***** Why Primes?
This piece is a bit ontological and cosmological with respect to the importance of the ‘early’ primes, 2-13, where of course 2, 3, 5 stand out as ‘extra primes’ because of their extra-ordinary importance in the matrix of space, but also 7 and 11, 13 to lesser degree, have very important roles because these numbers are involved in the transformation of sphere and vortex-torus, where bent-number becomes straight and straight-number, bent.
8/10/10
My recent diversions into the prime numbers, numbers only divisible by themselves and one ( 2, 3, 5, 7, 11, 13 etc.), may seem anomalous in the context of this website, but in fact for me it is going back to the first stages of the exploration of my new-found, old kind of mathematics that this whole website is based on. Here we find the rudimentary interaction of the primal numbers, which, as I argue, rule everything in vibrations.
I understand that prime numbers are not close to most people’s hearts or interests, but it was my exploration of the prime numbers, without knowing anything about them, just like you, that set me on the way I am still on, that is the way shown by the logic of the natural numbers themselves, irrespective of the conventions of traditional mathematics.
A proper appreciation of my analysis of the primes reveals the foundation of the whole number-logic and the related geometry that I have ‘unearthed’ and explained on this website. It is all about the first 6 primes and related numbers.
The deep obsession with precision may have blinded mathematicians for the beauty of the harmonies that whole numbers can create in their own ‘flexible’ number-logic and in the associated natural number geometry.
But don’t be mistaken, this is not a recreational oddity, on the contrary, it goes to the heart of nature itself, as I hope to show convincingly.
Here again mathematics shows that it is the ultimate tool to make ‘natural workings’ transparent.
The all pervading principle is that everything is expressed in (whole) natural numbers and the deeper meaning of this is that resonance is based on whole number relations; but that is not yet at stake here.
What is done so far on this website is showing how this system of whole numbers, applied to geometry, was employed by megalithic Stone Age man and the builders of the Pyramids (quite possibly partly contemporaneous)
It is just a gift that the model I developed was already known to two, even three illustrious civilisations, because I found it through inspiration by Sumerian cuneiform clay-tablets, but I still know virtually nothing about the Sumerians nor of their mathematics. I was not looking for anything specific, it was just curiosity, but once I found my nine-number system the primes popped up immediately and they haven’t gone away eversince.
Analysing the structure of the primes was what suddenly fascinated me and led me into a world of numbers nobody had ever told me about; and it all fitted beautifully once you understood the rules you could find yourself.
This remains the character of my mathematics, that it is self-evident, simple, transparent, and that it transpires integrity and harmony. Moreover, that it is easily understandable and creates beauty as a matter of course.
Initially the analysis of the primes showed me the exceptional character of the first three primes 2, 3, 5 , ( I will publish my initial analysis shortly) but regarding the repunits there are a further three 7, 11, 13 , which make these 6 principle prime numbers appear the pillars on which this whole-number-system is based.
A further two more peculiar primes are 37 and 101, because of their intricate relationship with 3 in 3 x 37=111 (R3) and 11 in 11 x 101 = 1111 (R4), these are the first primes to arise from the logic of the repunits R3 and R4. (Repunits are numbers related to powers of 10 minus 1 ; {(10^n)-1} divided by 9, consisting of only 1’s : 1, 11 (R2), 111 (R3), 1111 (R4) or in general 111………111= Rn).
The repunits in my view contain all primes as factors. Why is this so. This is so because of the reciprocal of a prime which holds all factors systemically bonded with the initial prime. Every prime, except 2 (0.5.) and 5 (0.2), combined 10 (0.1), do have a period in the reciprocal, 1/3 = 0.3 3 3 , periods of only 1 number. Note 1/27 = 0.037037037…, we see here why 37 is such a prominent prime, dat is because it is linked to the cube of 3= 3^3 = 27.
It, though, is not with the numbers themselves we are concerned but with the system that is ingrained in them and, in my view, is the way nature calculates, that is: through resonance. Resonance is not precise, resonance has always a margin to tune into, and resonance is always about whole numbers, like Pythagoras found out and based his musical theory upon and his mystic ontology. So this is where the floating value of the numbers comes in and how this incompatible but imperturbable logic of the numbers holds everything together and apart.
The heart of the matter is that the the primes form specific resonance patterns, which ‘materialize’ and out of which the diversity of things sprouts. The prime-associations decide what is and what is not possible. The idea is that the logic of the primes, as for instance exemplified in the structure of the repunits, is the model of the basic resonance of everything existing.
This logic is so simple that it all comes down to the ‘interactions’ of the first 14 natural numbers, where there are several doubles as 2, 4, 6 , 8, 10, 12, 14, that is 1 , 2, 3, 5, 7 , and 9 = 3×3 and 8 = 2×2×2 and 11, which relates to 9 in 10^2-1 = 99 = 9 x 11 and eventually 13, which remains a bit of an outsider of which the true function is not clear to me, but 13 rules 3-dimensional ball-packing (Kepler), like 7 does 2-D circle-packing (hexagon).
So what we are exploring on this website is the significance of the natural numbers in mathematics and specifically geometry, but in such a measure that the ‘received mathematical logic’ goes overboard. We build from scratch exclusively with natural numbers, no ‘irrationality’ whatsoever.
Nothing is precise, because everything has to resonate. The deepfield is characterised by incessant vibration and interaction of wave-fields.
Resonance is imperative throughout the deep-field. But resonance only occurs in whole number ratios.
By not being restricted by precision there exist margins of engagement in resonance. This is exactly the margin the natural numbers between them create and which makes that this model is reflected in the geometries and patterns of nature, like Rings of Saturn and Solar System.
I want to emphasize again that in principle the basics of these mathematics are not very difficult, especially because it is all very pictorial and can be ’seen’, but things are confusing because of the similarity of the numbers and because it is all extremely compact and it is switching between sets of ratios, which seem all very familiar: so it is more a matter of experience than of intellect which matters in this mathematics of mine (and of the people of old), but once you grasp its essence you will be surprised at the simple beauty this mathematics has in stall for you, irrespective of the Stone Age link.
One of the confusing moments is where 7 and 11 or another pair change to their opposite characteristic. 22/7 , the 11 is the arc number , the 7 is the straight line of diameter.
I am embarrassingly poor at mathematics, I tell you, and I must apologize for that, but I must totally rely on logical reasoning and junior high math and that is why I am so glad I found these simple, graceful and practically proven mathematics which have such phenomenal explanatory power in exegesis of papercuttings and far beyond.
The hidden geometry of Maeshowe expresses the doubling of square and circle by circumscription, square in circle in square in circle ……etc., but it also expresses the (Double-) Rainbow Proportion of 14 : 11 for the radius or in surface areas 1.62 : 1, ( 1.62 = .9×.9 x 2; note how close 1.620 : 1 is to 1.618… : 1= phi, the Divine Proportion and to (14/11)^2= 1.6198… area proportion, and it possibly also holds a cube of side 8. (be it with some margin, but still, 8 returns in other measures). These ratios and geometries only come to light in the analysis of the recent ground plans drawn up by archaeologists on the basis of excavations.
Then there is the lintel ring of Stonehenge which not only expressed the value of Pi in a mathematical formula through its inner circumference, as simple as 360 ulna / 162 half fibula, or 180 ME /81 MR (ME = Megalithic Ell, MR= Megalithic Remen (female fibula)) – [ note the predominance of the number 9 in these formulas], but which also incorporated the number 43, which is linked to the eclipse calendar, in the outer diameter of the lintel ring. This outer radius of the lintel ring is similar to the circle dimensions of the Stones of Stenness in Orkney which also feature the prime 43 in fibula bone measures and which were doubtless earlier.
The confirmation I found in Stone Age Orkney architecture and in the designs of the Pyramids is only a dreamt-of introduction to the simplicity and beauty of the mathematical basics I already had found.
After all, these monuments testify of a highly developed insight in geometry and in the harmony of the numbers, they have taught me the hidden corners of this marvellous system and given me incredibly exciting insights.
What I have added conceptually is seeing these mathematical complexes express the specific base dynamics of wave-fields (vibrations expressed in spheres and tori, circles and squares) as the substance of reality and closely related a theory of ‘lee-fields’ created by cosmic deep-field (urfield- or aether-) pressure to substitute the concept of attracting-gravity by a concept of ‘pressure-gravity’ in inertial reflection-fields. It is this inertial pressure which gives stability to space, the smaller the scales the higher the pressure.
May be many other things were known in those days. I have become deeply impressed by what I have found in the culture of the ancients and this is only the beginning….