SQUARING THE CIRCLE

H o m eA b o u t B r uA cb eo u t t h eC o n t a c t SearchLyons Co nt entB L – U JR U C E Y ONS N E X P E C T E FDeeds: OPosUts R CNomEmenYtsHuman HarmonicsArchive for April, 2010 GET UNPUBLISHED M e t h o CdONTE(NTP 1 1 )Squaring the Circle 24 Name (required)Posted in Human Harmonics on April 22, 2010 | Leave a C omment »24-METHOD FOR SQUARING-THE-CIRCLE w ith PRIME 2:1 (Post 11) Email (required)W e have seen one method for squaring the circle already. W e are now going to Submit »look at another method that starts w ith the same Prime 2:1 rectangle, ABCD.This time it w ill build the three grail tables on top of itself as if it w ere their THANK YOUmother. In fact the 2:1 acts like the mother and the father, not unlikeHexagrams #1 and #2 of the I Ching, w hich are complete inversions of one If this work has value for you,another. Line 1 is all solid light lines (yang) and #2 consists of all broken, dark, please contribute.Yin lines. They could be considered the “bellow s” of Lao Tzu from w hich themyriad creatures enter the w orld. This is one w ay to look at the first tw o CATEGORIESnumbers, 1 and 2, of Column I of Series E, or the next tw o: 5 and 10. Thegolden number, 1.618, is named by Column XIII. W e w ill see just ahead that Human Harmonicstubulin protein dimer subunits assemble into 13 slightly skew ed columns to form World Affairsmicrotubules. The 13 columns close up a hollow core interior consisting of RECENT POSTS‘ordered w ater’ that is free of all ions. It also seems to have a 3 nanometerthick layer of ordered w ater surrounding the tubes as if insulating them. The The Ukrainian Gamble andtotal diameter may be 29 nm w hich suggests some sort of optimum resonance the Global Truth C risiscapacity that might harmonize w ith hydrogen bonds in DNA. Some think the The Ukrainian Gamble andordered w ater may be the site of an event called ‘superadiance’ in w hich all the the Global Truth C risisphotons achieve a common resonance or quantum state. This might be a critical Squared C ircle Dynamics:aspect of consciousness. Microtubules seem to have multiple functions that Male Vesicas (P13)range from mitosis to synaptic repair, to memory, to information processing, to Squared C ircle Gateway ofconsciousness itself. But I w anted to emphasize that they form in 13 columns the Human Body (P12)and the tubules themselves bundle in a circle of 9 MT’s per bundle. W hen you Squaring the C ircle 24cut open a column and flatten it you see the dimers are staggered and w hen Method (P11)counted they have been grouped in a pttern that divides into 5 and 8 w hichgive 13. The golden proportion may be the means by w hich superadianceignites consciousness in w aves.Squaring-the-Circle: 24-MethodW e start by sw inging the unity circle around point A and w here it intersects thediagonal AC w e mark E. W e then golden section BC by sw inging the compassfrom CE to CF. converted by W eb2PDFConvert.com

This divides BC into BF and FC, w here BF is 3.81966 and FC is 6.18034. Bynow w e are very familiar w ith this pair of numbers. W e can note that (6.18)² =38.1966 so their golden section relationship remains harmonious in diversew ays. W e now take 3.81966 as the radius of a circle that w e create around thenavel, marked here as “I”. Its diameter (NO) w ill be 7.64. 382 and 618 appearnext to each other on Line 2 in Series E and 764 appears under 382 on Line 4in Series E, immediately before 1236. All this suggests that these numbers arepart of a process, a dynamic w eb that is regulated by the golden number. So inthe image above w e see the 3 grail tables centered over the navel. The circlehas a diameter of 7.64. The square has 6 on a side. The 2:1 rectangle is 4 x 8.The trick is finding the diameter of the circle w ith circumference equal to theothers, w hich is 24. The w ay to do it w ithout computation is to golden sectionthe Prime 5 x 10 rectangle. Series E rounds 3.81966 to 3.82. If w e took theactual golden section as 3.81966 and doubled it w e w ould get 7.639320119. Ifw e multiplied this by pi from Series E w e w ould get 7.639320119 x 3.1416 =23.999688. This is close to 7.64 x 3.1415926 = 24.00176. If w e split thedifference w e can use 7.64 and 24.The more I w ork Series E the more convinced I am that it w as one ‘Net ofNumbers’ know n to Moses and housed in the Ark of the Covenant. UnderColumn III on Line 4, w e find 24, because 4 × 6 = 24. 7 steps aw ay is 764under Column X, a new Unity, often heralded by ‘7’ steps. 22/π gives 7. So24/π gives 7.64. 7.64 is the diameter of a circle with a circumference of 24. Thisestablishes a pattern betw een Columns III and X. Take Line 6, Column III. It is converted by W eb2PDFConvert.com

36 and 36 ÷ π = 11.46. Line 8, Column III is 48. And 48 divided by π gives15.28. Line 24, it is 144 for perimeter w ith a diameter of 144 ÷ π = 45.84 ofColumn X. So Column III gives the circumference and Column X gives thed ia me te r.I’ll just briefly mention another w ay that Series E can ‘square-the-circle’. As anexample I’ll just take a number from Line 2. If w e take, say 6.18 and make it thediameter of a circle w e can find the square w ith equal perimeter by tripling Line2 to Line 6 and counting over 2 Columns to Column XIII w hich is 4854. W hat w efind is that 6.18 × 3.1416 = 4.854 × 4. If you take 1000 from Column XII, Line 2and go dow n to Line 6, Column XIV you find 7854. By using the decimal systemw e can see that 10 × 3.1416 = 7.854 × 4. So the exact squared-circle ratio 4/pi(or 1.27324) is built into Series E. 6.18 ÷ 1.27324 = 4.854. Another examplew ould be 7.64 of Line 4. Go to Line 12 (or 4 × 3) and count over 2 Columns toColumn XII. There you find 6000. So 7.64 × 3.1416 = 6 × 4 and 7.64 ÷ 1.27324=6Let’s return to 24 for perimeter.Line I above 24 is 6 and 24 is on Line 4. 4 x 6 gives 24. The circle has just beensquared. The 2:1 w ith the same perimeter is easy: it is the inverse: 24/6 = 4.The 2:1 w ill be 4 x 8. W e should just dw ell on Line 4 for a moment. W e arelooking to square the circle and w hat better line to look to than ‘4’. ‘4’ meanssquareness. Now in the K.C. the square w ith equal perimeter to the 5.236 x10.472 perimeter is 3/4th its length w hich is 7.854 of Line 6, Column XIV. 24 isthe corner of the first 3 x 4 rectangle: Line 4, Column 3. So 4 x 6 gives 24. ThenColumns X and XI give 764 and 1236 w hich w e have seen are the goldensection of a 1 x 2 rectangle .764 + 1.236 = 2. But 7.64 is now seen to squarethe circle w hen it is the diameter of a circle and 6 is the side of a square. Arectangle that is 4 x 8 then completes the 3rd Grail Table:4 x 6 = 24 = 8 x 3.Line 4 goes on to give 5236 again, the royal cubit value and then 13708 inColumn XVI w hich is the square of 4 and a member of the pow er of 2 Series.13708 is a valuable archetype because in physics it invokes the dimensionlesscoupling constant, 1/137.036, (Fine Structure Constant) that determines thestrength for the electromagnetic interaction at about the first Bohr Radius. Thisstrength is relevant in biology because it determines the coupling strengthsamong electrons of biochemicals critical for life-structures and life processes. Forexample, the creation of ATP from oxygen, glucose and phosphate bonds, is ahigh speed operation. The brain and muscles need trillions of these phosphatebonds to transfer information w hile thinking, moving and so forth. So the speedof the bonding and transfer process is critical for optimum function. The electronspeed has to be just right if it is to function properly and is determined by theFine Structure Constant as c/137 = 2188 km/s. W e have already seen theimportance of 2.618 in the calculation of π as 6/5 x 2.618 = 3.1416. Thisappears in Series E under Column XIV, the royal cubit column, on Line 24. Onceagain ‘24’ gives a circumference. 24 hours is a circumference of time and space.But 5.236 is Unity in the King’s Chamber, or 52.36 cm. 52.36 x 2.618 = 137.08.137 is also a reasonable measure for the overall length of Chartres excludingthe Saint Piat Chapel. It is simply 5.236 x 26.18 w hich is the diameter of a circlew ith the same surface as the Chartres/Sphinx square w ith 23.193 m on a side. converted by W eb2PDFConvert.com

Note that 84.72, 68.54 and 137 all appear in Series E. In cubits they appearagain as 161.8, 130.9 and 261.8 respectively. My guess is that the builders ofChartres possessed this Series E and understood it in a w ay that I have only aglimmering of.If you look at Column XVI you see 6854 in Line 2. This is the overall w idth forthe 2:1 rectangle that measures the w hole cathedral. 84.72 is the w idth of itscousin golden rectangle w ith length 137 meters. 8472 is next to 5236 on Line 4.137 is under Column XVI. To find the square w ith the same perimeter as this all-embracing 2:1, it is just68.54 x 6 ÷ 4 = 411.24 ÷ 4 = 102.81.Now , 411.24 appears as 41124 under Column XVI on Line 12. The square w ithequal perimeter is 10281 under Column XVI on Line 3. It is w ell w orth converted by W eb2PDFConvert.com

mentioning that the South Tow er at Chartres has been measured from its baseto the point of the steeple as 102.64 meters. The difference here is 17 cm. Thisis a small enough discrepancy over ~ 337 feet, to consider seriously thepossibility that the South Tow er is also the length of the side of a square w iththe same perimeter as the commanding 137.08 x 68.54 m rectangle. Forcenturies the South Tow er has been regarded w ith special reverence. There is asimplicity and harmony that satisfies immediately. It seems very likely that theheight w as taken from the measure of a square w ith the same perimeter as theoverall 2:1 that frames the complete cathedral. And as w e know from thehuman body, this length is ¾ the height or 1.5 x its w idth of 68.54 meters. Inour anatomy this is the place of the heart, the center of the Thoracic VesicaPiscis. I think many visitors to Chartres w ould agree that the South Tow er goesstraight to the heart.Here is another fine example of the Three Grail Tables. The diameter of a circlew ith the same perimeter as the 102.81 square and 137 x 68.54 rectangle isfound on Line 1, Column XIV as 130.9 meters. So you take 41124 of ColumnXVI, Line 12 and divide it by 31416 of Line 24, Column XIV to get Line 1, ColumnXIV. This is still a play upon ‘24’ because 24 Lines separates 1309 from 31416.Meanw hile if you take 130.9 as a diameter of a circle Series E w ill find for youthe circumference and the square and 2:1 rectangle w ith the same perimeter.That shared perimeter is Line 12, Column XVI: 411.24 Given the importance of converted by W eb2PDFConvert.com

the 100 x 61.8 meter golden rectangle for measuring interior measures includingthe transepts, it is w orth noting the harmonious difference betw een 100 and130.9. It is 30.9 w hich is ½ the transepts. And 30.9 is very close to 1 second ofarc at the Earth’s equator and is also ½ of 61.8, the exact internal w idth acrossthe transepts. A quick w ay to know the 2:1 and circle w ith equal perimeter isthrough the ratio of the common arm-span and the royal cubit: 137.08 ÷ 1.0472= 130.9 so that 137.08/130.9 = 1.0472. The difference betw een 137.08 and130.9 is exactly 6.18 meters or a tenth part of the interior measure across thetransepts. Chartres is an endlessly self-interacting crucible of harmony that seemsto be feeding itself with the inner wisdom revealed by Series E.Again w e have another pattern. Line 12 gives the perimeter w hile Line 1 givesthe diameter but 2 columns back. Let’s take 809 of Column XIII w e w ill find theperimeter on Line 12 at Column XV as 25416. 500 of Line 1, Column 12 w ill havea perimeter of 15708 on Line 12 at Column XIV. And this goes on until it goesout of phase. Series E is continuously ‘squaring-the-circle’ undoubtedly becauseof the presence of the golden number. So w e can see a sort of inversionoccurring here. W hen w e are on the right in the vertical Column 3 w e have theperimeter. W hen w e go to the larger numbers in Column X w e find the diameter.But w hen w e are in the horizontal Line 1 w e have the diameter and w hen w ehead dow n to the larger numbers w e find the perimeters on Line 12.137.036 is an interesting number. If you take the SCM as a constant ratio, say4.6558 it creates a curious progression.29.433 x 4.6558 = 137.036137.036 x 4.6558 = 638.0122638.0122 x 4.6558 = 2970.45722970.4572 x 4.6558 = 13,829.8546313,829.85463 x 4.6558 = 64,38964,389 x 4.6558 = 299,7926 steps gets from a speed that is close to the Earth’s circular velocity to thespeed of light. This is ~ 4.6558 raised to the pow er of 6 or 10,185Curiously, Sirius B used to be about the Sun’s size and has now collapsed into aW hite Dw arf w ith a diameter that is 80% that of Earth w hich is about 10,185km. If w e divided the diameter of Sirius B by 4.66 w e w ould get 2188 w hich isthe speed of electrons in the First Bohr Radius or 299,792/137. A W hite Dw arf isthought to be held up from complete gravitational collapse by a ‘gas’ ofdegenerate electrons. W hat bet their speed averages to about 2188 km/s andthat determines its size. In other w ords the Fine Structure Constant is affectingthe collapse ratio of a W hite Dw arf. And the SCM is involved in establishing ap ro g re s s io n .The more one w orks these numbers the more one thinks of the phrase underthe sculpture of the Ark at Chartres: “Here things take their course. You are tow ork through the Ark.” “Archa Cederis”. According to w hat w e are seeing,“archa” must refer to the relationship betw een the circle and everything else.W hen things divide square-ness sets in. Square-ness is part and parcel ofinverse square law forces: gravity and electromagnetism. Gravity andelectromagnetism hold together the solar system, the planets and biologicalstructures. The nucleus of the atom w ith their nucleons hold together thematter. And according to Capra the speed of that matter in its confined state isaround 64,374 km/s. This number occupies a position in the little chart justshow n above. Its relationship to the constant c is the SCM: ~ 4.6558, w hich isderived from the ideal SCM, 4.666 or 1.27324/.27324.According to this number, this relationship, 4.66, the speed of light in thevacuum is being altered w hen energy (E) is bent or curved (Archa) into sometype of enclosure or self-enclosure. The E reacts to its ow n enclosure andeventually w ill feel the reaction. It w ill become conscious of the reaction w hen athreshold has been reached. The square suggests an acceleration w hich isradius dependent w ithin a field. The circle is in part a reaction to the square andvice versa. It seems that w hen they are in balance – w hen they have the sameperimeters – something focuses. W hat focuses is an energy. Something opensup. The Eye opens and sees. W hen our vision is blurry w e feel ill. So health andresolution are equal. And resolution seems to depend in part from squared-circle resolution. The underlying geometry is the basis of health. The etymologyof the English “health” goes back to heath and the heather that is found there.This in turn came from a more ancient root denoting open, unploughed country.So health w as originally associated w ith the most natural and unrestricted stateof life. This w ould be the place of the W ild Mountain. The geometry that gives converted by W eb2PDFConvert.com

form w ould have to remain in communication w ith w hat is w ild to preservehealth. The golden number and squared circle geometry are probably doing justthat and in fact this open relationship betw een w hat is wild and w hat iscontained is likely a good w ay to characterize their function.Let’s review this 24-method for squaring the circle.The w ay to create this image is to simply golden-section the Prime 2:1, ABCD (5 x10), into 3.82 (BF) and 6.18 (FC). You then center a circle on the navel, point I.You take 3.82 (BF) as its radius. You inscribe a circle w ith diameter 7.64. Its’perimeter w ill be:7.64 x 3.1415927 = 24The relationship betw een 10 and 7.64 is 1.309, so the reciprocal of 1.309 is.764. Recall that 1.618 ÷ 1.236 = 1.309. And this ratio framed the Ra-Horachtystele from the earlier post. I cannot emphasize the importance of this ratioenough. It should be emblazoned on a flag and be seen fluttering in the w indoutside churches and courts of law . It is easy to use w hole numbers to create asquare and 2:1 rectangle that are 24 on the perimeter. The square is 6 x 6 andthe 2:1 is 4 x 8. 10/8 = 1.25 (w hich is the square of 1.118), the Major 3rd inmusic; and 10/6 is 1.66666, very close to A-natural (440) (440/264 =1.66666). This paradigm is packed w ith geometrical information that gives itremarkable self-focusing properties. For the moment I should just mentionagain that I am rounding up 3.82 and 7.64 as in Series E. In fact they arebothirrationals and appear in this paradigm as 10/2.618034 = 3.81966and 10/1.309016 = 7.63932.7.63932 x 3.1416 = 23.999 ~ 24The w ay to ‘square-the-circle’ w ith the prime 5 x 10 2:1 is through the goldenproportion. An ‘irrational’ diameter times the irrational pi produces a w holenumber; in this case 24. This is an inversion. Normally w e think of pi as irrationaland operating at the limitless circumference of a circle. W e think of the diameteras being finite. But here the diameter becomes ‘irrational’ and the circumferencebecomes ’24’. 24 is a nice number. W e have used it to divide the ‘circle’ of theday for a long time. The hour has relevance in human rhythms. 24 hours setsthe Circadian rhythms in the brain w hich according to the paradigm w e havejust seen fall in the King’s Chamber: Note how the floor of the KC divides theUnity Cube into .382 and .618! This is also the level of the Great Step. converted by W eb2PDFConvert.com

The floor of the Queen’s Chamber corresponds precisely to the ForamenMagnum w hich is w here the spine plugs into the brain proper.In any case, it is the golden division w ithin the 5 x 10 rectangle that sets thescale of the 3 Tables. But it is as if the 5 x 10 is the underlying support of the ‘3Tables that bear the grail’. This w ill have consequences w hen w e look at thenanometric scale of the tubulin protein dimers (4 x 4 x 8 nanometers involume) w hich may be information-processing automata in the cell, but also thescarab beetle that undergoes a metamorphosis from w orm to w inged insect ofextraordinary beauty. This does not just happen out of thin air. There must begeometrical forms that facilitate this remarkable transformation ofform. Something is ordering it in its cocoon. Three tables bore the Grail. The Grailis the essence (in the Stone) by w hich the Phoenix is burned to ash and fromw hich it rises again as lovely as before! converted by W eb2PDFConvert.com

1.309 is acting as a key of transformation and this must have something to dow ith the relationship betw een 1.618 and 1.236: respectively w ithin a 2:1rectangle, its golden number and its golden section. 1.236 is also the w idth ofits cousin golden rectangle w ithin w hich the female Pelvic Vesica is constructed.So 1.236 in the female is the relationship betw een heart and lungs above andw omb below . W hen it is related to the golden number w e get 1.309, at theheadw ater of Column XIV of Series E. So here it is the relationship betw eenparent and child; Prime 2:1 and grail circle: 10 ÷ 7.64 = 1.309. W e can also seein Series E that these numbers are lined up through a diagonal from 1236 to1500 to 1618 to 1309. And w e can note further that 1.618 ÷ 1.5 = 1.078689,the w idth that contains the male Thoracic Vesica and is also the armspan set atthe Idea Angle of botany w hich divides a circle by the golden section (137.5° +222.5°).If I w ere asked to be as specific as possible as to w hat I think “archa” refers toin the Latin inscription at Chartres, I think I w ould say the arcs that sw ing outthe golden section and golden number w ithin a 2:1 rectangle that in turngenerate the three grail tables. The Ark that contains the root of transformationfrom an angular to circular table is the 2:1 rectangle. Through it things take their converted by W eb2PDFConvert.com

course. Concern for equality of perimeter seems to reflect a concern for theconservation of energy or spirit throughout the transformations w ithin the 3tables; the 3 phases.This image is remarkable. This beautiful insect, carefully chosen by the Egyptiansas one of the symbols of the entire opus of man’s metamorphosis, has arisenfrom a w orm through this combination of three enclosures set over the ‘navel’ ofthe prime 2:1. This 5 x 10 rectangle that generated the circle w ith circumference24, remains active in shaping the scarab. It measures its w idth if the middleclaw s w ere tucked in slightly to touch the body. But the w hole length is framedprecisely by the 4 x 8 rectangle w hich extends a little above the 5 x 10 by theratio 1.0472. The “1”, or 7.64 – circle, exactly limits the antennae. The 4 x 8(EFGH) determines the main w idth of the body minus the middle claw s. The foreclaw s are limited by the 4 x 8 for extent, but are shaped by the diagonal of theprime 5 x 10 for angle of attachment to the body! They are in a precisecomplementary relationship w ith the opposite hind claw also determined by thediagonal of the Prime 5 x 10. The Square, IJKL, cuts through the eyes and marksdetails of the rear legs/claw s. The precision of these interactive forms can onlybe expected in view of the precision of the scarab’s natural beauty.But the key to this entire image is the relationship between the Circle with acircumference of 24 and the Prime 5 x 10 that created it. 10/7.64 = 1.309 =1.618/1.236. This then allow s the other 2 tables w ith perimeters of 24 to begenerated. They are all centered upon the nav el of the 5 x 10, or 6.18 from thebase DC. There is the distinct feeling that the golden section is at work in theprocess of metamorphosis that transforms the worm into a winged insect. It is thefeeling that the golden proportion is the “Stone” itself, the essence most pure,born in the midst of the activity of the 2:1 rectangle. The entire 5 x 10 seems tofocus itself at the navel as if it w ere a new umbilical link to the 3 new GrailTables. The volatile urge w ithin the w orm aw akens and flow s through the portalof that umbilical link as if magically. The 3 Tables that bear the grail limitthemselves as they distribute the extrusion of energy among the three sharedformats: square, circle, 2:1 rectangle. The 2:1 is the key to the limits andfunction of the main body of the insect. But the circle w ith equal perimeter converted by W eb2PDFConvert.com

carefully limits the antenna and the rear of the body.The squaring-of-the-circle is the geometrical means by w hich this w holedistribution of vital energy is facilitated and the golden section is the w ay thecircle-is-squared. Through this geometry, w hat w as in the w orm is conserved.Through the 3 tables the geometry can blossom, sharing the characteristics ofall three tables as w ell as the underlying Prime 2:1. Looked at this w ay, there isa striking parallel betw een the Egyptian symbolism of the scarab “Khepera” andthe Grail. Automatically, then, w e have to conclude that there is an even olderparallel betw een the Eye of Horus and the Grail. The Eye of Horus at one pointin the Pyramid Texts w as said to ‘go up from the head of Seth’. If it takes 3tables to bear the ‘grail’, one must empathize w ith the Egyptian tendency togive one phenomenon many ‘names’. Each name refers to different aspects ofits nature. The Egyptians w ere confident of unity and appeared not to bereductionists. I think w e have projected our ow n w estern reductionism on acivilization that w e did not understand. Their spiritual preoccupation w as w iththe final metamorphosis into pure spirit. This occurs w hen the plurality of namesreturns to the unity of spirit. The golden proportion and the squaring of thecircle seem to be the means by w hich this metamorphosis takes place.This paradigm also lends itself to a reinterpretation of the ‘brazen serpent’.There is the feeling that the 3 grail tables, generated through the goldensection of a prime 2:1 rectangle, is the means by w hich the serpent is raised inthe w ilderness. The w ilderness does not simply mean ‘sin’. It refers to the W ildMountain of the Grail romances; untamed forces; the chaos of the alchemist thatprovides the extra energy for spiritual transformation once it has caught itself,like the uroboros, in its ow n ‘grail vessel’.It is w orth looking at other examples of w here these 3 grail tables supported bythe navel of a prime 2:1 rectangle, seem to be functioning. One overridingfeature that seems to be common to all examples is the capacity to self-focusthe diverse energies supported by the four tables in response to thesurrounding environment. Obviously this self-focusing capacity must start small:at the microscopic scale. So I’ll show the tubulin protein ‘dimer’ first, based ondraw ings now familiar to many. According to Stuart Hameroff, w ho initiated theinterest in the role of microtubules in the phenomenon of consciousness, thesedraw ings are really quite schematic, ‘cartoons’ as he now calls them. But I w illapply them to the ideal geometry anyw ay in order to illustrate the principle.The w orld of tubulin protein is a science unto itself because they are at theborder betw een quantum and relativistic scales. They straddle and ‘partake’ ofboth behaviors – probably by alternation like most phenomena w e know of. To converted by W eb2PDFConvert.com

the human mind this alternation can appear as contradictory. Being at theborder betw een quantum and classical behaviors, they in a sense, appear toembody the ‘gap’ in our know ledge of how the mathematical descriptions of thetw o behaviors unite. Because Stuart Hameroff and Roger Penrose havepersisted in their determination to explain the role played by microtubules in thephysiology and physics of consciousness – in an effort to unify mind and brainmatter – it is w orth at least glancing at an image of one subunit know n to be adouble sphere occupying a tiny space that is 4 x 8 x 4 nanometers. Becausethey assemble into tubes consisting of 13 columns, they appear to either sideas 2:1 constructions. They contain a hydrophobic pocket that houses a single,relatively free electron that moves back and forth betw een the alpha and betaspheres – a bit like a built-in sw itch! Hameroff now tells us that thesehydrophobic pockets may be located in various parts of the double sphere. Thisschematic diagram here, then, is a sort of geometrical ‘w hat if?’, w here thegeometry can be seen as a bridge, a continuity that links the basic dimersubunit of cytoskeletal microtubules all the w ay to the new born human infant.The geometry might play a role in the internal self-organization of all early one-celled creatures w hich are capable of learning and reacting in accordance w iththat learned state to the changing environment that engulfs them. According tothis model, the golden section gets the ball rolling and may w ell be the meansby w hich the learning and adapting takes place, making of a living thingsomething much more than just a crystal.Note that ordered w ater, that behaves like crystal, is surrounding the tubes andis contained within the tubes’ cores, but the hydrophobic pocket has no w ater init at all. Its electrostatic properties have expelled w ater entirely from the pocketw here one single electron is housed. The change in dipole state of the dimerresults in a change in position of the electron. This is accompanied by a changein shape or conformation of the dimer so that it appears to open and close ornod at its ‘mouth’. In the image above I have show n it in transition betw een thetw o positions and am offering a geometrical solution as to how it distributes itsself-organizing mass during the conformational shifting. In its open state it is 4 x8. In its closed state it may go dow n to a shared distribution betw een hexagonand square w ith equal perimeter – meaning 24 nm. I am also suggesting thatthe hydrophobic pocket may be 1.888 nm w hich is the overlap of both goldensections taken up and dow n, so that 8 ÷ 4.236 = 1.888. 4.236 is the goldennumber cubed, w hich invokes a volume and enclosure of a high order of harmony.This might play a role in expelling the w ater from the pocket. This is a zone ofoptimum stability and harmony that keeps the slightly larger (56,000 Dalton)Alpha sphere in contact w ith the slightly smaller (54,500 Dalton) Beta sphere. Ishould also note again that each tube consists of 13 columns of dimers (slightlyskew ed or staggered) but microtubules assemble in groups of 9, yet anotherexample of an Ennead. Since MT’s are involved in separating self-replicated DNAduring mitosis, this Ennead is quite fundamental. It also appears in the tail pieceof the sperm and so is involved w ith a sort of w hip-like and rotationallocomotion that guides the sperm in its journey tow ard fertilization. 9 canhandle a fundamental acceleration/deceleration cycle generated by 3 x 3. This ishighly creative and interactive.To help picture the scale of operation here, note that 4 nm is 1/100 thew avelength of violet light and 8 nm is about 1/100 the w avelength of infrared.Each dimer contains about 900 amino acids; 450 per monosphere, alreadydisplaying the fundamental properties of 2:1. The conformational shifting of thedimers w hen assembled into tubes is important because it seems to correspondto different states of electrical polarization. In this w ay they may w ell becapable of processing electrical information and conducting that informationw ithin the cell and possibly to the synapses. But the tubes are also capable ofbecoming insulated by ordered w ater that may allow their hollow cores to act asw ave guidance systems or super-radiance devices w hereby quantum coherencebecomes a possibility. W ith 9 also involved w ith the 13 columns w e have arather complete picture of self-regulating, self-organization and informationprocessing. Recall that the golden number names itself in Series E at Column 13,Line 2. I w on’t go any further into the mathematics of the quantumw avefunction here (see Roger Penrose for clear explanations in “Shadow s ofthe Mind”, 1994)) and how MT’s may be involved w ith all their golden proportionrelations, but it is w orth mentioning that for decades (after 1971?) StuartHameroff believed that anesthetics w ere w orking by seeping the chemical intothe hydrophobic pockets of MT dimers, binding up the free electron and shuttingoff consciousness. And this is how the idea got going. There is so much more tosay about the behavior of microtubules in the cytoplasm of the cell. There is thecell’s sol/gel cycle involving calcium. There is a metabolic input. There is thenotion of feedback loops that w ould set up an amplification w ave needed togenerate the quantum w avefunction but also to contribute to the collapse of converted by W eb2PDFConvert.com

the w avefunction that causes matter to ‘choose’ a particular state over an arrayof possible states described by probability distributions. W hat I w anted to dohere w as to show the possible role of geometry even at this tiny scale, inguiding the morphology w ithin w hich quantum coherence might be able to thrivethereby allow ing mind and brain to cyclically act as ‘one’ w hile yet retaining theprinciple of difference through alternation, dipole behavior, and of course theunderlying exclusion principle of Pauli. I sometimes feel that the golden numberretains the secret key that allow s a stream of consciousness to be maintainedbecause it divides things unequally. This staggered asymmetry – yet harmony –allow s w hat is separated to be joined in a mobius like action that feeds backinto itself. There is no learning like self-learning. But self-learning is also thesuspense of self-transformation – or at least the potential for it. Just plainproliferation does not mean relatedness. The golden proportion and its familyallow s continuous relationships among parts w hereby proportion becomes thesecret ‘glue’ of the conscious present. As I have said repeatedly, the secretasymmetrical, but harmonious, signature of the golden proportion is .618.Now let’s look at a similar shape but at a larger scale: same geometry. This isthe very familiar human fetus. Though much larger in size it still conforms to thesame shape asthe dimers and is also prone to ‘nodding’. Its height is w holly contained w ithinthe ‘8’ rectangle (in blue here), but its w idth including large forehead and low erdorsal region, fill out the original w idth of the Prime ‘5 x 10’ rectangle: and onceagain, w ith amazing precision! The arms, ears, eyes and heart are containedprecisely in the area corresponding to the hydrophobic pocket of the dimer as ifthis slot w hich is 8/4.236 or simply 1 over the golden number cubed, w ere ofparticular importance. Here the heart is regulated perhaps. All the needs of allgrow ing cells w ill have to be supplied by the heart w hich distributes everythingthrough the blood. In this pocket a pressure differential is established andregulated w hich is one reason w hy electron ‘speed’ in the First Bohr Radius is socrucial. It is part of the efficiency w ith w hich oxygen and carbon dioxide aremanaged by hemoglobin and the iron atom that is at the heart of hemoglobin.Next w e w ill look at the same set of tables as they apply to the new born infantafter 9 months gestation. First of all note that crow n to knees fits in the 8×4.But the feet take it ‘back’ to the 10 × 5 (ABCD). The baby’s w idth, excluding thearms is exactly ½ the w idth of the 4 × 8, so ‘2’. But the height of the head isexactly ½ the w idth or ¼ the length of the 5 × 10! So the head is 1 × 1.25 orqr/ru. The throat of the baby, w ho does not have much of a neck, correspondsto the center of the thorax in the adult.Now note how the heart occupies the upper half of the ‘hydrophobic pocket’. Inthe dimer the upper half w ould be in the Alpha sphere w hich is slightly largerthan the Beta sphere and carries an excess of negative charge. The head isw hat develops most prominently first in the fetus and is proportionally large. So converted by W eb2PDFConvert.com

presumably the head is carrying a higher charge than the caudal pole. It w ouldappear to contain the seed from w hich all other grow th extrudes. Here theheart is lodged betw een the golden section of the 5 × 10,the center of the entire complex of smaller grail tables and the golden section ofthe 4 x 8, indicated by mn. The infant’s navel is the center of the 5 × 10 w herethe diagonals cross and the genitalia are at the low er point of golden section ofthe 5 ×10. To summarize, here w e see a real co-operation betw een the 4 x 8rectangle and 5 × 10 rectangle. Particularly striking is the head that has itsheight determined by the 5 × 10 and its w idth determined by the 4 × 8. Theprocess of dimidiation of the 2:1 rectangles seems to be in evidence all the w ayto the adult. Note that the heart seems to be angled by the diagonal EG, w hichis upper right to low er left of the 4 × 8 rectangle. The tw o hands appear to be‘plucking’ the invisible diagonals of the 4 × 8 as if they w ere musical strings –the strings that make the baby w ant to sing.Next I have show n the morphological similarity betw een a globalmagnetohydrodynamic simulation of the Earth’s Magnetosphere and the humaneye. I have placed the same tables in the upper half of a 2:1/hexagonal imagethat embraces the w hole eye right to the cornea. The ‘hydrophobic’ pocket fallson the anterior half of the lens. The lens complex w ith cornea and so forthdistributes its functions right through the grail complex as if the self-focusingproperties of the tables w ere their most important feature. converted by W eb2PDFConvert.com

W hat is important about this morphological comparison is the w ay the Earth isacting similarly to the lens of the human eye. W hen the geometry is added itseems w e are looking at the means by w hich energy has been gathered up, orgathers itself up, and self-focuses through the ‘grail tables’. Comparable shapesresult w ithin differences of density and medium. But basic ingredients remainthe same. Clearly for the medium to self-focus, the grail tables must build up aninner pressure: some of w hich is electrostatic. This then resolves the materialinto an ordered state w hich in the case of the eye permits perception.The Magnetosphere looks different w hen examined from different points of viewand in different w ays. One rather extraordinary cross-section stronglyresembles a lizard. The Earth seems to be acting like an electromagnet in theposition of the nostrils above the mouth. Snakes and presumably lizards are95% olfactory in character, w hich is to say their cerebral cortical development is95% olfactory derived. A human is 80% visual. An eagle is 95% visual! So it isfascinating to see a common geometry at both ends of the sensory spectrum. converted by W eb2PDFConvert.com

There is the sense of electromagnetic self-organization that involvesdecussation of electric current that w eaves together these forms includingvolume. Once a vessel has formed around the energy that has crossed over andcurved back upon itself, it is then able to build up. As it builds up consciousnessbecomes increasingly dominant as if it w ere the reaction to both internal andexternal stimuli. In this image the Earth acts like a seed around w hich lines offorce gather. The creature alw ays seems to have been formed around this littleseed as if consciousness itself w as vastly greater than the seed through w hichit is threaded!In the image below one can see that the decussation of optic and olfactory isstacked on top of each other at the same site. It is marked by EF w hich is thegolden section division of the Prime 2:1, ABCD. I have put in the ‘7.64’ circle topoint out that it seems to create the boundary for the visual re-association areaof the cerebral cortex. The ratio that dominates this boundary is once again1.309 or 1.618/1.236.Note that the angle separating the eyes is the same angle found in theSynodical Month, namely 29.1°. This angle runs to the back of the head. So in29.53 days from New Moon to New Moon, the Earth and Moon together travelthrough 29.1°. And from the Sidereal Month (27.3217 days) to the SynodicalMonth (29.53066 days), the Moon travels 29.1° in 2.2 days. converted by W eb2PDFConvert.com

Here in a slice through the brain at the level of the optic chiasm, w e see the29.1° recapitulated again.W ith a feeling for the morphological shape of the magnetosphere, I w ould liketo show the ‘teardrop’ shape that is familiar to many as an analogy to a ratherintriguing image of Hour Ten of w hat is in the Duat of the Egyptians. W e see anunmistakable portrayal of a w ell-know n breathing technique practiced atadvanced stages of ‘spiritual yoga’ w here the intention has become thereconstitution of the Eye of Horus. The technique involves raising the kundaliniby alternating breathing through the nostrils. The finger is used to pinch onenostril w hile one cycle is performed by the other. W hat happens is that theelectromagnetic pathw ays stimulated by the very primordial olfactorydecussation mechanism at the W hite Anterior Commissure, eventually w ithrespiration and heart rate registered in the pons and medulla oblongata,stimulate the spine and provoke the converted by W eb2PDFConvert.com

kundalini in the sacrum. This raises the ‘serpent in the w ilderness’ – suggestingthere can be a constellation of chaotic psycho-spiritual forces w hich makesavailable a large amount of energy. This then reaches an apotheosis in therealm of the ka w hereby the Eye of Horus self-organizes around the mysticalmarriage of Horus and Isis eventually resulting in spirit-state or spirit-form.W hat is striking here is that the tw o figures are not seated on anythingconcrete. There is no question that the figure on the right is using the righthand and arm to ‘pinch’ one nostril w hile the figure on the left is using the leftarm and hand to pinch the opposite nostril. There are tw o serpents for the tw ohalves of the spine. I placed the teardrop-shaped image of the magnetospherebelow it to suggest how this great form has been recapitulated in a humanendeavor on earth w ith a certain instinctual self-know ledge. W ith this breathingtechnique, it is not smell that matters but rather the meeting of various forcesthat converge electromagnetically to stimulate the kundalini. This undoubtedlyinvolves heart rate and chemoreceptors on the Aortic Arch w hich communicateinformation back to the Medulla Oblongata in the low er brainstem. This in turnw ill influence the spinal column and probably the state of the cerebrospinal fluidthat bathes the brain and runs dow n to the sacrum creating a cranio-sacralpulse. CSF is formed in choroid plexi that receive blood and then remove largepercentages of material from the blood, dripping a clear, colorless fluid w ith alow er specific gravity into the four ventricles of the brain. CSF is renew edaround the brain about 4 times daily, w hich is about the same as the number oftides in a day.The alternating breathing balances, amplifies and stimulates the completecranio-sacral complex. It is as if it acts upon a hydraulic pump that primes thew ell of the sacrum, draw ing that sacred fire-w ater up the spine in a w ave thatw ill reach the King’s Chamber in the head and reconstitute the eye.Possibly one of the most beautiful, startling, pure, compelling, inspiring anddirect expressions of this intention of the Egyptian way can be found inUtterance 524 of the Pyramid Texts (Faulkner translation is just fine for this one)from PT 1233 to PT 1243. Note also that the endeavor appears to be reunitingthe Red and W hite Crow ns w hich in various texts are referred to directly as theEye of Horus. They mean of course its function and its purpose w ithin a humanlife; not its ornamentation. Utterance 524 is called “a text concerning the Eye ofHorus”. It is a great one. It is complete. It is startling and it helps to understandthe meaning of the image above. It strikes me that the sphere you see converted by W eb2PDFConvert.com

materializing atop the tw o serpents is probably the same sphere the imagemaker sculpted into the Ark at Chartres. It is the same endeavor, the samepurpose, the same transpersonal inspiration:“I am he w ho prevents the gods from becoming w eary in seeking the Eye ofHorus; I searched for it in Pe, I found it in On [Heliopolis], I took it from the headof Seth in that place w here they fought [meaning Horus and Seth]. O Horus,stretch out your arm to me; O Horus, take your Eye; may it go forth to you, mayit go forth to you w hen I come to you. May the Eye of Horus come to you w ithme, upon me forever.” (PT 1242-43). The analogy betw een this and the story ofDavid and Goliath is striking. David takes Goliath’s head after slaying him byhitting him w ith a single stone in the middle of the forehead. Goliath is veryclose to the story of Seth. Seth is the material force that takes the Eye andimprisons it. The candidate for spiritual metamorphosis must retrieve the Eye. InEgypt it w as found on Seth’s head and must be returned to Atum – the Lord ofthe Horizon. The King’s w ork is not merely for himself; it is for the totality, godsincluded. W e can recall that π is the ‘horizon’ of a circle the diameter of w hich is‘1’. The King’s Chamber in meters has a perimeter of π x 10 or 3.1416 x 10 =31.416 m. One imagines that they intended it to be an inner gate or portal (sba)that opens the road or w ay to Him of the Horizon, Atum, the original, eternal.Entrance to the Netherw orld and the Golden SectionW ith this in mind take a look at the famous ceiling of Seti I of the XIXth Dynastyin the Valley of the Kings. This ceiling image portrays the entrance to theNetherw orld. It is very obviously designed. All I have done is highlight it.ABCD is an exact 2:1 rectangle. It is the same as the ceiling of the King’sChamber. This 2:1 captures a rotation of the heavens around a celestial pole thatshow s the summit of the circumpolar North Stars such as the Big Dipper, hereshow n as the Bull of Heaven chained or tethered like Seth to the ‘Thigh Bone ofthe Horus Eye’, guarded by the pregnant Hippo, Isis, w ith Draco? (AlphaDraconis?) (or Sobk perhaps?) surmounting her to join the rotation. Thestanding Osiris King w ith up-raised arm connecting sky to ground, is pointing tothe exact golden section of the 2:1 rectangle – the portal to heaven. The Bull isexactly ½ the w idth (AD or BC) of the 2:1 ABCD, implying that it has a value hereof 1.309 compared to the Thigh of the Horus Eye held by the Hippo w ith value‘1’. The height of the standing King w ith up-raised arm is also 1.309. In thiscontext the full length of the opening is 5.236 and its w idth is 2.618. InUtterance 524 just mentioned at PT 1238-39 it is stated:“Atum summons me to the sky, and I take the Eye of Horus to him. I am the sonof Khnum [Ram-headed Divine Potter], and there is no evil w hich I have done.Long may this w ord be in your sight, O Re; hear it, O Bull of the Ennead, openup my road, make my seat spacious at the head of the gods, that I may takethe Eye of Horus to him and that I may cause to reknit for him that w hich w entforth from his head.” (PT 1238-38, p196-7 Faulkner).Note, also that w hen the thigh-bone or thigh of the Horus Eye is taken as ‘1’w hich it is w hen enumerated in the W adjet Eye, it divides Unity also by thegolden section so that the length overall equals 5.236 w hich is the same as thearchetypal Pyramid Profile of the Great Pyramid. The top of the mnj.t or ThighBone is marked by the hands of Isis and the outermost curve of her pregnantbelly. The total Eye is 64. It is then dismembered by Seth. W hen it isreconstituted it adds up to 63, not 64. converted by W eb2PDFConvert.com

Unity remains the thigh bone of the Eye of Horus also know n as ‘qd’ and “mnj.t”w ith a value of “1”. In the Seti I ceiling Horus mounts to the sky on the “thighbone” itself, w ith the Bull supported by his harpoon and tethered by the mnj.t –the seed or essence of the Eye of Horus. In some instances the “thigh bone” isreferred to as a Mooring Post. In the Pyramid Texts the Mooring Post refersexplicitly to Isis or Nephthys. Isis w as associated in turn w ith Sothis or thebright star Sirius. The suggestion is that the Egyptians w ere treating Sirius assome sort of celestial Mooring Post, in turn associated w ith the axis of rotationof the heavens.It is this essence that has everything to do w ith the Grail – the essence of thestone by w hich the Phoenix purifies and renew s itself and cannot die. This is theinspiration that caught the minds and souls of the Templars and formerly, theentire Egyptian Civilization. W hen the essence is know n; w hen the keys to thekingdom have been recovered then ‘things take their course”. You w ork throughthe Ark w hich carries the Eye of Horus. It appears that the King’s Chamber w asdesigned to act as just such a portal: converted by W eb2PDFConvert.com

Read Full Post »Squaring the Circle: An Ancient Legacy(P10)Posted in Human Harmonics on April 22, 2010 | Leave a C omment »SQUARING THE CIRCLE: An Ancient LegacyIn the previous post I attempted to show some critical and diverse examplesw hereby squared-circle relations seem to be regulating aspects of Nature thathave influenced the very ability for life-forms to evolve, flourish and enjoy thecopious fruits of conscious experience. There appears to be a consistent and all-encompassing geometry that even extends dow n into the subatomic w orld. Thegolden number and its family seems to act as the ‘Royal Family’ of that all-embracing Net of Life or web of circumstances w ithin w hich spirit, the essence,the pure heart of the ‘stone’ is caught and is able to grow . The Egyptians andthe builders of Chartres seem to have taken this All-embracing net of life furtherand through know ledgeable architecture accumulated energies – the serpentpow er – to induce a qualitative leap in being, symbolized by the scarabKhepera. It seems that an underlying geometry must be capable of such ametamorphosis. Something must hold the Eye together. One factor that w eknow is alw ays involved is the arc of a circle. Most especially w e have seen thatarcs from opposite corners of a 2:1 Table w ill divide its diagonal by the goldensection. Before w e look at another method for squaring-the-circle, that I call the“24-method”, let’s go back to Chartres for a moment and ponder a smallsculpture on a pillar diagonal from the sculpture of Moses at the north-w estentrance, the Gate of the Initiates as it has been called. This sculpture isremarkable in more than one w ay. It is important to read the Old Testamentcarefully in order to appreciate this sculpture. converted by W eb2PDFConvert.com

The sculpture at Chartres depicts the Ark of the Covenant being pulled by a pairof oxen, not on a cart as stated in the bible, but affixed to wheels. It is notproportioned as stated in the Bible nor as others have reported. It seems to be1 x 3 w hen view ed from the side: the same proportions as the w hole ofSolomon’s Temple (20 x 60 cubits). Moreover, it has tw o Tables of the Laww ithin it and something else that is not mentioned in the Bible: it has a sphere ofsome kind to the right of the Tables (chipped by vandals in the sculpture).Now , the Tables w ere supposedly w ritten on both sides – law s composed byGod and w ritten by his own finger and delivered to Moses – alone. ‘Both’ sidesprobably means the Ten Commandments for the people, on one side, andesoteric, cabalistic mathematical law s for temple builders w ritten on the other converted by W eb2PDFConvert.com

side. Temples w ere the science of that era, just as they w ere in Egypt, India,Cambodia, Mexico, Greece, Rome and the Gothic period in France. The spheremight be the Earth, the Sun, the Moon, The Egyptian “Aten” or any circular body,including Plato’s Eternal Living Being w ho, according to the Timaeus, had manmade in his image or likeness through the means of a sphere. This w asaccomplished by w ay of the human head. The sphere could represent theHebrew , Yahw eh, but it could just as easily represent the Egyptian Eye of Horusor the ‘Spirit-in-the-Dndrw -Bark’ mentioned in the Pyramid Texts (e.g. PT 1637).Generally speaking, it w ould seem that the sphere points to the head in somew ay: the origin, the means, the w ay man is made in the likeness of ‘God’, thecosmos. But it also could just as easily refer to the principle of a circle sw ung bya compass. A circle in a sense refers to the w hole, totality, the All, Spirit. But it isalso a first enclosure; the first Grail Table. The perimeter of the King’s Chamberis the same as a circle w ith diameter 10 meters. Circles are intuitive, natural,instinctive, mysterious. The square is analytical, and is a play of the opposites.It is strategic and differentiated. It uses reason and sets dow n rules. The 2:1 isrevelation; the Alpha and the Omega.This head is Atum-Ra, Ra-Horachty and also “man”. The Sphinx reunites andjoins above and below ; around and w ithin; matter and spirit; square and circle;space and time. One also thinks of the head of Adam. In Egypt, like Genesis, itw as the Ram-headed Khnum w ho w as said to fashion both man and his ka on aPotter’s W heel. This is in imitation of the Earth spinning on its axis, the meansby w hich life processes are ‘sculpted’ by cycles of time and space. The Sphinxfaces east w here everything rises. W hat is on the Earth’s surface is sculpted byeverything that comes from the horizon – including the mysterious “sty” or‘perfume’ of the Eye of Horus. This perfume is caught by the vase of life, theGrail. In Egypt the first act of catching the perfume, the celestial w aters, w asperformed by Nut; and in a sense the last entity to become ‘pregnant’ w ith theaccomplished spirit of the ‘king’, w as also Nut, Saint Anne of the NewTestament: the Black Virgin w ho contains all the stars – mysteriously nourishingtheir fires w ith her eternal w omb. converted by W eb2PDFConvert.com

Note below the similarity betw een various forms and the vase that sits on topof Nut’s head. Of particular interest is the shape of the scarab’s dungball. Oneimagines that the Egyptians noted these forms in detail as they formulated theirunique style of hieroglyphic w riting. converted by W eb2PDFConvert.com

The head is the perfect container, the vase that transforms and regulateseverything else. In the Ptolemaic Period the Egyptians depicted the head of Raw ith a stylized scarab to symbolize the transformational gift of the head. Theears are like the handles of a vase.The image of Ra’s head is quite informative indicating that the interactionbetw een Greek imagination and traditional Egyptian principles w as at timessubtle. I have show n in the sutures of the skull and scarab similar geometricalratios as employed in this interesting head and triadic crow n. If the jaw to baseof crow n is ‘1’, from jaw to stylized scarab or brain cavity is .618. .382 includesthe stylized eyes of the scarab. The crow n of Thrice-Greatest Hermes rises upfrom betw een the eyes to complete an underlying 2:1 construction. In the skulland scarab the sutures seem to bridge .618 to .714. In the sba converted by W eb2PDFConvert.com

gate construction .714 measures the height of the pylons w ithin a 2:1construction, upon w hich the lintel sits. So .714 represents the opening of thegate, the height, 31.416/44.The head is sculpted by the w orld and in turn ‘sculpts’ the w orld. Its pow er andits influence are in evidence even at an early age. Personally, I rememberalmost the instant w hen the ‘head’ w oke up in my mind – as if it w ere a miracle.I w as hitch hiking w ith my camera from Big Sur to Yosemite, California. It w asApril and I had just seen Jacques Cousteau speak at Berkeley University. Hew as exhorting the crow d to fight on behalf of Nature and the Earth at exactlythe moment w hen w arplanes w ere carpet bombing Cambodia in one of thedarkest advances of the Viet Nam w ar. I had been picked up by a hyperindividual w ho had just gotten back from Viet Nam. He w as headed back toOregon. He could not stop his out-pouring of emotion that w as bursting from aperspective shift that had finally reached a threshold. He declared the w holew ar a complete w aste. A total tragedy. He said he thought he had served as hissolemn duty to the United States. But now that he had seen the extent of thedamage, how misguided it w as; w hat the w ar had done to people, flora, faunaand social order, he felt he now had to do something positive to compensatethe insanity. So he w as going back to Oregon to be a doctor. After many hoursunder a boiling sun I w as picked up on a dusty stretch of road by a pick-uptruck.This is the head of a 12–year old boy I encountered in the back of the pick-uptruck w hen I w as making my w ay through an endless stretch of grape fields. Hew as a farm w orker and had no rights. W hat amazed me during the ride w ashow life in California – the hot sun, w icked pesticides that had scarred his arms,long hours of labor, picking grapes – had sculpted his face, his head and theemotions that clutched his heart. I have neverforgotten that boy – his head – the dignity granted by God and promised byJefferson’s Declaration of Independence, but betrayed by one’s fellow humans.Tw elve years old and the Potter’s W heel w as already leaving its marks severely.Man has an enormous influence on w hat life sculpts so long as w e never forgetthe ‘clay’ that turns upon that w heel. This Mexican boy is a continuous reminderto me that each head is a child of the ‘eternal living one’ and is endow ed by lifew ith certain inalienable rights. The Sphinx echoes the heads of the ages. Thereis no head that the Sphinx does not reflect. It is absolutely fascinating thatsome Grail Romances depict the Grail itself as a head. Sometimes the head actsas an oracle. The Templars themselves ostensibly w orshipped a head called theBaphomet. Some have interpreted the ‘Baphomet’ as ‘Father of Understanding”.W hen you examine the skull, you w onder immediately w hether ‘understanding’w ould happen at all w ithout the golden section. The golden section is a dynamicprocess: a relationship. It is not a thing, like a crystal. It breathes w ith infinity. Itconducts and radiates the cosmic fire. Understanding rests on the cosmos; notmerely shape, but also a dimensionless w ell of potential energy. Note how thegolden section of the brain itself divides right at the Pituitary Cavity sunk in thesphenoid bone. The carotid artery bends around the Pituitary and then radiatesinto anterior and posterior cerebral arteries like branches of a tree. The w holecomposite brain/skull structure seems to be centered or rooted in that PituitaryC a vity.The Egyptian Nut, w ho carries the first vase that catches the w ell of potential converted by W eb2PDFConvert.com

energy dispensed in quantum ‘bits’ by the recondite vacuum, w as also calledthe Great W ell in the Pyramid Texts.Utterance 368 is a protection text that invokes first and last principles. It is aremarkable text but requires some background information first beforepresenting it in full. How ever, it is best to at least introduce a part of it so thatsome images start to seep in:“Your mother Nut has spread herself over you in her name of St-pt, she hascaused you to be a god to your foe in your name of ‘God’, she w ill protect you inher name of ‘Great W ell’, for you are the greatest of her children. Geb isgracious to you; he has loved you and protected you, he has given you yourhead, he has caused Thoth to reassemble you so that w hat w as on you comesto an end.” (PT 638-639)One can see that the notion of ‘the son of God’ is at least as ancient as thePyramid Texts and refers to a universal principle that involves a metamorphosisin a context of critical protection. One imagines the Pyramids w ere built to offerthat protection. Geb w as Nut’s male counterpart and w as associated w ith theEarth that had become fertile w ith seed. It is Geb in this instance w ho gives thecandidate his head. Thoth (Greek, Hermes) reassembles the w hole being, ananalogy to the reconstitution of the Phoenix and the Eye of Horus. This bringsan end to the ‘ash’ stage, the apparent death phase. So Thoth and the headare associated w ith the means by w hich the ‘King’ is reconstituted. This ofcourse refers to the ka or double, the assumption being that it lives on after thedemise of the physical form.Here you see the morphological similarity among inverted head, 12-day embryo,the eye and the 26-day embryo. The shape of the embryo is never lost. Itremains in the brain. The similarity betw een the eye and the 12-day embryo isparticularly striking. The embryonic endoderm + ectoderm is acting like the lens ofthe eye. And the primitive yolk sac is acting like the vitreous body of the eye.This strongly suggests that w ithin a spherical container electromagnetic forcesself-focus in a w ay that organizes information in biological material. Thatinformation is able to self-replicate as a living structure grow s. In the brainw hich w e are looking at inverted, the region of the Pituitary, W hite Anterior converted by W eb2PDFConvert.com

Commissure, hypothalamus, Third Ventricle, median eminence, optic chiasm,suprachiasmatic nucleus, mamillary bodies, etc. are involved in that central self-focusing region – acting as a sort of command central for many processes of thew hole body. W ithin the Egyptian Mysteries, the Eye of Horus played a similarrole for the soul, the ka and the spirit of the candidate. Its reconstitution w asthe goal of the Egyptian Way.Now under the sculpture of the Ark at Chartres there is a Latin inscription,presumably for initiates, since it is at the North-w est Gate. It is on the righthand side (south) as you mount the porch steps. I had to find a ladder to get uphigh enough to photograph it. So you must look for it or you w ill miss it.“Archa Cederis. Hic Amittitur. Archa Cederis”. According to Eugene Canseliet, thistranslates in the follow ing manner:“You are to w ork through the Ark. Here things take their course. You are tow ork through the Ark”.In the image below you can see the letters of the Latin clearly. But w ho amongus has thought of ‘working through the Ark’? And no mention has ever beenmade of placing a sphere in the Ark. Head, arcs, circles that become squares,orbits that maintain living things … the rotundity of the cosmos … a resonancechamber that transmutes all the motions there are to be … a compass thatsw ings out arcs and imitates circles…The Ark of the Covenant converted by W eb2PDFConvert.com

“You are to w ork through the ark”. Immediately one imagines there is anintended play upon the w ord Archa. One meaning is the arc of a circle, the role converted by W eb2PDFConvert.com

played by a compass in geometry. After all, it w as 1195-1220. Plato’s influencew as profound at Chartres as w as Pythagoras w ho supposedly spent 22 yearsin Egypt. The secret of the circle is part spatial and part temporal. The circle alsorefers to the secret of cycles and hence the cycle of the Phoenix. But the Arkw as also associated w ith the Oracle by w hich ‘God’ made know n his w ill.Therefore it w as associated w ith revelation, dreams, mediumism, holism.The Ark of the Covenant w as ostensibly kept inside the 20 x 20 x 20 cubit Holyof Holies at the end of a 20 x 40 cubit 2:1 Table in Solomon’s Temple also calledthe “Oracle”, the crystal ball of w holeness. Note the archetypal relationshipbetw een a Cube and the Sphere it houses: it is .5236 from Series E, the sameas the Royal Cubit. The cubit depends from π. It is the result of dividing the circleby 6. 3.1416/6 = .5236. The w idth of the King’s Chamber w as 5.236 meters. Thecubit as 1/6th the circumference of a circle – in the case of the King’s Chamber –depends upon a diameter of exactly one meter. This meter is 39.37 inches.Since this is the meter used today w e must conclude that the French elected togo w ith the Egyptian meter w hen in the 18th and 19th centuries w e could notfind agreement on the length of the meter. The Earth has too many variations inits surface. In those days there w ere no satellites.The w hole Temple of Solomon is 20 x 60 cubits; measures w e are now familiarw ith. The King’s Chamber has a perimeter equal to the length of the Temple ofSolomon, if the same cubit w as employed. This perimeter is 60 cubits or 31.416meters. And this 31.416 meters is the difference betw een square and circle inthe Great Pyramid and so represents the proportion of the ‘squared-circle-modulus’ (SCM) or 1/4.66 of the Pyramid Height of 280 cubits.Like the King’s Chamber, this Cube w as supposedly completely empty except forthe Ark. The Ark w as called variously, the ark of the testimony (e.g. Exodus25:22); the ark of God; the ark of the covenant. In Kings 8:1, it is called ‘the arkof the covenant of the Lord’. In Kings 8:4 it is called ‘the ark of the Lord”. InKings 8:6 it says it w as placed in “his place”, “into the oracle of the house, tothe most holy place…” It is of interest to note that in Kings 8:9, it is stated that“There w as nothing in the ark save the tw o tables of stone, w hich Moses putthere at Horeb, w hen the Lord made a covenant w ith the children of Israel,w hen they came out of the land of Egypt”.Another passage from Charpentier has haunted me since 1985 – sometimes thesign of an eternal clue; one that does not die even in the abyss of doubt. ForCharpentier the Ark carried much more than just the Ten Commandments. Hebelieves it w as a repository of measures. To puff ourselves up, w e love tobelieve that Temple builders w ere barely standing upon the shoulders of flint-carrying Neanderthals. Ironically, how ever, the mass of us do not hold this viewbecause w e ourselves are actually capable of building bombs, or computer chipsand artificial hearts. But rather, not only can the bulk of us not build bombs andcomputer chips, but w e are irked by the fact that w e cannot even design a converted by W eb2PDFConvert.com

porch let alone a temple. It is w e w ho have lost the know ledge andsignificance of the relation between man and cosmos and so w e are determinedthat ancient man could not have been capable of it either. It is us w ho see theArk as a magic talisman, not as a means, a blueprint for constructing a House ofGod w ithin w hich man is raised up. But it has alw ays been historically unfair forcontemporary cynicism, ignorance or just self-satisfaction, to disparage theaccomplishments of earlier generations.But no matter, there is no doubt about the Latin inscription at Chartres. ‘You areto work through the Ark’.“W orkmen are indispensable of course, but so is measure. Higher or low er, thepyramid of Cheops is only a fine heap of stones….One must have at one’sdisposal a valid measure, a common denominator betw een w orld and man. Itw ould seem that as regards the Tables of the Law , this w as a unit ofmeasurement w hich w as laid in the Ark in the form of Aaron’s Rod, the livingbaton. It vanished in Solomon’s time.” (Mysteries of Chartres, p. 64).The mention of the pyramid is appropriate since the square table at Chartres,23.193 x 23.193, implying a round table w ith the same perimeter w ith adiameter of 29.53 meters – easy to remember because it names the days in theSynodical month – is simply 1/10th the socket stone measures of the GreatPyramid. I have no doubt that the Hebrew took the measures of the GreatPyramid out of Egypt and had them placed in the Ark. If certain measures arelost the relation betw een matter and spirit can be lost. Man then reverts to aprimitive level that loses the capacity to regenerate spiritually. The balance islost; the covenant broken; the cycle of the Phoenix becomes impotent. Soconvinced w as Charpentier that the Ark contained some invaluable measure orsystem of measures, that he believed the Ark in some crucial respect w asrecovered by the Templars after the First Crusade:“There are no proofs of a removal of the Ark, or of a replica, into France. Noneexcept those that one does not look at because they are under your nose – theGothic Cathedrals.” (ibid, p77)Note again that Unity here – the ‘mouth’ of the triangle – is 14.765 meters. Thisimplies the diameter of a circle that is 29.53 meters. In this image I haveconcentrated only on the equilateral upon w hich the entire ogival arch rests, thefirst elevation and the highest point. It w as Jean Favier w ho pointed out thatthe highest keystone w as a little more than 36 meters. This w ould fit the use ofthe Square Root of 6 – the next root function beyond the square root of 5.2.44948 x 14.765 = 36.1667 meters. Note how aw kw ard these root functionsare. They are infinite values to the right of the decimal point. But w ithin a 2:1 converted by W eb2PDFConvert.com

construction, w ith just a line and stakes, one can be sure that one has ‘caught’the infinite in the proportion produced by the 2:1 itself. Also, note again that thefirst elevation of 9.794 represents the acceleration rate of gravity at the Earth’ssurface in one second of time. So the cathedral also gives the second. A fewextra centimeters and it w ill give the fall rate for the latitude of Chartres w hichis a little faster due to the Earth’s flattening. I suggest that the building has setthe second by the first elevation. Acknow ledging the acceleration rate forgravity, is juxtaposed to the understanding of how that gravity is overcome;how the spirit is raised. The Cathedral is a crucible w ithin w hich the essence ofthe stone is purified through a perfect quickening that escapes the serpentinecoils of the Earth. In the first elevation you have a triangle that gives the Earth’sradius, the fall of gravity and the means of overcoming it through spiritualenlightenment. Charpentier rightly points out that w hat determines the firstelevation is the ratio for the Minor 3rd in music, 6/5 or 1.2, recalling that 6/5 x2.618 gives π. Once again w e see the participation of 1.2 in the generation of πthat can be used in squaring the circle. 2.618 is the square of the goldennumber. The feeling is that the square of phi is a special acceleration that istranscended w hen augmented by 1.2. The first development of Series E is 1 + 5= 6 and 6/5 = 1.2. The King’s Chamber is a decimal play upon this principle: 12 x2.618 = 31.416 or 1.2 x 26.18 = 31.416 or .12 x 261.8 = 31.416. The w alkthrough the Chartres’ Labyrinth is 261.8.In this image you see the simple basis of the meter. The Earth Circle (EF) issquared (ABCD). A circle (HG) is placed in the square. The diameter of the circle(HG) and the side of the square (ABCD) are the same. The outer circle is1.27324 x larger than the diameter of the inner circle and side of square. Theside of the square and diameter of the inner circle are divided by 10,000,000w hich is a large decimal number that boils dow n to a human measure – know nto laborers and temple builders alike as essentially ½ a fathom, ½ an armspan.If somebody is my height w hich is 179.52 cm, I have an armspan that is almost1.0472 my height.1.0472 x 179.52 = 188 cm = 1.88 mHalf of this gives a measure of about .94 m or 37 inches. This is shy of the meterand a little larger than the yard.The meter directly measures the Earth. The King’s Chamber is a decimal fractionof the Circle-in-the-Earth-Square. Its perimeter is a 1/1,000,000th part of thisinner circle’s circumference. This is the inner circle of the alchemical ‘Pelican’. Inthe Pyramid Texts this Pelican is referred to as the King’s mother. This has converted by W eb2PDFConvert.com

nothing to do w ith one’s earthly or biological mother. Therefore it is the place ofthick darkness w ithin the Great Pyramid w here the Pelican transforms the King’ssoul into an eternal spirit that makes pregnant the w omb of Nut. This pregnancyw ithin Nut is referred to by different symbols – all referring to fermentation as aprinciple: beer, bread that rises, W inepress God, the bnn that fertilizes as ananalogy to sperm, etc. This spirit then passes out of the Pyramid – the firekindled in the earth. The Pyramid protects the metamorphosis so that itbecomes an inner gate indicated by the perimeter of the circle as 31.416meters. The w hole Pyramid enclosure, then, is acting like the Alchemical Pelican,the great w omb of the cosmic mother. Eventually it becomes pregnant w ith andgives birth to the Eye of Horus.This image of the Pyramid is identical to that of the ‘Squared-Earth’, it is just setat a smaller scale; 1:43,200. And this w e have seen is a key member ofSeries A27 54 108 216 432 864 1728 3456 6912 13824 27,648 55,296 110,592This scale is w hat creates a difference betw een circle and square at the top ofthe pyramid that is 60 cubits or 31.416 meters. And it is this that then becomesthe hermetically sealed enclosure of the King’s Chamber w hile also being thecircumference of a circle w ith diameter equal to 10 meters.A Master MeasureAs far as the history of architecture goes, this meter is a master measure. Itdoes not need to be belabored, but the Pyramid did involve labor to build. This31.416 meters – w hich is 60 cubits – w as extracted from the difference betw eenthe radius of the circle and ½ the square. That difference relates to the w holeheight – of w hich it is a part – as 1:4.66 just as the Moon (w hich makes thingspregnant) relates to Earth + Moon as 1:4.66. And just as Capra’s nucleonspeed relates to the speed of light in the vacuum as 1:4.657 as if it too w erethat w hich captures energy or light and makes the vacuum pregnant. W hat givesthe Great Pyramid its bulk, its w eight and its visible mass are the nucleons, notthe photons that heap up into varying fluxes of concentration in the vacuum;nor the massless gravitons. So the internal mass and the specific gravity thatheaps up in the pyramid concentrates energy and that energy becomes active,the w ay the yolk of an egg becomes active w ith electromagnetic and henceelectrochemical processes. This occurs in the empty spaces of the variouscorridors and rooms, w hich then act the w ay the megalithic dolmenic chambersa cte d . converted by W eb2PDFConvert.com

These chambers accumulated energy that w as utilized by the Druids and othersfor purposes of spiritual initiation into the higher states of human existence.The King’s Chamber is completely lined w ith granite – a very high-pitched stonethat has a high quartz content. Quartz is capable of conducting piezoelectriccurrent w hen subjected to a compression – decompression cycle that the massof the Pyramid w ould undergo just by terrestrial tidal gravity alone. The w holeEarth’s crust breathes w ith gravity. It is quite dynamical because of theinfluence of the Moon w hich shares a center of gravitational mass w ith the Earth1700 km below the Earth’s surface. This focal point is alw ays shifting becausethe Earth rotates faster than the Moon orbits the shared center. So the internalcenter and the combined outer influences of Sun and Moon acting togethermake for a potent variation cycle that is memorized by biological material activeon the Earth’s surface – a surface that is intermediate betw een outergravitational cycles and inner gravitational cycles. In humans the Circadian andInfradian biological clocks are located in the suprachiasmatic nucleus on eitherside of the anterior w alls of the Third Ventricle just above the optic chiasma.This is part of that self-focusing region of the brain that is quite important indirecting many aspects of our life. Moreover, tw o shafts also target the King’sChamber: one from Orion and the other from Alpha Draconis. These shaftsperfectly fit the description of the w ay the ‘perfume’ of the Eye of Horus comesfrom the horizon of Amun and is captured, concentrated by and in the Stonew hich w ill eventually reconstitute itself as the Eye of Horus. This internalquickening of the ‘egg’ is w hat the Egyptians meant by the bnn and henceBenben Stone. In the Pyramid Texts it adopts many names one of w hich is thew ork of Sokar and Isis.Most readers w ill sense that the Great Pyramid is an Arq Ur or Great Measure.That the difference at the summit of this ‘Mundsalvaesche’ betw een square andcircle should be none other than 31.416 meters – the very meter used today –is a master stroke of scale. But to incorporate that very masterful measure intothe perimeter of one of the most mysterious and talked about chambers onEarth – the King’s Chamber – is also a masterpiece of know ledge and of therelationship betw een matter and its behavior and spirit and its behavior. This isnot to be compared to rocket science. It is not to be compared to nuclearw eapons nor nuclear reactors w hich w ill drive hair driers and T.V. sets. This is aspiritual science capable of balancing and healing the Earth and its inhabitants.This is not easy to do. Illness persists more readily than the know ledge that cancure it. Best, then, to preserve the cure through thick and thin.Below I have placed a Unity Cube in the Pyramid as if it w ere the starting pointof the entire construction. In that cube is the head of Atum w ho becomes Geband eventually man himself. The relationship betw een this ‘source’ and thepyramid is the golden number. So the ½ base is 1.618 and the apothem is2.618 w hile the height and sides of the cube are unity. The King’s Chamber isfound at the golden section point of the cube taken in three directions! On thatbasis I decided to see w hat part of the head corresponded to the King’sChamber, Queen’s Chamber and Subterranean Chamber. converted by W eb2PDFConvert.com

It w ill require a separate post to expound upon. How ever, it is clear that theSuprachiasmatic nucleus does fall w ithin the King’s Chamber. It does seem thatthe ‘root’ of the Uraeus falls in the King’s Chamber. It seems that the w holebrain rallies around a ‘seed’ of some kind that then escapes the ‘coiled serpent’to borrow a term from the Pyramid Texts.Moreover, the Unity Cube extends as a Root of 2 rectangle very precisely dow nto the Subterranean Chamber as if the Subterranean Chamber w ere acting as aroot. W e can see this relationship below betw een a ‘germ’ taken as Unity andits root, w hich becomes the square root of 2. In the case of the Great Pyramid itis as if the Vagus Nerve w ere rooting itself in the Aortic Arch w hich w e knowcorresponds to the golden number, 1.618, in the w hole canon. The same root 2rectangle also contains the spine as far as the first Thoracic Vertebra. Nervesfrom these first 8 vertebrae innervate the heart stimulating it to beat faster. TheVagus Nerve reaches the heart from the medulla oblongata via an anteriorro u te . converted by W eb2PDFConvert.com

W ith this simple scheme it is very significant to see the Uraeus emerging fromthe brow on the golden section of the Unity Cube. W e can recall from theprevious post that the Uraeus also rests on the golden section of a head cubein a Karnak bas relief show n below . Note that the Grand Gallery rises up to andrests upon the golden section latitude of the Unity Cube. This also correspondsto the top of the cerebral peduncle. The King’s Chamber is the meeting of theforebrain and anterior extremity of the thalamic complex and Third Ventricle.Here I have taken the serpent itself as “1”, so it is “2” to the vertex. From baseof Uraeus to base of jaw is 3.236. The relationship is 1:1.618 just like the floorof the KC in the Unity Cube. The KC appears to be about 44 meters from theplatform. Here, the 44 meters is represented as .618 of the Unity Cube, or inother w ords as the Golden Section. This corresponds to exactly 84 royal cubits.The Queen’s Chamber appears to be 42 cubits above the ground. converted by W eb2PDFConvert.com

In Exodus, it is stated that only the ‘testimony’ is to be put into the ark. Thetestimony w as given to Moses at the top of Mount Sinai. Mountains are oftenassociated w ith enlightenment, testimonials, salvation and so forth. The GrailCastle is called Mundsalvaesche or Salvation Mountain. The Pyramid w as ahuman mountain w herein an extraordinary form of salvation w as to take place.The Osiris-King, according to the Pyramid Texts, was not seeking his ownsalvation for himself alone. The top of the mountain is meant symbolically. W hatis really meant is that the serpent is raised up in the W ild Mountain. The infrastructure of the Great Pyramid seems designed to raise subterranean energiesup to the King’ Chamber. The w ilderness is teeming w ith savage life-force. Itspow er must be tamed, and raised. It is draw n up the spine; into the oldbrainstem; over the cerebral peduncle; through the Thalamus via a slitcorresponding to the Third Ventricle; and finally into the narrow domain w hereforebrain and thalamus meet. It is as if the candidate has returned to the fetus –its cause; its germ; its origin in the w omb of Nut. From this the Eye of Horus w illbe reborn. It is Seth, often symbolized by an ox w ho must ‘carry’ the Eyeforevermore. It is Horus w ho must overcome Seth w ithout killing him and w homust place him ‘under the king’, ‘under the eye’. The Eye w as sometimesdepicted as being carried in an Ark or Barque. ‘You are to w ork through the Ark’could perhaps be stated otherw ise. ‘Here things take their course. You are tow ork through the Eye of Horus.’ But one could also say: ‘Here things take theircourse. You are to w ork through the Grail.’“Take me w ith you O Horus; ferry me over, O Thoth, on the tip of your w ing asSokar w ho presides over the Bark of Righteousness. Horus is not asleep behindthe canal, Thoth is not boatless; nor am I boatless, for I possess the Eye ofHorus”. (PT 1429)The boat, the Ark, the Bark of Maāt or Righteousness – the means of passage– is one and the same as the Eye of Horus. In ancient Egypt the King w asexpected to w ork through the ‘Observances of Maāt’. He w as to follow the pathof the ‘Bark of Maāt’. This w as also called the “Right W ay” in the Pyramid Texts.W hen you follow this path, the ‘path of righteousness’, then things naturallytake their course. The start point of this path and the end point of the pathseems to be the 2:1 Table. In the Great Pyramid this is the King’s Chamber.During the w hole process the candidate sometimes feels as if he w ere going togo mad as there is much that must be shed; much that must be burned to ash,much that must be exposed in the w ilderness. The ‘madness’ accompanies theloss of one’s initial frame of reference. This is Dionysius. Chaos precedes orderas if by magic. Just w hen you think chaos w ill rip apart mind, soul and body, ittransforms, self-organizes into the Eye by w hich one is delivered: through abrilliantly ordered self-amplification. Since color is involved it seems thatelectromagnetism must be part and parcel of the ordered self-amplification insome sort of hermetically-sealed sphere of protection. There is a remarkableimage of the scarab pushing the Eye (dung-ball) out of the pyramidal mountain converted by W eb2PDFConvert.com

w here it has been reconstituted. The image show s the transformation from a 3-4-5 triangle to an equilateral triangle. The equilateral is featured at the site ofthe Sphinx. I w ill have to show this image in another post. It w as first identifiedby Schw aller de Lubicz and constituted one of the most importantbreakthroughs in his understanding of the ancient Egyptians. The King isdepicted as the hypotenuse of the 3-4-5 triangle, w hich is to say as the number5. A serpent that is undulating forms the remainder of the triangle. So you haveserpent = 3 +4 = 7 + King = 5, giving 7 + 5 = 12 for the full triangle. W ith thearms reaching up over the head the hypotenuse becomes 6 establishing theratio 6/5 and an equilateral triangle is then formed. The Templars used toportray an Eye w ithin an equilateral triangle. The equilateral triangle is relevantat the latitude of the Great Sphinx w here the Sun casts a shadow at Noon onthe Equinox that is 60 degrees.It w as only years later (2000) that I came upon more than one reference to theArk w hich w as described as being 2 x 4 x 2 feet in size (e.g. “The Hiram Key,1997). By that point it came as no surprise to learn that the Ark may havebeen based on a 2:1 table. In Exodus, it is given quite different proportions,namely: 2.5 x 1.5 x 1.5 cubits. How ever, the Court of the Tabernacle thathoused the Ark w hen the Jew s w ere w andering in the desert, w as proportioned1:2. The table built for offerings w as also 1 x 2 x 1.5 or perhaps 20.6″ x 41.2″ x30.92”.The Ark is featured in a singular w ay at Chartres at its north-west entrance, as ifit had been regarded w ith special interest by its builders, The Order of theTemple. Incidentally, w hile the south-east entrance to Chartres features Christ,the north-w est entrance features Saint-Anne holding the infant, Virgin Mary, asif somehow the key to the w hole mystery w as the axis draw n across thetransepts from Saint Anne to Christ. Moreover, it cannot be stated enough timesthat the internal measure of the cathedral that joins Christ to Saint Anne isnone other than 61.8 meters. This is a remarkable measure. It is 2 seconds ofarc of terrestrial surface. Half is 30.9 m. 1,296,000 x 30.9 = 40,046,400 m. Thediameter of this circle is 12,747,165 m. If you divided this diameter by 1,296,000you w ould get 9.835. This is the fall rate of gravity at the North Pole in secondsof time, or 9.835 m/s². It is alw ays w orth repeating that the escape velocity atthe Sun’s surface happens to be 618 km/s or 10,000 greater than the spanacross the transepts at Chartres. The Earth’s escape velocity is 11.18 km/sw hich is 100 times greater than the height of the North Tow er at Chartres, or,11,180/111.8 = 100. 61.8 alsp participates in a golden rectangle the height ofw hich is 100 meters. The theme of Chartres seems to be the vessel thatcaptures a complete cycle: the incarnation; the rebirth in spirit and the finalliberation or resurrection of the spirit. In this sense to w ork through the Ark is tow ork through the complete cycle of the Eye of Horus.W hether the Ark w as a 1 x 2 construction or a 2.5 x 1.5 construction, thisinscription rang true for me immediately. I suppose I took it on faith. It w as saidthat ‘God himself w rote the law on both sides of the tables of testimony therebyforming a covenant w ith both Moses and the Hebrew people. Both sides mustmean exoteric and esoteric. The Ten Commandments are relevant for socialbehavior but cannot teach a Master Craftsman how to build a Temple, let alonea place like Karnak, or Luxor, or Chartres or the interior design of the GreatPyramid. Nothing has inspired me to press forw ard w ith a geometry of humanproportions quite like this simple instruction – or reminder – to the builders ofpossibly my favorite sanctuary on earth. The emphasis w as on ‘w ork’. This w asnot art for its ow n sake. This w as w ork, Virgo, precision, structure, purity ofdesign, efficacy of function; the capacity to heal, the art of perfection and aconfidence in that function that keeps all detail spare. It is easy to miss thissculpture as it is small and a ladder is essential to get up to its level in order tophotograph it. converted by W eb2PDFConvert.com

I w ould not have noticed it had Charpentier not draw n attention to it in hisbook. It is w ell w orth looking for it if you can get to Chartres. Note theconspicuous sphere next to the tw o damaged Tables of Testimony. I am not yetsure w hy Charpentier did not mention the sphere. I noticed it only w henexamining the photo that I had enlarged and is now on the w all. Lomas andKnight (1997) mention that 3 things w ere put in the Ark, the tw o tables oftestimony, but also Yahweh himself. And they also mention that the Ark w asproportioned 2 x 4.This sphere is an interpretive addition made by the Grand Master or MasterCraftsman at Chartres. The only reason for adding it w ould have been if thebuilders believed it w as somehow the essence of the entire w ork; too importantto leave out. Of course w e know that the Ark w as supposed to house the divinepresence, the Lord of Hosts, God. For Plato there w as no better w ay torepresent God than a sphere. W e see spheres in the sacred barques of theEgyptians and references such as “Spirit w ho is in the Dndrw Barque” in thePyramid Texts (PT 1637). But in the Pyramid Texts, the King himself has becomethat spirit. And that spirit is also the Eye of Horus. It is my best guess that thesphere represents the ultimate relation betw een God and man. This is the realbasis of the covenant. The Eye of Horus, the All-Embracing sphere is the meansby w hich the covenant is established. The Ark is the support w hich links time tos p a ce .They may also have felt it w as important to portray the antiquity of the principleof of the Ark that likely predated the time of the Old Testament. The sacredbarques of the Egyptians, such as the Hennu Boat, seem to be as old as thePyramid Texts that, in turn, are probably much older than the first dynasties.The hand of the clock points to a legacy that had returned to the Nile after somesort of hiatus. It is highly likely to me that the Hebrew w ere a part of that legacythat now dissolves into pre-history, frustrating the instincts of many of us w hoknow know ledge did not start formally w ith the Greeks, but predated them byuntold millennia. The Ark itself w as taken out of Egypt by Moses, so ostensibly itrepresented critical know ledge inherited from the Egyptian civilization tow ardthe end of the 18th Dynasty.To learn that the Ark may have been 2×4 feet is significant in light of this entirediscussion. One could say: “Here things take their course. You are to w orkthrough the principle: 1:2. Everything emerges from it and everything returns toit.” And ‘Ark’ (arc, archa) is also a circle. Geometers imitate the circles of Naturew ith their compasses. Circles and squares bring measure into the w orld. Thecircle is the first enclosure w here time and space function together w ithperiodicity and rhythm. Things become differentiated w ith the square. W ith the2:1, everything is related to everything else. It relates, purifies, transcends andtransforms. In Exodus the altar w as a 5 x 5 cubit square. The offering table w as converted by W eb2PDFConvert.com

1 x 2 cubits. It received only sacred objects.In the sculpture here on the south side of the north-w est porch, the side of theark is proportioned 1 x 3. The w hole Temple of Solomon w as 1 x 3 or 20 x 60cubits. It w as divided as 1/3rd and 2/3rds. The Holy of Holies w as 1/3rd and therest 2/3rds. If the cube w as the oracle, it is important to repeat that the headhas a close affinity w ith the cube. Egyptians, Tibetans, Hebrew , Aborigines, allused specific head gear to enhance the flow of energy in the head for theoccasion of the annual oracle. The human head is part and parcel of divination,not at all of the coffee table variety. Rather the purpose of the divination w as tokeep above and below in the right balance. This is a profound dimension of theGrail itself, w hich concerns spirit as much as flesh and time as much as physicalspace or mass. It unites them in the place: the place w here a meaningful Goddw ells.The Templars w ere also interested in the “Grail”, that mysterious vessel or‘stone’ that is both cornucopia and altar simultaneously, or perhaps alternately.It is also w ell-know n that the Templars apparently w orshipped a recondite headcalled the “Baphomet”, in some w ay connected to the means by w hich w isdomenters the w orld from all around and is gathered up into a living testament. Thehead w as supposed to have brought fertility to the land: the source of riches,grow th, health and strength. It even made the trees blossom. These gifts w erealso attributed to the Grail as if the Baphomet and Grail were one and the same.In Egypt one thinks of the head of Atum-Ra. In Greece one thinks of Apollo orZeus. Then there w as Orpheus and the Celtic “Bran”. There w as Osiris,Geb, Horus, Rahu of India…In Egypt, Nut w as the immense black sky thatcontained all the stars. Geb w as the Earth. Atum became Geb on his w ay tobecoming man. The most conspicuous link betw een God and Man has alw aysbeen the head. The skull is certainly reminiscent of a ‘gral’, a bow l, a vesselundergoing a mysterious transmutation draw ing pow er from the roots of thes p in e .The building of a cathedral is a testament to a total know ledge; not its finalgoal, but a means by w hich the spirit of the pilgrim can be perfected, quickened;purified, lifted up tow ard sublimity. It offers an unparalleled relief; to feel againthe w ell-spring of the divine that can be forgotten in the humdrum. converted by W eb2PDFConvert.com

The cathedral w as designed to testify to specific law s by w hich the ‘Grail’ reveals itself to the w orld. The image of the head w ill not go aw ay easily. Remember in Greece that old saying: Athena was born fully grown from the head of Zeus. Athena w as the Egyptian Neith w ho w as linked to the Eye of Horus. Plato dedicated the Timaeus to Neith. Neith w as know ledge, w isdom, Sia. In the Pyramid Texts the King becomes Sia. He departs this w orld as Sia and sits at the ‘right hand of Re.’ “I become Sia w ho bears the god’s book, w ho is at the right hand of Re; O you w ho are protected by my hand, it is I w ho say w hat is in the heart of the Great One [feminine Goddess], in the Festival of Red Linen. I even I, am Sia, w ho is at the right hand of Re…” (PT 268). If one is looking for a good definition of ‘humanity’ I can offer a clue. Humanity is that extra gift in man that offers transpersonal inspiration; an inspiration that the individual or a group of individuals endeavor to bequeath to successive generations long after they themselves have left the delights of Earth. Charpentier has left just such an inspiration. And Chartres is w hat inspired him. Under the discussion of the Ark of the Covenant and the w ay it w as portrayed by the “image-maker” at Chartres, Charpentier points out w ithout apology, w ithout couching his co n victio n : “There is more in the Gothic than a series of technical solutions. There is a building of temples that are gates to the Kingdom of God; and this requires a higher science than that of calculation of forces and resistances. It demandsknow ledge of the law s of numbers, matter, spirit and, if it is to w ork in the soulsof men, know ledge of the law s of physiology and psychology. Someonerevealed all this. If it is not the Ark, if it is not the Tables of the Law , the knightsTemplar must have brought back an extraordinary initiatory document to theW est.” (Mysteries of Chartres Cathedral, p.77-78).In 1985 I took this passage seriously. I already believed that it all w orkedtogether. My 1980 dream demonstrated sufficiently to me that man w as thebeing of grand unification. The question w as: w hat w ere those ‘law s’? And theansw er inevitably started w ith the 2:1 and the arcs sw ung by a compass w ithinand around that 2:1 construction. Everything grow s from the 2:1, right from thefirst cell division of 1 into 2. It also seemed possible that the Ark containedinformation derived from Egypt; Tables of Numbers such as Series A, Series Eand so forth. It seems it could have given the Earth’s size and rotation rate; theMoon’s size and distance from Earth; the Sun’s size and distance from Earth.The Templars apparently taught Columbus that the Earth w as round. They mayalso have taught him its size and how to navigate its seas. Man must be in converted by W eb2PDFConvert.com

harmony w ith his Earth or w e could not survive the vicissitudes. One seed mustgrow into a diversity that remains in harmony w ith all its parts, including manh ims e lf.If, for example, the Templars w ere taken to Egypt by, say, the Fatimids, it ispossible that they w ere show n the implications of a shadow cast by the GreatSphinx and any obelisk that w as 66 feet high and placed at the latitude of theSphinx or its neighboring temple. In round figures the shadow cast w ould havebeen 11.6 meters. The theme of the Sphinx’s location is 6. A 60° angle is cast bythe Sphinx at Noon on the Equinox. The 11.6 shadow can be doubled into asquare w ith 23.2 meters on a side. A circle can be put in this square w ith adiameter of 23.2 meters. This diameter can be taken 60,000,000 times and w illgive a diameter of:23.2 x 60,000,000 = 1,392,000,000 meters.Today astronomy texts give a diameter of the Sun, the Egyptian Aten, as1,392,000 km.If w e take the Moon’s diameter as 3476 km or 11404176.67 feet and divided itby a member of Series A11404176.67 ÷ 172800 = 66 feet.The shadow cast at the latitude of the Sphinx is about 60.025° and gives alength of 38.064649 feet or 11.602 meters.23.2 x 4 = 92.8 meters.92.8 x 432,000 = 40,096 km = Earth’s Equator.In essence then, the 66 Foot Sphinx and its shadow are giving 3 figures atonce: the size of the Earth, the Moon and the Sun:29.53 x 432,000 = 12,756 km = Earth Diameter66 Ft x 172800 = 11404800 feet = Moon Diameter11.6 x 2 x 60,000,000 = 1,392,000 km = Sun’s Diameter.The Sphinx gives the square. W hen w e square the circle w e get a diameter of29.53 m and a radius of 14.765 meters w hich also sets the scale for theelevations at Chartres. 29.53 is easy to remember because it is also the numberof days in the synodical month. In this instance 1 meter corresponds to 1 day.In the next post w e w ill go directly to w hat I call the “24-method” for squaringthe circle.Read Full Post »Squaring-the-Circle (P9)Posted in Human Harmonics on April 21, 2010 | Leave a C omment »SQ U ARING-THE -C IRC L EThe building of a cathedral is a testament to a total knowledge; not its final goal, buta means by which the spirit of the pilgrim can be purified, quickened, perfected andlifted up toward sublimity. It offers an unparalleled relief; to feel again the well-spring of the divine that can be forgotten in the humdrum. The human body canperform a similar function.It is March 12th, 2010. The sun is blazing through a baby blue sky over NovaScotia. It is cold and the resolution is flaw less even as the Earth quakes andtrembles as if in the midst of the labor of rebirth. All creatures must commiseratetogether even if only unconsciously – the magnitude of the labor is so great. AsI attempt to penetrate the secrets of w hat makes cathedrals masterpieces ofholism, and our bodies masterpieces of expression, it becomes increasinglyurgent w orld-w ide to transform our differences into a source of creative energycapable of protecting and enhancing the w orld’s highly interconnected w eb ofresources. W e cannot master these differences if w e cannot masterourselves. Know ledge can inspire and guide. But it must reach dow n to the verydepths of our shared humanity, a humanity that includes every creeping,peeping sentient creature here under the sky.I have had occasion to reread sections of Louis Charpentier’s book on ChartresCathedral and find it even more impressive than I remember back in 1985. Itreminds me of the mountain of w ork that still lies before me. How do I containthe cornucopia? How do I represent the legacy? W hat do I choose to leave out,given that most people are already overstuffed w ith information? converted by W eb2PDFConvert.com

Charpentier invokes for me an inextinguishable path of transpersonalinspiration. You must not give up no matter how stony the path may get; nomatter how many thorns may block your w ay. Belief guides your aching feet.The Sun lifts you. The basics do not abandon you.The 2:1 Table can be given many names. From it arise all the contents of thecornucopia. W e ourselves are that cornucopia. W e ourselves arise from the 2:1.W e ourselves are the Grail and its content and have the potential for some sortof qualitative leap, a ‘mutation’ of the soul if you like – even an improvement inour physical constitution. The spirit can heal an ailing vessel from within. W eourselves are subject to the path of 3, three tables, three qualities bound byone essence. The 2:1 has been called the Mystical Table about w hich nothingcan be said. But in my experience everything can be said about it. That’s thereal problem: there isn’t anything that cannot be said about it! As the root ofeverything, the door through w hich phenomena enters the w orld and becomessquare or round or square again, it is the parent(s) of everything. For thisreason I w ill show tw o methods by w hich the 2:1 rectangle can ‘square-the-circle’. For several purposes at once, I w ill concentrate on equal perimeter for thetime being. It has proven to have real relevance in this w ork. In this post I w illshow one method first. But w e’ll take a short detour first. There is alw ays adetour to make in the Labyrinth. But every path leads to the center and thecenter leads to the periphery.The King’s Chamber Squares the CircleFor the sake of a legacy, that w hich is ancient, I w ill remind the reader again,that the King’s Chamber, 44 meters above ground in the Great Pyramid – builtfrom 100 large blocks of granite, including 9 ceiling beams up to 29 feet long (50tons each!) – is an exact 2:1 rectangular shape w ith a height that is ½ its ow ndiagonal or 1.118 x Unity. I w ill also repeat that its dimensions, 5.236 x 10.472meters, are derived from its perimeter w hich in meters names π, 31.416 meters.And this length that has become a 2:1 rectangular enclosure, comes from thedifference betw een the square and circle w ith the same perimeter: the geometrythat forms the basis of the Great Pyramid as a w hole. Only ½ the configurationis above ground, so it is 280 cubits (radius) minus 220 cubits (square) leaving60 cubits, w hich is 31.416 meters. Note that the basic configuration here aboveground is based on a semi-circle around a 2:1 rectangle: JKPQ. The differencebetw een semi-circle or radius and the 2:1 is TS, 60 cubits, or 31.416 meters. A2:1 is 1/2 a square but also is itself a double square. Nature likes dimidiation.In the previous post I show ed the geometry of the ‘sba’ gate w here theopening w idth is 10 and the height of the opening is 31.416. This is framedw ithin an overall 2:1 construction. If the 31.416 height is turned into a circle,the w idth of the door w ill be its diameter. If that is turned into a 2:1 rectangle, itw ill be 5.236 x 10.472 in dimension (10 x 20 cubits) w hich w e see in theillustration of the KC below . converted by W eb2PDFConvert.com

The golden number squared is 2.618. 12 x 2.618 is 31.416. Recall the w alkaround the labyrinth at Chartres is about 261.8 meters or 500 cubits. Thediameter of the labyrinth at Chartres is close to 13 meters. It’s possible that itw as supposed to be 13.09 w hich is the Great Diagonal of the King’s Chamber(DG above). Here w e can see that 13.09 meters measures the Labyrinth andthe opening across the Royal Portal. It measures betw een the pillars of theNave.These numbers all appear together in a single Fibonacci-Series show n below .The depth and breadth of this series is one of the delights of this w ork. I havefelt for some time that ancient sages have long know n this series and hadrecourse to it. It strikes me that the Templars may very w ell have gotten theirhands on the same series and w ere instructed as to how to use it. It is aunique play betw een the meter and the royal cubit. It starts simply as 1, 5, 6,11… and then it also builds in the vertical plane w ith 2, 10, 12, 22, etc.; 3, 15,18, 33, etc.; 4, 20, 24, 44, etc. Eventually it names the royal cubit (.5236, Line converted by W eb2PDFConvert.com

4), the golden section (1.236, Line 4), the golden number (1.618, Line 2), 1.309(Line 1) w hich is 1.618/1.236 and by Line 24 it names π as 31416. Note thatthe outside measure of the transepts at Chartres is 130.9 cubits (Line 1,Column XIV) or 68.54 meters that appears on Line 2, Column XVI. This Series Eis a genuine cornucopia of number. Moreover, number and phenomena seem toarise together in an ineffable embraceSeries E is characterized by “5”, just as pentagonal geometry opens the goldenproportion family. 1 is common to any Fibonacci series. It is as if this Series Erepresents a ‘leap’ of some kind: a qualitative transformation of the PrimeSeries w hich is 1, 1, 2, 3, 5, 8, 13, 21 … etc. W hen 5 and 1 are added togetheryou get 6. 6/5 = 1.2 and 1.2 x 2.618 = 3.1416, an excellent version of pi thatappears on Line 24, under the 1309 column. In any case 118, 309, 1309, alloccur on Line 1 of this series. 382, 618, 1618, 2618, etc. all appear on Line 2.5236 occurs on Line 4 and 10472 occurs on Line 8. 31416 occurs on Line 24.At Chartres, 13.09 is also the radius of the round table w ith the same surfaceas the Chartres Square Table w ith 23.193 m on a side. It also seems todetermine the round point of the choir. Now , if I’m right and a 100 meter tablew as really used for the interior measure of Chartres for Nave + Transepts +Choir, then it is interesting that 13 w ould correspond converted by W eb2PDFConvert.com

to the proper proportion for the head of a figure that w as 100 meters in height.I’ll come back to this w hen I discuss the head more specifically. I w ill mentionagain that the perimeter of the Chartres Square Table identified by Charpentieris about 92.772 meters. This is 1/10th the measure around the ‘socket’ stones ofthe Great Pyramid noted by W illiam Fix in 1978 as 927.72161 m. W hen theChartres square is multiplied by 432,000 one obtains a very reasonablemeasure for the Equatorial Circumference of the Earth: 92.772 x 432,000 =40,077,504 meters. The scale of the Pyramid w as set at 43,200 of the Earth.Charpentier did not have accurate data for the socket stone measure aroundthe Great Pyramid. So he did not quite realize the exact correspondencebetw een the Chartres Square and the socket stone perimeter of the GreatPyramid. But he sensed it. The number 927 that appears in Series E on Line 3,Column XI, under 618, has turned out to be yet another important number. converted by W eb2PDFConvert.com

Some cornucopia! The Grail feeds glutton and ascetic alike! Let me just pointout for now that if w e take the Astronomical Unit for a date that is a little pastApril 4, the day of the mean (149,597,870 km), w e can easily accept a roundfigure of 150,000,000 km. No astronomer w ill haggle over that. The Earth isonly ever at the mean position tw ice a year, otherw ise it is on on one side of itor the other w ith a range of nearly 2,500,000 km on either side. In Series E,1500 is right next to 927 on Line 3. So if w e perform our archetypal goldensection to the AU that is 150,000,000 x 75,000,000 w e get ~ 92,700,000 km.Around April 17 it w ill be 150,108,000 ÷ 1.618 = 92,773,000. W hen I laid theincomplete geometry for an image of the Earth+Moon orbiting the Sun in 1998,the numerical information brought Series E to life when I used the meter. I alsofound it instructive to use royal cubits and at other times, the “light-second” or299,792.458 km. converted by W eb2PDFConvert.com

W hen I collapsed the golden section value into a circle, I recognized it as thecircle w ith the same perimeter as the Chartres Square and Great PyramidSocket Stone Square that gives the Earth’s Equator. Same number, just adifferent scale. Above w e see the w idth of the Pelvic Vesica as 30,924,598 km.Below w e see the diameter of the circle w ith the same perimeter as the‘Chartres Square’: 92,773,794/3.1416 = 29,530,746 km.I began to fine tune the geometry as if it w ere self-adjusting. The Vesica Piscisof course is 1/3rd of the interlocking circles. In the female it is 1/3rd of 1.236 orthe large segment of the golden section. Here, this is say: 92,773,794. 1/3rd isthen 30,924,598. At the Equator of the Earth 1 second of arc is 30.922 m, w hich converted by W eb2PDFConvert.com

is also the w idth of the Parthenon and ½ the transepts at Chartres. 309appears on Line 1, Column XI. It is ½ of 618, 1/3rd of 927 and 1/4th of 1236.The measure across the Pelvic Vesica is 30,924,000 but the diameter of thePelvic Circle is ~ 92,773,000 ÷ π = 29,530,000 km. As it turns out this is thecircle w ith the same perimeter as the Chartres Square: 29.53 m w ith a radius of14.765 m. This becomes the base of a triangle that determines the elevations ofChartres all the w ay to the ceiling keystone. Jean Favier mentions that near theW estern Tow ers it exceeds 36 meters from floor to keystone. If a radius of14.765 is used as unity of a 2:1 w e can see that the Ogive springs from thesquare root of 3 at a height of 25.57 meters. The keystone height w ould seemto have used the square root of 6 w hich gives 36.167 meters – a very, verygood guess for the intended height of the original ceiling. The root of 6 is thediagonal of a “Root-5” rectangle w hich displays very harmonious properties andsimply arise through a progression that I w ill show in another post. I’ll just notethe relationship betw een 30,924,000 and 29,530,000 is 1.0472, that of theroyal cubit or pi/6 = .5236/5.An Eternal Paradigm: 2:1W ith the 2:1 rectangular table, you feel your ow n w orthiness above you, belowyou; w ithin you and all around you. And w hen you trace out tw o equal circlesw ithin each of the tw o squares, it is hard not to think of the Sun and Moon justhaving separated after New Moon, or just about to enter conjunction; or thefirst cell replicating its ow n nuclear information and then suddenly dividing intotw o, new , equal ‘daughter’ cells. Right aw ay nuances abound, it is true. Nothingis ever quite identical to anything else, but yet there is the Platonic hint ofperfection that surrounds that division. The w hole story starts to tell converted by W eb2PDFConvert.com