## Posts Tagged ‘rainbow proportion’

### Menkaure, Maeshowe & Mathematical Mind

Saturday, November 1st, 2014

The Geometry of Square Root 2                           1/11/14

Perfection of megalithic Maeshowe design

–
Original Icahm base-plan Maeshowe 1946

Introductions
(This piece is a summary of the philosophy of science and can be appreciated even without any mathematical knowledge)

Natural Number Geometry

This website is an effort to bridge the gap between mystical knowledge and scientific exploration of ‘existence’ or ‘reality’. This new ontology (ontos= authentic essence of being) revolves around a supposedly ancient, but simple mathematical natural number (1, 2, 3, 4, 5, … etc.) theorem, applied to the geometry of circles and squares, with evidence and clarification given in many chapters. This ontology is based on the assumption that mathematics underlies the manifestation of Nature, a modern version of Pythagoras’ ‘All is Number’, as resonances in vibration.
I’ve called this theorem by many names, ‘Geometry of Square Root Two’,  ‘Pyramid Proportion’, ‘Maeshowe Theorem’ and ‘Rainbow Proportion’, reflecting its intriguing contents and versatility, but the  ‘ Lost Menkaure and Maeshowe Theorem’ is an appropriate historical name, I think, because the theorem went lost for over 4000 years, although its quintessence still stands in ancient buildings to this day. The crucial ratios of the theorem have been solidly recorded in buildings of at least two ancient ‘megalithic’ (big stone) cultures, that is in well-known Giza in Egypt and in Orkney, an archipelago off the northern coast of Scotland.

For Orkney it means going back into the late Stone Age some 5000 years ago, 3000 BCE, to Maeshowe and its first European squared space, for Egypt it means going back to Pharao Sneferu’s Meydum pyramid with ratios 275 : 175 (11:7) in Royal Cubits (RC) for base length and height, preceding, but like the Great Pyramid = 440RC : 280RC = 11 : 7 and the Third Pyramid Menkaure at eastern platform level = 198RC : 126RC = also 11 : 7.
Meydum was the first ‘true’ pyramid, after having been started like Imhotep’s step-pyramid-type (Saqqara) and its design in ratios is mathematically similar to the Great & Third Pyramids at Giza, but earlier, so this means going back to at least some 4600 years ago, 2600BCE, to Pharao Sneferu at the end of his long reign. The two totally different, but ‘megalihic’ cultures may have been partly contemporaneous.
Both the Atlantic and the Mediterranean ‘Megalithicum’ ‘eternalized’ their scientific/cosmological knowledge in megalithic buildings and both erected huge standing stones to exalt the sun and the cosmos (my definition of a ‘Megalithicum’); some standing stones also functioned as sun dials (Obelisks – Egypt, Grand menhir-brise – Brittany, France).
It is an early manifestation of the awareness of rhythm and cycles in Nature and the Cosmos, of scientific interest.

The Lost Theorem can be seen as on a par with or even complementary to Pythagoras’ famous ‘right angled triangle and squares-theorem’ (a² + b² = c²), of which the ratios appear in Giza in the Second Pyramid (3²: 4²: 5²) Khafre, though long before Pythagoras’ time. The ‘Lost Theorem’ itself also happens to be a ‘square-theorem’ as we see it in the Great & Third Pyramid and in Maeshowe’s chamber (Orkney), but this lost theorem contains the relation of squares and circles (and eventually of torus and sphere), so you bet a more intricate one, and indeed it is different, very different; so different with its seemingly imprecise and ‘hidden’ rules, that it got lost and the lesser but apparently more precise Pythagoras-theorem (3²: 4²: 5² -> 9+16=25) became a preferred design with later pyramid-builders and survived to this day as one of the cornerstones of Euclidean geometry.

equilateral triangle Maeshowe ground plan

Maeshowe’s plan with hidden Pythagorean triangles and parallels

The analysis of Maeshowe’s ground plan, shows perfect Pythagorean triangles and parallels at the heart of the building, and much more. (see below and at The Measure of Maeshowe)

Maeshowe: Circle-Square-Circle Theorem and Rainbow Proportion
big yellow square perimeter equals red circle circumference; their areas relate 11:14
red centre square side=9Megalithic Ell (4.71m) with inner blue encompassing circle segment=10ME (5.236m), inner blue circle = 40MEll (ME=0.5236m) (MR=0.37025m)
big blue circle = 80 Megalithic Remen (MR) equals inner diameter Stonehenge!= 29.62m
radii ratio inner blue circle to red circle = (Double) Rainbow Proportion = 11:14

My ‘natural-number-logic logo’: yellow 9-grid with orange square perimeter in blue circle. I conceived of this symbol of my mathematical theorem before I found it in the pyramids and in Maeshowe, both were spectacular findings and experiences, “I had understood and did understand their message, I was working on it”. Rare moments in a lifetime, but this mathematical work has given me several profound ‘recognitions’, as the ‘little theorem of Fermat’ in relation to repunits and primes, which was a huge confirmation that my math was all right.

If this number-crunching is too much for the reader just skip these parts, which are necessary for the scientific argument and its (circumstantial) proofs, but don’t go away, it’s not all like this, continue, say, at ‘Sophistication’

Its True Significance

What the Lost Theorem does is expressing ad infinitum the ratios of ‘squares in circles in squares in circles….’ (inscribing, encompassing) in natural numbers as we see it in the picture, that is, in a specific set of fixed unchanging integer ratios, like 11:7 and 11:14 and 10:9 and 162:100, which are the quintessential ones, here. (To remind you: in standard maths this is only achieved through the irrational transcendental number Pi, π, which though blocks any smooth relation between natural numbers in circles and squares, and also through the irrational golden mean number 1.618… =Phi, which is here 1.620 (+0.002). Nowhere does the theorem differ in the hundredths, always only in the thousandths, so it is very close to conventional math.
The eventual order is achieved in the Lost Theorem by using a ‘rational’ approximation of π as a squareroot-2 number= (20/9)V2 or 3.14 2696… (ratio circle circumference and its Euclidean diameter, π = 3.14 159265…) and by a rational value for π²-squared ( 9.87654…), respectively by the rational Pi-numbers: 22/7 (3.14 2857 1428…) and its complement 2800/891 (=3.14 25 36…) and the new Pi-squared as 9.87654321 (= 22/7 x 2800/891 = 800/81), all expressed in natural and rational numbers, the undubitable basis of any early mathematics.

The theorem’s true significance though lies in ‘squaring the circle by circumference’ (this is different from the famous and notorious ‘area-squaring of the circle’), which we see here (picture above) realized in the yellow square perimeter being equal to the red circle circumference. The big blue circle diameter is 10, the red circle diameter is 9, as ratios. The big blue circle perimeter 40, the yellow square perimeter is 36, which is again ratio 10 : 9.
(The 10/9 ratio is the basis of the 1.11111…., 2.2222….., 9.9999…, 11.11111…. nine-number system which rules the algorithm and this, in turn, is a bridge to the repunits and their root primes, number waves and more)

This ‘squaring the circle by circumference’, as mathematical operation, gave us the ‘Great Pyramid’ as the geometrically square abstraction of the (hemi-) sphere (globe), that is, of the Earth.
In Orkney though, the theorem, in a peculiarly extended but more rudimentary form (8: 9: 10), lies hidden in the lay-out of Maeshowe’s megalithic chamber and comes into the open in the dimensions of the several man-made circles of the nearby Ring of Brodgar ( its standing stone circle and rock-hewn moat with 2 sloping edges give 3 ratios), there though expressed in the big numbers of Giza (99 or 198 and 140 or 280). This is the full natural-number-solution for the ‘rationalisation of number-irrationality’, i.c. of ‘square root 2’ now as 140/99 and 99/70. (see Rationalizing the Ir-rational).

Megalithic Pi
What could make this website suspect for many in this respect is that I found that practically the same unit of measure as Egypt’s established Royal Cubit (RC= 0.52375m, or 0.524, less precise) fitted perfectly and mathematically meaningful in major Orkney megalithic works (and all over the British Isles, for that matter) and I have inferred that the Megalithic Ell (ME= 0.5236m) was used in Orkney and elsewhere in the Isles, possibly (much?) earlier (Newgrange, Ireland?), than in Egypt. On top of that I found this measure (ME) based on two male ulna bones (26.18cm, under-arm, ell(-bow), which was a gift), this measure has, as diameter-size, an ingenious mathematical relation to a slightly revised Megalithic Yard (A.Thom).
My MY= 0.8228m and is thus 6.2mm smaller than A.Thom’s megalithic yard =0.829m, but usually better fitting the data and always with mathematical meaning, because this revised Megalithic Yard turns out to be equal to the half-circle segment of a circle with diameter 1ME=0.5236m, and equals two male tibia bones (= 2 x 0.4114 = 0.8228m, another gift, average height Neolithic male 1.75m, same as Egyptians). It results in the formula for a Megalithic Π (MPi) as 2MY/1ME (2×0.8228/0.5236= 22/7)
My only other defence for this rather ‘incredible’ but nevertheless striking situation must be that this mathematical model I found(ed) and use has connected many ‘incredible’ things in the course of my exploration, events that I personally experienced as great gifts (from heaven) not only because they were completely unexpected and enhance the beauty and profundity of the model, but also because their enigmatic occurrences in my personal life keep me highly motivated to pursue this long quest into the deep past; there is a treasure to be found at the end of the (double?) rainbow, as you know.

Megalithic Ell
My earlier mentioned fixed measure of 0.5236m as I came to use it for Giza’s Royal Cubit (RC), elsewhere usually given as .524m, is a gift in still another way, because as Megalithic Ell it not only fitted Orkney better than it does Giza, but it turned out to be exactly 1/6 of Pi (6x.5236=3.1416) and 1/5 of Phi^2  (5 x .5236=2.618) as I only realized during my Orkney-calculations. This means that a (stone-) circle diameter measured in metres gives multiplied by 6 the number of megalithic ells (ME or RC) in the circumference (6ME/1m = Pi ); a very handy gift, this one, because it may give a first indication of the possible number of stones in the original circle, the more so because also the yard and remen are at hand as measures.

To make things worse for the sceptics I show that the diameter of the stone circle of Orkney’s Brodgar is equal to the side of the Third Pyramid at (eastern) platform level, and equal to the distance from the King’s Chamber floor level to the top of the Great Pyramid, both 198RC (103.67m); and that the Brodgar ring’s circumference is equal to the ground-diagonal of the Great Pyramid (880 Remen= 325.82m or 396 Megalithic Yard = 4×99).

Natural number Logic of Menkaure design
Mathematical height (from Eastern platform level) is 9×14 = 126 RC, the side at that level is 2×99 = 198RC, the diagonal there is 280 RC, which is the height of the Great Pyramid. We see that 126 is the smallest grain to directly relate to measures of GP and to express the mathematical theorem, which would be even more rudimentary expressed as 63 and 99 and 140 for the double cubit of 104,72 cm. Here we see the geometry of sqrt2 in the ratio 140/99, or half-diagonal for 70/99.
(John Legon found a possible even more basic expression of the Theorem in (900 palms for the height 67.32m, 1000 for half diagonal = 748m, full diagonal 2000 palms = 1496m and finally a side of 1414 palms (1000V2) as 202 RC of 105,8m. This the ground level of the base of the Third Pyramid, 9, 10 and 10V2, at the ‘mathematical level’ it is a side of 1386 palms (198RC), of 1960 palms diagonal and a height of 882 palms, at sun-platform-east level some 2.5 RC above ground level)

Moreover it shows the intrinsic numerical relation between the Great and Third Pyramid in Giza (20:9), all this insight in relations thanks to the, possibly contemporary, measures of Brodgar and Maeshowe!
My important finding that the Third Pyramid must hold the mathematical key and theoretical blueprint to the Great Pyramid and relates in volume virtually as 1 : 11, comes straight from the analysis of the Orkney ratios!

Ratio of Great Pyramid same as Menkaure (-math)  280:440 = 126:198

This is of course all a bit too much to believe in for most people and certainly for the professional archaeologist who will dismiss it as ‘lunatic fringe’ science, but, reader, I had the same problem, I was not out to get these things at all and at first not even really happy when I found it, for this very reason (this is ‘too much’), but I’ve checked it all many times and I am not in the habit of fooling myself, nor others; it’s in the data and especially in the ratios. (I compare with Lehner, Cole and F.Petrie data). In case of differences they are all too close to call, or just ‘controversial’ in this Megalithic-context, with differences expressed in centimetres over lengths of hundreds of metres. (Lehner’s data for Gr.P.-sides are all 230.33m – possibly a misprint-  Cole’s average = 230.36m-;   230.33m  is definitely wrong).

The inevitable bickering about the correct length does a lot of damage to a serious approach to the logic of the designs, because it is about (number-) logic integrated in design, it is about the intention of  the design, not about perfect execution, it’s about the genuine probability of a deep insight and a great Cosmic Idea, ‘Earth as a sphere’ for one thing, the discovery of Pi as 22/7, the change to 7 palms in the Royal Cubit, it is not about cynical 20th century, so called critical modern scientific scepticism. The data I use are solid, the differences or inaccuracies are trivial compared to the overwhelming mathematical logic that is revealed.
It’s about possible synchronism and about a near mystical (historical) Enigma: how two so widely differing cultures could come up with the same mathematics, the same units of measurement and the same ‘cosmic length’ at about the same time.

Sophistication
The high mathematical sophistication that speaks from my analysis of the  late Stone Age designs in the British Isles poses a problem; in the first place for me. Is this really possible? I am not on this quest for many years to pursue and produce an ‘impossible’ story, or trick my readers, so I had to go a long way before I could convince myself of the ‘real possibility’. What convinced me most were those moments of complete recognition, where I know I could not have found any of it on my own had I not been led by the analysis of their ratios and had I not understood the mathematical logic in their designs; I am not a mathematician, only logician. Those were great moments of ‘communication and revelation’, a 5000 year gap, but One mathematical Mind, it was, and is, as from the Beyond, timeless, it’s living the experience: there is no time, their mind is still here, there is a record, a communication, it is history, no longer pre-history, they have communicated  in the most universal manner possible, the language of mathematics!  So for me there are too many instances of ‘striking’ confirmation that I could reasonably doubt Orkney’s Stone Age Man’s ability and sophistication. Maybe I am tricked by fortunate coincidences (but then, so many?), but I also see it confirmed in their superb building techniques, their orientations, in their obvious involvement in cosmology and calendar making (solstices) and, finally, in the calculating and recording of numbers that all this must have involved.

Without having signs for numbers they realized this by incorporating ratios of numbers in the dimensions of geometrical designs and by placing them in circles and marking numbers of standing stones for counting their calendrical and cosmological cycles. Avebury is about recording the moon cycle, with 3 circles of which one has the diameter of Brodgar, again 103.67m, Stonehenge is obviously dedicated to the sun. (See further pictorial analyses of the Orkney design in the ‘Maesure of Maeshowe’ in triangles, squares and circles, it’s fabulous)

Near Maeshowe, at the now famous Ness of Brodgar site, situated between the (huge) Stones of Stenness (ever 11 or 12 standing and with less than a third left standing some near 6 m high, it still holds some of its original echo in its centre, manmade!), itself one of the earliest stone circles and henges, if not the first (having virtually the same outside measure as Stonehenge, mind you!), these Stones of Stenness on one side and the huge Ring of Brodgar (ever 60 or more stones) on the other, there is clear evidence of paint-making at the Ness, paint which could have been used to mark the stones of the two nearby Rings with different colours for counting and recording different cosmological time cycles. Here the standing stone circle becomes a record holder, a calculator and a geometrical playground, like connecting certain stones with ropes, making a square with the four cardinal points, like in Maeshowe, knowing the diameter as 198ME and consequently the side of the square is 140 ME = 73.30m; so possibly it was an educational place as well, in all it was so much more scientific/cosmological than rigidly ritual in practice.
Not only the amount of stones holds numbers, these are also in the dimensions of the works, where the ratios get geometrical and arithmetical meaning. I have argued that the two standing stone circles with perpetual drumbeat together with a huge pendulum in Maeshowe (see picture), were instrumental in creating day-time, clock-time, at the equinoxes.

Pendulum Maeshowe + starry sky

This is what the Ness of Brodgar and its environs were possibly about and probably famous for: the ‘Creation of Time’, a spiritual cosmological centre with people flocking here as ‘Pilgrims of Time’ from far and wide, to hear the heartbeat of the universe in the drums that kept the rhythm through day and night at the equinoxes  and to compare it with their own heartbeat and take that home as a measure of time, but also to see the many rainbows and marvels of the Northern lights, to hear the echo of their voices at the centre of Stenness, as in caves, to being at the end of the ancient world, beyond the North Winds (Hyperborea).

Shamanism
My explanation for the mysterious mathematical relation between Giza and Orkney has moved from Egyptian naval expeditions visiting the ‘fabled’ archipelago (Hyperborea, Atlantis) with on board the great architect and healer Imhotep in his youth (who then later built the  Saqqara pyramid), to ‘morphic resonance’, same (evolutionary) things occurring in unconnected places at the same time (Sheldrake), onto the shamanic ‘Supernatural’, of which I now think the last one is the most probable, but morphic resonance is a close second. As shamans claim they derive their knowledge about use of medicinal plants in trance from the (spirits of) the plants themselves and they climb the Rainbow, I have considered that a geometrical form of their beloved Rainbow might have revealed its numerical/rational/pictorial make-up to the shaman in a similar way. (shaman Joska Soos’ paintings are highly geometrical, as are some of his contentions, see ‘Shaman and standing stone’). Since it is very well possible that Giza and Orkney were, at least partly, contemporary, a synchronic shamanistic and supernatural revelation in both cultures must be reckoned within the  possibilities, it could be that the Megalithic Ell, as well as the equivalent Royal Cubit, do indeed represent the ideal ‘cosmic unit of length’, each occurring in some local revelation and showing again ‘man as the measure of all things’ as we see it in palms, feet, thumb and finger measures and that indeed this sacred length was found by or revealed to both scientific Megalithic cultures as they appear to use the same number-logic as well and came to the same ‘crucial length’ of 198 Megalithic Ell or Royal Cubit (198=2x99) = 103.67m.
It’s all about the ratios of 11:7 and 10:9 and their ‘interactions’. We see this length returning in the diameter of Brodgar’s Ring and in that of one of the inner circles of Avebury’s lunar clockwork  (chapter), even the (irregular) stone circle of Newgrange (103.6) is thus reported, but, more importantly, this length is also equal to the square base length of the 3rd Pyramid at platform level, 198RC.
Lehner’s unreliable data suggest 196RC = 102.63m (L=102.2) and 200RC = 104.7m (L=104.6) but this makes no difference for the relevant value of the diagonal. (I think a satellite and computer imaging should do these jobs by now).
This has consequences for the angles of the slopes, but these seem hardly different from the Great Pyramid’s, so I maintain that the Third is the prototype top of the First, measured exactly at airshaft exit levels, and there must be a correlation between the different sides of the Great and Third Pyramid

I stick to the size 198RC because it also appears as the distance of the floor level of the King’s Chamber to the top of the Great Pyramid, 198RC (280-82). Intriguingly it is also the pyramid side lengths at the exit levels of the air-shafts (see picture John Legon), so that the top 1/11th volume of the Great Pyramid upwards from shaft-level is 126RC (280-154, Legon) high and consequently identical with the Third Pyramid at east-platform level. This is the reason for the angles of the shafts, they had to mark out on the outside the ‘theoretical mathematical principle’ that is topping the building as its ‘mathematical brain’, a visible horizontal mark and a practical airshaft at the same time (there were most probably people in this building going about their business whatever it was, see gallery, no one was ever buried there), so a visibly marked top with ten times its own volume beneath it. (always note this play with numbers: 9, 10, 11, 14)
The number 11 (22/7) is the number of the Great Pyramid (440), with 9:10 hidden, 37 (3×37=111) of the Second Pyramid (100+37; 3 x 137= 411) ,  9 and 10 and 9 and 14 of the Third Pyramid.
The height of the Great Pyramid is equal to the diagonal of the Third’s ground floor at platform level =√(198²)x2 = 280.
The differences are very small here but can be decisive in our argument when it comes to an overall picture; the accumulation of arguments within the same framework. It is only because they had so great reverence for the building technique and genius of their ancestors (Imhotep, Sneferu) that even the Menkaure pyramid, the key to the mathematics, was built, where it is so much less impressive than the others, close to being an anomaly on the site. It may even be that the foundations of all three pyramids were laid at the same time still by Sneferu or soon after. Obviously its authentic value and scaled(!) design was seen as crucial to the cosmological (scientific) message of the whole site. This is what I read in it: when the temple is harmonious, the universe is in harmony.

Tibetan Buddhism
The shamanic connection, has become fundamental in my understanding of the Stone Age spirit. Time and again I emphasize how much I try to appreciate the world-view of shamanism as it emerges the world over in the Stone Age and with this fascination the Tibetan Buddhist connection comes to the fore. I am aware that shamanism is a sensitive topic in Tibetan Buddhist circles, because it would be seen by the outside world as not genuinely Buddhist. During the recent Kalachakra in Ladakh (’14), which I attended, the Dalai Lama mentioned explicitly this perception by critics of Tibetan Buddhism, possibly within Buddhism, that Lamaism and shamanism are not true Buddhism.
But what is true Buddhism? Buddhism always takes the flavour of the culture where it flourishes, like Ch’an (Zen) in China, Nichiren and Zen in Japan and Vajrayana and Tantrism in the Himalayas. The early Buddhist monks were compelled to show the Tibetan population that their Buddhist teaching could produce the same magical powers as the shaman possessed in order to convert them and gain their support.
I consider the shamanic flavour of Tibetan Buddhism as one of its great attractions, which does not at all interfere with the sincerity of the Tibetan commitment to the real great Mahayana ideals of compassion and universal liberation. On the contrary Tibetan Buddhism seems designed to heal the soul and who else than the Buddha was also called the Great Physician, the Great Healer (bhisakko), the supreme surgeon ( sallakatto anuttaro) and in that respect many Tibetan Lamas are outstanding healers.

How could there be anything ’embarrassing’ about being the heirs of spiritual traditions and techniques that go back to the unfathomable depths of the Stone Age and to the first great awakenings of the ‘human’ mind in that age; after all, several Buddhas are supposed to have preceded our historical Buddha and they don’t come by every few centuries, it seems. Besides that the original Tibetan shamanic Bon-religion has now effortlessly been incorporated in the Tibetan Buddhist brotherhood, so it is all very close, but not at all decisive.

To me the Tibetan Buddhist and shamanistic parallels as: chosen-ones, rain-making, oracles, divination, drumming, fast travelling, form the living bridge to a ‘spiritual atmosphere’ and wisdom of the Stone Age. These techniques though are peripheral in the central teachings. The logical, dialectical and magical mindedness of the Tibetans reflect the historical situation of the tradition. It is not well-known that Tibet in its Buddhist florescence for centuries culturally dominated the whole of Central Asia to deep in Siberia. The similarity with Mongolian Buddhism is evident and that the latter also share in a shamanic tradition cannot be doubted whatsoever.
What fascinates me in shamanism is the extra-ordinary (suggestive) powers of the human mind, because those must in origin have been universal, as shamanism was, and those powers are still available to us all, in principle, I think.
Tibetan Buddhism is possibly the only highly organized tradition which has preserved and still practices these age-old techniques, most of which are beyond scientific comprehension (at the moment) and rock the foundations of the Western rational world view; “this is not possible”, we say. This same Tibetan Buddhism is now also closest to modern scientific approaches of reality  (Kalachakra) as we will see shortly, which again shows the extraordinary sharp intuitive mystical insights it is based upon.

Shamanism has been the spiritual development and exploration of the human mind through the Stone Age the world over in different places with different techniques but always with extra-ordinary healing mind-powers as a result. The first development of language must be thought of as within the shamanic horizon. Those who study root-languages like Proto Indo-European (PIE) know all too well how much insight and intelligence went into the formation, derivation and meaning of words, and there were sounds only, no symbolic frame work. Here again we see unfathomable wisdom and capability in the deep past.

As I have argued elsewhere: the very fact that shamans could risk their lives for the benefit of others places them on a spiritual level that is beyond any religion and at the same time expresses the highest form of spiritual attainment, that is: self-sacrifice for the right cause ( Jezus, Socrates, Buddha-teaching).
Shamanism is in this view pre-religious and pre-philosophical enlightenment expressing a rich and integrated spiritual life in which the whole world is ‘spirited’ and open to contact, even communication.

Context
What I have stated so far is only the historical and cultural context in which I place the mathematical theorem that I found independently of these rather ‘solid historical records’. First it was ‘Giza’ that surprisingly fitted my model, then a few years later ‘Orkney’, both these  places were just other incredible ‘gifts’ to sustain my ‘improbable’ findings in ‘natural number geometry’ and some pertinent claims in other fields, but whatever their status as scientific confirmation (at least in History), these (pre-) historical places have no bearing on the mathematical validity and importance of this model, as such. The model stands on its own; when grasped  it is amazingly ‘solid and aesthetic’.

********

Part I

Warning

At first sight the complementary natural number theorem I have ‘uncovered’ (it has always been there of course), looks like a ‘Kindergarten mathematics’ and you certainly could make a nice puzzle for very young children on the basis of it and making them acquainted with numbers and geometry in one go, it is very pictorial as well, but when you get to the amazing intricacies of it, it can become dizzying, however simple the ingredients remain, because only the numbers 1-14 are involved.
I am not a mathematician and I can only do very simple things, so most people with education can follow this exposition and enjoy math maybe for the first time. It may also be the reason why I have done what no mathematician would obviously ever do, that is changing the rules of mathematics by holding the integrity of the natural numbers as ‘sacred’ and follow where they lead. The new rules are: only natural or rational numbers, complementarity, transparency, approximation, resonance in ratios. So irrational numbers, like sqrt2, or transcendental numbers, like Pi, are off limits. Now one could argue that this is just a nice set of rules to make exquisite designs with squares and circles involving the golden rule, so: an aesthetic device, but I claim not only that it was discovered already thousands of years ago, but also that it concerns the basic mathematical rules that govern Nature as such. That is, in all its simplicity: a profound scientific device.

Given the fact that it chimes very well with the new drive for a fundamental paradigm-shift in Science, which places Mind at the centre of reality, I hope my work can contribute to strengthen this movement (Laszlo, Church e.a.) towards a spiritual foundation of science and philosophy.

The mathematical model

Decimal nine-number system (1.111…; 2.222…./ 9.999…(=10); 11.111…)
Initially this peculiar geometry evolved from a ‘decimal nine-number system’ (for lack of a better expression), that was inspired by cuneiform clay tablets from ancient Sumer (Iraq) I saw in a newspaper (’98) and worked out.  This 9-number system, Sumerian or not, is a rational number system and still at the heart of all the calculations I do here, as it is the ratio 10:9, which produces the rational numbers (10/9  =1.11111…. to 9.99999….=10, then: 11.11111… etc., so 9 rational numbers in the space of 10 natural numbers) and it is perfectly tailored for the calculations of the derived geometry; they cannot be separated. What makes this ‘natural number-logic’ such a sure and fast calculator is that it is self-correcting and self-contained and based on  natural and rational numbers only. As soon as unsuitable input is involved the logic of the numbers crashes, moreover the system is such that the answer is already at hand and could in principle be immediate. Here we may see how ‘immediacy’ in physics actually functions, it’s a mathematical necessity, outside of time (another proof time does not exist), and, given certain specifics, the answer is logically inevitable and through timelessness becomes ‘immediate’, and easily ‘non-local’ (space-less, without distance). ‘Immediacy’ functions ‘non-local’ through the Zero-dimension, I claim, the inner border-point of space, without locality, as I will describe below.

Fine structure constant*
Our model produces ‘theoretical’ values which means that our theoretical answer is usually not precisely matched in the dynamics of Reality and it shouldn’t; this shows nicely in the universal ‘fine structure constant’/α (alpha), alias, ‘coupling constant’/e (0.085424 55….) which in my system turns out to be (repunit, R3)  111 x  (10/9)^2 = 137.0370370370…= 3700/27 = α, a rational number at the heart of our model and as e it is √(27/3700) = 0.085424 21…. [because it is about repunits  (numbers consisting of only ‘ones’, 111….111) and the ratio  10 : 9, this squared = 1.234567..]]

Richard Feynman wrote about the number e, the ‘coupling constant’: “There is a most profound and beautiful question associated with the observed coupling constant, e , the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.085424 55... (My physicist friends won’t recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to Pi or perhaps to the base of natural logarithms? Nobody knows. It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the “hand of God” wrote that number, and “we don’t know how He pushed his pencil.” We know what kind of a dance to do experimentally to measure this number very accurately, but we don’t know what kind of dance to do on the computer to make this number come out, without putting it in secretly! “

This is about a ‘magic’ number, a BIG number, in short, and my system seems to show ‘how HE pushed his pencil’. I can present it in different formulas which each may show the deep-structure of the number (and without secretly putting it in anywhere).
R3, 111,  a major repunit, is involved and our central ratio 10:9 (1.11111…….) ‘squared’ (1.234567…) is involved but the number also can be read very plainly as 3700/27 = 137.0370370370… , though scientifically defined as 137.03597….. , a difference of 0.0010…., one -thousandth) The numbers 37 and 27 have a peculiar relation in 27 x 37= 999 → 999/9= 111 (R3), the numbers 3 and 37 in R3 are firmly related to one- third of the repunits in 3 x 37 = 111. We can also produce the Feynman  coupling value of 0.085424 55… as the square root of 27/3700 = 0.085424 21…, with difference of 0.00000034…., that is less than 1-millionth. Not bad (and rather better than in the ‘alpha’ version of a thousandth!).
So we see that the shape of this ‘Holy Grail number of Physics’ is rather trivial in the rational numbers 3700/27 or the square root of 27/3700, whichever  way you like (the number is apparently known in different shapes).
You won’t believe me now, but time will tell. You may think the prime 37 is random, but the repunits (111….111) show it isn’t:  3 x 37 = 111 (R3). Repunits are the key to the calculator and the fundamental wave-patterns as they reflect so closely the 10/9= 1.111111111….. relationship. Then there is the number 27 = 3 x 3 x 3, a basic cube of the pivotal prime 3. The number 27 appears also prominently in packing theory with circles in hexagons (Kepler density quotient pi/V18= 0.74048222… in my theoretical system is 20/27= 0.740740…).
(Possibly this is a key to the  enigmatic hexagon at the pole of Saturn!)
This is no longer  ‘recreational mathematics’, that ‘repunits’ are deemed to be in professional circles,  this is the ‘real stuff’, however hidden and enigmatic it still may appear now. It is the powers of 10 in relation to 9, with only one unit difference; formula repunit, only one spark changes the structure of numbers. In the powers of 10 the extra-primes 2 and 5 are stored, plus or minus 1 produce a sum of totally different primes, either 111….111 or 100….001 and multiplicated they form a new repunit and new primes.

I have given here two examples of the stunning approximations I can make with this number system and with immediate numerical transparency. But my exploration of the number system brought a large variety of natural constants to light.

Rainbow Proportion
As my personal contribution to clarifying this ‘pre-historic mathematics’ I regard the insights that the system’s logic describes a basic 10:9 resonance, which appears between spherical and toroidal aether waves at all levels, as I understand it; that this resonance is found in the Solar System data and visible in the rings of Saturn, that as other example there exists a steady 11:14 (double) Rainbow Proportion resonance and that the 2-D circle and square natural number ratios can stand for sphere and torus (ball and ring) geometries in space and for the necessary interaction of their wave-systems in natural number resonances.

The magnetic field is the effect of the horn-toroidal shape of spatial fieldlines. The electric field has spherical incoming and outgoing fieldlines, so presenting the interrelation between sphere and horn-torus mathematically as fundamental for space geometry seems more than justified.

Resonance is always a whole number phenomenon, keep that in mind, this is also the ultimate scientific ‘rationale’ for this peculiar mathematical model I developed and employ.
This last insight then is seen as the fundamental geometry of space down to the Planck-length. The mathematical model in my view could describe the resonances of the deep field vibration of physical reality, analogue to super-strings. Nevertheless it is simpler and more straightforward than super-strings, I think, (no ontological questions: what is a string made of?) and it works on all scales, be it  not with 11 dimensions but only  5 or 6, depending on what is included and how you count. (is the zero-dimension a dimension?).

Here we see what the Theorem does: it connects seemingly completely unrelated phenomena by shedding unexpected light on certain relationships, always touching on the deepest levels of reality. It’s like a magic wand sometimes. The dimensionless universal constants, for example, have no place in any existing scientific physical theory, but they find a natural translation in this model and that is a feat of great scientific importance when right, I would say, as it shows that something fundamental is missing in gravity theory regarding resonance; and numbers.

Since I have never stopped thinking about the implications of these fundamental number ratios I have naturally come to a rather complete frame for ontology and cosmology. I am aware this is pretentious, but I had no choice, it grew as of its own logic. Besides that  it was supposed to be a theory of everything (TOE), that was the challenge in those days, maybe still is, but I still wish to formulate something, find a language, that is a real bridge from science to the mystical experience and the Mind and I hope it is consistent and universal and that what I do with my very limited knowledge is setting the first feeble Kindergarten steps in the revelation of its entire scientific and mystical scope, which might be epochal.

Part II

What reality?
Reality is an important concept in philosophy and hard to define but it could be said to be that which we experience as ‘the world’ (which is ambiguous in itself, but you know what I mean, by context). What we perceive as ‘reality’ though, cannot be severed from our faculties. We perceive a world as it presents itself within the scope of our senses and capacities. Our, limited, senses ‘create’ the world as we ‘experience’ it. This insight is in the West usually attributed to the philosopher Kant, heralding the European ‘Enlightenment’ epoch, but it was an analysis the Buddha (and others) had made already over 2000 years earlier. Today the influence of the mind on reality is dramatically shown in quantum-physics where scientists have lost their grip on their concepts, creating ‘contradictios in terminis’ and other logical monstrosities, like: ‘vacuum-energy’, ‘wave-particle duality’, ‘probability wave’ and, of course, the ‘BigBang’….., that even spiritual people feel forced to believe in; such is the force of a scientific paradigm.

Kalachakra

That there is a ‘dependent origination’ of reality is another of the Buddha’s insights which scientists now have to grapple with. The link to Buddhism is in my work most ‘material’ in the concept of the ‘space-pixall’, reminiscent of the ‘space-particle’ of the Buddhist Kalachakra philosophy, in which there are five types of particles, related to earth, water, wind and fire and the aether/space as fifth. This last one is the smallest, ‘aetherial’, but most fundamental one. It is what remains when a world-system disintegrates: space-particles. The Buddhist analysis entails an emphasis on the ‘granularity of space’ as well as gives it a ‘body’ and even permanence. This characteristic makes it compatible with the concept of an ‘aether’, since this is understood the world over as ‘the stuff filling space’; the ‘body’ of space, the fabric, the energy of space.

Dalai Lama
A space consisting of space-particles generates an other cosmology than the BigBang as we will see. (note the space particle in the following Buddhist quote, as the ‘fundamental con-substantial cause of the entire physical world’, so it is the first and most basic ontological unit).
The Dalai Lama describes it as follows: “Buddhist cosmology establishes the cycle of a universe in the following way: first there is a period of formation, then a period where the universe endures, then another during which it is destroyed, followed by a period of void before the formation of a new universe. During this void, the particles of space subsist, and from these particles the new universe will be formed. It is in these particles of space that we find the fundamental con-substantial cause of the entire physical world. If we wish to describe the formation of the universe and the physical bodies of beings, all we need do is analyse and comprehend the way in which the natural potential of different chemical and other elements constituting that universe was able to take shape from these space particles. It is on the basis of the specific potential of those particles that the structure of this universe and of the bodies of the beings present therein have come about.”

Note here the exceptionalpermanence’ of the ‘space-particles’, where nearly everything is impermanent in Buddhism, but it brings these particles on a par with the Mind, which is of great importance as we shall see. The great lama actually sums up what has become a major challenge of this website: ‘All we need do is analyse and comprehend…. how the natural potential of… elements… could take shape from these space-particles’.
Unwittingly I have for years worked according to the Dalai Lama’s ‘program’ in my efforts to give the space-particle (-pixall, -granule) the fundamental place (mathematics) and properties (resonance, field) it needs to fulfil its basic function. This is a ‘realisation’ I’d never expected when working on the ‘pixalls’ although the Dalai Lama’s talk of space-particles indeed originally had inspired me to go back to my erstwhile visions of ‘sparks filling space’ (Formentera ’72), subsequently triggered by the fundamental mathematics I found when in Ireland (Beara ’98/’99).

Einstein
The following is another gift, this time from Einstein, himself a bit of a mystic , where he describes exactly the characteristics of  a ‘Deep-field’ by naming ‘singularities’, extremely dense  point-forms of energy, as the fundamentals (in 1909, before GTR). He describes effectively an aether in my view ; the point here is the granularity, which disappeared in the General Theory of Relativity and with it the ‘basic field interferences’, the ‘oscillating field’.
Einstein (1909): “I imagine to myself, each such singular point surrounded by a field that has essentially the same character of a plane wave, and whose amplitude decreases with the distance between the two singular points. If many such singularities are separated by a distance small with respect to the dimensions of the field of one singular point, their fields will be super-imposed and will form in their totality an oscillating field that is only slightly different from the oscillating field of our present electromagnetic theory of light.”
Put for ‘singularity’ the term ‘space-pixall’ and it says what I could not say better, the oscillating field is the ‘deep-field’, the aether. The pixall is the ‘valve’ of the zero-dimension, which ‘carries’ the pure light; maybe the pixall annihilates when sparking.

Max Born
A  very good description of the classic ether-concept, is given by Max Born, it helps to clarify the difference between ‘somethingness’ (aether) and ‘nothingness’ (relativists)
Born (1924): “The undulatory, or wave theory, (..) sets up an analogy between the propagation of light and the motion of waves on the surface of water or sound waves in air. For this purpose it has to assume the existence of an elastic medium that permeates all transparent bodies; this is the ‘luminiferous ether’. The individual particles of this substance merely oscillate about their positions of equilibrium. That which moves on as the light wave is the state of motion of the particles and not the particles themselves.”
We see here another suitable description of the deep-field and the ‘space-pixalls’ as I propose them, only that the pixalls are not really ‘individual particles’, but interlocked singular tiny vibrating fields (down to Planck-length region), like Einstein’s description above. (It must come close to Descartes’ ‘vortexes’ which also Maxwell mentions; these are typical ‘scientific intuitions’)

Eternity
These quotes of prominent proponents of mysticism and science illustrate perfectly where the two converge in the concept of discrete fundamental units and how the Big Bang-cosmology is made obsolete in one stroke (by the permanence of space-particles and by recurring cycles).
If there were a beginning of time how could there be eternity? Eternity can only exist and be felt because there is no time, so how can there be a ‘beginning of time’, as cosmologists claim. Eternity is not material, it is space in its ‘suchness’.
We see that Einstein intuitively describes an ‘aether’, a fundamental ‘field-filling’ of space – possibly the reason he abandoned the idea (because of his adagio: no aether)- his ‘singularity’ has a field, which, I say, it can only have because it spins in absorbing  and emitting waves. In every point of space there is a spherical incoming wave-front as the sum of all the cosmic wave-field fronts.
This front creates spin in every point and creates a reflex wave going outward, this creates a standing wave field (oscillating) and gives the centre stability and inertia. It is this interaction of the incoming and outgoing wave, the order of the standing wave which relates to the number 9, that our mathematical model describes or else, how a spherical wave transforms into an outgoing toroidal wave, that is what this website’s peculiar mathematics seems created for.
At specific frequencies the pixalls lock into field-mode and get energized, this is the reality we see and the light it is made of. This spin is also seen as a vortex to negative infinity and, as such, a border-point of space opening to the zero-dimension, the pure light.
Space only has an inner boundary, like there is no ‘other-side’ to the centre of the earth. When you can imagine that there opens a new dimension at the centre of the earth, which maybe we can visualize by taking the volume of the horn-torus as our curved space, and going through the centre point, aka borderpoint of space, we come into the space surrounding the torus surface, that is the zero-dimension of pure light (the 3D horn-torus is peculiar because its one centre point borders its whole surface and in 2-D its surface is a square).
The horn-torus, 4. π².r²  (indeed  the square of the circle =(2. π. r)², with two equal radii), is the pivotal geometry of space on this website and shows consequently that its surface equals a square, but is bordered by one point only; this now is what ‘space-curvature’ can do in mathematics, I suppose, but here I miss all the tools to continue; for instance this may also be the ontological key to the holographic aspect of reality, the whole surface of the horn-torus is reflected in the central border-point, in every point of space.
At least it is reported that the mysterious centre of the earth appears to have clockwise and anticlockwise motion, which is perfectly feasible in a horn-torus geometry and as such the doorway to the zero-dimension.
No better geometrical way to see how all is one.

Pure Light

The ‘pure light’ of the zero-dimension, although ‘outside’ of space, is in every pixall, so every pixall is a ‘carrier’ of light (‘lumini-ferous’ aether), which makes it literally true that everything is ‘made of light’ and this is why light does not travel and ‘speed of light’ is a misnomer. In this conception the ‘ray’ is a string of sparking stationary pixalls, which makes it appear discrete as a photon in observation, but the photon has no self-substance, it is just a rather randomly hit and sparking local pixall. The notorious double-slit experiment becomes trivial when you realize that the whole interference pattern of the ‘deep-field’ changes when you open or close a slit. The deep-field lines change, so do the the pixalls in their alignments along the field lines, there are myriads of wave-fields going through the slits, so that the pulse travels through a completely different local deep-field in either case. At quantum level what we see as matter, the sides of the slit, is merged with the surrounding space, it is blurred, besides that the photon, has no eigen-substance, is a travelling excitement of  space-pixalls. The whole ‘quantum enigma’ may disappear when you have an aether, a deep-field, and no ‘self-substance’; the ‘virtual particle’ is the ‘dormant pixall’, nothing virtual about it, except for its permanent inner metamorphosis.
There is a deeper layer to reality than meets the eye and scientific lens, a layer that has to be inferred because by nature it cannot be ‘detected’, it moulds everything, it is the zero-dimension at the heart of every space-pixall.
I do not think quantum-mechanics is as mysterious as it is made out to be, it is a matter of the right description, I predict, and of giving up long cherished and stern intransigent views about the ‘non-aether’, by embracing the aether again, however modified and ‘aetherial’. That there is something rather than nothing after all.

The notorious ‘wave-particle duality’ gets also dissolved in our description, because the wave is the form, the configuration, whereas the ‘particle’ is the observed momentary pixall-contents, the substance, of the, always ‘passing’, configuration through the deep-field.
The wave is the pulse, the form; the space-pixall is the medium, the substance. The ‘relativity’ here is that the deep-field is always at rest; no ‘energy- ‘forms’, though, are ever at rest, they are always changing, moving. From the point of view of the ‘form’, it is itself at rest and the deep-field flows through it, this is the ‘relativity’-aspect and caused by the substance of the form being fundamentally at rest; that is the paradox of the moving form (we feel at rest while constantly moving through the deep-field, our substance is always at rest, like being at rest in a seat in a moving vehicle).
The form moves through the featureless fixed pixalls of the 4-D space screen, the deep-field, so the form (image) has no substance of itself, no ‘self-substance’, its ‘material’ content is the seemingly fleeting deep-field. Nor does the deep-field have form of itself, it is Substance as an aggregate of space-particles, formless, ‘unborn’.
Only together  form and deepfield create an ‘appearance of endurance’.
’Form is emptiness, emptiness is form’. (Heart sutra, Buddha)

So what we try doing in the following is finding a description of the ‘One-ness’ in personal experience and reality, an ‘enlightened ontology’; or how mind and space (-pixall) merge in the zero-dimension, how matter becomes mind, how duality disappears. That is the crux.

Part III

Space and mind

To get to grips with ‘matter’ as manifestation of the mind, we have to carefully describe how it occurs in space. We have to become more aware of this deep relationship of space and matter, and of space and mind (where time falls away), because when you thoroughly catch that insight you must be halfway on the road to enlightenment, to ‘true liberation’. Experiencing the ‘ideality of reality’ is a key to understanding mysticism and concepts like Maya and Emptiness.
A way of understanding space as mind is seeing that space is no ‘volume’, and has no ‘abode’. A volume is finite and is in a place, but space nor mind have a boundary or location.
Our concept of physical space is wrong, because we see it as a ‘vacuum’, ‘void’  containing ‘things’, whereas it is the ultimate ‘plenum’ and the ground of all existence as the manifestation of the One (Mind).
Your life, your ‘being (thrown) in the world’, your existential ‘Dasein’ (Being around) is, however you look at it, at basis and in last analysis only: ‘experience’. This is what makes our lives ‘mental’: our body produces ‘experience’ and experience produces ‘memory’ (past) and ‘expectation’ (future), both ‘fill our mind’, it is our ‘stream of consciousness’, ‘our world’, the ‘myth’ we believe in and live by. Our seemingly solid world is no more than the background of our individual and collective experiences; that is the real stuff ‘our world’ is made of. How strange. It is here now and gone the next moment, a flux
We don’t understand the nature of our experience because we do not realize the workings of reality, that is: ‘of our mind’. Again, our mind shapes the experience (you feel buoyant, world is bright, you feel bad, world is bleak), so the mind is the essence of it all, not matter, matter is the surface, the surface of the mind. (see No matter at all)

99% space

What we know about atoms, the entities that give all the ‘qualities’ to ‘matter’, is that they form a neat mathematical system: the ‘Periodic Table’, one of the basic proofs of the mathematical basis of reality, and that more than 99% of the atom’s ‘body’ is space! It’s the physics-teacher’s golden moment when he baffles the class with this truth, matter is 99% space, wow! You would think this discovery was more important than Copernicus helio-centrism, but, no. This startling fact namely implies that we ourselves are 99% space. It was already a shock to find out we are some 70% water, but 99% space really beats it all. What ‘matter’ are we still talking about then, you wonder? We are the key to understanding matter, because we are matter ourselves, that is: 99% space. When all that bodily matter is (mostly) space it becomes easier to understand feelings and consciousness, it is just the state of space in the body. The brain is also 99% space, as if we didn’t know. Through the brain we are one with the deep-field and the zero-dimension of pure light.
We are plugged into the timeless universal storehouse of experience and have instant memories of a distant past, another indication time is not involved. The concept of ‘karma’ is also outside of time, as seem all ‘dreams’ coming from the ‘universal storehouse’. (A long dream compressed in a few seconds, no time again)
The most enlightened state of humankind is the bliss of the pure light (‘clear light’ Buddhists say), becoming one with the deep-field, Akasha.

Aether

One of the central points in my approach to ‘cutting edge’ theoretical physics is the re-introduction of the concept of the aether. It is good to see that over the years more and more scientists come round to an aether concept again. Referred to is, for instance, the Hindu Akasha-field, the Chinese Tao/Dao. So we see also here a re-introduction of very ancient human knowledge, but knowledge based on enlightened insight.
In many Eastern philosophies, as in ancient Greece, the popular 4 elements : earth, air, water, fire are invariably philosophically accompanied by a fifth:  ‘aether’  or:  ‘space’. In my system this ‘aether’ is usually called ‘deep-field’, as the actual ‘substance’ of reality, although, it must be said,  this goes beyond the classical aether-concepts.
Scientific concepts cut reality up in fragments, but this present ‘aether’ is integral with the One, an ‘experience’. Its concept is as in the East: a rather all-encompassing element, space , an aggregate of space-pixalls.

This ‘aether/space-as-substance concept’ is an illuminating way of describing the inmost of ‘surface-reality’ (holography) and with it elements of the mystical reality, like Spinoza’s Substance. It is a way of describing the ‘emptiness’ of ‘particulars’, how it is all of ‘one taste’ as the Buddhists say. How it is at the same time ‘Nada Brahma’, as the Hindus assert, the primeval sound, the ground-vibration. (Sound can serve as a door to liberation and -sudden- enlightenment).
How could ‘the Ultimate’ not be these things, these qualities, since these are words expressing the highest awareness and insights of quite diverse human cultures, levels of experience where science plays no part, where ‘enlightened intuition’ rules supreme. So our ‘scientific’ world-picture should contain these elements.

‘Experience is: the world’

Our immediate environment, that is the way we know the world. It seems a fragment but through Mind it represents the whole. Understanding the character of this experience of the ‘here and now’ as the whole is the doorway to liberation. We can begin to appreciate that our experience is the ‘world’ and that the seeming permanence and firmness of the world ‘out there’ delude us as regards its true character, it has no own substance, it’s mental,  that’s why the Buddha called it ‘empty’, an illusion, a dream.
In the Lankavatara Sutra the right understanding of reality is expressed as follows: ”When an objective world is no longer grasped, there is neither disappearance nor non-being, except something absolute known as Thatata-vastu, Suchness, the realm where the wise have their abode”.
We see here the ‘Suchness’ of the world brought back to the subjective experience as deepest ground.
Does our body represent a solid world? How does ‘solid’ feel like? In essence our body is only fleeting feelings, sensations, moods, images, nothing solid, it’s mainly space, as we saw.
Herein lies the big mistake, the source of our ignorance, that we separate matter, our body, from our consciousness and from the rest of the world; a double existential mistake. Our body, as it is to us, is only in our consciousness and it is not separate, but the centre of our world. We tend to think of the body as a thing, but in last analysis it is the centre of ‘experience’. When unconscious, there is no world or body at all.
Things only really start to ‘exist’ in our experience, when not perceived the world is in a limbo-state of ‘tasteless’ potentials, that only ‘materialize’ through consciousness into the forms we experience. Nous sommes le Monde, we are the world, we even ‘create’ it. Experience is our ‘being in the world’, one could say that the important Buddhist distinction of ‘sentient beings’, refers to beings that ‘experience’ a world due to their senses.
So, again, the faculties of our mind create the world we experience and because this is so we can improve the world we experience by enhancing our faculties and intuitions. Animals differ from humans in this important respect that they cannot improve their collective and individual conditions, their mental capabilities are exhausted, their evolution of consciousness stopped, where they lack past and future in their consciousness (although they do remember by resonance), they cannot reflect and plan other than in an immediate situation or by collective instinct. We are definitely ‘more enlightened beings’ than animals are (although in many ways they far surpass us in sensitivity), because of our sense of eternity where past and future melt into the One, where the here and now gets expanded with past and future, in distinction to animals, it gives us in principle infinite possibilities: we are reflective and prescient (if only we were).
It is in enhancing our individual and collective consciousness that our only hope for humankind can rest. The Juggernaut we are on collectively is heading for the abyss because there is still no really integrated collective control or any solidly agreed perspective for improvement, a lot of words so far. But the real cause is of course the ingrained competitiveness and self-centred-ness of the industrial age, the socially corrossive capitalist order and economy, there are no common perspectives, it is any for his own, a bonfire of greed, until its collapse.
Another problem is  that our collective crisis seems not very acute because it seems to hit the periphery, whales, polar bears, ozon-layers, rain-forests (rather  ‘peripheral’ as vital climate and  genetic storehouses), oceans in cms per century; it does not affect our daily lives, until recently. But in the mean time humankind has become a devastating plague to its own natural environment, by totally overstretched production and waste in every area (also finances), an ominous condition for the crash of a civilisation.

In the ancient past one of the incentives to stone-building was to build for many, many generations, that should be again the perspective of collective endeavers.

*******

### Stonehenge, a gigantic graveyard?

Friday, March 15th, 2013

Intro

Ramilisonina came to Stonehenge, as the story goes, and immediately proclaimed from his gut-feeling: ‘these stones were put up for the ancestors’, and that was it, enough ‘proof’ for MPP to accept his theory and write a book about it. Nowhere else has this connection been substantiated since nowhere else any significant numbers of burials are found in connection with henges or stone circles. Some pit circles seem to have burials, but you can’t have it both ways in Stonehenge, it’s either pit or standing stone. This by itself already completely undermines the ill-founded theory of an ill-informed foreign archaeologist, a theory which by now has become the most prominent one in the media in Britain, probably America, possibly the world; British archaeology is squarely put back to the death cult ‘cul de sac’ it has been in for ages.
One wonders whether it will ever want to work its way back to reason.

Woodhenge

The fact that most of the examined bones from Stonehenge come from the upper layers of back-filled pits, the well-known Aubrey Holes, 0.6 to 1.15m deep, shows that these pits were most probably originally intended to hold enormous wooden posts, like it was custom in the area at the time. Like Woodhenge (pictured, with close-by tree-lined Durrington Walls’ green in upperrighthandcorner) more and more of these timber and pit circles come to light these days. Such deep pits as the 56 of Stonehenge were certainly not for burials as burials were, as observed, usually in the upper fillings and not over a metre deep in the ground. Here I quote Atkinson, the first scientific excavator in the fifties of the last century extensively, with my comment in brackets and bold script: “The sides are steep, the bottoms flat. Their contents were extremely mixed. In general, however the filling consisted of chalk rubble originally dug out of the hole, which had apparently been deliberately shovelled back soon afterwards, some of it having been disturbed by the digging of later holes into it, often right down to the bottom, which were filled with burnt soil containing fragments of charred wood. In most of the holes there were deposits of cremated human bones, either in compact masses (a hat full) or scattered throughout a large volume of filling. Sometimes these cremations were in the primary filling, but more often in the later disturbances.”(…) “The main concentration (of other burials) is near Aubrey Holes 14 and 15, with smaller groups in the ditch

Analysis
What can we learn from this, when we don’t start with preconceived ideas? That there was a rather well-measured circle of evenly spaced deep holes, as all the pictures show, that the regularity implies they were dug in the same short period and that they were part of a design which by now has been proven to be highly likely cosmological, pertaining to the moon cycle and eclipses. (Burl says the pits were not so regular, but this happens when you start digging at your reference point and lose it that way, worsened by others taking over). There were 56 pits in number relating to 3 moon cycles in years (3 x 18.6) and to twice 28 relating to the female fertility cycle in days. After having been dug completely(?) (were the shallower pits ever finished?) they were then back-filled rather soon, it seems (but really it is high time 2 or 3 fresh holes are meticulously and, if possible, objectively excavated). This could mean a change of plan from holding wooden posts to holding standing stones, but this is by no means certain from the evidence because the crushed chalk at the bottom could just as well have been from heavy wooden posts later dismantled. (Is there no report from Woodhenge on this?) By all means the Aubrey-circle was primarily a spiritual/scientific/cosmological place (which were ‘one thing’ then) where days and years were counted and recorded, eclipses predicted, so absolutely not a cemetery. That it got used for possibly ‘clandestine’ burials may have been the very reason for the quick back-fill by the cosmologists, but it is useless speculating until a thorough investigation of preferably several new holes is done. And what about ‘scattered bones throughout a large volume of filling’? This happens when you start digging for your own family burial at an auspicious site in the soft material of a back-fill, very convenient, and that you find out too late that someone had already been buried there, the place was occupied, so you back-fill and try find another back-filled hole. It is this which most probably caused the scattering of the earlier burial. Besides that, again, it was most probably done ‘clandestinely’ at times it was not much used because the place was not a burial ground, but a lunar observatory in the first phase.

The whole picture is one of haphazard burial by private groups of people (not the kind of large gatherings of today) at some preferred but random places (nr.14, 15 due south-east of centre and in the ditch) over a long, but possibly even short, period of time, just as you would expect from a place which was not intended for burial, but auspicious for other reasons as it happens throughout history.

Spotted bluestones from Preselis
The spotted bluestone as shown in the picture, is reminiscent of the night sky relating to the Milky Way, the moon, fertility, the cosmic cycle. Some claim now they were brought to the area about 3000BC, this is 500 years or more earlier than has been presumed until now and has not been substantiated yet. Some claim now they were burial markers completely ignoring the question as to why they would take the trouble of getting them from the Preselis in the first place and then would have placed the stones subsequently in the Bluestone Circle on the bank of the Avon at the end of the Avenue. I have no doubt that the spotted bluestone was coveted for its special starry sky-like appearance, the fairytale-like landscape it originates from where (holy) springs abound and possibly for its healing powers, as others have suggested. Even in the latest settings at Stonehenge the bluestone numbers are related to the moon cycle in the numbers 19 (horseshoe) and 23 (earlier oval)(230 moon cycles in 18.6 years, 235 in 19 years, Metonic cycle; you have to know your numbers to give meaning).

Giant graveyard
We see from the above down-to-earth analysis, that there is absolutely no indication of organized burial at the site, let alone 56 reservations for members of a royal family for the next millennium, on the contrary it has all the features of, as said, occasional ‘clandestine’ burial, just as in the megalithic refuge chambers, mostly a handful over time-spans of many hundreds of years, but we find in the Guardian this quote of Parker Pearson: “The first bluestones, the smaller standing stones, were brought from Wales and placed as grave markers around 3,000BC, and it remained a giant circular graveyard for at least 200 years, with sporadic burials after that”. This is just completely unsubstantiated kladderadatsch, because it suggests that for every burial they went to Wales to get a stone which everybody can surmise will never have been the case. These projects of hauling stones were of course big long term enterprises with a lot of mainly men involved over doubtless many, many years and seasons, but inspired by some great spiritual vision, because an enormous amount of ‘enthousiasm’ (etymology: by a godhead inspired) is needed to motivate people in undertaking it. It is inconceivable the transport would happen every time someone, a child, a woman or a man died and was interred at the site. There is absolutely no connection between a standing stone and a burial, except that some people may have liked to bury or be buried near standing stones, but that is a completely different perspective. The idea of the Aubrey Holes being originally dug for the Blue Stones is nowhere substantiated.

Hawley and Cunnington
Hawley, who excavated about 30 Aubrey holes between 1919-26 and discarded all the bones he found and which have just now been investigated, into one pit nr.7, Hawley initially thought the holes were for stones, indeed, but changed his mind when he saw with his own eyes Maud Cunnington’s excavated pits at Woodhenge which were exactly the same. Since there is absolutely no doubt about Woodhenge holes being for wood, this is for me full proof the Stonehenge holes were initially dug for placing wooden posts, not burials, so the concept of a cemetery is false. The closeness of Woodhenge is significant because that seems a very interesting building with a circular beamed roof possibly ( the biggest posts are in the middle rings) and an open space in the middle. This woodwork would come back in the typical connections of the stones. I am pretty sure Woodhenge is earlier than the  sarsen period, but may have been contemporary with the early Bluestones, of which some also have the ‘wood-connection’ fo lintels, this may have been the architecture of the Bluestone circle in the bend of the river Avon, later brought to the centre of Stonehenge. Bluestone chips in some filling, may be of a much later date, because the holes were dug out again and again over a long period of time. The holes are round like tree trunks are, like Woodhenge, the bluestones are not round. It is noteworthy in this respect that in the Y and Z holes only one bluestone chip in each was found placed at the very bottom, a foundation burial of sorts; this, to me, is clearly a symbolic act and emphasizes the bluestones had a specific spiritual meaning, maybe the Preselis in Wales  where they came from were seen as a holy place with its profusion of sacred springs and the quarry for these magical stones. (the Dragon’s Back). It was also almost certainly related to the moon and fertility since there were 59 Y and Z holes equal to 2 synodic moon cycles of 29.5 days. There were 23 bluestones in the centre: 59 +23 = 82, this is 3 x 27.3 (sidereal months), all connected to bluestones. You see here again how Stonehenge abounds in meaningful numbers: 29 and a half sarsen (nr.11) in the ring. All coincidence? (the half sarsen in the outside ring would not have supported a lintel, so in design there were 28 lintels and an opening with a sun-dial in the ring to the south, with the sun in zenith. (28 + 5 central lintels = 33, which times 10 is 330, the number of days of waxing and waning sun volume, the sun cycle) The sun and moon cycle became numerically integrated in the whole design. A further problem with a very early hauling of the bluestones for a two hundred years burial span, as would follow from some theories, is that it suggests that there was a time gap of some 500 to 700 years between a practice of moving huge stones over long distances which in my view is highly unlikely since people don’t take up practices of a long gone ancestry. A circle of bluestones in the Aubrey Holes is contrary to the evidence in the excavation records of the pits.

Bluestonehenge
The chance discovery of Bluestonehenge in 2009 at a ford of the River Avon at the end of the Avenue is a major find, because it is the final proof the bluestones were transported by water all the way, that is, not only by sea but up the river Avon as well. Atkinson proved this possibility already in 1954 in a television program! (Quote: It was clear that the raft could have been propelled at least in slow-flowing water, by a single man).This means the widely published overland route from the Bristol Channel coast

is at least not correct for Stonehenge, it was by river, the easiest way.

I happen to know and have investigated the river Avon (pictured) some 15 years ago when I was researching for a novel with the title ‘The building of Stonehenge’, which did not get past its 36 pages when they found evidence for a Beckhampton Avenue at Avebury, which Stukely had reported 300 years ago, a man I hold in high esteem, for his phenomenal intuitions. It ruined my set-up, but that is another story. (William Stukely, I recently found out (Burl) derived the Druid’s Cubit from Stonehenge and it measured 20.8 inch, that is 0.5283m, which is just 5mm difference from my Megalithic Ell of 0.5236m, remarkable. My Meg.Yard differs 6mm from Thom’s, nevertheless both Thom and Stukely have priority when it comes to these units, of course). The Avon is a smoothly flowing rather shallow river about a metre deep without any cataracts and with a firm level sandy riverbed from Pewsey to its mouth at Christchurch. It is found to be the river with the most species of fish in Britain, by the way (Wikipedia). [In my next post which I hope to get out soon, I will show how the huge sarsens of Stonehenge (up to 50 tons) were transported by water over the Avon river. I think I am the first to suggest this and carry this idea for 15 years now, obviously it’s about time it gets out.] The new Blue-stonehenge circle of purportedly 25 standing stones (I bet it’s 23 or 22) is 10m diameter (19 Megalithic Ell= 9.95m!) and is right on the riverside, where there is an easily accessible natural ford (wading place) which is unique just in this section of the river down from Durrington Walls because the river cuts through a ridge with steep riverbanks in this area. A ford is essential for and used by living people, not by the dead, so the theory of a stone circle as symbol of a domain of the dead where the living keep away from ends here. You don’t make an exclusive domain of the dead at the only place for miles where the living can cross the river. It is more likely this circle, if it was a bluestone circle, was placed as a symbol of spiritual connection with the sacred Preselis in South-Wales and as marker for the main entrance of Stonehenge as cosmological centre, the spotted stones as symbolising the night sky, the Milky Way. These 23 Blue-stones would then eventually have been taken up and placed at the heart of Stonehenge in the horseshoe.

Fallacy

Again and again archaeologists make the mistake, their persistent scientific fallacy, the Achilles heel of a beautiful discipline, that when they find burials at a prominent site they think that that is the ‘raison d’etre’ of the site, whereas of course the opposite is true, a site is prominent for spiritual reasons and this is the ground some people bury their dead there so as to give them an auspicious passage to the afterlife. All the subsequent bronze age barrows testify to that. Would the Beaker people and Bronze Age chiefs honor Stonehenge as a funerary site for the ‘conquered’ elite that were buried there? Give me a break. The practice of interring at such sites in the late Stone Age was moreover just as rare as cremation still is today in Europe, or even more so, because comparatively very few burials are found of these ages. They just did not make a difference between people in those halcyon days, even children were treated as equals (no babies though it seems). It was probably a burial tradition in some families or in certain spiritual convictions or circles, nothing more. It is a practice you find all over the world at spiritual sites. This is why people get buried in and around churches, caves, waterfalls, places of outstanding natural beauty, their own estates. No church was ever built for the purpose of burying people in or around, everybody knows that, neither were megalithic refuge chambers, as I maintain. Do you think there were Stone Age guards around a bare henge or a chamber for hundreds of years to prevent ‘commoners’ from burying at the Royal Cemetery? It is even known that until quite recently druids did burials at Stonehenge. Quote Atkinson: ” Well within living memory the latter-day Order of Druids buried portions of the cremated remains of their deceased members within the Stonehenge enclosure, a practice now forbidden.” How about that? Well, that’s what happens, that’s what people do.

Time span
Archaeologists often seem obsessed by burials, and by finding them, because it indeed often are the richest sources of insight in former cultures in their field. This is exactly the problem: Because burials are so important for archaeologists, they assign a totally disproportionate importance to them in the assessment of the cultures they investigate, the whole thought of ‘royalty’, of any structural ‘power’ hierarchy is squarely at odds with the shamanic spirit of the Stone Age, which is indeed marked by indiscriminate burials of men, women and children, a rather sure sign of an egalitarian and largely ego-less society. If there is one thing that characterizes the watershed between Stone-age and Metal-age culture it is just this: the birth of the ego from competition and inequality, following horse-riding, superior weapons and wine (signs of nobility to this day)

Another solid proof
According to Alexander Thom and Aubrey Burl (Stone Circles Br.Isles I) the dimensions of the Aubrey holes ring are as follows expressed in their data and in my units of length, see how close Aubrey hole circle: Perimeter: 271.60m = 330 Megalithic Yards = 330 x 0.8228 =  271.52m (Thom= 327.6MY) Diameter:    86.40m = 165 Megalithic Ell       = 165 x 0.5236  =  86.39m  (Thom = 104.2MY) This is another striking example of my formula of Pi as 2MY circumference and 1 ME as diameter Pi = 2MY/1ME. (330/165) This outcome is far better than Thom’s 131 Megalithic Rods (271.5m), where the prime number 131 means absolutely nothing and his Megalithic Rod (2.5MY) looks like a desperate attempt to make things fit where his Yard failed. In my model nothing is ‘forced’, I don’t do anything but apply the data, it just always fits meaningfully as this website shows over and over again. It is sad Thom was wrong with his Megalithic Yard by just  some 6 mm and never got what he so rightfully deserved. The rationale of the 330MY can be found in the sun cycle of 33 years after which an alignment with the sun at the equinox will be exactly the same as 33 years earlier, so posts set every 10MY (8.23m) on this circle can be markers for the count of years.(Heath, 1998, Mackie, 2003) A cache of 33 quartz pebbles was found close to an equinox alignment near Argyll, Scotland. (33 is also the amount of lintels in the design, with 28 in the ring and 5 in the horse-shoe, the number 10 is in the horse-shoe sarsen uprights) [28 = 30-2 at the south half sarsen nr.11, 1/2 of 29.5 days moon cycle] Just now (may, 2015) I read that the sun has also an internal cycle of 330 days waxing and waning, another ‘year-cycle’, by which its volume and activity waxes and wanes, this cycle the ancients could have known by shamanic insight, like most of their mathematical and cosmological knowledge.
The overall diameter of Stonehenge (plus ditch) is given as 110m (Burl), which is 210 Megalithic Ell (210 x 0.5236 = 109.96m) so we find again the Rainbow Proportion, since 210/165 = 14/11 = 1.272727.. or 110 / 86.4 = 1.273 which is also 14/11 = 1.2727272…. (you want more precision?)
A diameter of 210ME gives a circumference of 210 x 22/7 = 660 ME (2 x 330), which is of course 420 MY, (since 11ME=7MY), again 420/210 = 2MY/1ME, which is Pi, isn’t it neat?
The ring of 660 ME can also be used for the sun cycles of 33 years and 330 days of course with markers every  2 or 20 ME (1.05m or 10.5m) on the circumference, possibly aligned with those posts in the Aubrey ring. There always is astronomical or mathematical meaning in this system, or both, it just works infallibly.

(photo) The Aubrey Holes are the biggest yellow ring of dots which relates to the outer ditch perimeter as the Rainbow Proportion, 11 : 14, (as area ratio it is 100:162 or better 1 : 1.620, but also 1 : 1.618, the golden mean, since sqrt(1.6180……) = 1.272 0196….  and 1.272 72727….. =  11 : 14  (differences in the thousandths are of no consequence, they function identically in our system, they resonate, tune in.
***

At the Ring of Brodgar the stone circle is related to the outer circumference of the sloping ditch as 198ME : 252ME or 103.67m : 131.94m = 11 : 14, also the Rainbow Proportion. These two world famous henges, one in the south, the other in the far north of the British Isles, relate exactly in the ratio 5 : 6, a proportion which figures prominently in the amazing double square design of Structure 1 at the Ness of Brodgar in Orkney. (See: Math at the Ness)

Double Rainbow proportion between stone circle and outer circumference ditch at Brodgar.

Isn’t it again all perfect coincidence. Well, at least I do nothing but relate known scientific data in an ordered manner with a perfect mathematical model, just desktop science. You cannot keep on saying that all successive mathematical fits and facts are mere coincidence. I try to interpret it all as ‘consciously designed’, if that is not the case then it is of miraculous subconscious design, because the maths does not budge and the data don’t go away, and the neglect of coincidence as ‘meaningless’ is a fallacy every Buddhist will raise his eyebrows on.

***************

Afterword: After publishing above post an important citation of Hawley came to my attention which comes from his preliminary report for the Antiquaries Journal in 1921, his first and biggest excavation, Hawley:
“The holes vary very little in size and shape: the biggest is 3 ft. 5 in. deep, its maximum diameter 5 ft. 3 in. and the minimum 4 ft. 6 in. The smallest is 2 ft. deep, maximum diameter 2 ft. 6 in., and minimum 2 ft. 5 in. They are as a rule sharp and regular cuttings in the chalk, and are all more or less circular. ( Trees are circular, bluestones are not. YG) Many have the edge of the chalk crater shorn away, or crushed down, on the side towards the standing stones of Stonehenge, this being apparently due either to the insertion or withdrawal of a stone, probably the latter. From their appearance and regularity there can be little doubt that they once held small upright stones; for, in two cases at least, a portion of the excavated chalk appears to have been returned, as if the hole had been too deeply dug to suit the intended height of the stone. This returned rubble was extremely hard and compacted, as if a very heavy weight had rested upon it for a long time. (Note this crucial argument. YG) With the exception of four holes, all bore evidence of cremated human remains having been deposited in them, and at least three showed signs that actual cremation had been carried out in them.”

This was in 1921 when nothing was known of big post-holes anywhere, until Maud Cunnington caused a sensation by excavating Woodhenge with its big post-holes in 1926-27, posts not bigger than the Aubrey holes, I know from seeing the concrete stumps myself, the largest being at most 1m diameter, if I remember well.
Seeing this excavation is what made Hawley change his mind on stones having been set in the Aubrey Holes, it would have been big wooden posts. QED.