## Posts Tagged ‘permanent creation’

### 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 worked 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.

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. (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). The eventual order is achieved in the Lost Theorem by using a ‘rational’ approximation of π as a squareroot2 number= (20/9)V2 or 3.14 2696… (ratio circle circumference and its Euclidean diameter, 3.14 159265…) and by a rational value for π²-squared ( 9.869…), respectively by the rational numbers: 22/7 (3.14 2857 1428…) , its complement 2800/891 (=3.1425 36…) and the new pi-squared as 800/81 (9.87654321.= 22/7 x 2800/891), all expressed in natural and rational numbers, the undubitable basis of 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’), the squaring by perimeter 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….. 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. (Maybe they thought the Earth is only a half sphere, that there is no other side to it, it is actually the same as I claim down the line, only in an ancient way)
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). See 99 is a rep-digit (repetitive digit) of rep-unit (R2) 11 times 9.

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) 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. 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 (0.4114m, 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 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

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!
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  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 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). 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, it is not about cynical 20th century scientific scepticism.
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 ‘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 then, 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. Avebury is about recording the moon cycle, with 3 circles of which one has the diameter of Brodgar, Stonehenge is obviously dedicated to the sun. (See my 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, 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 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 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 9, 10, 11, 14)
The number 11 (22/7) is the number of the Great Pyramid (440), 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.
These 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 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 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 ‘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 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), 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 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, squared = 9.87654321]

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 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 0.08542455… as the square root of 27/3700 = 0.08542421…, 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’, which ‘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.

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.
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 (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.
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 (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 set 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 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, -grain) 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.
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 views about the ‘non-aether’ by embracing the aether again, however modified and ‘aetherial’.

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-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 they one of the incentives to stone-building was to build for many many generations, that should be again the perspective of collective endeaver.

*******

### Gravity = the Cooling of the Cosmos

Friday, November 11th, 2011
Gravity = the Cooling of the Cosmos

Introduction ‘Gravity’

In previous pieces I have advocated the idea that ‘gravity’ is the result of cosmic field pressure, emerging because of a ‘lee’ in the counter-pressure of the cosmic deep-field around a body. Although I was sitting in the bath, like Archimedes, when the idea came to me; unlike Archimedes, I stayed in the bath, not yet sure of my second ‘Eureka’ on gravity. I found just recently that Newton and Lorentz and several others had played with similar ideas a (long) time ago (see Wiki, history gravitation, paraphrased here), but although they all eventually dismissed it, I want to give it another try, from a different perspective. After all, gravity is still a mystery and here is a real (not abstract) and even understandable explanation.

Similar theories
Here are some points of similarity with those earlier theories:
1)Lorentz used electromagnetic radiation, like I do with Poynting vectors of EM-fields. 2) Newton and Riemann argued that aether streams carry all bodies to each other, similar to my principle of ‘source streams to sink’. 3) Newton and Euler (1760) proposed a model, in which the aether loses density near the masses, leading to a net force directing to the bodies, which amounts to the same as my insight of ‘depressions’, or ‘lee-fields’ near the bodies. The ‘depression’, loss of pressure density, is what Einstein calls ‘curvature’, but that is too much a 2-D description of a 3-D reality and is only mathematical (Riemann); in my picture it is a loss of cosmic field-pressure (loss of density) in the spherical ‘lee’ of the object (shielding) which is mathematical but has ‘mechanical’ components, as deepfield-density and cosmic field-pressure.

It is indeed the deep-field which reacts to the presence of the object, in this it is in full agreement with Einstein, but the object is on the deepest level part of the deep-field through which it passes, it moulds the deep-field in its passing. Gravity and electromagnetism are not separate distinct fields, as Einstein maintains, they are both emerging aspects of the one deep-field, but since electromagnetism is the deep-field of all ‘matter’ the whole concept of gravity becomes obsolete. The  EM-field is  probably the main push of the pressure-gravity.

When you light a candle, you light the deep-field, the candle is not the source of the light, but the trigger of the deep-field. This is why the speed of light is independent of the motion of the so-called source, which is no source. The field is already there only has to be triggered to emerge. When you push the candle it will fall, the pressure-gravity field was already there, gravity ’emerges’ because of imbalance. When the candle falls, does its light fall? Can light fall? Newton thought the Earth was attracting the falling candle, Einstein claimed that as far as the candle was concerned the whole universe made a somersault, but I think it is safer to speculate it is space  itself that pushes you down when you lose equilibrium.
Space wants everything in a steady place. At the same time there is a kind of vortex, a sink in the deep-field, which induces rotation, like all orbiting in ‘free’ space. So the change in pressure of the deep-field is caused by the density and geometry of the deep-field. The energy absorption by all bodies from space is a kind of ‘sucking-in’ which is the aspect of the vortex which then
in extremis becomes the Black Hole. It is also some kind of contraction and by all means the concavity of the torus surface is the best example of the mathematical contraction of space. It is this contracted state which induces the acceleration, but it is as with expansion it is the state of local space which induces a dynamic. The local state of space defines the rate of transformation (local time). This is why the universe is in a steady state, but its convexity is perceived as expanding, redshift, but space in our model is just as steady as the surface of a torus, with local contraction (concave) and local expansion (convex).

So my present description combines these insights and gives, I think, a more understandable picture of what really happens on all levels.

An authority on what I try to say all the way with my ‘deep-field’, is the physicist John Bell in Wiki at ‘Aether theories’, who actually uses the same kind of reasoning I do about Lorentz, superluminal speeds and quantum behaviour, elsewhere he said that the ‘ether’-concept should be chosen if only because it is so much more adequate in making things easier to explain. But nobody listens. The concept of ‘aether’ has become completely ‘out of the question’, in physics, eradicated, and see what damage is done. I think the concept of the cosmic deep-field opens complete new vistas, if only one gets the (zero-)point.

Let me insert here an appropriate quote from another authority on the matter. ( I am pleasantly surprised by uncovering such unequivocal support for my own findings by several unquestioned authorities recently).

Robert B. Laughlin: Nobel Laureate in Physics, endowed chair in physics, Stanford University, had this to say about ‘ether’ in contemporary theoretical physics:

 “ It is ironic that   Einstein’s most creative work, the general theory of relativity, should boil   down to conceptualizing space as a medium when his original premise [in   special relativity] was that no such medium existed . . .The word ‘ether’ has   extremely negative connotations in theoretical physics because of its past   association with opposition to relativity. This is unfortunate because,   stripped of these connotations, it rather nicely captures the way most   physicists actually think about the vacuum. . . . Relativity actually says   nothing about the existence or nonexistence of matter pervading the universe,   only that any such matter must have relativistic symmetry. It turns out that   such matter exists. About the time relativity was becoming accepted, studies   of radioactivity began showing that the empty vacuum of space had   spectroscopic structure similar to that of ordinary quantum solids and   fluids. Subsequent studies with large particle accelerators have now led us   to understand that space is more like a piece of window glass than ideal   Newtonian emptiness. It is filled with ‘stuff’ that is normally transparent   but can be made visible by hitting it sufficiently hard to knock out a part.   The modern concept of the vacuum of space, confirmed every day by experiment,   is a relativistic ether. But we do not call it this because it is taboo.”[3] ”

A relativistic aether’, let’s leave it at that. But we will return to this important issue because the conceptual reinstatement of the aether may turn out to be a key to solving the huge incompatibility problems in theoretical physics.

In the following I explain how I have deducted from the mathematics of natural number geometry the possible interaction of spherical and toroidal wave patterns of resonance which would pervade everything and go down to Planck levels, a grid of singularities in Einstein’s description, here called the ‘deep-field of space-pixalls’.

One circle rotating around an axis gives us the sphere, two interconnected circles rotating around perpendicular axes give us the (horn-)torus. The one is how energy manifests in absorption (contraction, spherical compression), that is: spherical stars, the other how energy translates in emission (toroidal expansion, radiation, momentum), that is: toroidal (standing) waves.

What I do here is constructing in my own language a scientific ontology which is based on natural number logic, geometry and harmonics (musical, overtones). It is completely based on logical reasoning on the basis of what the numbers my model generates mean in the reality of your everyday world and in the world of physics, possibly in a big way.

It looks like ‘Kindergarten mathematics’ to the professional, so this is how simple and understandable my model is, or rather, begins. This model’s ‘simple’ mathematics though could break the present mould of science. It is a different paradigm.

Permanent Creation
It should be borne in mind that my view of the cosmos is that of an integrated cyclical system, permanent creation, in which heating and cooling are two complementary phenomena. The heating is caused by radiation, which very much sustains the fabric of space by feeding into the space-pixalls, this is the pressure part. Absorption is excessively so when ‘matter’ (condensed/excited space-pixalls) is involved as a concentration of energy in the cosmic deep-field. This absorption creates the ‘lee-field’ around an object, it shields the general deepfield-pressure from the direction of the object, resulting in net-pressure towards the object, which is falsely seen as ‘attraction’, and called ‘gravity’ (gravitas). (some call this approach ‘push-gravity’ but this involves pushing particles, which is not the case here, also see Newton, Euler, above, I would prefer ‘pressure-gravity’, if ‘gravity’ is to remain as term; the best term would be aether- or deepfield pressure, it keeps everything restrained and in order).

In this logic the cosmic radiation and pressure is transformed by inducing spin, that is, into ‘mechanical’ unlimited motion and momentum in a reflection wave-field. All spin creates waves. This is the object’s inertial field. (And this is why Lorentz’s thermo-dynamic objection of ‘over-heating through absorption’ is void, the absorbed energy is transformed into momentum and field).
It are these inertial fields which give the final rigidity and high pressure in the deep-field (Dark Matter?) so in that sense Mach was right in claiming that inertial space was caused by the totality of the matter in space, but he and science in general forgot about the inertia of the spin of all these bodies ( like gyroscopes), this is the missing ‘dark matter’, it is ‘dark inertia’. It are possibly the reflection fields of the large heavenly bodies which feed into the high pressure of the deep-field at quantum level.
This draining of energy from the deep-field can be seen as cooling the deep-field to sustain the mechanical cycle of supplying and draining, to sustain the transformation by transfer of energy in radiation, or by draining, so that is: ‘cooling the cosmos’

So this is why the principle runs:

“Gravity is the cooling of the cosmos”

In the following I will set out how this relates to my present, much further developed, view of the cosmos. I now understand much better what I intuited at the time 14 years ago, but I would not have used those terms today probably and I actually had forgotten about it, I must confess, because it is so long ago I found it, but it remains a powerful comprehensive statement in its own right. And a complementary principle, added today, can run :

“Radiation is the warming of the cosmos”. (It could mean Dark Energy)

Entropy
My cosmology revolves around principles, like rotation, cooling, contraction, least resistance, continuity, equilibrium, harmonics, not the usual rigid physical laws which are derived from mathematics and usually poorly understood by scientists themselves because the mathematics is clear, but what it signifies isn’t; because the laws are not properly understood they do not interrelate which makes for the lack of a comprehensive picture. All laws are presented as independent entities like in the case of the concept of Entropy. The notorious Second Law of Thermo-Dynamics is almost sacred to physicists, unfortunately it is a dead end street. In my model there is no disintegration other than as part of regeneration, but the Bigbang cosmology is a one-way alley, from the Bang to….. where no one knows for a long time now, but it seems to be dark and cold there. Wouldn’t it?

My description of the space-pixalls ‘aligning’, ‘contracting’ and ‘expanding’ is an attempt at really describing what ‘happens’ at the quantum level of the deep-field. The more so because this deep-field is the ‘screen’ on which ‘geometrical forms’ materialize. This sounds like holography. The object is a concentration of excited pixalls in a form which influences the geometry of its environment by its reflection-field. This ‘organisation’ of space around the object results in a ‘lee-field’, which functions as a ‘sink’ through pressure-differential. The general pressure of the cosmic deep-field accelerates all objects towards each other up to the point where there is an equilibrium in the pressure of the reflection fields, that is when they are in resonance and stable orbit.

As a metaphor the deep-field reaches to the deep of the ocean, motionless and under high pressure, but the deep-field is also the currents, major and shallow, it is the waves of the ocean and, eventually, between these huge forces Life emerges as the foam on the waves, sometimes abundant but always fragile in every bubble.

Canonical Pi is a Euclidean number

The most obvious fallacy of science is that, with much talk of ‘curvature of space-time’, expansion, acceleration etc. nobody seems ever to wonder what happens to Pi (as a Euclidean number), in a non-Euclidean setting like curved space. (True, Einstein mentions it, but his π’s are smaller than canonical Pi because he measures a convex space, they should be bigger than Pi to express the contraction of the radius relative to the circumference in most cases, a concave space, this is the ‘pull of gravity’).
Except for the rings of the giant planets which are their gyroscopic razor-thin absolutely Euclidian flat inertial fields, which help to stabilize the planet in its rotation, as the moons do, there is no flat space. (without the stabilizing effect of the moon orbit, higher life would not be possible on earth, probably, it would wobble like ‘hell’). Except for these huge stabilising rotating inertial fields there is nothing Euclidean in space and certainly not at the quantum level, whatever scientists say about ‘flat’ space. The rigidity of flat of the Saturn rings is mindboggling, over some 280,000km it has a thickness to exceeding 1 km, that is effectively pure Euclidean space, but most of all shows a rigid underlying geometry.

In my system the differing values of Pi could actually be the measure of space curvature, which will show in the specific number use and geometric place a measured value takes between two or more mathematically fixed standard values.

Pi=sphere, Pi^2=torus

This system is built on two different incompatible approximate values for Pi and Pi-squared (²), all rational numbers, which both are based on contraction of the radius as we would expect in a vortex. Pi is for the sphere (axial rotation circle), Pi-squared for the (horn-)torus (tangential rotation circle). So because of the contraction of space they are slightly bigger than Pi, but only in the thousandths, as always in this system. (Canonical Pi = 3.14159265… squared = 9.86960440..):

Pi- Sphere (7) = 22/7 = 3.142857 142.. sqrd=9.8775510..

Pi- Sphere(11) = 2800/891 = 3.14253647.. sqrd=9.8755355..

Pi- Torus = 800/81 = 3.1426968.. sqrd = 9.87654321.

Pi- Cube = 359/198  or 360/198  x  sqrt(3)  = 3.14 0 43…. smaller   or  3.14 9 18…. bigger than Pi.

We remenber that the circle formula is 2..r

the formula for the surface of a sphere is 4..r²

the formula for the surface of a horn-torus is 4.².r²

(note this is the square of the circle 2..r )

the formula for the volume of a horn-torus is 2.².r³

(note that the last formula is identical to Einstein’s formula for Riemann’s spherical space (4th dimension) which, thus, turns out to be a horn-torus volume).

These formulas are the core of these geometries and in this system the ‘horn-torus’ is named ‘corus‘, as a contraction of ‘core’ (point), ‘compact’ and ‘torus’. This is what it seems all about: the secret versatility of the torus.

The torus

The torus is among my most valued tools and in relation to the sphere it is the heart of the cosmological model I present in these pages. The torus (ring) incorporates the important ratio 10:9, in my system, which is the crucial ratio in the natural number logic on which the ‘geometry of resonance’ is based and which, as I have shown, pervades the solar system (see Solar system resonances).

As Huygens laid down the patterns of light waves, I hope to lay down here the patterns of the ‘inertial’ waves of the reflection fields which we find in the ring-systems. It are essentially these emission wave-fields of the giant bodies which form the pressure of the deep-field. All the visible and invisible heavenly bodies produce in resonance this all pervading pressure-field, which seems to increase with ever smaller dimensions. The shorter the wavelength, the more momentum it carries, the higher the pressure. That we don’t feel that pressure is the same as that we don’t feel the atmospheric pressure around us which is dramatically shown in the famous Magdeburger Hemispheres, where two span of 8 horses could not pull apart two vacuous hemispheres of 50 cm diameter. That is the pressure we live in without feeling it, believe me, there are higher pressures we don’t feel.

Two span of 8 horses cannot pull the vacuum spheres apart

That an electromagnetic field carries momentum and thus has considerable inertia seems overlooked (Dark Matter) by scientists, because of the ‘Nothingness’ of ’empty space’, and the wave without a medium. (In Wikipedia on relativity ‘ether’ is now equal to ‘nothingness’, all thanks to ‘special relativity theory’ and its parlance)

Momentum

The essence of a wave is its ‘momentum’, that is: ‘velocity times mass’, and this can only be carried by a medium.  in fact electromagnetic fields carry momentum, are momentum. Waves are momentum, because they move a medium, stir other things. The higher the wave the more mass it carries, this is the volume and energy of its momentum, still the substance remains in the same place.

The wave has no self-substance

Just imagine a wave rolling to the beach, its momentum is just as big as the volume of water it is able to move, this hangs initially together with the force of the wind, but even when the wind is gone the waves still carry its momentum, it is kind of stored in the volume of moving water. But now be attentive, because this is the crucial thing: the wave moves the seawater only up and down , it does not take the water with it, neither does it take you when you are in there as you know (except in the breaker, the collapse of the wave), what goes through you as feeling of the passing wave is the up and down, the wave uses the water, and you in there, to carry its momentum, but it has no ‘eigen-substance’ (self-substance), the wave is the momentum carried by the medium, it is the push of the gaseous wind over the liquid water, because there must be a medium to carry momentum, the medium materializes the wave, by carrying it as momentum. If we understand this thoroughly we can also see that any ‘object’ is just a bundle of waves carried by the deep-field and that no object has an ‘Eigen-substance’, which is the centre of my argument. We are only waves, we have no ‘own’ substance, our substance is ‘space’, ’emptiness’.

Energy sustains space

All the energy which is radiated out in space is needed for the very sustenance of space, because the space-pixalls need to be fed to keep their wave fields intact, otherwise space itself collapses as in the black hole, a border point of space, which eventually absorbs an old star or galaxy, as it ‘dies’.
Space is internally bordered by the essence of matter, a vortex obscuring the pure light, the zero-dimension. Every object is, after all, a border point of free space, it occupies space and gives it an ‘inside’, but where is ‘your inside’, all that ‘matter’ of you, where is it located; without looking around, you would have no idea.
You can see our 3-D world is the inside of a horn-torus (below) and we walk on the contracted inside surface of that torus, thinking we walk on the surface of a solid sphere below us. Every point in our space is like the border point of the zero-dimension which pervades everything but has no dimension. The pure light sparkles in every point of space, we are made of light, if only we would see.

‘Corus’ (Horn-torus), this surface is bordered by one point in the centre, inside and outside.

Geometry of universe and space-pixall

The best way to visualise this border point of our space is by imagining the volume of a ‘corus’ (horn-torus, 2.².r³, Einstein’s 4th dimension !) as our universe, this universe is bordered by one point in the centre and it is this one point, in every point of space, which keeps us unaware of the ‘dimensionless pure light void’ which surrounds us and connects us because it is One in every point of space. The space-pixall is hiding the ‘pure light’ in its heart, the pure light is all pervading emptiness itself, the zero-dimension, like the white of the page around the pictured torus and the blackness of the centre zero-point.(above). Every surface of our our everyday world is the surface on the inside of the horn-torus, around it the emptiness of the zero-dimension of pure light.

I will use the model of the torus surface to explain the contraction and expansion of space in a steady state model of the universe. In my model the whole universe is a torus, but not necessarily like the one below.

Universe as primordial cosmic wheel

The surface of the torus is the answer to the question of the expansion of space. Three quarters of the ‘corus’ surface is convex , means: in a state of expansion and one quarter is concave means: in a state of contraction; but nothing moves, it is just a state of space in which the geodesics contract and expand, which, when wrongly interpreted, gives the idea of seemingly expanding space, where only the fabric of space is changing, the deep-field density and the permittivity-speed of the field (red shifts).

Concept gravity wrong

My analysis of the solar system (see: Solar system resonances) shows the prevailing concept of gravity must be wrong because it cannot explain that the 9-fold dominates the orbital resonances of the system, but crucially that the ratios of the masses of the planets themselves are also in that 9-fold resonance. This whole concept of resonance is alien to science at the moment when it comes to gravity, because gravity is, notwithstanding Einstein’s geometry, still seen as a ‘force’, whereas in fact it emerges as the lack of something, that is, lack of counter-pressure.

In my approach gravity is the effect of the ‘lee-field’ of an object and this ‘lee-field’ of any massive object creates a ‘depression’ and ‘contraction’ respectively in the pressure and the density of the cosmic deep-field. The lee-field of an object is thus a depression in the general field, because each object absorbs pressure by rotation and so shields its vicinity from general cosmic field-pressure, at the same time it structures this spherical lee-field geometrically by a partly toroidal ‘reflection-field’ with high resonance, which results in an equatorial standing wave-field, as we see it in the ring-fields around, especially, Saturn, showing extreme rigidity in its equatorial plane (1km thick over 280,000km diameter) but also other planets and of course the Solar System centred on the sun itself.

Tunguska

Since the deep-field pressure ‘hits’ every object spherically the object transforms this impact through rotation by creating a toroidal transverse reflection field. It is not so difficult to associate the outward-rolling torus as the essence of the momentum of the wave. When energies collide in a point, they create a border-point of space from which energy bounces back, this energy is the torus geometry, sphere and torus are the essence of the transformation of space. The torus just does not play a fundamental part in science’s picture, most scientists don’t know the formula for a torus by heart (try it!, they’ll tell you they can derive it) whereas in my picture it is the essence of the spindle-torus as geometry of rotation as we see it in the equatorial bulge of inertia of a rotating body, like stars and planets (Saturn -> 10:9= equ:pol).

A nuclear explosion is in fact local destruction of the deep-field, the gigantic pressure in every point of space is unleashed by the destruction of the space-pixalls constituting the nuclei taking part in the fission. So the space-pixall turns inside out and dissolves in a gigantic release of pressure. This explosion has a toroidal shape.

The most dramatic natural example of a giant explosion showing toroidal vacuum at the very centre is the meteorite that exploded in 1908 over Tunguska in Siberia at several hundred metres height in the atmosphere. At the epicentre of the blast all trees were still standing, stripped, but upright, no side-ward pressure, but in a ring around it the damage is still visible today, a hundred years on, the red ring shows the torus of destruction. (Scientists have no explanation for this torus-phenomenon, though also at the epicentre of the Hiroshima bomb the memorial building is still standing)

Tunguska, 1908-2009

Reflection-field

The geometry of the reflection field, the transformation of spherical wave-fields into transverse wave-fields is the most fundamental mechanism in nature and determines the reflection-field of the object and its emerging inertial field.

We have to appreciate that every object is extended in the deep-field far beyond its appearance (with a sharp enough lens you are visible from space) this is its (your) reflection field, the beginning of which may show in the aura. It is a standing wave field, which is at the same time an inertial field and its ‘con-firmation’ of the deep-field, it adds to the stability (inertia) of the whole. So every aspect of the transformation sustains the whole as an organic process and this is also reflected in the energy equilibrium like the cosmic micro wave background radiation (CMBR) at 2.73 degrees Kelvin, 1/100 of melting ice at 273 degrees K (1 + 99), but coincidence, of course.

In my approach we see the cosmos as a self-contained integrated whole in which every aspect has, or reflects, a function. In the BigBang cosmology though everything runs in separate categories from a contingent beginning to a fading end, like an old fashioned alarm-clock unwinding its spring and ‘freezing in silence’. Instead my perceived cosmos is preferably cyclical, continuous and only locally entropic whereas the Big-Bang universe is blind and contingent, our universe ‘sees’ and has ‘purpose’, even if only it were to preserve ‘continuity’, but most of all our cosmos is ‘intelligent’ and ‘formative’. We see logic everywhere in nature, a logic of harmony and of beauty, a logic of economy, of how everything is recycled, nothing is wasted.

How nothing gets lost, until completed. (Law of Karma).

Cosmic Deep-field

The imperturbable rest of the deep-field is the basis of uniform motion, as in waves, and as is manifest in the electromagnetic fields which all have the same local speed depending on the condition (curvature) of local space. The uniform inertial motion of any object is the objects natural resonance with the deep-field, it is embedded in the motion of the field, because it is made of it. As soon as outside pressure is applied, the deep-field resists change by slowness, inertia. Inertia is in that sense the ‘stretching of time’, it is ‘slowing-motion’. But it is also the transfer of energy by increasing momentum of the object through increase of excited pixalls involved in the movement at any one moment. The higher the speed of an object, the stronger the inertial field by increasing numbers of space pixalls being involved at the same time, the higher the wind the higher the waves, thus increasing the ‘substance’ and thus the momentum.

Momentum is stored in the deep-field as the momentum of an ocean wave is stored in its movement, the more volume the wave has, the bigger its momentum and still the water (the medium) does not move, but up and down, in a cycle, the wave has no eigen-substance, is only momentum.

Entrainment

This is why momentum can be transferred in ‘entrainment’ (Huygens), (transfer of momentum and phase through space) because there is a medium; how could it be transferred through ’empty space’, this is a crucial argument for an ether

Lorentz commenting on Einsteins ‘absolute relativity’ wrote: “I cannot but regard the ether, which can be the seat of an electromagnetic field with its energy and its vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter.” (Lorentz, 1906)

This is the Cartesian view, which was held by most scientists, who nearly all presupposed an ether to explain the fact that space can transmit a force and waves of light. Newton even stated that no one in his right mind could entertain the idea that force could be transmitted through empty space, but Einstein convinced the whole scientific community that you can, through curvature of space, that is of ‘Nothingness’.

Here it is important to see that in our approach matter is an ‘excitation’ of the deep-field and that we have always to consider the paradox of the moving form through the ‘unmoving’ medium. The substance of the form is anchored, at rest, in the deep-field, this is its inertia, this is why the electro-magnetic field speed (light) is always constant relative to the object. Its substance does not move relative to the waves of the field, how could it, it is made of these waves. This is the puzzling paradox of a body’s substance at rest in the same frame of reference as in which its shape is moving, just like the moving shapes on an immobile pixel-screen.

No Space-time

This is a different approach from the Minkowski-Einstein explanation with regard to curvature of space-time, but it confirms that in a profound sense we are at rest in the deep-field, because it is the stuff we are made of; this is quite different from Einstein’s insistence on an inertial frame for every individual thing, which could be seen as my idea of ‘inertial fields’.
The ‘separate thing’ does not exist in the deep-field, it is like the volume of a wave, the momentum, it has no eigen-substance. I am often very close to Einstein’s insights, because he became aware general relativity cannot do without a medium, but was not listened to anymore in that respect, all too happy as scientists were to have gotten rid of that persistent antique concept of intangible ‘aether’.

All objects will move in the direction of least resistance in the deep-field, because of the omnipresent cosmic pressure-front of cosmic radiation, generated by the energy fields of the galaxies, neutron stars etc, so bodies will move in the direction of each others ‘lee-field’. The push of the cosmic pressure field, which secures uniform motion in the neutral deep-field, causes the acceleration in the lee-field of the object, the closer to the object the less the resistance of the counter-pressure from that direction, which falls off with the square (surface: r^2) of the distance (radius: r), and the higher the acceleration, even though the pressure of the general deep-field does not change. (It is G and very weak).
So ‘gravity’ (heaviness) is more caused by a lack of force rather than an act of force, but it is in fact an imbalance in the cosmic pressure field. This imbalance shows in the ‘curvatures’ of the ‘elastic’ deep-field, but is better expressed as local contraction or expansion of space, where the strength of the inertia in the deep-field, the permittivity of the medium, decides over the speed of a process. So with a proper use of the term inertia as the cause of a time-frame, we can probably make the concept of time in physics obsolete and have a definition of inertial space. QED.
(The ‘proof of relativity in GPS’ is due to the difference in ‘gravity’ on earth and in outer space, that is: the intensity of the lee-field, the state of the deep-field; no ‘time’-dilation, it is deep-field-dilation)

Cosmological models

The major and decisive difference between my model and the Bigbang is, that mine shows cyclical (rhythmic) and continuous order (‘permanent creation’), whereas the BigBang is a sudden origin out of nowhere, with no mention of order, no explanation of what is now (as order), but winding down eventually into disorder (entropy, linear time). So they know everything of the beginning and of the end, but cannot connect it to the world we live in. It is maybe misplaced to call that ‘cosmology’, it’s theoretical astrophysics.

Whereas scientists are again and again baffled by the subtle order of the processes in Nature, this bewilderment originates in their ignorance of the cyclical and objectively ‘intelligent’ character of the Universe and Nature as a whole, because of harmonics. Cosmos means order, Chaos means disorder. Overall we see order, not chaos, chaos is at the lower levels and in the struggle for life, cosmos is when you look up to the night sky, huge silent order.

Stone Age people may have known this and seen the deep harmony of the cosmos which they sought to express in the mathematically harmonic designs of their ‘megalithic works’, their ‘cosmic architecture’, which appear to hold the principles of resonance.

Stars and Black Holes.

What is interesting about the mathematical approach is that ‘mass’ is ignored and everything centers on what happens to points in space and their connections. This makes it immediately related to my model of space-pixalls and the mathematical foundation of reality. Riemann used the term ‘Stoff’ (dust, stuff) for the (liquid) aether which he presupposed, take note that Riemann thought granular [the liquidity of dust, the vortex of the hourglass, this is the mechanics of space (-pixalls), stretched in time, the black hole as the vortex of a galaxy].

The black hole cools the cosmos as the star heats it up, it is equilibrium in a process of regeneration. There is no conservation of energy, it is a constant stream of renewal in equilibrium with decay, but, yes, very big cycles. The Second Law is more an aspect of local decay, not a deterministic overall law, I intuit. We see in this black hole geometry the vortex, which has the dynamics of a torus, perpendicular circling creating the abyss, the cyclone.

Cyclone is like galaxy

It is similar to magnetic field lines towards a negative pole. The black hole is a 4-D monopole. It is interesting in this respect that the amount of entropy which is supposed to be in the spherical black hole is 1/4 of its surface area. Nobody mentions that this means a reduction of 1 dimension since the spherical surface as border of 3-D space gets as ‘information’ compressed into a flat one-sided 2-D circle area, .r², since the spherical surface is 4 times the great circle area = 4..r²

In my view this implies the black hole is not spherical but a one-sided flat disc, so to speak, a monopole, the border-point of 3-D space, opening to the zero-dimension. It seems to me this 1/4 reduction is rather important but nobody seems to notice it. It could also signify the 1/4 concave surface of the horn-torus
Space is limited on the inside by the zero-dimension, so a sphere becomes a one-sided circle surface with respect to the zero-dimension. The earth has no centre, no signals can penetrate it through the heart, they all bounce off because there is no other side to the centre, it is outside 3-D space, it is the zero-point as border-point of space.(Look at the ‘corus’ again)

Horn-torus or Corus

Here the importance of the torus-geometry and especially the horn-torus becomes apparent. What makes the horn-torus unique as mathematical form is that on the one hand its surface area is bounded by one single center-point and on the other it is also expressed in a 2-D square. These two unique properties give it a special relation to the sphere which properly speaking is also a unique moment in the torus-geometry and transformation of space.
In my conception of the geometry and dynamics of space the torus is pivotal, because it is the geometry of rotation. Although stars and planets look spherical they are due to their rotation flattened and consequently in my system spindle-tori. This rotation is also the origin of the waves it causes in its surroundings which are then carried by the deep-field and form a reflection field which is at the same time the ‘lee-field’ of an object. It is the ‘pressure-gravity’ emerging in the depression of the deep-field, the ‘lee’ around an object, which keeps everything rotating. The rotation absorbs the pressure and emits this energy as waves by which it shapes the geometry of the deep-field in its vicinity. So the objection of (over-)heating (Lorentz himself abandoned his own idea for this), which is held against this model is not valid, the absorbed energy is transformed into reflection wave-fields, which indeed affect the geometry of inertial space.

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More on this subject you will find in the chapters under the heading ‘Cosmology’