon exerts about 2.18 times more tidalgravitational influence on the Earth than the Sun does. The Moon is moving 2.2times faster in its orbit around the Earth than the Earth is moving at its Equator:1.023/.4651 = 2.2. The Earth rotates faster in a day because it has far lessdistance to go. At the Equator it has to go about 40,075,035 meters. It doesthis in about a day. But the Moon has to go much further even though it istraveling 2.2 times faster. It has to make about 2,415,262.7 km to get aroundthe Earth in its 27.3217 day Sidereal Orbit. This is about 60.26 times greater indistance. So, naturally, 60.26 ÷ 2.2 = 27.3, w hich is the days in the siderealmonth, the Moon also being .273 or 27.32% of the Earth’s diameter. The Moonis locked into a synchronized roll as it orbits the Earth. It rotates the same ratethat it revolves as if the friction (and gravitational resolutions) w ere acting like afixed axle and it w ere a cart on w heels constrained to a gravitational path. Butthis imparts cyclic regularity to the Earth/Moon/Sun dynamic. For the ancients,the fixed regularity of these cycles of motion of Moon, Earth and our relationshipto the Sun constituted the most basic law s governing all aspects of life on Earth.Everything w as subsumed under these cycles of motion. The constellations likeSirius, Orion, the Great Bear, Alpha Draconis, Regulus and so forth mixed theirinfluences in w ith this basic Triadic Paradigm. Man himself w as sculpted on thePotter’ s W heel by these cycles or arcs of motion.These examinations encouraged me to treat Capra’s ‘nucleon second’ in asimilar fashion. I w as imagining an inversion w here a balance w as struckbetw een macroscopic resolution (and regularity) and microscopic or quantumbalance w here, through confinement, the one energy slow s dow n in one respectsince it is changing from massless energy to mass-energy through the curvatureand self-enclosure of spacetime, but by containing that energy forces it to speedup according to specific rules or at least proportions. I strongly believed thatproportion w ould have to play a role because the vacuum w as being involved inthe curvature or self-gravity; or self-attraction process. The spacetime vacuumw as involved and proportion w as one indicator that described the involvement.It w as curving itself and reacting to its ow n confinement; its ow n self-enclosure.I could easily picture the squared-circle effect as a self-reaction: a geometrictendency tow ard dynamic equilibrium akin to hydrostatic equilibrium. W ell, oneday I simply related Capra’s figure to the speed of light:299,792.458 ÷ 64,374 = 4.657I definitely gulped w hen I saw this. It invoked w hat w e had just seen abovew ith the w ay the 5 x 10 rectangle squared the circle:6.3673 ÷ 1.3673 = 4.6578 = AG ÷ NG converted by W eb2PDFConvert.com

W ith time I came to call this 4.6578 factor, the “Squared-Circle Modulus”(SCM) because I found a path from the Fine Structure Constant all the w aythrough Capra’s nucleon speed to the speed of light w ith some interestingstops along the w ay – all through the number 4.6578 or there abouts. I w illshow this path later. As a ratio it w as behaving similarly to the golden number.But w hat is this factor? And w hy do w e find it also associated w ith theEarth/Moon proportions w here by a sort of inversion, the Moon is actinganalogously to the internal agitation or activity of the highly confined nucleons –the carriers of w hat w e call mass-energy: energy that is densely confined andso starts to behave like matter? To repeat: in the one instance the SCM isreferring to speed or a rate of propagation of an energy relative to the vacuum. Inthe case of nucleon momentum, it is not to be pictured like a speeding bulletmoving from A to B. Rather it is a self-contained distribution of motion-energy,highly confined and relative to its position (or confinement). In the case of the Moonit primarily refers to diameter or the amount of space occupied by a celestial body ina gravitational field. In the case of the nucleons, the speed (64,374 km/s) iscertainly offering resistance to gravitational collapse. It also seems to beimparting stability to the identity and lifespan of protons in particular. In thecase of the Moon, speed is certainly playing a role in its position but the SCM isdescribing the volume of space that it occupies as if Earth and Moon had beensculpted proportionally out of a single mass. So w hat is so interesting here isthe proportion itself, namely ~ .2146, or 1/4.66, that links speed to volume.The Moon appeared to me like a point of macroscopic inversion in a gravitationalfield intimately shared w ith the Earth and dominated by the Sun w hichdetermines w ith its mass and distance the speed the Earth and Moon can travelaround it (29.786 km/s as the mean).10,000 ÷ (4.6578/1.619) = 3476 kmTen thousand kilometers is the Circle-in-the-Earth square. 3476 is the Moon’sdiameter. 1.619 is intermediate betw een the golden number and the square of4/π. 4/π is 1.2732395… The square root of the golden number is 1.2720196.Their ratio is 1.000959, so they are very close. One could say that the squareroot of phi is involved in determining the height of the Great Pyramid and helpsto set the difference betw een square and circle. Probably one of the mostfundamental coincidences in the w hole of geometry is that betw een 4/π and thesquare root of phi. W hen 4/π is used the corner angles of the Great Pyramid areabout 51.854 Degrees.Here is another observation that may add another section to Ariadne’s threadthat helps us to keep connected inside the labyrinth of know ledge. W e saw thatto obtain the SCM- factor in the Great Pyramid – so that it w as 31.416 meters converted by W eb2PDFConvert.com

– it meant dividing the Earth by 43,200. This gives a height of about 147.1469including a 1/2-meter platform for the Earth’s Polar Radius. Minus the platformgives a height of 280 cubits. W ith a 220 cubit square 60 cubits remain. 60 x.5236 = 31.416 meters. W e also saw that w hen w e used an Astronomical Unitfor the day the Earth is 150,108,000 km from the Sun very interesting numbersare spaw ned. W e can also take the same AU and divide it by 43,200 since it issuch an interesting proportion in its ow n right:150,108,000 ÷ 43,200 = 3474.72 ~ Moon’s DiameterCuriously, back in the 1980’s a team from MIT measured the Moon’s diameterand got 3474.8 km, not 3476 that w e see most commonly in use today. Ichecked w ith a member of that team back in 2000 and he still insisted that theMoon’s diameter w as 3474.8 km. But in any case it is close enough to make thepoint. W here there is life, harmony tends to be operating on multiple self-interacting levels and w ith effort humans can glean some of those levels andthe nature of some of the harmonies themselves. This becomes quite intuitive,like composing music, and it is true that ultimately it is not prone to analysisbecause by its very nature it holds together as a web of existence, life, reality.The life of a ‘thing’ is in the web that it shares with other ‘things’. In this instanceyou have two proportions dovetailing on an AU of about 150,108,000 km. When Iused this date the numbers broke down harmonically in such a way that I startedto fine tune the canon of human proportions by using those numbers! And whenthe Moon is used as a measuring rod, it measures the same distance 43,200 times.Moreover, the Sun measures to nearly the same distance 108 times, anothermember of Series A.So w hat might be going on here? W hat might this tell us about squared-circlerelations? And w hy did the Egyptians take the same difference that concerns ushere – recalling that in a sense, the Capra speed is acting like a differencebetween mass-energy and massless energy – and turn it into an ’empty’enclosure as if it w ere an inversion of mass-energy, the mysterious Cavern ofSokar or Broad Hall of Osiris? W ere they not attempting through the enclosure tobring about an acceleration, a quickening, a metamorphosis that theysymbolized by the scarab beetle? Moreover, they often replaced the scarab w ithvarious forms of ‘bnbn’ w hich is none other than the Benben Stone brought bythe Phoenix w hich in turn burns itself to ash in the House of the Phoenix only torise again probably as Horus, symbolized by the falcon or the Eye of Horus. Itseems these inner caverns w ere designed to accumulate energy, spirit as afood for the ka to facilitate the very ‘leap’, the very spiritual ‘mutation’ that manyof us seem to crave. If the Capra nucleon speed refers to the matter pole(Egyptian “Seth”), perhaps the empty caverns w ere referring to the ‘spirit-pole’.The same proportion w as being applied to opposite ends of the spectrum. This isa good point to mention Eschenbach’s definition of the Grail in Parzival.The Grail and the PhoenixSo, this enclosure determined by the SCM, brings about the proportional size ofthe King’s Chamber. Not only has the difference of the Squared-Circle Modulus(SCM) become the perimeter 31.416 meters or 60 cubits, w here 60 is acommon number for measuring time, but 31.416 meters is also exactly 1236.84Br. inches. In 100 years there are 1236.8 synodical months. Half the perimeteris 618.42 inches symbolic of 50 years and 618.42 synodical months. 1/4 of theperimeter is 309.2 inches symbolic of 25 years and 309.2 synodical months. Allthese numbers are found in Column XI of Series E. There is the feeling that theKing’s Chamber w as also a clock and that the clock w as tuned to both small andgreat cycles of time. It acted like Solomon’s Holy of Holies w hich w as closed upall year except once, admitting the High Priest alone to enter its pristine statelike an oracle. Here is w hat Eschenbach says about the ‘stone’, as if the stonew ere acting like a ‘pyr’ or an accumulation of electromagnetic energy capable ofundergoing a metamorphosis in the thick darkness pregnant w ith suspense andmys te ry:“By virtue of this Stone the Phoenix is burned to ashes, in w hich he is reborn. –Thus does the Phoenix molt its feathers! W hich done, it shines bright and lovelyas before! … This Stone is also called “The Grail”. (Parzival, p. 239)W e all know the Phoenix burns itself to ash in a singular act of self-immolationupon an altar of its ow n making. The self-enclosure is also the ‘altar’. Sincethere w as nothing in the King’s Chamber except the coffer, the coffer w as likely,then, one and the same as the altar upon w hich ‘the Phoenix burned itself toash’. The Grail, then, is the essence of the Phoenix itself, the mystery of theeternal spirit w ithin and its relationship w ith the surrounding universe, theCosmic W eb. It molts; it does not die! The coffer w ithin the King’s Chamber hasbeen called a ‘fount of spirit’. For the Egyptians and Gothic Builders at least, theSquared-Circle seemed to act as an eternal gate w hen Circle and Square have converted by W eb2PDFConvert.com

been reunited; when their difference has been transformed and possiblytranscended. The King’s Chamber must have been seen as the Cavern ofOsiris/Sokar w ithin w hich that union and transformation is realized. Thediagonals of rectangles have long been treated as transcendental functions. Inthe King’s Chamber you have 15 cubits in the end w all, 22.36 cubits in the floorand 25 cubits in the Great Diagonal w hich is also 13.09 meters – so prominentat Chartres. Recall that at Chartres the 13.09 circle seems to determine theinternal round point of the choir. W e can see 1309 below at the head ofColumn XIV, the same column that also contains 2618, 5236, 7854, 10472,15708, 31416. The w idth of the King’s Chamber is 5.236 meters; its length is10.472 meters and its perimeter is 31.416 meters.So much more can be said about this famous chamber – especially w hen oneexamines the Pyramid Texts – but I w ill have to do this at a later point – it is toodetailed. W hat should be said, how ever, is that w hen ‘circle’ and ‘square’ arereunited, all the opposites are reunited, probably in part due to the presence ofthe square root of phi (1.2720196…) in the radius of the circle (Height of theGreat Pyramid). In Egypt, Horus w as the Eye or Circle; Seth w as the Square, theone w ho dismembers, opposes, obstructs and imprisons the coveted luminary:the principle by w hich light (and sound) become intelligible. Seth is the matterpole that must be transformed from passion into w isdom. W hen theTw o Combatants, as they w ere called, are reconciled by Thoth-Hermes throughthe agency of Isis – undoubtedly by w ay of the altar supported by the 2:1 Table– the “Eye” is restored; the Phoenix is reborn; the scarab transforms from aw orm into a w inged insect of startling beauty. It is my belief that the ancientEgyptians believed in this metamorphosis sufficiently enough to build the GreatP yra mid .SQUARED CIRCLE MODULUS (SCM) AND HUMAN GEOMETRY: THE MOUTHBefore demonstrating the second method for squaring the circle that also startsw ith the 5 x 10 Prime 2:1 rectangle and also uses the golden section divisionof 3.82 and 6.18 (also from Series E, Line 2, Columns X & XI), I should just notethe first prominent application of the SCM in a human being. It has already beenalluded to, but now that a bit more has been discussed, it is w orth looking at inbetter detail. W e are interested in that difference betw een circle and squarew here a sort of inversion takes place at a limit. At the macroscopic limit w e havethe Moon that has assumed the same angular diameter in the sky as the Sun.The Moon has harmonized w ith the Earth to set the monthly rhythm thatgoverns female ovulation that alternates month-by-month, ovary by ovary. It isa clock-like oscillation. In the male there are no ovaries but there is a longing inthe depths of the psyche and soul for another form of birth that has likelycontributed fundamental elements to initiation rites of all races and all creeds –in pursuit of the mystical marriage of the inner man w ith the inner woman insuch fashion that a gate opens for the spirit to find its passage into openterritory. It is as if the ‘squared-circle’ w ere a fundamental analogy for themystical marriage of male and female. W hen the marriage is successful a converted by W eb2PDFConvert.com

candidate experiences a state of exaltation that stands outside sexuality, butyet also overflow s w ith a higher level of energy.At the other pole w e find another limit set by the mean rate or energy ofagitation, movement, speed, in a state of severe confinement far removed fromthe electrons that mediate all biological activity that supports conscious life onEarth. This energy is deep in the atomic nucleus, w here the mass-energy hasreacted proportionally to its confinement. More important than the highlysuggestive ‘speed’ offered by Capra, w ho made the calculation himself w ith theaid of Heisenberg’s Uncertainty Principle along w ith a few other factors, is itsproportional relationship w ith the massless constant w e call ‘c’ that also maydetermine the speed of gravity in the vacuum, if indeed gravity has an‘exchange particle or mediator’, similar to photons. And that relation is299,792.458 ÷ 64,374 = 4.657. But this is the squared-circle modulus (SCM).And it has show n up w ith the Moon – that is also partly a planet – and hasdetermined several biological and possibly spiritual rhythms. So, (Earth + Moon)÷ Moon = 4.66. At one pole the SCM applies to comparative speeds and at theother pole it applies to comparative diameters. Through an inversion the SCMrelates speed to diameter. Earlier w e saw how the ratio betw een Solar pulsesand Earth shouts related as 9/69, just as the head relates to the w hole bodyheight as 9/69 or ~ 13/100. And since the Sun and Moon have the sameangular diameter w hen view ed from Earth, one w onders if the head is not amarriage of both Sun and Moon and the respective ‘motions’ each imparts tothe head’s formation.The SCM has also has show n up in a most fundamental w ay at the GreatPyramid – determining the dimensions of the King’s Chamber (perimeter = 60cubits = 31.416 meters) – w ithin w hich most likely occurred the apotheosis ofthe Pyramid Age. W e see it below as the difference betw een the radius of thecircle TR (280 cubits) and the 1/2 square SR (220 cubits).Now let’s look at the human female w here the square PQTU replaces JKLM seenin the Pyramid image above. Let’s take the Prime Circle w ith length “2” (or150,108,000 km) and let’s square that circle by equal perimeter and see w herethe SCM falls. converted by W eb2PDFConvert.com

The circle is OV and w hen it is squared the square becomes PQTU. Thedifference betw een the 2:1 PQNM and the radius of the circle is clear. I did notput a letter in, in order to avoid cluttering the space. How ever w e w ill take themeasures arithmetically to satisfy all curiosity. But the first point is obvious. Thedifference falls on the mouth of the adult. PQ passes right through the opening ofthe mouth. In other w ords the upper side of the square PQTU passes throughthe mouth of the standing adult. One could argue that the geometry of thesquared-circle is the underlying cause of the position of the opening of themouth of the standing adult. Incredibly, as some may know already, the King’sChamber w as associated w ith a recondite ceremony or ritual know n as the“Opening of the Mouth”. It w as also called “Splitting open the Mouth” and“Splitting open the Eye”. In human anatomy, how ever, the functions are socomplex, that the mouth position w ould have to be caused by more than onefactor alone. How ever, the coincidence w ith the squaring of the circle is aremarkable one.The distance from the mouth to the vertex (O) is acting like the 31.416 metersat the top of the Great Pyramid that becomes the perimeter of the King’sChamber. It is acting, proportionally, like the ‘nucleon second’ compared to thespeed of light. By becoming denser the speed has been slow ed and has alsobecome absorbed into the properties of the nucleons in their condensedconfinement. It is also acting, proportionally, like the Moon relative to the Earth +Moon, w hich stimulates and regulates biological processes probably in morethan one w ay.Now if the diameter of the circle is 2, its radius is 1. Its circumference w ill be 2πor 6.2831853. The square w ith equal perimeter w ill be 1.5708 on a side. Halfthat w ill be .7854. These numbers appear in Series E on Line 6 and Line 12: converted by W eb2PDFConvert.com

If w e add 1 to this .7854 w e get the height from the ground: 1.7854. Anotherroute to get to the mouth is to divide the height simply by 1.118 (1/2 thesquare root of 5) w hich goes in the opposite direction from the diagonal. Thediagonal of a double square is obtained by multiplying the length by 1.118giving 2.236. To obtain the mouth from the diagonal it is 2.236 ÷ (1.118) ² =1.7888 = 2.236068 ÷ 5/4. The difference betw een this and 1.7854 isnegligible. It is for all intents and purposes exactly coincident. So: 2 ÷ 1.118 =1.7888 = 1 + .7854. Note that in the King’s Chamber the diagonal of the endw all is 7.854 meters. W ith this as the side of a square you have a perimeter of7.854 x 4 = 31.416 w hich is the same as the King’s Chamber itself and alsothe same as a circle w ith diameter 10.31.416 appears on Line 24, Column XIV above. The 3 Tables that bore the Grailare instantly evident in the King’s Chamber (Circle has diameter of 10; Squarehas side of 7.854; Rectangle is 5.236 × 10.472). How interesting that thesame factors are literally opening the mouth of the standing adult! The ‘place ofcoincidence’ and the ‘line of difference’ are the very factors that open the mouth.In the Pyramid Texts the Egyptians refer to both ‘Opening the Mouth’ and‘Splitting open the Mouth’. They also interchange this w ith ‘Splitting open theEye’ by w hich they mean the Eye of Horus. But in an important reference toSokar they also mention ‘splitting open the egg’.I should mention that just as male blood pressure tends to be around 120/80w hich is 3/2 or 1.5, the center of the thorax from the ground, the female bloodpressure tends to be 110/70 w hich is 1.5708. The relationship betw een 1.618and 1.5708 is 1.030048 – probably the most common female armspan. The malecan be looked at as 1.618/1.5 = 1.078689, w hich I w ill make as the overallarmspan for the male as it is 1.03 × 1.0472 w hen in the angled position w ehave been seeing. The relationship betw een male and female blood pressurestandards is none other than the ratio of the Royal Cubit: 1.5708 ÷ 1.5 =1.0472 = π/3. The w oman has a larger range and her systolic pressure is low erthan the male. By a conservation law , these nuances show up in differentfu n ctio n s .Let’s check the ‘mouth’ of the female Thoracic Vesica. It divides unity by 3, sothe horizontal cross is .333333 or W X here below . Half that w ill give the ½ base(W N) of an equilateral triangle or .16666666. The base of this triangle is show nbelow as W X. The apex is unmarked but falls on the mouth. 1/2 W X falls in thecenter of the heart, marked N. converted by W eb2PDFConvert.com

The height of the triangle is easy to determine as it is the root of 3. So you have.1666666 × 1.73205 = .288675. Since the middle of the Thoracic Vesica sits onthe 1.5 latitude marked above, w e add 1.5 to .288675 = 1.788675. So w enow have the follow ing: 1.7888, 1.7854, 1.788675. In the image above I havemarked 1.7854 to label the upper side of the square w ith 1.5708 on a side.Once again they cannot be distinguished from one another. This is extraordinaryharmony w ithout any question. It is w ell w orth enumerating.A. Height divided by half of the square root of 5 = 2 ÷ 1.118 = 1.7888B. Squared-Circle falls at exactly 1 + .7854 = 1.7854C. The mouth of the female Thoracic Vesica Piscis falls at 1.788675.The fact that these prime geometrical factors converge on exactly the samepoint, indicates that the mouth is capable of genuine refinement as w ell asbeing a cornucopia of flow , an exchange betw een inside and outside, diastoleand systole, inhalation and exhalation, inspiration and expiration. The moutharticulates and shapes w hat has been formulated in the vocal cords (throat) bythe motor activity that comes from the brainstem via the recurrent laryngealnerve that w raps around the Aortic Arch of the heart after having left the VagusNerve (N.X). The Aortic Arch is at the latitude of the golden number (1.618) fromthe ground. The Aortic Arch signals the medulla and pons as to the state of theblood: oxygen and carbon dioxide levels. It strikes me that the recurrentlaryngeal nerve needs to maintain that somew hat cumbersome route to reachthe larynx because it is related to respiration and the emotions associated w ithrespiration and heart rate. The lungs dominate the upper half of the ThoracicVesica, demonstrating that they are formed w ithin the unity circle. The breathsupports the vocal apparatus. The heart is also very much involved w ith speechas is the brain and brainstem. Circuits that drive the larynx also pass throughthe heart and are undoubtedly related in a prime w ay to Nerve X, the VagusNe rve .The motor control of the larynx and mouth can be manipulated by yoga toconserve the almost automatic flow that engenders ideas, emotion and speech.W hen a peak is reached – especially w hen the kundalini is added to theequation – it is possible to experience some sort of mystical initiation. Herew ords are experienced differently. They have great pow er and authority andcan bring about transformations. They induce dramatic changes. But it is as ifyour ow n w ill is not the source of the vocal energy. W hen the Tibetan kudenhas donned his 30 pound helmet and has entered his oracular trance, he iscapable of extremely pow erful and authoritative displays of w ords. But laterw hen he has recovered from his mediumistic trance he has no recollection of thecounsel he gave. So the source of w ords has a mysterious origin and there isboth consciously acquired know ledge and deeper levels of know ledge that canuse the same vocal apparatus. To see these fundamental geometrical functionspredetermining the position of the mouth indicates that the source is complexand in part transcendental. No w onder Saint John begins his gospel w ith “In thebeginning is the w ord…” In the Pyramid Texts it is said at one point: “I am theGreat W ord”. And this Great W ord had liberating effects!It seems the best w ay to assimilate unusual information is thematically. Thememory likes themes, probably because cognition itself holds togetherthematically; in patterns. So I should mention w hile w e are here that there isyet another convergence on the mouth of note. This one is the tip of a GP-pyramid, the base of w hich is 1.236 or 2 × .618, the same span and same converted by W eb2PDFConvert.com

latitude w ithin w hich the Pelvic Vesica Piscis is constructed, namely the width ofthe Golden Rectangle, EFGH. In the accompanying illustration it is base RS set atthe level of the pubic bone or ½ the height. The apex of the pyramid falls on themouth. The apothem of the pyramid, moreover, is Unity.This is another striking example of harmony, so proof is in order. If w e put thecompass point alternately on R and S, open it to Unity at E and F and thensw ing it into tw o interpenetrating circles they will intersect on the mouth w ith theapothem of the pyramid as 1 and the ½ base as .618034. It is easy tocalculate the height of this archetypal pyramid from the pubic bone. W e justtake the square root of (1 – .381966) = .6180434. So the square root of.618034 is .78615. W e add unity to this to get the distance from the ground:1.78615. Once again w e can see how close these four convergences are:A. Height divided by half of the square root of 5 = 2 ÷ 1.118 = 1.7888B. Squared-Circle falls at exactly 1 + .7854 = 1.7854C. The mouth of the female Thoracic Vesica Piscis is 1.788675.D. The apex of the 1.236 pyramid is 1.78615W e can also go the 4/π route as w ell, giving .618034 × 1.27324 = .7869. W henadded to unity you have 1.7869.These convergences are not inconsequential. They are not trivial geometricalcomponents. Rather they are the most significant and fundamental geometricalcomponents that relate directly and harmoniously to the Prime 2:1 that spaw nsand supports them.THE SIGNATURE OF THE GOLDEN NUMBER: .618It is quite interesting to see how versatile and harmonious .618 in fact is. And.618 is the signature of the golden number. It is the difference, the proportionthat gives the golden number its meaning and operating capacity. The reciprocalof .618 is 1.618, the golden number itself. The square of .618 is its ow n mate inthe golden section: .381966 w hich w ill play the pivotal role in the secondmethod coming up for squaring the circle. Recall that .618 ÷ .382 = 1.618. And.618, the ½-base of this golden rectangle pyramid, can be used tw o w ays toobtain the height of the pyramid that reaches the mouth from the pubic bone.The square root of .618 gives a height of .7861 and so 1.7861 from theground. And it also can be used as .618034 × 4/π = .7869 = 1.2732395× .618034. This architecture is so strong and so flexible and so harmonious inthe w ay inside relates to outside that grow th, cell-division and multiple activitiescan co-function in a dynamic environment such as the Earth’s surface. Themouth’s versatility is astonishing. converted by W eb2PDFConvert.com

In the meantime w e can see that w e are dealing here w ith several points ofconstructive harmony – especially the constructive use of .618. Not only is it ½the base RS, but it is also SJ and RI. This links the pelvic bone (1/2-point) to thegolden number (1.618) that marks the horizontal armspan and the Aortic Arch ofthe heart. So IJSR is an important 2:1 rectangle that w orks harmoniously w ithPQNM, another important 2:1 rectangle that links the Pelvic bone to the mouthvery precisely. As archetypes they relate as follow s:1.5708/1.236068 = 1.2708. This number appears in Series E on Line 6, ColumnXV next to 7854 and .7854 is the height of this ‘1.236’ pyramid. .7854× 1.618 = 1.2708.I w ill confess to the reader that there are times w hen I w ish I could assign atone to each of these geometrical ratios. I then w ish I could ‘play’ the orchestraof sounds that have come together in the human body. That w ay theexperience could be direct and non-analytical. Here, the reader must supplymuch of their ow n imagination to experience the interactive significance of thesefundamental ratios. W hat I have found is that contemplation has proven to be alittle more important than analysis. But contemplation takes time. In any case,there is no question that in the female, the golden rectangle, w ith w idth 1.236,plays a marvelous, even beautiful role, in the w ay it w orks w ith the Prime 1:2rectangle. The mouth emerges as the fount of life and w isdom as the traditioninsists! The geometry helps us to understand how it can be the source ofw isdom. converted by W eb2PDFConvert.com

The Human FaceIt is now important to examine the geometry of the face to see w here themouth falls relative to its immediate environment and then see how thatharmonizes w ith the 4 methods already cited w hich apply to the body as aw hole. I w ill start w ith a brief synopsis of how I became convinced of onestatistic that demonstrated that the head tended to be 13/100 of the w holeheight. I found this particularly interesting at Chartres because the 100 metersw as in evidence as an important internal measure. Its diagonal seemed to begiving the height of the tallest tow er (North). And the inside measure across thetransepts suggested a golden rectangle w as also determining important interiormeasures, namely 61.8 meters. The fact that a 13 meter circle w as settingeverything from the round point of the choir to the entrance to the Royal Portaland the diameter of the Labyrinth, I decided to take the 13/100 seriously. Butthen I came upon a curious w ork called “The Opening Eye” by Frank McGillion(1980) that referred to a New York Times article (mentioned earlier) fromJanuary, 1976, w ritten by W alter Sullivan called “Doubts are raised on w hy theSun shines.” It discussed different scientific teams w ho had discovered a pulsein the Sun that w as like a gigantic heartbeat – every 160 minutes – or 9 beatsdaily. Another impressive example of a Great Ennead. But this little book alsomentioned something called an Earth ‘shout’ that is an electrostatic retort fromthe Earth’s ionosphere as if in response to the Sun’s pulses – or in any case abuild up of electrostatic energy as if in a large resonance cavity. The Earth shoutis 69 times a day (see L. W atson, The Gift of Unknow n Things, 1977). Therelationship betw een the Solar pulse and the Earth ionospheric ‘shout’ is13/100, or more exactly .13043478… So I made this relationship betw een theSolar ‘heartbeat’ and the Earth ionospheric ‘shout’ the proportion of the humanhead.Now I w ill introduce the head of a young w oman w ithout the geometry and w illthen put the geometry in to show the position of the mouth.In the case of this young w oman I have divided the height of the head in half atthe rims of the upper eyelids. I have divided other faces in half at different pointsof the eye w ith equal success. But the first operation is to divide the particularhead in half. That becomes the length of a 2:1 rectangle. The 2:1 is expandedto a golden rectangle (W XYZ) and it is also doubled to a Prime Square (EFGH).The Prime 2:1 (ABCD) is then able to be broken dow n into smaller 2:1rectangles w hich can be further broken dow n by the golden section and sofo rth . converted by W eb2PDFConvert.com

W hen the Prime square, EFGH, is divided in half at IJ through the upper eye lids,the mouth immediately becomes a very harmonious place geometrically-speaking. The diagonals IG and JH immediately determine the angle of the upperlips. It is exact. I never associated the diagonals of a double square on its sidew ith beauty. But here the angle formed by the descending diagonals isobviously creating a bew itching beauty. The angle HGI is 26.56°. The low er lip isfurther defined by another diagonal of a smaller 2:1 rectangle, KLCD, that alsodescends at 26.56°. KLCD is ¼ of the Prime 2:1 rectangles and 1/8th of thew hole Prime square. By extending CK and DL, the base of the ear lobes aredelimited, so in fact a larger pair of complementary 2:1 rectangles are involvedlinking V to D and U to C. These are 3/4th the Prime 2:1 rectangles and theyalso overlap, reaching across the Prime 2:1, ABCD.The opening of the mouth can be looked at tw o w ays: w ithin the w hole squareand w ithin a ¼ 2:1 rectangle, “abcd”, that exactly measures across the w idth ofthe mouth from corner to corner. So the w idth across the crease of the mouth is1/4th of the Prime square and ½ of the Prime 2:1 rectangle. Its height is ½ theheight of the w hole head. The mouth is opened very precisely by the golden converted by W eb2PDFConvert.com

section of this 2:1 rectangle, ‘abcd’. ‘xd’ becomes .382 and ‘ax’ becomes .618.This means that from the vertex or crow n of the head to the crease of themouth is 1.618 and from the base of the head to the crease is .382. And 1.618÷ .382 = 4.236 = (1.618)³. Also notice that just like the Vesica Piscis the noseis exactly 1/3rd the width of the Prime 2:1 and 1/6th the w idth of the PrimeSquare. Its triangular shape is precisely determined by the diagonals of thePrime 2:1, ABCD. Meanw hile the ears meet the face exactly at the boundary ofthe golden rectangle. W hat is most striking for me about this geometry is thew ay the opened eyes from upper eyelids to xy, or the opening of the mouth,w orks w ith the golden section to produce the overall feeling of concentratedalertness and sense of purpose that this face exudes. The next remarkableobservation is the coincidence of the intrafacial measure from mouth opening tovertex (1.618) and the overall measure w ithin the body taken as a w hole(.2146). W ithin the head taken as 2 the SCM length is 1.618. W ithin the w holebody height taken as 2, the same span is .2146. Tw o significant harmonies acttogether to open the mouth. According to the infrafacial geometry, the openedeyes play a significant role in determining te opening of the mouth in thisparticular person.W e can now readily compute the intrafacial position of the mouth and see how itrelates to the other overall methods that integrate the mouth into the w holebody. As it turns out w ith a total height of “2” for the body w hen w e add thepercentage of the w hole represented by the base of the jaw to mouth portion,namely .0249085, to the height of the body as far as the base of the jaw or.8695652 w e get .894473709 of the w hole, so:2 x .894473709 = 1.7889474W e can now add this to our list of geometrical factors responsible for openingthe mouth.A. Height divided by half of the square root of 5 = 2 ÷ 1.118 = 1.7888543B. Squared-Circle falls at exactly 1 + .7854 = 1.7854C. The mouth of the female Thoracic Vesica Piscis is 1.788675.D. The apex of the 1.236 pyramid is 1.78615W e can also go the 4/π route as w ell, giving .618034 × 1.27324 = .7869. W henadded to unity you have 1.7869.E. (.618 x 4/π) + 1 = 1.7869F. Intrafacial location (.049821653) added to 1.73913 = 1.788947First of all, note again that I did not use exactly 13/100 for the head size. I usedthe ratio betw een 9 and 69 sensing that this relationship betw een the Sun’spotential pulses and the Earth’s ionospheric response (w hich is also tidal by thew ay), is probably fundamental and helping to support electrical and magneticbrainw aves – rhythms that support patterns, themes and musical-like w avesthat support cognitive processes and memory patterns.9/69 = .130434782This leaves a body height to the base of the head of .869565217. The jaw -to-mouth % of the head is .190983 and this is .024910829 of the w hole body. Thisis added to everything up to the jaw :.024910829 + .869565217 = .894476029This is 89.447% of the w hole height or the height divided by 1.118 as w e haveseen. So, .894476 is the reciprocal of 1.118. Remember that 1.118 is the ½diagonal of a 2:1 rectangle and is the ratio betw een length and diagonal. Theheight of the KC is 1.118 × Unity or 11.18 cubits or 5.854 meters.W ith a height of “2” w ith this configuration w e have from the ground:.894476 × 2 = 1.788952 converted by W eb2PDFConvert.com

This next illustration show s how Nature has fine-tuned the sculpting of this face.The same ¼ 2:1, here IJKL, w hen golden sectioned the other w ay across ‘ut’determines the opening of the nostrils. So in one rectangle, golden sectioned inboth directions – dow n and up – w hat is determined is both points w here air istaken in and breathed out. uM or tN have a value of 1/(1.618)³ or 1/4.236. It isa particularly stable region and w e w ill see w ith cytoskeletalmicrotubules that this region houses a relatively free electron in a hydrophobicpocket. In the image above also note now the even smaller 2:1, here ‘abzy’.W hen it is golden-sectioned from below it forms the bottom limit of the lower lip.The V of the upper lip that completes its beauty is formed by the golden sectionarcs of IJKL, the same arcs that determine the crease or opening of the mouth.W hen I make the jaw -to-mouth distance “1”, the mouth w idth is 1.309 and1.309 is 1.618/1.236 = 1.309. W e are back to the proportions of the EgyptianRa-Horachty stele. The rectangle, MNKL is part of w hat makes this mouthbeautiful, edited, functional. This individual happens to w rite very w ell, and triesvery hard to articulate her truest thoughts and impressions. She is as giftedw ith imagination as w ith the desire for ‘truth’.Splitting Open the Mouth = Splitting open the Eye.It w as mentioned earlier that the Egyptians used different phrases to say thesame thing. One event or phenomenon had several aspects to it. So “Splittingopen the Mouth” also w as referred to as ‘Splitting open the Eye.” The Eye ofHorus w as depicted in various w ays, one of the most important being theUraeus on the brow . This w as the raised serpent or kundalini. In an image fromKarnak it is striking to see that the measure of the jaw -to-mouth is identical tothe measure of the Uraeus itself that is seated on the brow . Note that theUraeus (Maāt, Eye of Horus) sits on 3.236 from the base. Above it is 2 to thevertex. 3.236/2 = 1.618. So Splitting open the Mouth or ‘Splitting open the Eye’also refers directly to the golden number and golden section of the w hole head.In the Pyramid Texts it is stated that the Eye of Horus is recovered from theforehead of Seth. I w ill discuss this in more detail in future posts. converted by W eb2PDFConvert.com

This image below combines these same geometrical factors w ith squared-circlerelations and angles. I did this in 1990 to demonstrate a principle, not attemptto draw an actual head. converted by W eb2PDFConvert.com

In the next post I w ill demonstrate another method for squaring the circle andhow it seems to be used by Nature to w ork a few w onders. W e w ill also returnto the Astronomical Unit to get some clues about the male geometry and theorigin of the heart. The human being is an unapologetically profound creature.Our depth cannot be separated from the geometry that supports us.Read Full Post »Squared-Circle: The Unexpected Vessel(P8)Posted in Human Harmonics on April 21, 2010 | Leave a C omment »“Three tables bore the Grail, a round one, a square one and a rectangular. Allthree have the same perimeter and their Number is 21”. (The Mysteries ofChartres Cathedral, p.92, p.133)W hen I first read this I felt I had been involuntarily pulled into a ritual. The ritualw as cosmic. It w as a w ave-action like a heart-beat. I accepted it before Iunderstood it w ithout know ing w hy.By this time I w as already thinking in terms of 3-ness because of my 1980dream (that I’ve been referring to all along) w hich had occurred right on theoccasion of w hat every tradition of astrology ever know n has called the‘progressed New Moon’. This is based on the synodical month w hich dependsfrom 3 bodies: Sun, Moon and Earth. It is about 29.53 years from one pNM tothe next, so a year corresponds to about 1° w hich ‘equals’ one day. Nature is acontinuous relationship betw een storage and release; systole and diastole;enthalpy and entropy, accumulation and discharge, yin and yang, seed andflow er; implicate and explicate. The pNM is the point of maximum contraction,the shedding of the old, the last vestige of exhalation, the seed, a newimplicate order aw aiting grow th. But it also possesses the potential for innerillumination; a light born from the darkest dark. This is the light of revelation; the“Fire of Saint John,” w hen one has been taken back to the seed and itsmysterious and even formidable cavern, the Broad Hall of Osiris. In the imagebelow w here a five-fold serpent is biting its tail, the fallen Osiris figure has ascarab on his head – the symbol of spiritual metamorphosis. Above this cavern,the fire of 3 serpents is about to burn the enclosed contents of 3 chestscontaining head, w ing and animal loins. One imagines three parts of the temple:the court for the pelvis; the covered w ay for the spiritual heart and the secretsanctuaries for the head: the origin and place of return. At Chartres you haveNave, Transepts and Choir: Round, Square, Rectangular. One can speak of 3fires: Sagittarius, Leo, Aries.Though the progressed New Moon is the product of 3 bodies, the fruit of theirharmony is a fourth. The fourth behaves differently from the other three. Theyare all recapitulated w ithin it. In the inspired and w ell-know n Emerald Tablet,the Sun is its father, the Moon its mother and the Earth is its nurse. The fourththat concerns us rather uniquely is none other than man, often symbolized bythe head w hich distinguishes us.At Gizeh there are three great pyramids; three chests ‘efficient for burning’;three “pyres” capable of reducing and purifying the ash of the Phoenix. Thelargest, show n below , canonizes the squaring-of-the-circle. The other tw o converted by W eb2PDFConvert.com

celebrate other significant geometrical principles. But there are also 6 smallerpyramids, suggesting that behind the Sphinx you have the Great Ennead. Atumw as said to become the Great Ennead. He w as both Primordial Mound and GreatEnnead. 9 is the square of 3. It is the sum of 3 + 3 + 3. It is a 3-fold w ave ofamplification that transforms into a 10th, Horus of Egypt: the spiritual essencethat the Nine Bow s release into the Netherw orld.Here w e see 3 ruined pyramids next to the south-w est pyramid (Mycerinus).There are three more small pyramids in front of the Great Pyramid seen here inthe distance at the right, bringing the total to 9. Horus w as the tenth. Oneimagines the three large pyramids to refer to Atum, Geb and Osiris. It is difficultnot to think of the Great Sphinx as being both the fourth and the tenth. TheSphinx represents man “made in the image of – ”. converted by W eb2PDFConvert.com

The human imagination is difficult to satisfy – but w ho w ould w ant it any otherw ay? Reductionism is the first step on the road to dictatorship. Better to takean alternative path w ith bare feet and the shirt on your back if it avoids thedebacle of subjugating others in order to dominate their freedom. The Grail islike the number 64. It invokes totality. The w elfare of the w hole is in itsembrace. And to celebrate that totality it spaw ns many children to bear w itnessto it. How ever everything great finds its ow n limitations. The Grail Castle did notopen its gates to just anybody at any time. W ounds sometimes hold the solekey of entry. In Parzival a bleeding lance possesses as much mystery as thecornucopia that satisfies all the heart’s desires and quenches the thirst of monkand glutton alike! Parzival w as supposed to ask about the lance and the bloodthat w as dripping dow n its shaft. A lance pierces. It can kill. But it can also letsomething extra enter the vessel. This sets in motion a transformation. Passion,self-satisfaction and pride yield to spirit and its w ider frame of reference thatincludes the tribulations and joys of others encountered beyond the boundaryof one’s ow n vessel.W ere the builders thinking of man’s genesis in the image of the three tablesw hen they spoke of the Grail? W ere they thinking of the manner by w hich ‘Godfashioned Adam on his Potter’s Wheel’ as depicted at Chartres echoing the w aythe Ram-Headed Egyptian neter, Khnum fashioned a man and his double (ka)also on a Potter’s W heel at Luxor, Egypt? The emphasis at Chartres w as onAdam’s head. converted by W eb2PDFConvert.com

Chartres w as under the spell of Plato’s Timaeus at that time. Plato saw thegods fashioning the W orld Soul first as a sphere. The head w as created inimitation of both W orld Soul and the Eternal Living Being w ho w as spherical. Thebody then follow ed as a matter of practical necessity to stabilize the sphericalhead. But in any case Charpentier is quick to point out w ithin the context of hisuse of the past tense, “bore the Grail”, that:“… even the bare mention of the Grail show s clearly that there is no question oftrifling and that this “trade secret” had, in its application, an initiatorysignificance and, especially in the case of a cathedral, a bearing on initiatoryaction.” (ibid, p.133)W ere the pyramids also built w ith a mind to initiatory action? And w as the Eyeof Horus the fruit and blossom of that action? Unadulterated instinct, of course,says “yes”. The politics of history and religion engages in polemics in order topromote a current brand name; a label. But this is just an earthly substitute fora spiritual frustration; initiation obstructed; the Eye shut up in darkness. AtChartres all such argument seems to cease. W e are born from an earthly mother.But there is an essence that yearns for rebirth in spirit. This is a path, a quest, ajourney. It proceeds in steps: traditionally three.THE KING’S CHAMBER: GRAND UNIFICATIONNote first, at the summit of the Pyramid, I have marked in the difference inmeters betw een the square and the circle. It is 31.416 meters or 60 royalcubits. Recall from earlier posts that the 1/2-base is 220 cubits and the Pyramid converted by W eb2PDFConvert.com

Height is 280 cubits w hich is the radius of the circle w ith the same perimeter asthe square. 280 – 220 = 60 and 60 royal cubits is 60 ×.5236 = 31.416meters. This becomes the perimeter of the King’s Chamber set at the point ofgolden section of the Unity Cube, ABCD, taken as “1” w hen the ½ base is1.618 and apothem is 2.618. The Great Step is mounted at the north-southmidpoint of the Pyramid. The King’s Chamber can now be seen as the module ofthe whole. Its width (10 cubits) fits into the difference betw een square and circle6 times. It fits into the 1/2 base 22 times. It fits into the w hole base 44 times. Itfits into the height 28 times. It fits into the length of the Great Sphinx 14 times.Not only is the Sphinx length in a pi relationship w ith the Pyramid Base but theperimeter of the King’s Chamber names pi in meters as 31.416 meters (modernpi is 3.1415926…). Right aw ay w e have stumbled upon the three tables thatbore the Grail – in the King’s Chamber itself. The round table has a diameter ofexactly 10 meters. The square table has a side that is 3/4th the length of theKing’s Chamber as show n in the previous post, or the diagonal of the end w allw hich is 15 cubits. 15 × 4 = 60 cubits = 31.416 meters. The rectangular table is10 ×20 cubits w ith a perimeter that is 10 ×6 = 60 cubits = 20 × 3 = 31.416meters. So w hen the start point is a circle w ith a diameter of 10 meters andcircumference of 31.416 meters, the royal cubit can be used as the means to‘square-the-circle’. One simply divides the circle by 6 using a 6-pointed star, andturns it into a 2:1 rectangle w here the width is equal to 1/6th of the circle. Theradius of the circle is 5 but the w idth of the KC w ill be 5.236. To find the squarew ith equal perimeter of 60 cubits one can simply divide by 4 but it is w orthnoting that if the height of the w alls are 1/2 the diagonal of the floor, thediagonal of the end w all w ill be exactly 15 cubits (7.854 meters) and this givesan equal perimeter of 60 cubits or 7.854 × 4 = 31.416 meters. The King’sChamber is a celebration of the ‘three tables that bore the Grail’ allinterconnected w ith each other in a single volume that incidentally is 1000 ×2.236068 cubits³ or 1000 times the square root of 5 = 2,236.068 cubits³ = 321m³.All this seems unnecessarily complicated initially. But in fact it is remarkablysimple and even more remarkably harmonious. W hat is important, how ever, isto learn the significance of that 31.416 meter difference that w e find at the scaleof the Great Pyramid, w hich happens to be 1:43,200 compared to the Earth.Something about that 60 cubit difference betw een radius and 1/2 square w as offundamental importance to the Egyptians. It w as considered so significant thatthey took that difference and made it the perimeter of the King’s Chamber, itselfa fine example of the ‘3 tables that bore the Grail’! 60/220 = .2727. W e cannote immediately that our Moon bears the same ratio to the Earth as 60 does to220. In mean terms: 3476/12,732 = .273. A common ratio used today is3476/12,741 = .27282. I w ill come back to the Earth/Moon relationship as w eproceed. At this stage of our understanding, this ‘squared-circle’ relationshipbetw een Earth and Moon is a genuine mystery and in my view raises significantquestions about the real history of the tw o bodies. Harmonious forces w eresomehow able to ‘shape’ this relationship. I am certain that one aspect of theshaping w as gravitational. Moreover, I w ould hazard that it w as a sharedgravitational field operating for a long time – almost as if the Moon w ere at onepoint w ithin the Earth and a bit like a “polar body” in biology, w as somehowexpelled from the Earth. The analogy is very general because of the fundamentaldifference in scale. Nanometric forces are at w ork in an ovum for example. Soelectromagnetic energy is w orking w ith a volume overload. In the case of Earthand Moon a straight collision by a large entity (“Giant Impact Theory”) seemstoo accidental. Perhaps iron and magnetic fields played some unknow n role w iththe Moon already pre-formed near or on the Earth surface during a precisephase of rapid self-gravity.In the Great Pyramid there seem to be three levels. W ith the Unity Cube in thecenter, the Subterranean Chamber falls right on the square root of 2, quite as ifit w ere acting as a root. The next level is the Queen’s Chamber that I w ill haveto discuss at another time. The King’s Chamber rests on the golden section ofthe Unity Cube at 44 meters from the ground. The north w all of the KC is thegolden section from North to south. And the East w all is the golden section fromW est to East! It is not easy to sum up the significance of this level of harmony.Moreover, historians tend not to credit the Egyptians w ith a know ledge of thegolden proportion. But it looks as if the King’s Chamber has been situated inaccordance w ith both ‘squared-circle’ geometry and the golden proportion. Onecould readily argue that they understood the relationship betw een thesegeometrical factors and the coveted spiritual metamorphosis symbolized by thescarab beetle, Khepera (“Transformations of Ra”) and the Eye of Horus. For nowI w ill just introduce the theory that w hen the 1/2-base of the Great Pyramid is220 cubits, the Unity Cube that the Pyramid encloses, w ill be almost 136 cubitsor about 71.194 meters. The golden section of that “Unity” is 44.0012 meters. It converted by W eb2PDFConvert.com

seems the Queen’s Chamber is 22 meters from the ground and the King’sChamber is 44 meters from the ground or the golden section of a Unity Cube.The Cube can be thought of as the Holy of Holies, such as at Solomon’s fabledtemple. But in the case of the Great Pyramid, this Cube w as enclosed by theprinciple of the squared-circle, pointing to an internal transformation ormetamorphosis that the Egyptians regarded as significant, as it maintained acosmic balance betw een ‘above’ and ‘below ’. This they called Ma-at. Ma-at alsomeant ‘justice’ and ‘truth’. So the Great Pyramid w as also a testament built instone.Three TablesAn All-embracing roundness becomes square through division and differentiation– possibly under pressure; a necessity in the cycle. The Grail is cyclic. Its sourceis eternal: the bountiful universe, the ‘black’ w omb of Nut in ancient Egypt. Itsaction is tidal. Squareness involves acceleration. Acceleration is an aspect ofinverse square forces such as gravity and electromagnetism. Squareness alsoinvolves 4-ness. W e speak of 4 forces of Nature w hich have difficulty beingunified mathematically. The ancients spoke of Four Elements. Psychologistsspeak of the Quaternary. So w ith squareness, gravity or ‘self-gravity’, is bornand things become separate and differentiated: Atum becomes a separate ‘hill’.He surges up into being from unknow n depths and distinguishes himself as aPrimordial Hillock consisting of a Great Ennead of neters. Just as w e speak of 9planets that react to the Sun w e also speak of 9 hormones that react and moveand activate other processes in the body. Once things become separate andactive, there is now competition in a shared field, and w hat is born is a quarrel,a struggle that demands a quest for harmony; a longing for peace. Gravity actsa bit like Seth w as said to act. He stole the Eye of Horus and sw allow ed it.Horus has to get it back again. Christ had to descend into hell to w in back thelight. The creative hero has to overcome his ow n miserable inertia to w in from itinspirations that ache to be born. The opposites strengthen themselves, likeHorus and Seth, male and female, light and dark, w ar and peace, matter andspirit through the square or ‘square-ness’, w hich includes electromagneticradiation. Matter steals the light w hich is reborn in the belly of the Sun. W henaccumulated in the head and heart it too can be reborn until the w hole being isa vessel full of light, w hen the ‘Sun once again rises from its ow n dark ash’.W hen the pilgrim arrived at Chartres – usually having endured multiple dangersto get there – he or she entered through the Royal Portal. I must mention thatthis w as carefully designed and seems to have been acquired from theEgyptians and their generic gate know n as the ‘sba’. It is normally constructedw ithin a 2:1 rectangle w ith w idth 22 and height 44. The Opening is 10 w ith 6 foreach pylon. The height of the door opening isthen 31.416, echoing the difference betw een circle and square at the GreatPyramid, namely 31.416 meters, the perimeter of the King’s Chamber. If thatw ere collapsed into a circle its diameter w ould be the w idth of the opening, 10.This gate symbolizes the gate to the horizon of Atum, or sometimes referred toas Horachty, Horus-of-the-Horizon. In Christian terms it is the gate to Heaven.The pilgrim had made his w ay to Heaven-on- Earth. The Rose W indow sitsabove the gate. Presumably, then, it represents the heavenly sphere, heavenlysplendor. This w ould explain its emphasis on the color blue. converted by W eb2PDFConvert.com

In the image below I have modified Charpentier’s original sketch of the threetables that bore the grail. He has made them of equal surface. I have added thecircle w ith equal perimeter to show the difference. All my figures are in red. The29.53 circle is the circle w ith the same perimeter as his square w ith diagonal32.8. It adds to his overall length of 97.04 m by 3.36 meters, giving an overalllength of 100.4 meters. I have indicated w here I think exactly 100 meters hasbeen applied by the builders. The square table seems to be encroaching slightlyinto the rood screen. The scheme seems to w ork. Charpentier gets 32.8 fromthe middle of the w alls of the nave. The inside measure across the nave w all tow all is about 32.2. The 29.53 circle seems to give the length across the navefrom the base of the pillars. converted by W eb2PDFConvert.com

Charpentier then pointed out the follow ing:“The rectangular table is that of the Eucharist. The mystical table, Christian, thatw hich supports the altar and, indeed, the choirs of Christian churches are as arule rectangular. There have been other rectangular tables, as in Egyptian andGreek temples…But the choir at Chartres is rectangular.” (ibid)Charpentier means that the original table w as rectangular before it w asrounded, probably in the image of the rounded crow n of the head. But w hatmatters for now is that he refers to the rectangular table as mystical, that of theEucharist. As many know the Eucharist w as symbolized by a w hite w afer w hichin numerous Grail stories w as associated w ith the Grail or w as carried by theGrail or w as brought to the Grail as if the Grail w ere one and the same as thealtar. The altar is the place of a sacrifice, offerings, making sacred. Here matterand spirit undergo an exchange. Each receives from the other. Here square andcircle act as one. The altar keeps the essence pure. The Grail is inextricablybound up w ith the altar and w ith the essence. Everything about the altar mustbe effective, genuine. Altars w ere places associated w ith fire and incense.Originally they w ere associated w ith burnt offerings in imitation of the action ofthe Phoenix. W hen Eucharist, altar and choir are put together w ith the idea ofrebirth, or a second birth, the notion of 3 tables suddenly becomesfu n d a me n ta l.Charpentier continued w ith a relentless penetration into the mystery thatalready had me under its spell but w hich w as not yet fully radiant: you w ant converted by W eb2PDFConvert.com

your ‘tree of know ledge’ to liberate and purify the soul, but it is easy to beconfused by the mysteries. W hen myth is used to convey eternal truths, w etend to latch onto the symbol and fail to sense the process for w hich it is a vitalmetaphor only. Often science itself becomes trapped by its ow n myths:assumptions that cannot be verified because w e lack the time and instrumentsto measure w hat is infinite or, conversely, w hat is infinitesimal. So w e accepttheories as if they w ere axiomatic. There is a very fine line betw een effectivesymbol and even unintended propaganda! And how subtle one must learn to beif you w ish to describe the w orld of spirit – that other plane w hereconsciousness can feel more real than it does w hen saturated w ith a glut oftangible things. The meeting of the tangible w ith the intangible is the boundaryof the enigma. Circle and square seek reconciliation. But at Chartres the choir isrectangular. In fact the w hole cathedral seems to have been laid out by a 2:1rectangle, but I could not see this all at once.“There w ithout doubt w as the w ay into the mystery of the cathedral’sconstruction. But it w as still necessary to solve the riddle of the Number 21. Theansw er is simple in fact. W e are to read, not 21 but 2 and 1. W e are confrontedthen, w ith a rectangular table w hose length is tw ice its w idth.” (Mysteries ofChartres Cathedral, p 93)To repeat, the choir at Chartres, like the table held by Moses, is rounded at theNE extremity. But it started as a rectangle. It is likely the same w ith the w holecathedral. It is also important to note right aw ay that this choir w as oncecompletely blocked by a gorgeous, thick, stone ‘rood’ screen, not removed until1763. No one – not even the Knights Templar – w ere allow ed entrance to thismost holy place except the ‘High Priest’ and even then, as in ancient Egypt andSolomon’s Temple, only once a year! It w as the place of the High Altar. Clearlythis choir had gathered up something so pure, so vital that the temple priestsdid not w ant to violate or disturb it in any w ay. It w as acting like a dolmen, aspiritual fertility stone. The ‘Grail’ w as traditionally associated w ith fertility, theBnbn of ancient Egypt. The Eucharist invokes some sort of sacrifice, oftenassociated w ith altars. In Christianity the sacrifice w as that of Christ, by w hichhis blood and his flesh w ere capable of ‘feeding’ others. But it has to bementioned that the builders of Chartres placed no crucifixes in the Cathedral.The Templars did not share the Christian view of the crucifixion. Nor did theyshare the Christian view of Christ.All Roads lead to the 2:1 Construction.W hat is it to be called? A double square? A 2:1 rectangle? The octave? A magiccarpet? A gate? A portal? A sacred enclosure? The Table of the Law ? The Tableof Rectification? I responded by learning different w ays to illustrate it. TheBenben Stone? The Mystical Table? The Table of the Altar? The Tabernacle? TheTable of the Sacrifice? W hat sacrifice? W hen God became man? W hen potentialenergy first coagulated and divided from One into Tw o and started the processof both differentiation and relationship? Everything about the 2:1 enthralled me.For some indeterminate spell I felt like the luckiest man on Earth. Charpentier converted by W eb2PDFConvert.com

had reinforced w hat I had already met w ith in Doczi’s book, that Egyptian andGreek temples w ere based on 2:1 tables. As Vitruvius noted, this w as thefoundation for human proportions. I w as an instant convert. In fact I w as notconverted at all. The 2:1 rectangle and its keys and inner patterns, w erealready in me ready to be fertilized. The real fertilizer, w hat caused the seed togerminate, w as the journey to New Zealand and the idea that the w ay into theconstruction of Chartres w as none other than a 2:1 rectangle. I knew I hadfound the means for constructing the canon of a human being. But I had no ideathat it w as overflow ing w ith geometrical information. The 2:1 is the cosmicchip. It is the means by w hich the w eb of circumstances arises from the greatvoid. It is a generator, a processor, a purifier and a rectifier. My converted by W eb2PDFConvert.com

confidence in the little 5 x 10 cm rectangles I w as draw ing several times a daybegan to grow in a w ay that felt mystical and practical simultaneously. It w as aremarkable feeling the day I first expanded the 5 x 10 to 6.18 x 10 by simplydropping half the diagonal dow n from each corner to the adjacent corner adding.59 to each side giving: .59 + .59 + 5 = 6.18. This is IJKL at Chartres. It w aslike being introduced to one’s true name. I did not see the length converted by W eb2PDFConvert.com

across the transepts at Chartres until 1988 after I had been there. How can theheart fall in love w ith a number? 6.18 is not a number. It’s a proportion, abuilding block of life, as important as DNA! I have never seen this 61.8 x 100meter rectangle mentioned in print. Few people associate know ledge of themeter (39.37 inches) w ith the Gothic Age. But all my w ork indicates that not onlyw as it know n, but that along w ith the royal cubit it w as partly responsible forthe unique fertility of the time. The meter by its very definition comes from theprinciple of the ‘squaring-of-the-circle’!It w as not this measure across the transepts that gave me the idea to use agolden rectangle for the female pelvis. But w hen I found Houvet’s measure forthe interior w idth of the transepts, I admit, my heart did nearly seem to stop. Itw as as thrilling as it gets in this business of human and architectural biometrics. converted by W eb2PDFConvert.com

The 2:1 also seems to encompass the entire construction, excluding of coursethe Saint Piat Chapel at the extreme North East. It strikes me as quite possiblethat the Templars recovered both the royal cubit and the meter from the HolyLand if not Egypt itself. The Prime 2:1 here, ABCD, encompasses everythingincluding the front steps and outside w alls at the far end. It includes the mainw alls and inner porch, but requires the golden rectangle EFGH to include theouter porches, north w est and south east. At Chartres, the 61.8 meter w idthacross the transepts is an interior measure. It contributes enormously to thefeeling acquired from being amidst the transepts. I have included the 29.53circle around the labyrinth. It too is an inner measure. The beauty of this converted by W eb2PDFConvert.com

ABCD rectangle above that appears to be 130.9 x 261.8 cubits in dimensions, isthat it provides the overall form to the mass of the building. All that specificgravity! It is the foundation of the volume. It completely comprises the length ofthis magnificent Ark. Once this enclosure has been settled, the mind is at peace.The heart feels right. This is about 68.54 x 137.08 meters. Regarding length,nothing is excluded. This is the length overall of this ship of stone. To totallyinclude the outer part of each porch, a golden rectangle is needed w hich takesit to 84.72 meters, able to encompass all steps that lead up to the porches. Themeasure across the outside porches minus the steps is 73.4 w hich is not farfrom the length of the Great Sphinx (73.15 meters). The 61.8 meter length is aninner experience, the inner w idth across the transepts. The 100 meter lengththat completes the golden rectangle, is also an inner measure betw een thetow ers and the rounded part of the choir. All visitors can feel the sacred natureof that measure at Chartres. W hen you enter the nave from betw een thetow ers you can see to the rounded inner extremity of the choir w hich is veryclose to 100 meters aw ay, or say, 328 feet. W hen you mount the modest stepsto enter at the Royal Portal you are entering an all-encompassing 2:1 rectangle.The mass of the building rises up w ithin that enclosure. converted by W eb2PDFConvert.com

You feel yourself betw een the tw o massive tow ers. They are also hollow . Sothey also ascend. They do not just descend. You then stand at a thresholdbetw een C and D. This is w here I think the 100 meter rectangle also begins.Immediately you enter a smaller 2:1, ABCD above, that is perhaps 13.09 x 26.18m in size. The first square prepares you for the Labyrinth that is containedw ithin the second square. I have placed the larger 29.53 circle around theLabyrinth as it determines the elevations of the cathedral by using its radius asthe base of a triangle that builds through its hypotenuse. The labyrinth is a longpath that w as probably intended to be exactly 261.8 meters long or 500 royalcubits. That is ten times the diameter of the circle w ith the same surface as thesquare w ith a perimeter of 92.7714 that I have indicated above. As one w alksaround the Labyrinth one is also inside the 13.09 x 26.18, 2:1 rectangle. As youproceed the rational faculty is expelled. W hat is instinctive, vital, moving,natural, propels you tow ard the center: the place of the nucleus w here energyis most concentrated. W hen you get there you confront yourself. The darknessof the Minotaur is the darkness of Seth: a primal pow er that is accumulated andso offers energy to be utilized. In the Labyrinth one must confront this pow erand not deny it; not repress it. The ego is to be reigned in. Seth is to bebrought dow n or laid low , but not destroyed! To destroy Seth is to destroy thatextra energy that w ill be needed to take up the spine, the living pillar. converted by W eb2PDFConvert.com

Vitruvius pays homage to the Greeks, but it is w ell to remember that the Greeksspent some time on the Egyptian throne (after 305 B.C.?)! They fully restoredplaces like Dendera and Edfu. And now Charpentier added that the 2:1rectangle w as somehow the key to the equivalence of the 3 Tables ‘that borethe Grail’. 3 Tables – ? 3 phases or qualities of one essence, perhaps – thethree parts of the one philosophy, the one mystery – one miracle like the bodyof Shiva, shimmering w ith billions of luminous parts. Initially I had to pinchmyself. Something as simple as the relation betw een 1 and 2 w as possibly thekey to a place as fantastic as Chartres? W as it possible? Chartres grew from atable with a length twice its width and this table somehow was the means by whicha round, square and rectangular table could all be calculated to have equalperimeters? And more: w as I to assume that these tables also bore humancharacteristics a bit like Jung’s psychological “types” rooted in the deepestarchetypes of the collective unconscious?An unexpected destinationSo, each unexpected fork in the road had arrived at the same destination: arectangular table with a length that was twice its width. It w as a w ork-horse w ithw ings. The mystic germ capable of unfolding into visible life and returning to aw orld of spirit. The fount of the altar. For me it w as like a universal omphalos,only it was a rectangle, a double square. I w ish I could describe how it felt uponarrival, w hen I first stumbled in to the clearing to touch the ‘cosmic chip’.There w as nothing to say. No comments proved fruitful. Initially I tried to hide it:the omnipotence of its simplicity. W hen I tried to talk to others about it I turnedinto a stammering fool. They almost felt sorry for me and my childish draw ings.It all looked so bare and insignificant on the page – like a boy’s torn schoolbook! But finally I had cause to truly keep my nervous lips sealed. I w anted toshare my excitement, but I w as going to have to get to w ork, not squander thepropitiousness of the moment on talk. A strange silence binds the tongue ofacceptance – especially in restless people like me – alw ays afflicted bydissatisfaction. New Zealand w as a nice part of the w orld to be confronted w ith converted by W eb2PDFConvert.com

such an enigmatic experience. W hat do you do? You breathe and enjoy thestillness. W hile Kely and Vincent W ard researched the Black Death that struckEurope around 1348 – about 30 odd years after the Inquisition against thebuilders of the Gothic Cathedrals – I asked myself about the simplicity of the 2:1construction, the primordial octave: “How can this be”? But there is no answ er.It just is. Such a relief! The 2:1 is not man’s doing. It’s the nature of things: theprimordial flow . Draw ing the 2:1 w ith precision w as a bit like the Sun rising aftera frigid daw n. The frost melts and drips back into the roots of living things.Green abounds. You see at last that meekness does not mean w eakness.W eakness is the belief that impatience and might are all there is. Having beenan outcast, you feel as if you have reinherited the Earth, the place w here‘above’ and ‘below ’ unite. You yourself are that point of union. If Vitruvius w asright, I w anted to prove it. The body must be formed the same w ay. W e areborn of that 2:1 tablet, w here 1 has become 2 and then everything happensbetw een them like the bellow s of the Tao, the heart of the Tai’chi. An ovum isneutral until fertilized by a sperm w ith equal DNA. Then suddenly its neutrality isgone. Meiosis, once suspended, converts to an endless mitosis until deathshuts dow n the ‘w ater factory’ and the 2:1 becomes the final looking-glass. It’sdiagonal, so easy to draw , presents itself as a mystery, filling the soul w ith aw e.And so you start to sw ing the compass. You learn to measure. From the 2:1 thegolden rectangle evolves w ith such ease. In time you find more than one w ay tosquare the circle. The more you look, the more you see. Very gradually yourealize: 1 and 2 are not numbers. This is not an enumeration. It is a cosmicprocess. It is a field of activity active in the void.In the W est, w e insist upon reducing everything w ith a name to a physical thingthat can be labeled and pointed to. W e have a conscious infatuation w ith the“tangible object”. In my view this infatuation is not merely a product of empiricalscience or the advent of the modern ‘scientific method’. Rather, to me, thescientific method is a product of an infatuation w ith the ‘tangible object’, aninfatuation that has been w ith us for a long time. W e cling to our ‘attachments’for practical reasons, but w hen things become ‘fetishes’, the light soon fails toleave the rim of the cup. During the Middle Ages pilgrims w ere obsessed w ith‘relics’, tangible ‘proofs’, hard evidence that the divine w as at w ork on Earth in aspecific place and time. This obsession became the basis of Christian Dogma,w hich is w hy influential spiritual leaders such as Saint Bernard of Citeaux, w hohelped inspire the movement that lead to the Gothic Cathedrals, constantlyreminded everybody that a cathedral is but a means only. The end is thespiritual perfection of the individual pilgrim w ho is making a passage, a journey.Nature respects hierarchies, but there is a point w hen you can no longer w aitaround for the divine to send another savior, w hen w hat is called for is that yousummon your ow n light from its ow n little hideout. I am the last to say that thisis easy. The light assumes many forms and many roles.The Grail and the HeadAt one point by 1990 I had come upon enough references that compared theGrail to the head, that I w as inspired to put all these ideas together in oneplace. At that stage I also knew that the Templars kept and ‘w orshipped’ amysterious head called the Baphomet, possibly meaning ‘Father ofUnderstanding’. I know nothing about this recondite head, but the w holediscussion sparked my interest in the focusing pow ers of the head – by w hich Ido not just mean the eyes. I mean a collective pow er for the mind to self-focusin singular acts of conscious aw areness. I w as amazed by it! So I attempted toapply w hat I knew to create a head from nothing. I used the angles of‘squared-circle’ geometry and the golden section as generated w ithin a 2:1rectangle. I left the lines visible to provide a sense of somethingintelligent arising from the void as if it w ere a self-organized vessel thataccumulates the light, thereby piercing the w orld of appearances as if all atonce – overflow ing all the w alls of the inner labyrinth. At that moment the headstruck me as the ultimate mystery w here everything is united in the ‘place’: thatcenter of centers that could be called an ‘essence’ so pure it cannot bedestroyed. The head also transmutes its ow n content to the point ofoverflow ing the container, shedding its light on the w orld for better or forw orse! This head above is one geometrical recipe w ith some elements commonto all recipes. I chose a recipe that w as relevant to the main theme. Thesquared-circle w as doing something fundamental. It w as not just asuperstitious conceit.In the W elsh version of the Grail, a head on a platter replaces a chalice! Thehead is w hat is being served at the feast. The appearance of the Grail issupposed to prompt a question from the hero: “W ho or w hat do you serve w iththe Grail?” The miracle of the human head or the Grail, is a means only – apassage perhaps. W e feel the Grail is linking tw o w orlds: the visible and the converted by W eb2PDFConvert.com

invisible; the transitory and the eternal; the finite and the infinite.In Egypt the head w as associated w ith Horus, Ra, Atum-Ra and Osiris. At RoslynChapel in Scotland, the Grail is associated w ith the Sun and the head. InW estern astrology the Sun is said to be ‘exalted’ in Aries. Aries is also said to‘rule’ the head. In a complex w ay, the head absorbs the sun’s light, responds toits gravity and transmutes the energy into an endless field of activity. In anycase, I w ill use the face of this young w oman show n next as a standard for thefundamental geometry I have found present in all faces, the means by w hichthe head and face self-organize w ith amazing consistency. The geometry hasnuances, face by face, and yet alw ays plays w ith the same fundamentalprinciples! Here it is w ithout the geometrical lines and markings in place, w hich Iw ill show later. converted by W eb2PDFConvert.com

The quest for the Grail is itself an out-and-out adventure if ever there w as onebecause the experience cannot be distinguished from one’s ow n transformation.W hat, then, is this ‘Grail’ that w e variously label: ‘cup’, ‘head’, ‘Eye of Horus’,cathedral and that w hich overflow s each of these containers?The EnneadW hen the Templars initially formed somew here betw een 1100 and 1114, theyformed in a group of Nine Knights. W hen they first planned Chartres, theyintended to build Nine Tow ers. They ended up w ith tw o only. The Egyptianscontinuously refer to The Great Ennead above and the Great Ennead below orthe Double Ennead. The Templars likely w ished to demonstrate the GreatEnnead here below that reflects the one above. Nine is the square of 3 and sobrings about a transformation. It probably w orks in a double direction: spirit tomatter and matter back to spirit. Nine supports the 10th, a new Unity.Nine pyramids invoke nine planets. In 1976 the New York Times reported thatscientists w orking independently in France and Russia discovered that the Sunw as pulsing – in their w ords – quite as if it w ere simulating a gigantic heartbeat. It discharged this gigantic pulse 9 times a day or every 160 minutes. As asort of echo, perhaps, to this solar pulse our ow n ionosphere apparently buildsup electrostatic energy in its ion population, w hich is discharged like anelectrostatic ‘shout’, 69 times a day. The relationship betw een 69 and 9 is7.666… or inversely, .1304347… W hen I found out that the mean size of thehuman head w as 13/100 of the adult body height, I started to take this 9/69relationship seriously. And in fact I eventually came to use the exact ratioof .1304347, as it helped refine the position of the mouth in the standing adult.I realized the Egyptians w ere discovering multiple properties in the principle of“9” and that the “9” pyramids, like the symbol of the Grail, w ere superabundantin meaning. 9 governs, regulates and transforms. The head is a magicalcauldron that springs from the circular actions of 3-ness. How did Plato put it inthe Timaeus? ‘The head is endow ed w ith all the varieties of motion there w ereto be’, and for this reason the body w as designed to serve the head, “thedivinest part of us that controls all the rest.” (p. 60, Timaeus). One imagines thatthe 9 pulses have somehow been internalized in the head and that the 69Earth shouts have translated into the body. It’s as if the 9 solar pulses w erethe source of the 69 shouts, just as the head is the source of the commandsthat govern and regulate the body. The head also contains the Pituitary Glandthat is divided into tw o parts: an anterior and a posterior. The formerbiosynthesizes 7 hormones and the latter, 2, so 9 w hen taken together. The converted by W eb2PDFConvert.com

posterior is part of the Central Nervous System. The anterior part is not. Mostbody processes are regulated by these 9 hormones or stimulators.Castle Mundsalvaesche, home of the Grail, also invokes a magical mountain ofsome kind. In the Pyramid Texts Atum becomes the Primeval Hill, the PrimordialHillock. He rises up like a Pyramid out of the Nun (void) as a primordial mound.In PT 1652, it is said that Atum-Khoprer ‘became high on the height’. He rose upas the bnbn-stone in the Mansion of the Phoenix. The bnbn-stone is the BenbenStone brought by the Bennu Bird that appears to be a cyclic phenomenonassociated w ith the Phoenix. As every school child know s: the Phoenix isfamous for its uncompromising act of cyclic self-immolation. After it has burneditself to ash it rises again as resplendent as it w as before.But w hat is less familiar to everybody is the relationship betw een the Phoenixand the Grail. Eschenbach is fairly clear about it. The Grail, he says, is a stone byw hich the Templars of Mundsalvaesche are nourished. He stresses that they liveby the essence of that stone w hich is particularly pure. He calls it Lapis Exillis.“By virtue of this Stone, the Phoenix is burned to ashes, in w hich he is reborn.Thus does the Phoenix molt its feathers. W hich done, it shines dazzling brightand lovely as before!” Eschenbach then goes on to insist that anyone w ho seesthe Stone is immediately made young again and that, by it, all illness isbanished. “This Stone is also called “The Grail”. (p. 239, Parzival)The similarity betw een this and Utterance 600 of the Pyramid Texts is striking. Aprayer is being made for the king and his pyramid.“O Atum-Khoprer, you became high on the height, you rose up as the bnbn-stone in the Mansion of the Phoenix in On, you spat out Shu, you expectoratedTefenet, and you set your arms about them as the arms of a ka-symbol, thatyour essence might be in them. O Atum, set your arms about the King, aboutthis construction and about this pyramid as the arms of a ka-symbol, that theKing’s essence may be in it, enduring forever.” (PT 1652-53).The text goes on to invoke the protection of the Great Ennead w hich it calls theNine Bow s. Atum-Khoprer refers to the scarab beetle and its capacity totransform. The bnbn-stone takes its meaning from bn or bnn w hich has manymeanings but the root is to rise, to fertilize, to make rise. There are tw o birthsthat this can refer to: physical and spiritual. The essence here concerns spiritualrebirth. The pyramid w as designed to keep the essence pure. As if describingthe pow ers of the Grail, PT 1278 says the follow ing:“A boon w hich Geb and Atum grant: that this pyramid and this temple beinstalled for me and for my double, and that this pyramid and temple beenclosed for me and for my double. This Eye of Horus is pure: may it belong (?)to me.” (PT 1277-8)The translator w as unsure of the w ord ‘belong’. For the ow ner of the pyramid,the Eye of Horus must manifest; it cannot just be an expectation. Like the Grail,it does something. It bestow s something upon the King and upon his double.W hat it bestow s is the essence w hich is then protected. W ith this in mind w ecan return to the subject of the ‘squaring-of-the-circle’.Sacred MoundsLong before Chartres w as a cathedral, the place itself w as famous for itsmound. Its w ater, the vegetation, etc, w as legendary. The Druids practiced asecret form of ‘w ater baptism’, initiation rituals in a crypt w ithin the mound. converted by W eb2PDFConvert.com

Supposedly a dolmen is buried w ithin it to enhance its spiritual and healingproperties. The current cathedral is simply one in a long history of beneficentmanifestations associated w ith the hillock, tertre, or ancient mound of Chartres.The Great Pyramid w as also a legendary mountain know n throughout history.Supposedly the building itself has been built over and around a 30 meter highhillock that w as as legendary as Chartres. The Great Pyramid is a celebration ofthe Squaring-of-the-Circle as if it w ere the key to keeping the Eye of Horuspure; the Grail effective. And it is this that nourishes the Templars.Reflected in the faces of the men and w omen sculpted in stone at Chartres, yousee a common horizon that liberates and uplifts. The peace is immense andtireless. It is a shared mound; a universal sanctuary: an immense reminder thatechoes w ith the voices w e cannot forget. Just reading Charpentier in 1985 – Iw as hooked. I couldn’t w ait to get to Chartres. W hen I got there by the fullmoon at the end of May, 1988, not only w as there no let dow n; it w as theopposite. Chartres vastly exceeded anything I could have imagined about it. Ittransported Kely in the same w ay. Despite her burdens at that time – mostlyfinancial and professional w orry – I could see she w as not expecting Chartres tobe so exalting; so gracious; an immensity of love. W hat a gift to have bestow edon the generations w ho have lived since 1220 A.D. At Chartres you are notafraid to love. The w ord is fulfilled and carries no shame. I exist because I love. Iam because I love. This has nothing to do w ith romanticism; nothing to do w ithsentimentality because at no time can the experience of Chartres be reduced.The overflow is superabundant. And somew here the squared circle had alreadyprimed the pump of the everlasting as if a priori. Incredible really. Everything theheart already know s and the mind has already forgotten. And then you takeyour turn and climb the hill to Chartres. Am I exaggerating? No. Chartresexceeded in every w ay imaginable anything I had ever thought or learnedabout it before getting there. I’m afraid to put a photo in here because I amreluctant to reduce the energy of the place to an appearance; a category orstereotype of the mind. Something about Chartres exceeds all appearances andall history w e have of it.The Great Pyramid PrincipleOf special interest here: if the ½-base is 1, the w hole GP profile w ill be 5.236,the number of the royal cubit (.5236 m). And the difference betw een the ½square and radius of the circle (TR) is TS w hich is 60 royal cubits or 31.416meters. W e can recall that the perimeter of the King’s Chamber is none otherthan 60 cubits or 31.416 meters! The question to be asked is w hat significancedid the builders place on that difference betw een circle and square of equalperimeter? I am going to address this in more than one category as w eproceed. As it turns out it appears to be fundamental. Also note in the imageabove that w hat links the height of the Pyramid (w hich can also be taken as theEarth’s radius or polar axis) to the 1/2 base of the defining triangle, is noneother than the golden number w hich is very close to the square of the ‘squared- converted by W eb2PDFConvert.com

circle’ coefficient, 4/π or 1.27324… So, 1.618034 is close to 1.27324 x 1.27324 =1.6211389… If you rounded the former up and the latter dow n, you w ould haveabout 1.62. Curiously, in meters, the mean height of an American or Britishfemale is 1.62 meters. And w hen you add the Moon and Earth together you getabout 16,217 km. The meter is not only useful, it also carries w ithin it an intrinsicharmony that allow s diverse phenomena to function interactively. W e w ill seethis in other posts w hen w e come to the circumstances of w hat w e call theAstronomical Unit, or the mean distance that separates the Earth from the Sun(149,597,870 km). The AU can be roughly expressed as 500 “light-seconds” orjust 150,000,000 km. “15” is an easy number to remember. And if a w omanknow s that her height is average, say 162 cm, she automatically know s the sizeof the Earth + Moon. She simply multiplies her height by 10,000,000. Thedecimal system can be pleasant.Read Full Post »Squared Circle: More than meets the Eye (P7)Posted in Human Harmonics on April 11, 2010 | 2 C omments »W hen I first picked up Louis Charpentier’s book called “The Mysteriesof Chartres Cathedral” in June, 1985, I could taste it somew here deep insideme. It w as an indescribable food – not quite esoteric – just an unprecedentedinspiration – but I had to w ait three more years before it w as my turn toexperience the beneficence of the place itself. And yet I could taste it as if itw ere just dow n the road from our hotel in Auckland. This echoed my feelingsabout Chartres back in 1971 w hen Kenneth Clark commented on it in his seriescalled “Civilization”. I confess again: Chartres lives in my heart and the feeling isthat it has alw ays been there. Though its presence defies logic and all theories Ihave ever entertained about know ledge, somehow it is supposed to be there.Chartres is ‘heart-know ledge’ and resists all labels, all categories, all w ays byw hich the mind disarms the living fire only to chain it to some cold part of thebrain. The brain need not become a prison. But vigilance is required to keep thefires stoked. Moreover, there is no one on Earth w ho I can think of – w hetherfriend or enemy – w ho I do not w ish could visit Chartres at least for one day intheir lives. Chartres is for everyone. I repeat, in some ineluctable w ay Chartresis supposed to exist. So every w ord that Charpentier committed to print seemedto be an affirmation of a know ledge so deep it w as as if I had been born w ith it.And if I w as born w ith it so, too, must the rest of humanity have been born w ithit. But the secret of this know ledge felt as if it w ere imprisoned in an infernaldarkness. My urge w as to descend into my ow n depths and w rest it from itsjailor provided I could overcome the tw o greatest adversaries: time and fatigue.I lived under a cloak of terror that somehow I w ould run out of time. I had faith,but not enough to just drift through life without knowing the secret. I w as notborn illuminated. But I craved it.I believed humanity had emerged through some sort of pattern; some sort ofmeans. Surely it w as just a question of w here to look. Like all living thingsknow ledge w ants to grow . W e are the effects of that grow th even w hen mostof its root system remains submerged in the unconscious. Significantknow ledge is not merely a matter of connecting the dots or finding acorrespondence betw een an effect and a cause. It is not mere imitation. converted by W eb2PDFConvert.com