11/1/11
Preface
On several occasions I have made comments on some basic ideas of the cosmology that I have developed over the years which this website is ultimately about, but only recently I reached firm ground in an exciting confirmation of the factors of repunits (11, 111, 1111 etc.), which I introduced here earlier, with respect to the frame work of the ‘dimensionless universal constants’, as there are the ‘fine structure constant’ , the ‘mass ratio of electron and proton’, the ‘gravitational coupling constant’ and the ‘strong coupling constant’.
Holy Grail
Any Grand Unified Theory (GUT) or Theory Of Everything (TOE), the Holy Grail of modern science, must incorporate these constants and there is none yet that does, these constants are complete enigmas to science, so what I have got here is pretty good, if only it were because at least I have a coherent framework, whereas most of the others don’t even know where to look for one. (The Higgs-field, you say, but that is about gravity, not about universal constants, it is though conceptually close to my cosmic deep-field and in that sense the LHC may find that I am right, not by finding the Higgs-boson, but by coming to understand the deep-structure of space by finding no ‘god-particle’, because the only possible ‘god-particle’ is the ‘space-pixall’, but that is no particle in the sense other particles are deemed to be particle, if you get what I mean, I wrote this 11/1/11, which was before the international hoax on the Higgs- boson, which may be a particle, but not what they were looking for; scientists are not at all happy with what they found)
If I am right, my (possibly ‘shamanic’) mathematics explains why the universal constants are interlocked in a huge frame work of basic resonances, vibrations based on natural numbers, concentrated in the first 5 (or 6) primes and why it cannot be otherwise. It explains why some things can and others cannot exist, by the states of constructive and destructive resonances; simple and transparent. This world is not the best of all possible worlds (Leibniz), this world is ‘the only possible world’, because its basics, the interacting vibrations, expressed in numbers are based in fundamental natural number relations and cannot be otherwise.
It also shows that evolution is not a haphazard blind force, but a mathematically well organized development of ever higher frequencies and intricate natural patterns. So the tendency of nature is towards higher frequencies, higher complexity, higher refinement, higher intelligence. All the beautiful patterns in nature, from flowers to a spotted animal hide, are based on mathematics, but they are never ‘exact’ or the ‘same’, everything is unique, has its own unique vibrational space, signature and history, by which it is recognized, like you by your face and voice. Everything grows from an ever new present Nature is not rigid, but flexible, it is built on iron-cast logical principles but it calculates by resonance and resonance is not rigid and precise, but it interlocks. If it were different, nothing could exist.
Who knows?
In the following I make an attempt to do justice to the ‘incredible’ regularities I have discovered, but this does not mean that I understand any of it, I can only show, I cannot penetrate into these mathematics and geometries like others may, who are trained to do so. The only thing I can do is point at the peculiarities of the resonance model, its numbers, its symmetries, it’s beauty, all on a plane that is understandable by an educated public.
First though some quotes of scientists to stress the importance and the enigmatic nature of these universal constants, with the fine-structure constant as the ‘prima donna of scientific mystery’
The fine-structure constant
Feynman (1985): “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! “
-Richard Feynman
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Mac Gregor stated: “The mystery about α is actually a double mystery. The first mystery — the origin of its numerical value α≈ 1/137 has been recognized and discussed for decades. The second mystery — the range of its domain — is generally unrecognized”.
—Malcolm H. Mac Gregor.
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“If alpha [the fine structure constant] were bigger than it really is, we should not be able to distinguish matter from ether [the vacuum, nothingness], and our task to disentangle the natural laws would be hopelessly difficult. The fact however that alpha has just its value 1/137 is certainly no chance but itself a law of nature.
It is clear that the explanation of this number must be the central problem of natural philosophy.”
—Max Born.
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Analysis of the dimensionless universal constants
I publish this analysis although I am aware that with the state of knowledge of the involved science that I am in, it would be doubtful I could add anything worthwhile to the topics at hand. I do this because I feel a duty towards the number knowledge that I acquired over the last 15 years, because I cannot bear not to point out to my fellow men what has been such an enrichment of my own life.
This whole (website-) investigation has brought me in regions of the mind and the world I would never have thought I’d ever go and I still struggle to express satisfactorily what I deem of great importance if found beyond doubt to be indeed true and working. This is why I would plead with those scientists that are experts in fields that I touch on here to judge this work with sympathy and with the realization that at basis we stand before a profound mystery. I try to find a description with principles that make it easier to cross the barrier of mind and matter by dissolving the individual Eigen-mass of things in the ‘Substance’ of the deep-field, of Space.
The fine structure constant
In the following I give a number of ways of writing the constant in an attempt to lay bare as much as possible from its possible associations. The only thing I can do is show the versatility of the natural number ratios within the mathematical logic of the model I employ, these numbers and ratios may hold keys to understanding the universe as system.
Alpha
The fine structure constant α ≈ 1/137 and α^-1 = 137.0359 9908 (in 2012……., it still changes), this is the constant of the physicists as Feynman noticed, I claim it is 137.0370 37037 with difference 0.001037…, one-thousandth+ and it gets better in the following. The number 137.0370 370… is actually the astoundingly simple rational number 3700/27, but in the form of the mathematicians as coupling constant α= 0.0854245429….. , this value becomes even more conspicuous because the square root of 27/3700 (= 0.00729 729 7..) is this coupling constant e mentioned by Feynman and this square root is 0.0854242195… which differs from the official alpha a mere : 0.000 000 323… Maybe you can pronounce it, but it is an awfully little difference. We see that my constant is purely mathematical, a simple ratio in which 37 and 27 play the key roles and then it is good to know that 27 x 37 = 999, a number bearing the third repunit 111 R3 (3 x 37). so you can also write this number as 111 x 100/9 x 9 = 11100/81, in this form it relates very well to our value for Pi-squared the hallmark of the torus geometry as 800/81. (9.87654321)
We see these numbers being able to share a compatible order.
We continue by showing just by different presentations how the number sheds light on deeper structures and geometries
In my system this strange lump ratio can be expressed in many different ways, for instance as:
136900/999 = 137.037037037… (1369 = 37^2)
factorized this is
37 x 37 x 10 x 10 / 9 x 3 x 37 = 136900/111 x 9
3700 / 27 or (37/27) x 10^2
also
(37^2 x 10^2) / (37 x 3^3)
this is 37 divided by the cube of 3 times the square of 10 or even further broken down in
(370/3) x 10/9 or even
370^2 / 999
370/3 = 123.333333…. = 1110/9
1110/9 x 10/9 = 11100/81 = 137.037037037
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(10^2 / 9^2) x 111 = 137.037037037
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81/11100 = 0.00729729729… = 729/99900 (729 = 27^2 )
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27^2 / 3^2 x 10^2 x 111
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[9^3] / [3^3 x 10^2 x 37]
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81 / 11100 and 11100 / 81
27/3700 = 0.00729729729……..
3700/27 = 137.037037037…..
it is also 0.085424 219… which is the root of 27/3700
[alpha = 0.085424 549….. diff. = 0.00000033 !!!, diff. 33/millionth!!!]
3 x 137 = 411 and 10/9 x 370 = 411.11111……. 3700/9
6 x 137 = 822 and 20/9 x 370 = 822.222222…..
9 x 137 = 1233 and 30/9 x 370 = 1233.33333…..
10 x137 = 1370 and 37 x 37 = 1369
3700 / 9 = 411.111111….
411.111111….. / 411 = 1.000 270343336036766693701 00027034333…..
factors of period 270343336036766693701 are R24 and all early primes etc. the usual lot
these are the factors of RR 2, 3, 4, 6, 8, 12, 24
this is where the resonance takes place between 137 and 37, it is at multiples of 411 and at multiples of 10/9 x 370 being 411.11111111111……..
It is of course remarkable how close this gets to the following constant of mass ratios
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Constant of mass ratio for electron and proton
1 x 1836 = 4 x 27 x 17 ( 2^2 x 3^3) x 17 = 108 x 17
1/1836 = 0.00054466231
.544444444….. -> 49/9 = 5.44444…
49 / 90000 = 0.0005444444….. square root 49/90000= 7/300 0.023333..
period 54466231 x 1836 = {(10^12)-1}/9 = 1111….1111 [R12]
R48 factors are: RR 2, 3, 4, 6, 8, 12, 16, 24
3, 7, 11, 13,17, 37, 73, 101, 137, 5882353, 9901, 99990001,
9999999900000001.
these are 13 crucial primes and they all have a structural relation in this number, look how this can be broken down and recombined in factors of 10 (n+1) and 10(n-1)/9:
3 x 37 = 111 ;
7 x 11 x 13 = 1001 ;
73 x 137 = 10001
101 x 9901 = 1000001
17 x 5882353 = 100000001;
10001 x 99990001 = 1000000000001
1000000000001 x 9999999900000001 =
1000000000000000000000001
111×1001 = 111111 R6
111111x 1000001 = 111111111111 R12
111111111111(R12) x 1000000000001 = 111111111111111111111111 R24
111111111111111111111111 (R24) x 1000000000000000000000001=
111111111111111111111111111111111111111111111111 R48
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These are the layers of the relationship of the electron and the proton, represented by the primes
This is the hidden structure of the repunits and matter, the resonance base.
This is the final victory (and I wasn’t looking for it)
We see repunits R3, R6, R12, R24, R48 and more importantly we see powers of 10 plus 1 (10000…0001) and their complementary deep structure primes and we see powers of ten minus 1 represented by repunits (1111….111) and their deep-structure primes.
The emerging numbers are absolutely early crucial primes and repunits, so this reveals the structure of matter as regards the elementary interaction and geometry, whatever it means to us now. The repunits have a supposed bearing on quantum jumps and resonance frequencies.
Involved are the factors of 10 to the power of 1, 2, 3, 4, 6, 8, 12, 24 each plus 1, which are each part of a repunit, which is a power of 10 minus 1, divided by 9.
Is there anyone who can better this analysis?
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Given the logic of the prime numbers the natural constants are exponents of the only possible way that nature can exist ‘mathematically consistent’ and this is achieved by resonance and harmonics (harmonious ratios).
The fine structure constant is most probably a geometric necessity as it would be expressed in the formulas above
The unit which has the measure of 10^-38 or 10^-39 is and may be a repunit because both the factor 10^38 -1 and 10^39 -1 have as factors the deep-structure numbers of the repunits and a prime repunit being R19, so here again there is a clean numerical approximation in the root primes, either
R38 -> 10^38-1 : 11 (R2) = 1111111111111111111 (R19)
909090909090909091 (R38)
or
R39 -> 10^39-1 : 111 (R3) = 1111111111111 (R13) 9009009009009909909909901 (R39)
We see that these are not ordinary numbers and primes but numbers that reveal the structure of the infinite repunit building in which all the primes find their place. note the peculiar 9 numbers which are reminiscent of the reciprocals of repunits. Every new repunit only adds 3 to 7 new primes to the whole which means that the amount of primes remained nominally constant on average, but that the amount of other numbers involved grows with factor 10 in every new repunit.
We see here dramatically how few primes there actually are in the totality of numbers which is infinite.
A different approach comes to a different value but again with very clear factors, even better.
R36 -> 10^36-1: R2, R3, R4, R6, R9, R18, R36
Remember all these are exceptional repunits in their factors, all the ‘early primes’.
Again we are able to translate all the vital constants of nature into our system of approximations in a very elegant way, without any forced logic, although by no means the ratios are clear, or yet intelligible to me nor anybody else probably at first, but they consist of specific significant numbers, all early primes, unique period primes, a host of circumstantial evidence which cannot be dismissed as trivial. All these regularities still fit seamlessly in my system of crucial numbers, the celestial proportion. (I do not use the word ‘sacred’ geometry, although I may pay reverence in my terms).
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Gravitational coupling constant
1752 x 10^-45 is the electron-mass divided by the planck-mass, squared. (1752 = 73 x 24) 73 x 137 = 10001 = (10^4) + 1
this number has related primes in its repunit deep-structure :
11 17 73 101 137 R16
RR 2, 4, 8, 16
again we see here crucial primes like 137 and 11 and 101 also 73 x 137 =10001 especially the 17 of R16 is remarkable because it comes with the prime 5882353 this prime minus 1 is 5882352, which then relates to an enormous amount of primes via the prime number 61 which is factor to R60.
R60 covers RR, 2, 3, 4, 5, 6, 10, 12, 15, 30 and 41 which relates to R40 and there is a 7-squared,
The repunits suddenly dominate the scene.
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Strong coupling constant
0.1178 +- 0.0001 (+.0081 -.0095) 2 x 19 x 31
1178 relates to : R90, R45, R30, R18, R15, R10, R9, R6, R5, R3
116 : R7, R14, R28
117 : R5 R6
119 : R48
Here again a cluster of very special repunits
I am amazed at how strong the model stands, everywhere I get meaningful confirmation, it is not just some numbers that fit, it are outstanding numbers that fit. What I call the early crucial primes, that have generated all other primes.
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