Maeshowe, Giza, Mathematics

This post has been added to the pages under the title Third/Menkaure pyramid theorem

The Geometry of Square Root 2                           1/11/14

Perfection of megalithic Maeshowe design

Introductions

Mathematical Integer Theorem

This website is an effort to bridge the gap between mystical knowledge and scientific exploration of ‘existence’. This new ontology (ontos= authentic essence of being) revolves around a supposedly ancient mathematical whole number (integer-) theorem with evidence and clarification given in many chapters and pictorials. I’ve called it by many names, ‘Geometry of Square Root Two’,  ‘Pyramid Proportion’, ‘Maeshowe Theorem’, ‘Celestial’ and ‘Rainbow Proportion’, reflecting its contents and versatility, but the  ‘Lost Giza Theorem’ is an appropriate historical name, I think, because it went lost for over 4000 years, although it still stands in Giza. The crucial ratios of the theorem have been solidly recorded in buildings of at least two ancient ‘megalithic cultures’, in Giza, Egypt and in Orkney, Scotland, an archipelago (megalith = big stone). For Orkney it means going back into the late Stone Age some 5000 years ago, 3000 BCE, to Maeshowe and its squared space, for Egypt it means Pharao Sneferu’s Meydum pyramid, 275 : 175 = 440 : 280 = 11 : 7 (first ‘true’ pyramid, after Imhotep’s step-pyramid-type), and the Great & Third Pyramids at Giza, up to some 4500 years ago, 2500BCE, but possibly partly contemporaneous.
Both the Atlantic and the Mediterranean Megalithicum ‘eternalized’ their scientific/cosmological knowledge in stone buildings and erected huge stones to exalt the sun and cosmos of which some probably also functioned as sun dials (Obelisks – Egypt, Grand menhir-brise – Brittany, France).
The Lost Giza Theorem can be seen as on a par with or even complementary to Pythagoras’s famous ‘right angled triangle and squares-theorem’ (a² + b² = c²), of which the ratios appear in Giza in the Second Pyramid (3: 4: 5), though long before Pythagoras. The ‘Lost Giza Theorem’ itself also happens to be a ‘square-theorem’ as we see it in the Great & Third Pyramid and in Maeshowe (Orkney), but this theorem contains the relation of squares and circles (and eventually tori and spheres), so you bet a more intricate one, and indeed it is different, very different; so different with its hidden rules, that it got lost and the lesser but seemingly more precise Pythagoras-theorem (9+16=25) survived to this day.

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

Maeshowe Circle-Square-Circle Theorem and Rainbow Proportion
Yellow square perimeter equal red circle circumference; areas 11:14
Integer-logic logo: yellow 9-grid orange square in blue circle (or.=red)
red centre square side=9ME blue encompassing circle segment=10ME
big blue circle=80MRemen= inner diameter Stonehenge= 29.62m
inner blue circle to red circle = double rainbow proportion

What the Lost Giza Theorem does is expressing the ratios of ‘squares in circles in squares in circles….’ (inscribing, encompassing) in integers (whole numbers), that is, in a specific set of fixed unchanging integer ratios, like 11:7 and 10:9, the quintessential ones. (To remind you: in standard maths this is only achieved through the irrational transcendental number Pi, π, that blocks any smooth relation between numbers in circles and squares). The eventual order is achieved by using a ‘rational’ approximation of π (ratio circle and its Euclidean diameter, 3.14159…) and one of π²-squared ( 9.8…), respectively 22/7 and 800/81. Its true significance though lies in ‘squaring the circle by circumference’ (this is different from the famous ‘area-squaring of the circle’).

It is here that the interaction and interference of sphere (ball) and torus (ring) geometries take place, where the ratio 10:9 is in the resonance between the two geometries sharing the same centre, the incoming sphere bounces back as a horn-torus(square), this a standing wave pattern, with intermittent resonance points, appearing as discreteness. This ‘squaring the circle by circumference’ as mathematical operation gave us ‘the Great Pyramid’ as the geometrically square abstraction of the (hemi-) sphere (globe, the earth). In Orkney the theorem, in a peculiarly extended but most rudimentary form (8: 9: 10), lies hidden in the lay-out of Maeshowe megalithic chamber and comes into the open in the dimensions of the several man-made circles of nearby Brodgar ( its standing stone circle and rock-hewn moat with 2 sloping edges, 3 ratios), but here expressed in the big numbers of Giza (99/198 and 140/280), it is the full integer-solution in the ‘rationalisation of number-irrationality’ (see Rationalizing the ir-rational) and of the incompatibility problem of the irrational numbers like  square root 2, 3, 6 = √2 , √3, √6 (which are here now rationalized as follows: respectively
√2 = 1400/990 = 140/99       or   99/70
√3 = 1715/990 = 7³/2×99      or 400/3×70
√6 = 2445/990 = 489/2×99   or 943/5×70

1400 : 1715 : 2445 = 280 : 343 : 489 = 40 : 49 : (70)
(see also Pyramid proportions)

Megalithic Pi
What could make this website suspect for many in this respect is that I found the same unit of measure as Egypt’s established Royal Cubit (RC= 0.52375m(FlP) 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, but (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), has, as diameter-size an ingenious mathematical relation to a slightly revised Megalithic Yard (MY= 0.8228m, is 6.2mm smaller than A.Thom’s yard (0.829), but usually better fitting the data and specially the mathematical logic), because this revised Megalithic Yard (RMY) turns out to be equal to the half-circle segment of a circle with diameter 1ME=0.5236m (2×26.18 ulna), and equals two male tibia bones (0.4114m, another gift), average height Neolithic big male 1.75m). It results in the formula for Megalithic Π (MPi) as 2MY/1ME (2×0.8228/0.5236= 22/7) [The Royal Cubit seems derived from an original ‘ordinary’ cubit of 6 palms (44.88cm, often 45cm) by adding a 7^th palm (7.48cm) we get a Royal Cubit of 52.36cm. Often it is given ‘officially’ as 52.375cm (from authorative Fl. Petrie, but not right), ‘my’ Megalithic Ell is the 52.36cm from supposedly 2 male ulna bones, so it would seem the two units have developed independently. (I would like to stress here that Powell made measurements of New Grange and Knowth, which would reveal units of 13.1m, this is exactly 26,18cm / 2 = 13.09cm = 13.1 x 100 = 13.1m, Powell number!, I’ve written about it.
My only other defence for this ‘improbable’ but striking situation must be that this mathematical model has connected many ‘incredible’ things in the course of my quest, events that I personally experienced as great gifts not only because they enhance the beauty and profundity of the model but because their enigmatic occurrences in my life keep me highly motivated to pursue this long quest into the deep past. Still new insights occur and are interwoven in the existing texts.
There is a treasure at the feet of the (double?) rainbow, as you know. Double Rainbow Proportion is 11 : 14

Megalithic Ell
My fixed measure of 0.5236m, was chosen (over the better 0.52355 Borchardt/Cole) on esthetic and pratical grounds as I came to use it for Giza’s Royal Cubit (RC), elsewhere usually given as .52375m or .524m, this fixed measure is a gift in still another way, because as Megalithic Ell it not only fitted Orkney better than 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 on the amount of stones planned in the original circle.

To make things worse for the sceptic I show that the diameter of the stone circle of Orkney’s Brodgar site 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, with 198RC (103.67m) as side of GP at airshaft exit levels; and that the Brodgar ring’s circumference is equal to the ground-diagonal of the Great Pyramid (880 Remen= 325.82m). Moreover it shows the intrinsic 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.
( 20/9 x V2 = 3.14269680, the Qute, squared = 800/81  =  22/7  x  2800/891(=7x4x10^2/11×9^2) or 22/7 x 28/8.91) =  2^3 x 10^2 / 9^2 = 800 / 81 = Qute^2
My important finding that the Third Pyramid must be 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 Brodgar ratios!
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 and at first not even really happy when I found it, for this very reason (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.
In case of differences they are all too close to call, or just ‘controversial’ in this Megalithic-setting, with differences expressed in centimetres over lengths of hundreds of metres and very rough and contingent material (Lehner’s data for Gr.P. all 230.33m,  Cole average 230.36m).
This inevitable bickering about the correct length does a lot of damage to a serious approach to the logic of the design, because it is about (number-) logic integrated in design, not about perfect execution, it’s about genuine probability and a great Cosmic Idea, Earth as a sphere, for one thing, not about scientific scepsis; it’s about possible synchronism and serendipity; and about a near mystical (historical) Enigma: the same ‘cosmic’ length, its unit and mathematics occurring in 2 widely differing cultures at about the same time some 5000 years ago

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 ‘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. 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 so many?), but I also see it confirmed in their superb building techniques, in their involvement in cosmology and calendar making 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 cosmological cycles. (See my pictorial analyses of the 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 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 by connecting certain stones with ropes, possibly an education place, in all, 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 drumbeat together with a huge pendulum in Maeshowe,

(Pendulum Maeshowe)

were instrumental in creating day-time, creating clock-time, at the equinoxes. This is what the Ness of Brodgar and its environs were 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, to see the many rainbows and the Northern lights when lucky (last year!), to hear the echo of their voices at the centre of Stenness, to being at the edge of the ancient world, beyond the North Winds.

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 (the first in stone, ‘square’ from Maeshowe and with a ‘revolutionary’ roof-corbeling technique which was already long standard in megalithic chamber building!), 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 Sheldrake 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, maybe 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’ and that is also the basis of my whole number logic that fits the data so well by being mathematically coherent. The principles of my natural number logic were in place before I got into Giza and Orkney and the use of the algorithm has honed the calculus and theory to perfection. We see this length returning in the diameter of Brodgar’s Ring and in that of the inner circle of Avebury’s (lunar clockwork), even the (rather sloppy) stone circle of Newgrange (103.6) is thus reported, but, more importantly, this length is also equal to the square base length of the 3^rd Pyramid, 198RC. at eastern sidewalk/platform level (Lehner’s 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 have no explanation for Lehner’s rectangle in this context, is it right?(I think a satellite and computer imaging should do these jobs by now). Nevertheless it may be an, as yet for me, hidden teaching: 196=14×14=14² = 2².7² and 200= 2x10x10=2x2x2x5x5= 2³.5².
This has consequences for the angles of the slopes, but these seem hardly different from the Great Pyramid, so I maintain that the Third is the prototype top of the First, the Great Pyramid, otherwise there must be a correlation between the different sides of the Great and Third, but Lehner gives what seem to be unwelcome sloppy data (230.33m) for all the sides of the GP and this is pertinently wrong considering the excellent work done by Petrie and Cole, largely in close agreement, in the past and, worse, Lehner’s measurements can never translate into the slope that he gives for the Great Pyramid; his data are intrinsically incompatible, so this makes me wonder what it is this carelessness about.

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 1/11^th volume of the pyramid upwards from shaft-level is 126RC (280-154, Legon) high and consequently identical with the Third Pyramid, this is the reason for the angles of the shafts, they had to mark out on the outside the theoretical mathematical principle topping the building as its ‘mathematical brain’, a visible mark and a practical airshaft at the same time (there were people in these buildings going about their business whatever it was, see gallery, no one was ever buried there, but this explanation puts the mathematical theory superior to astronomical considerations), so a visibly marked top with ten times its own volume beneath it. 11 is the number of the great Pyramid, 37 of the Second Pyramid (100+37).
The height of the Great Pyramid is equal to the diagonal of the Third’s ground floor =√(198²)x2 = 280 (also with Lehner’s 200 RC and 196 RC data, the crucial diagonal, is still 280 RC; count for yourself).
These differences are very small but can be decisive in our argument when it comes to an overall picture. It is only because they had so great reverence for the building technique and genius of their ancestors (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 om 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.

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) 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 is 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 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 Buddha’s 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 decisive.

To me 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 must still be available to us all, in principle, I think, I hope. Tibetan Buddhism is probably the only 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 worldview; “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 intuitive insights it is based on.

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 (Buddha, Jezus, Socrates). 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 ‘solid historical records’. First it was ‘Giza’ and a few years later ‘Orkney’, both these  places were just other incredible ‘gifts’ to sustain my ‘improbable’ findings in ‘un-mathematical mathematics’ 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 may have deep roots, but it stands on its own.
Try to grasp it, it is amazingly ‘solid, while transparent and aesthetic’.

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Part I

The mathematical model

Decimal nine-number system (1.111…; 2.222….)
Initially this peculiar geometry evolved from a ‘decimal nine-number system’, inspired by cuneiform clay tablets from ancient Sumer (Iraq) I saw in a newspaper and worked out.  This 9-number system, Sumerian or not, is still at the heart of the calculations, as it is the ratio 10:9, (10/9  =1.11111….) and it is perfectly tailored for the calculations of the derived geometry; they cannot be separated. What makes this ‘number-logic’ such a sure and fast calculator is that it is self-correcting and self-contained and based on whole 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. We see here 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 reality; this shows nicely in the universal ‘fine structure constant’/α, alias, ‘coupling constant’/e which in my system turn 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) = 0.08542421…. (because repunits and ratio 10 : 9, squared)

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 0.08542455. (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, a BIG number, in short, and I seem to show ‘how HE pushed his pencil’. I can present it in different formulas which each may show the deep-structure of the number. R3, 111,  a major repunit, is involved and our central ratio 10:9 (1.11111…….), squared is involved but the number also can be read very plainly as 3700/27 = 137.0370370370… , though scientifically defined as 137.03599….. , 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 0.08542455… as the square root of 27/3700 = 0.08542421…, with difference of 0.00000095…., that is less than 1-millionth. Not bad (and rather better than in the other version). So we see that the shape of this ‘Holy Grail number of Physics’ is rather trivial in 3700/27 or root 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 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 is 20/27= 0.740740…) This is no longer  ‘recreational mathematics’, what repunits are supposed to be in professional circles,  this is the real stuff, however hidden and enigmatic it still may appear now.

Rainbow Proportion
As my personal contribution to the significance of 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 waves, 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 (closely related to the Golden Section) and, last but not least, that the 2-D circle and square integer relations can stand for sphere and torus (ball and ring) relations and for the necessary interaction of their wave-systems in whole number resonances (resonance is always a whole number phenomenon, keep that in mind, it is also the ultimate scientific ‘rationale’ for this peculiar mathematical model I 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 the manner of super-strings. Nevertheless it is simpler and more straightforward than super-strings and works on all scales, be it  not with 11 dimensions but only  5 or 6, depending on what is included and how you count. 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 physical theory, but they find a natural translation in this model.
Since I have never stopped thinking about the implications of these fundamental integer 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, that was the challenge in those days, but I still wish to formulate something that is a real bridge from science to the mystical experience and I hope it is consistent and universal and that what I do with my very limited knowledge is only set the first feeble steps in the revelation of its entire scientific and mystical scope.

Curved Space (appendix)

Since Einstein’s work the term ‘curved space-time’ has become a household concept in physics, although no-one really understands what it actually designates. I claim on this website that the term is a misnomer because time does not physically exist and curved space is nothing new, moreover I think the term has caused major confusion in theoretical physics and blocks insights in the real ‘curvature’ of space as I will argue now. Because we deal with balls (stars) and rings (ring systems) in outer space, we can see spheres and tori (plural  of ‘torus’, ring) as representatives of ‘materialized  mathematical entities’ in physics and, as such, as ‘actualised geometries’ in ‘organic’ space (aether), so the ball and ring are the actual representatives  and outcome of space curvature. The major difference in my approach with Einstein’s is that in my view space organizes energies in balls by producing an even (electromagnetic-) field pressure on all sides (similar but different from le Sage’s ‘push-gravity’) and that this is why the sphere is a fundamental geometry of space; this is how space organizes itself in its excited state. Also in my approach ‘matter’ does not exist other than as a configuration of space (-vibration) and we see that the space-matter dichotomy is ‘dissolved’. Matter should be an obsolete concept in physics, it’s all mathematical vibration patterns around qualities/harmonies. Take our earthly atmosphere, the curved cloud cover, that is curvature of space, you can see it when you know it, like the curved sea-horizon, that is real curvature, what clearer experiential curvature of space do you want? But this is not what scientists mean with their ‘curvature of space-time’, there a ball thrown vertically in the air and coming down has described a straight line in space-time, of which they concede they don’t know what it really is, it is a totally abstract description actually. So if the curved cloud-cover does not signify curvature of space, what then? Is the terrestrial atmosphere not curved space? Is the ground we stand on not curved? How does it become curved? What tension works there? We, and even scientists, do not realize that our whole perception of perspective and distance is due to the specific curvature of the earth’s surface. That became clear on the moon.

Astronauts (appendix)
The astronauts on the moon could not deal with distance because of the different curvature of the (smaller) moon sphere (that is my explanation), everything seemed nearer and smaller than it was, also the perception of time changed, in my view due to the different gravity.  Buzz Aldrin 1969: What really impressed me was the difference in distances. After we were back inside again, looking out at the flag, the television, and the experiments, they looked as though they were right outside the window. In fact, on the surface, we had moved them a reasonable distance away. So I think distance judgment is not too good on first setting down. The tendency is to think that things are a good bit closer than they actually are. This says they (meaning the boulders) are probably a good bit larger than what we might have initially estimated”. They had felt as though they were standing on a large ball rather than on land surface.  Armstrong said, “I was surprised by a number of things, and I’m not sure (I can) recall them all now. I was surprised by the apparent closeness of the horizon.”
This then is curvature of space: ‘standing on a large ball’, with a horizon close by in stead odf on a flat ‘landsurface  as on earth. But this is the trick. Aren’t we standing on a large ball with a horizon close by, as well? It’s just that we are used to the curvature of our slightly larger ball that land surface and sea surface seem straight and flat to us, not? But it is obvious that the curvature of the moon surface and the space right above it work as a tele-lens, there is nothing wrong with the ‘judgement’ of the atronaut, the environment does indeed appear differently, nothing ‘illusion’, it is as real as it can be, but the whole environment vibrates in a different mathematical mode, this now is the effect of ‘space contraction’ near an object, in my view. Al Shepard remarked: “It’s crystal clear up there – there’s no closeness that you try to associate with it in Earth terms – it just looks a lot closer than it is”. Astronaut Pete Conrad mistakenly judged a 500 m diameter crater that was 4500 m from his position as only 35 m in diameter and 300 m away.
 As far as I know there is no scientific comment on this ‘moon-space- perception-distortion’, let alone an explanation given, they probably think it’s a ‘problem of the astronauts’, as the astronauts tend to think themselves obviously, (“the tendency is to think that….”) as if it is a matter of just ‘getting used to it’; but what is it then?
Real curvature of space doesn’t suit the scientific theories. Going on a mission to the moon to study space curvature is still a bridge too far for our scientists, they rather have astronauts race around in buggies and collect ever more stones than find out what is really interesting and not understood. A setting sun and a low rising moon also seem bigger (closer) because of the telelens of the curvature of our own terrestrial space (because of the small angle there is of course much more really curved space in between object and observer at those times). In our own atmosphere looking up the mountain, things seem nearer, looking down further away, the gradient of a steady climbing road can seem horizontal (‘false flat’), again, different perception because of curvature of space based on general surface-curvature. The round Earth is the result of the curvature of space, caused by the universal spherical cosmic wave-front-pressure generated by the energy fields of stars and the like, pressing in every point of space, in short it is the result of the way things are. So no mystery about gravity any more when you realize it is the very weak universal (electromagnetic) wave-field-pressure (G) accelerated by the geometries of local space (lee-fields). This pressure is absorbed by rotation and emitted as inertial-reflection-field, causing inertia. Because this process of transforming wave-pressure into inertia means energy is lost in free space, Gravity is effectively a ‘Cooling of the Cosmos’, as I have claimed and explained before elsewhere.
Gravity can be explained, you see! It can be explained without mysterious ‘attraction’ and without even more mysterious ‘space-time-curvature’.(see Gravity= the Cooling of the Cosmos). It is a matter of the right understanding and the right description.

Unknowns (appendix)

Unfortunately science speaks a lot in concepts scientists don’t understand themselves: ‘unknowns’; between them there are the most common household words, ‘gravity’ is one, ‘mass’, closely related, then ‘wave-particle duality’, ‘space-time curvature’, ‘probability wave’, ‘black hole’ are others. What they have is ‘a name for an unknown’, for many ‘unknowns’, nevertheless suggesting they know what they are talking about, which is usually no more than an aggregate of qualities and/or conditions. ‘Dark matter’ and ‘dark energy’, big ‘unknowns’. Embarrassingly big. So they use a lot of key-words in their communications which may have no meaning whatsoever and are often even blatantly self-contradictory; for instance the mentioned notorious ‘Dark matter’ which is in reality, as argued, ‘unexplained inertia’ and no matter at all (chapter). It seems not to occur to scientists that a theory with so many crucial ‘unknowns’ as they adhere to, should invite to wondering whether there may be something deeply wrong with the theory itself, that is, its whole conceptual foundation. They stare themselves blind on the confirmations of their theories, they ignore the refutations and the growing number of ‘unknowns’. The situation is even worse when age-old intuitive concepts get abolished because they cannot be measured, yet, concepts that could have saved their theories a lot of trouble, like the ‘aether-concept’, kicked out and ridiculed by Mach, Einstein and the logical positivists, but now dearly missed.

New cosmology (appendix)
I present a rather original cosmology here with a new set of (some old) concepts partly based on a new mathematical whole number paradigm, which bases everything  on resonance -an integer phenomenon!- and I relate it to what I understand of (Eastern) mystical insights in Reality which far surpass the confines of science (and Western philosophy and thinking).  The true scientific aim should be a wholly different, that is, ‘enlightened’, concept of Reality, but that is not in the cards today. Only a few centuries ago though Science was still referred to as an all inclusive ‘Natural Philosophy’ (Descartes, Newton), but today Philosophy is hardly an issue in a ‘rationally’ fragmented science, which shows often in its narrow-mindedness and loss of greater perspective. Ever, science was a spiritual treasure to shape a philosophy and world view, now it is big business. There is though no clever Big Picture, only a rather superficial Big Bang. I hope I have succeeded in presenting a first outline of what such an ‘enlightened description’ of reality would look like in the following text; may its concepts evolve with deepening insight.

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’. 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. Our, limited, senses ‘create’ the world as we ‘experience’ it. This insight is in the West usually attributed to Kant, heralding the European ‘Enlightenment’ epoch, but it was an analysis the Buddha 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 monstrosities, like: ‘vacuum-energy’, ‘wave-particle duality’, ‘probability wave’…..

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, but most fundamental. 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 energy of space.
A space consisting of space-particles generates another cosmology than the BigBang as we will see. (note the space particle in the following Buddhist quote, as the ‘fundamental consubstantial cause of the entire physical world’, so the first and last 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 exceptional ‘permanence’ 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, -grain) the fundamental place (mathematics) and properties (resonance, field) it needs to fulfil its basic function. This is a ‘realisation’ I’d never expected although the Dalai Lama’s talk of space-particles inspired me to revisit my erstwhile visions of ‘sparks filling space’, triggered by the fundamental mathematics I found when in Ireland (’98/’99).
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 (1909, before GTR). He describes effectively an aether in my view ; the point is the granularity, which disappeared in the General Theory 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.
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 fields (down to Planck-length region), like Einstein’s description above. (It must come close to Cartesian ‘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 (permanence of space-particles, cycles).
If there were a beginning of time how could there be eternity? Eternity can only exist and felt because there is no time, so how can there be a ‘beginning of time’, as cosmologists claim. 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. 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, which we can visualize by taking the surface of the horn-torus as curved space, with one centre point bordering the whole surface of the torus of which the surface points all have an equal distance to the centre circle of the ring and consequently to the centre of the torus, possibly the only regular mathematical 2-D curved surface to do so.
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, it is the square of the circle formula (2. π. r) and consequently its surface equals a square, but is bordered by one point only; this now is what ‘space-curvature’ can do in mathematics. 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.

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 (‘luminiferous’ 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 ‘eigen-substance’, no self (-substance), it is just a rather random 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.
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 metamorphosis, maybe you could characterize it as ‘in statu nascendi’, yet ‘unborn’.
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, 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 stern views, embracing the aether again.

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 of the, always ‘passing’, configuration through the deep-field.
The wave is the pulse, the form; the space-particle 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. 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. 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 ‘eigen-substance’ (eigen=self), 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.

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’, 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. 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. (No matter at all)

99% space

What we know of atoms, the entities that give all qualities to ‘matter’, is that they form a neat mathematical system and that 99% of it 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, how about that? It was already a shock to find out we are some 80% water, but 99% space really beats it all. What matter are we still talking about then? 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. We are plugged into the timeless universal storehouse of experience and have instant memories of a distant past, another proof time does not exist. The concept of ‘karma’ is also outside of time, as is the ‘dream’ coming from the universal storehouse. (A long dream compressed in a few seconds, no time again)

The Creation of Time
The ‘Creation of Time’, the title of this website, expresses the conviction that ‘time’ is a creation of the human mind. It started in the Stone Age with cycles of the moon, then the sun, a first calendar was made, the first ‘creation of time’, then seconds (heartbeat), minutes and hours followed, the creation of day-time, clock-time. I’ve tried to trace it back; how it began.  Today, some 5000 years later, we talk about ‘slowing of time’, even ‘time standing still’. From a creation of the human mind time has become a physical dimension and created the all controlling tyrant in our daily lives, the clock. (Every morning millions chain themselves to their wrist watches; in ultimate freedom) So, claiming ‘there is no time whatsoever’ must have some implications for our world-view and will in science necessarily have ‘repercussions’ for theory in which time plays  an important role.
In bird’s eye view I further present the ontology of my cosmology and please note that I really do have a frame work to give ‘explanations’ for concepts science has no grip on, like: inertia, gravity, aether, singularity, black hole.
Science can only describe them, not explain why they are necessarily around; I try doing just that.

No time
When there is no physical time, there cannot be a ‘space-time’ either, so the whole concept of ‘curvature of space-time’ hangs in the air as well. The point is that without time without endurance, space cannot ‘exist’, it remains abstract, mathematical, so ‘organic’, ‘living’ space has intrinsic duration, this ‘continuity’ is a  4^th dimension, but a dimension of space, it is the eternity of space, forward, backward, spaceward, it is not space-time, but a dimension of energy, without beginning, without end, it is Suchness.
The concept of ‘distance’ involves time, distance is time, distance defines speed, speed is expressed in time but it is not time, it is movement in basic space, comparative movement is the basis of time, but a concept.  Our concept and experience of time is a property of the transformation of space, not in space, because matter is a manifestation of space and of its duration, its existence, its continuum. We have seen that matter is 99% space, so it is correct to say that matter is space ‘packed together in a mathematical way’. We speak of the ‘fabric of space’, so we base our speech on something fundamental existing in space, its fabric. You cannot do that with a vacuum or a void, let alone with ‘Nothingness’, but you can do it with an aether and its ‘particle-fields’, or better, its ‘granularity’.

Inertia (appendix)
The elimination of time as concept does not make it go away from our successful formulas, so which  physical reality is still there that can be measured, when time is ‘out’? Inertia, in my view. Inertia is the real ‘king of transformation’, the real ‘rate of change’, the actual source of duration. Inertia is linked to gravity, together they create a local rate of change. It is the substance of the Earth and its inertial field that cause the rotation on which one time-cycle is based, the day, the other cycle is the heartbeat, only two cycles can create a time (-frame) (Time and space on the moon is experienced differently, because of different gravity and curvature in my analysis). Every movement on earth falls under (pressure-) gravity  and is harmonized by it, it takes energy to stand up and stay on foot, it affects all equally in principle, we’re built for it.
Inertia is the reflection-field of an object, its anchor in the fabric of space, which tunes the space-pixalls for the object’s passage. The source of inertia is spin, like we see it in the gyroscope. Spin creates ‘particulars’, the space-pixalls, space-grains (there are four types of spin in quantum theory, spin ½ for ‘matter’ and  0, 1, 2  for forces , but since there are neither ‘forces’  nor ‘matter’ either, only geometry remains). Since spin in this analysis is a fundamental aspect of space  itself, I see it as a dimension. (Possibly it can, as vortex, replace the ‘curled up’ space as concept of a 5^th dimension. I can only suggest here.) When we realize that matter is space itself we can see spin as a property of space. This spin is essential to sustain the fabric of space, the pixalls, a pixall without spin is impossible, the pixall ‘is’ spin and ‘creates’ field, without spin it annihilates, without field no distance, no space. The pixall hides the pure light in its vortex. Pixalls are tiny black-holes in every point of space that hide the pure light in the curvature of their vortexes, which open and ‘spark’ when touched by the right vibration. (or something like that, or different)

Wave-particle duality (appendix)
The pixalls of space embody, like pixels in a screen, the ‘wave-configuration’ which we identify as ‘matter’ or ‘energy’. So here the ‘wave-particle duality’ becomes obsolete, since the wave is the ‘form’ of the moving ‘object’, whereas the particle, the mass, is in the pixalls that constitute the object at a certain point in transformation. When the ‘object’ is hit by an observation, it are its accidental constituent pixalls which are ‘materializing’ in that observation, falsely suggesting it consists of these specific entities permanently. Because the contents of the form is ‘fleeting’ one can maintain that the form is ‘empty’ by nature. The river is only a form, the fleeting water is the ever-changing substance, without a ‘body of water’ there is a riverbed, no river.  So we see here how the Buddhist concept of ‘emptiness’ can be derived from an analysis of physical reality, that the form has no ‘eigen-substance’, that it is empty. Its content is ‘fleeting’, impermanent, in constant renewal, like it is so visible in living organisms, where all kinds of cells constantly renew, but all in their own time-frames, their own uniform motion, there own ‘Chi’. Renewal is the basic pattern, also in the cosmos, it is the ‘permanent creation’. So here we see that ‘Chi’ as well as ‘Emptiness ‘, both central concepts from two completely different mystical cultural backgrounds, that both concepts have meaning in our ontological description of the ‘basics’ of reality. This is what I am after: a scientific model which absorbs the great mystic intuitions from all time and transforms them into a new spiritual and scientific worldview for the elevation of humankind.

Photon? What photon? (Appendix)
The photon concept does not stand up to scrutiny when you look at things without preconceived ideas. Einstein admitted at the end of his life he still did not know what the photon was and did not believe anyone else did.  I think he was right, the situation has not changed, because, as I claim, the photon does not exist in the way science treats it. I suppose the reader agrees with me that this photon must be seen as a tiny ball/spark of light, an individual entity shining in all directions and because there is no other way of conceiving it (since how could it ever be a torch shining in one direction, which one?), this is also the reason it must be a wrong concept. I will tell you why: because we only see light that comes in our direction, like a wave. How could there be shadows when it were differently, how could we have the dark nights that we have, thank goodness, if it were spherical light balls/sparks shining all around. The whole solar system is bathing in light from the sun, see our days, but also look at the full moon and the planets at night, bathing in light with us in the dark, also our galaxy, bathing in the light of billons of stars, with us in the dark. Still we see only the reflected light from the moon and we miss all the bright source light that is passing the earth, us, by, how could that ever be possible when photons were balls of light shining in all directions. The photon is another persistent fallacy of scientists and obviously a fallacy that with some simple logical empirical reasoning is easy to reveal and do away with. The photon as individual entity does not exist.
There are galaxies just like our Milky Way that we perceive as stars, ‘solid’ balls of light, but like our own galaxy they  must appear dark inside to an observer. How is that possible? How can such a source of bright light be dark inside? Because we only see the light that comes our way, directly or reflected. On ‘pictures’ of our own galaxy (see below) you also see this glowing centre of light, but we don’t see that (nothing to do with dust clouds), it’s all a matter of very great distance where the light of individual stars starts to overlap giving the appearance of a solid ball like the sun. The stars in our galaxy are just too close by and far apart to overlap, that is why our galaxy seems dark inside, we cannot see the ‘invisible light’ that passes us by, but it is there, also like the stars we don’t see.  See picture below, where it is still hard to imagine there is really so much darkness at the centre and around us.

In my model (pure) light is emitted by the (toroid) space-pixalls when they open their cores by being aligned through their axes, like beads on a string, the string is the ‘light-ray’. This opening occurs when the deep-field through the electro-magnetic field adopts the ‘light-mode’, like it can be in ‘electron-mode’, ‘quark-mode’ etc. The specific wave configuration configures the space-pixalls and when observed together with the intermittent wave pattern of the deep-field-resonance this creates the illusion of discrete quanta, but in reality the wave pattern opens, in the case of light, the core of a pixall and reveals the zero-dimension of pure light. So it turns out space is saturated with ‘invisible light’; light which is invisible, either because unexcited pixalls hide their light through curvature of the vortex of their tiny black holes, or their orientation by the EM-wave-field is such that we don’t see their sparking cores (we’re in the ‘shadow’). In short, there could not be shadows, nor night-time darkness if light were ‘moving photons’ shining all around. Again, the photon does not exist, it is another conceptual fallacy. QED.

Note: The whole problem of ‘dark matter and dark energy’ disappears because the massive inertia of the ‘reflection-fields’, plus the permanent electro-magnetic excitation of the space-fabric (dark matter) and the massive amount of energy involved (dark energy) shows that the term ‘dark matter/energy’ should properly be ‘effects of invisible light’. What it means is that the inertia and pressure of ‘big space’ is 95 times bigger than scientists calculated for the mass of the ‘visible’ matter content of the universe; an embarrassing blunder. The whole model is simply wrong, ‘matter’ does not exist as a self-substance in our model, it is space itself being occupied and taking shape.
It is, for instance, electromagnetic field pressure (pressure-gravity) which appears as expansion of space, but is in fact an optic illusion. Space does not expand linearly, but is locally in states of contraction or expansion; a dynamic but static condition.

Aether

One of the central points in my approach to ‘cutting edge’ theoretical physics is the re-introduction of the concept of the aether. In many Eastern philosophies, as in ancient Greece, the popular 4 elements : earth, air, water, fire are invariably philosophically accompanied by a fifth:  ‘aether’, also:  ‘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.

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 world-picture should contain these elements. ‘Nada Brahma’ means to me: all is vibration; ‘one taste’ : an indivisible experience without separate qualities. It all means that ‘Experiencing-the-One’ is the Great Way (Tao).

‘Experience is: the world’

Our immediate environment, that is the way we know the world. It seems a fragment but through the 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 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’, our ‘Dasein’, our ‘Etre’, 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, they cannot reflect and plan other than in an immediate situation. 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 no integrated collective control or any agreed perspective for improvement. But the real cause is of course the ingrained competitiveness and self-centred-ness of the industrial age, 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), it does not affect our daily lives. But in the mean time humankind has become a devastating plague to its own natural environment, totally overstretched (finances), a typical condition for the crash of a civilisation. Only a more enlightened awareness of the ‘world-crisis’ can start to solve our collective problems, of which one is of paramount importance: peace, creating a collective aversion to war, the strong conviction that violence is ‘not done’, is no option, it is already dragging us into barbarity although we don’t want to know .
We need create conditions for real cooperation, solidarity and respect. What happens is the truth, religions are not so relevant. Today it is not important to which religion or spiritual creed you consider yourself belonging, a spiritual intent can help bridging gaps in communication in every situation. This is what the spiritual path today is about, I think:  awareness of the fragility of the natural environment, care for a future humankind and opening your heart and communicating, very down to earth; but difficult enough.

The Qute (Appendix)

One of the first great gifts of this theorem is the square root of the new Pi-squared rational number 800/81, the factor for the torus formula, and this root is 3.14 26980…., I named it Qute (symbol Q) to bring it close to Pi and because it is a ‘cute’ number. It is the only ‘irrational’ number in the system, I believe, but being one of my ‘magic’ numbers it works wonders in packing theory, for instance Kepler’s density coefficient: π/√18 = 0.740481… suddenly becomes rational, 0.74074074 = 20 / 27, that kind of thing, and so by being irrational itself  the Qute is a key factor in ‘rationalizing’ other square-root-2 numbers.
Another packing grade with number 27 is that of 7 circles in a hexagon, this is supposed to be π/√12 = 0,906899…, but becomes 10√6/ 27 = 0.907218… or with a rationalized V6 = 2.44948 → 2425/990 = 2.44949494….. to 2.45 = 49 / 20, so density packing becomes 49 : 54 (27×2) =0.9074074074… and we see that the number 27 is prominent in this packing density and this throws a new light on the 27/3700 of the fine structure constant.
This is how revealing this calculator works. It is all based on the clear and close whole number approximation of the ratio of the perimeter of the circle and its inscribed square as 10:9. It means: “the mathematical square was discovered by the neolithic cosmologists”.
After 22/7 as the perfect integer ratio of circumference and diameter and 11/7 the ratio of half circle and diameter,  then this 10/9 ratio between square side and quarter circle was the great scientific discovery in deep-antiquity (and for me) and this is what made the integration of circle and square, sphere and cube, globe and pyramid, possible in integer ratios, which was all they had. Diameter and diagonal suddenly were the same.
This great find and its numerical solution in 99 (9×11) and 140 (10×14) as rational substitutes (140/99=1.41414…) for square root(2) (1.421…), all went lost because the Pythagorean (Second Pyramid) precision was superior, that is: in Euclidean space and the mind of man.
However when circle and square are taken as 2-D representations of respectively a sphere and a horn-torus, then the model becomes a universal representation of the vibration patterns and interferences of sphere and torus on the largest and the smallest scales, this is the ‘raison d’etre’ of the space-pixall (space-particle), the ‘substance’ of the permanent creation.
This is why this model is so crucially important, it places the torus ‘squarely’ in the ‘circle of creation’, sphere and torus are the fundamental geometries of space vibration; that is the message.

Value of the model (Appendix)

In terms of present day mathematics my model probably is, at best, considered a nice approximation system based on integers, but nothing deeply mathematical about it, just ‘one of those things in maths’, so I beg to differ here in opinion because in my view this system is the mathematical basis of all the resonances in nature. Resonance is about ‘flexible’ whole numbers, because resonance is not precise and this system is exactly that. In words: the theory is based on two standard rational values for ‘Pi’ one for circle 22 circumference with 7 as diameter, that is 22/7, the other 2800 circumference with 891(11 x 81 and 9 x 99) diameter, forming 2800/891 (I have not found any use for this Pi yet, but it is related to 99 a pivotal number in the model), they are complementary; the product of these two produces one standard ‘Pi-squared’ with the rational value 800/81. The approximations of the system always only differ in the ‘thousandths’, so at the third digit and when two numbers differ only from the thirddigit, they are treated as equal and interchangeable within the system, their resonances are equal; this is why the Golden Section (1.618….: 1), the Rainbow Proportion:  14:11 (as squared: 1.619….: 1) and the crucial ratio of our system 162:100 (or 1.62000….: 1) (double horn-torus in cube, torus-cube), are closely related and interchangeable in the system, this is its flexibility, it connects differing systems. Foregoing is the absolute quintessence of the whole number geometry, this is where it all started and this is where early (sacred, pharaonic?) geometry began in my view and possibly the earliest development was in the British Isles. So the truly revolutionary finding is that a circle with circumference: 10, holds ‘exactly’ a square with perimeter: 9, this is the core of Maeshowe (9 x 0.5236= 4.71m squared). This system results in the Pi-squared of 800/81 = 9.87654321.(another gift) In mathematics the Pi-squared is the hallmark of a torus formula (2 circles) and forthwith the torus and its geometry and dynamics (vibrations) should be treated as equal and complementary to the sphere and its dynamics; then everything will be solved and fine, I predict.

 Complementarity (Appendix)
A great theoretical physicist, the Dane Niels Bohr, was convinced of the fundamental state of complementarity in Nature.The Chinese Yin-Yang symbol expressed it all for him. In my approach something similar happens where the 5-D space, (cosmic) black, is internally bordered by a zero-D space, (pure light) white, which mutually inter-penetrate in (circles or) spheres (stars). The pixall is the white spot in the black space, the opening to the infinity of pure light. The black spot is the black hole in the pure light, opening to the infinity of space. To put this in a different way we can use the horn-torus, here called ‘corus’ as a model to visualize how to turn our 4-D space ‘inside-out’, it is going as ‘surface’ into the curved vortex of the corus-centre and comes out on the other side as ‘pure light’. As I‘ve put it elsewhere: There is no other side to the centre of the Earth, it’s where the zero-dimension begins. All signals bounce off the core of the earth because of this, they cannot penetrate through the centre because there is no ‘other side’, only infinite density, the zero dimension.
This is a daring perspective. It means that every surface is the ultimate boundary of 4-D space, behind which the zero dimension begins. It is the consequence of the fact that 4-D space is bounded on the inside and boundless on the outside, because it is a complement of the zero-dimension of pure light. Projected on the horn-torus we imagine the ground we stand on as the concave surface inside the torus, its volume is our space and is bordered by one point, if we go through this point (black hole) we get outside the volume of our space- torus into the density of the pure light, the zero-dimension, being everywhere. In the theory of the black-holes ‘entropy’ plays a surprising part, where it is stated that the entropy of the black hole is a state of maximum information. According to Dutch Nobel laureate Gerard tHooft, originator of the ‘holographic principle’ in cosmology, this means that this information must be compressed on the surface, the border, of the black hole as in ‘holography’. tHooft wonders though how we can ever get to the information on the ‘surface of the universe’, describing what happens in our world. When you though see the picture inside-out, the border of the universe is on (behind) every surface. The boundary of the physical universe is the ground we are standing on. We have to realize that we always observe surfaces in space. We are kind of surface ourselves. We are ‘die Grenze der Welt’, as Wittgenstein put it, the boundary of the world, where the zero-dimension opens, the mind. Every time you cut something open you get a new surface, you never get to the inside of matter, until you reach the space-pixall, itself a border-point of space. The space-pixall is something like the old atom, it cannot be cut up, it can only annihilate, ‘uncurl’, releasing pure light and be replaced by a new one in the open point. But it is nearly wrong to speak of individual pixalls, since they only exist in a field, not independently. The deep-field when damaged heals immediately through environmentally induced spin. I think the geometry of the horn-torus, with its total surface bordered by only one point reflecting the whole curved surface can be of great value in the holographic/information approach (Suskind) which seems to be very close and compatible with the tools I use to pin the space-pixall down. In excited state the pixall is a horn-toroid field, like the magnetic field around the earth. The magnetism is the fundamental toroid geometry of space, not a force, but a state of absorption and emission, of circular motion, a state of stability. Nothing shows the existence of the aether as does magnetism in its field lines and electricity in its plasmas.

The system I reveal on this website is complementary to the Pythagorean ratios as this complementarity got forever embodied in the three pyramids of Giza where the full theorem is completely inherent in the ratios of the different pyramids: The Great and Third Pyramid express the above most important ‘Lost Giza Theorem’ whereas the Second Pyramid expresses the lesser Pythagoras theorem, highlighting the prime 37. (274/2=137=100+37). Both concern squares, Pythagoras in relation to the triangle, the ‘Lost Theorem’ in relation to the circle. It is inevitably more intricate and more important. I guess that the ‘Lost Theorem’ I present here in these pages will eventually prove more profound and far-reaching than Pythagoras’ triangles.

The Lost Giza Theorem
The  ‘Giza Theorem’ went lost because of its intricacy and abstraction compared to the straightforward and precise Pythagorean ratios (3, 4, 5) of the Second Pyramid, which would be followed in the designs of many later Pyramids, but the Great Pyramid theorem was never used again in Egypt although it is the more cosmic and profound of the two with its roundness, its resonances and non-EUCLIDEAN consequences. It is a theorem for curved space, for real space, but there was no other than cosmological use for it; in Egypt it was possibly a pharaonic and secret science (measuring the spherical earth!). The theorem fell into disuse at the end of Pharao Sneferu’s ‘mathematical lineage’(father, son, grandson & great grandson, Cheops, Chefren, Mycerinus/ Khufu, Khafre, Menkaure) and disappeared, so that the Greek scholars, like Herodotus and Pythagoras, who studied in Egypt some 2000 years later, didn’t even know it ever existed.
Pythagoras would probably have less agonized over the ‘irrationality of square root 2’ had he known, the ‘rationale’ of the irrational, the mathematical whole number solution of square root 2 by pertinent logic (‘Rationalizing the Irrational’), found 2000 years earlier and standing there magnificently embodied in the Great and Third Pyramids, also in his day; if only he had known. I am sure that the development of mathematics would have been different had this Maeshowe- and Pyramid- theorem survived since antiquity, had Pythagoras indeed known it for example, but maybe it is good that present-day mathematics with its ‘rigid Euclidean canonized Pi’ has run its entire unobstructed course and that this new concept of a flexible  π  expressing a measure of space tension or curvature, can only now be fully fathomed and appreciated, now that non-Euclidean space has come to the fore and physics is at a conceptual loss as to how to speak about what they don’t know; a century in theoretical crisis now, because of the ‘Loss of the Aether’, no end in sight; except in these pages. I expect that the theorem’s impact on theoretical physics will be profound once its value is fully appreciated and that the same will happen in mathematics when the practical ‘physical’ results will force the mathematicians to admit that sometimes a mathematical theorem is proven by reality itself (empirically), in contradistinction to current mathematical logical proof (mentally). But it will take some time because it rocks the foundations of Big Science. It is just based on different axiomas and perspectives. It is a mathematics where ratios of integers are of paramount importance, not precision. It’s a different way of thinking. It’s got the tolerance of resonance. It shows there’s space, character and beauty in the numbers. (End)

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