davelook wrote:Ok, this is getting weird!
classical electron radius = alpha^2 X bohr radius = 2.81794028E-15
charge^2 to mass ratio = e^2 / mass_e = 2.81794028E-8
OK, here's what I think is going on here...
Larson uncharged electron mass= .00057870
Larson Charged electron mass = .000548741
uncharged/Charged ratio = 1.054595884
h-bar value = 1.054571628 X 10^-34 J*s
1.054595884 / 1.054571628 = 1.000022997E+034
Larson's actual number for the uncharged electron is .0005787037037.
Now, I've begun to notice lots of 4's and 3's, 12's, 144's running around when playing with natural ratios & multiples. It is often said that light is "144" in the "magic" way of thinking.
(e*c^2=144, fractal)
Anyway, you don't have to read geomantic literature very long before coming across constant references to the "magic" number 1728 (12^3).
There is something called the duodecimal (base-12) system, which according to Wikipedia (yuk, I know) is a much easier system for working in fractions, and isn't Larson's system all about fractions? It also the ancient basis for timekeeping and cyclic reckoning.
According to this notation, duodecimal 50 expresses the same quantity as decimal 60 (= five times twelve), duodecimal 60 is equivalent to decimal 72 (= six times twelve = half a gross), duodecimal 100 has the same value as decimal 144 (= twelve times twelve = one gross), etc.
Now I've also been trying to figure out what to use as the NATURAL number for electron mass, since it's co-created counterpart, the positron, is always created along with it. The electron is the first manifestation of light into mass (pair production).
Now, care to guess what the reciprocal of this cube of the natural number twelve is? 1/1728=0.0005787037037. I found that somewhat interesting!
Reciprocal Geometry
Re: Reciprocal Geometry
davelook wrote:
Reciprocal Geometry
First, read about the "Golden Angle" here and here...
http://www.popmath.org.uk/rpamaths/rpam ... lower.html
and http://maven.smith.edu/~phyllo/About/fibogolden.html
"In order to optimize the filling, it is necessary to choose the most irrational number there is, that is to say, the one the least well approximated by a fraction. This number is exactly the golden mean. The corresponding angle, the golden angle, is 137.5 degrees. (It is obtained by multiplying the non-whole part of the golden mean by 360 degrees and, since one obtains an angle greater than 180 degrees, by taking its complement). With this angle, one obtains the optimal filling, that is, the same spacing between all the seeds (figure 3).
This angle has to be chosen very precisely: variations of 1/10 of a degree destroy completely the optimization. (In fig 2, the angle is 137.6 degrees!) When the angle is exactly the golden mean, and only this one, two families of spirals (one in each direction) are then visible: their numbers correspond to the numerator and denominator of one of the fractions which approximates the golden mean : 2/3, 3/5, 5/8, 8/13, 13/21, etc."
1728/4pi = 137.50987083
360/Phi^2 = 137.50776404
The Golden Angle in both cases.
http://www.popmath.org.uk/rpamaths/rpam ... lower.html
and http://maven.smith.edu/~phyllo/About/fibogolden.html
"In order to optimize the filling, it is necessary to choose the most irrational number there is, that is to say, the one the least well approximated by a fraction. This number is exactly the golden mean. The corresponding angle, the golden angle, is 137.5 degrees. (It is obtained by multiplying the non-whole part of the golden mean by 360 degrees and, since one obtains an angle greater than 180 degrees, by taking its complement). With this angle, one obtains the optimal filling, that is, the same spacing between all the seeds (figure 3).
This angle has to be chosen very precisely: variations of 1/10 of a degree destroy completely the optimization. (In fig 2, the angle is 137.6 degrees!) When the angle is exactly the golden mean, and only this one, two families of spirals (one in each direction) are then visible: their numbers correspond to the numerator and denominator of one of the fractions which approximates the golden mean : 2/3, 3/5, 5/8, 8/13, 13/21, etc."
1728/4pi = 137.50987083
360/Phi^2 = 137.50776404
The Golden Angle in both cases.
Reciprocal Geometry
davelook wrote:
Larson identified the "Life unit" as a combination of material and cosmic atoms in Beyond Space and Time, so what we may be looking at with the Phi ratio is a LINKAGE between the two sectors, not something that is totally inanimate... though I would expect that any combination of motions exhibiting motion in time as well as space may also have these characteristics.
I think the first evidence we would see of that linkage would be in the classic neutron, where a proton and anti-neutrino form a temporary rotational combination.
Also, if we consider the RS2 proposition that the electron is actually the cosmic positron (not a material particle as Larson indicates), then your use of 'e' in the constants may have that special significance of "linkage", acting more as a life unit than an inanimate particle.
Also, since atoms do tend to capture electrons... perhaps looking at the atom as a "life unit" (aggregate motion of material and cosmic particles) might have some additional insights.
[/]
You might want to check out these books:First, read about the "Golden Angle" here and here...
http://www.popmath.org.uk/rpamaths/rpam ... lower.html
- Toward a Phenomenology of the Etheric World, Bockemuhl, Lindenau, Maier, Muller, Poppelbaum, Rapp, Schad
- The Plant Between Sun and Earth, George Adams, Olive Whicher
- Sunspace, Olive Whicher
- The Heart of the Matter
Larson identified the "Life unit" as a combination of material and cosmic atoms in Beyond Space and Time, so what we may be looking at with the Phi ratio is a LINKAGE between the two sectors, not something that is totally inanimate... though I would expect that any combination of motions exhibiting motion in time as well as space may also have these characteristics.
I think the first evidence we would see of that linkage would be in the classic neutron, where a proton and anti-neutrino form a temporary rotational combination.
Also, if we consider the RS2 proposition that the electron is actually the cosmic positron (not a material particle as Larson indicates), then your use of 'e' in the constants may have that special significance of "linkage", acting more as a life unit than an inanimate particle.
Also, since atoms do tend to capture electrons... perhaps looking at the atom as a "life unit" (aggregate motion of material and cosmic particles) might have some additional insights.
[/]
Every dogma has its day...
Reciprocal Geometry
Just found this while researching my connections...
http://arxiv.org/abs/physics/0509207
Sommerfeld introduced the fine-structure constant into physics, while he was taking into account the relativistic effects in the theory of the hydrogen atom. Ever since, it has puzzled many scientists like Eddington, Dirac, Feynman and others. Here the mysterious fine-structure constant, alpha = (Compton wavelength/de Broglie wavelength) = 1/137.036 = 2.627/360 is interpreted based on the finding that it is close to 2.618/360 = 1/137.508, where the Compton wavelength for hydrogen is a distance equivalent to an arc length on the circumference (given by the de Broglie wavelength) of a circle with the Bohr radius and 2.618 is the square of the Golden ratio, which was recently shown to divide the Bohr radius into two Golden sections at the point of electrical neutrality. From the data for the electron (e) and proton (p) g-factors, it is found that (137.508 - 137.036)= 0.472 = [g(p) - g(e)]/[g(p) + g(e)] (= 2/cube of the Golden ratio), and that (2.627 - 2.618)/360 = (small part of the Compton wavelength corresponding to the intrinsic radii of e and p/de Broglie wavelength) = 0.009/360 = (1- gamma)/gamma, the factor for the advance of perihilion in Sommerfeld's theory of the hydrogen atom, where gamma is the relativity factor.
I wonder how the pure electron mass 1/1728 plays into this.
By the way,
pi/Phi^2 = 1.1999816... which is why I think the ancients picked 12 as the cyclic numbering base.
http://arxiv.org/abs/physics/0509207
Sommerfeld introduced the fine-structure constant into physics, while he was taking into account the relativistic effects in the theory of the hydrogen atom. Ever since, it has puzzled many scientists like Eddington, Dirac, Feynman and others. Here the mysterious fine-structure constant, alpha = (Compton wavelength/de Broglie wavelength) = 1/137.036 = 2.627/360 is interpreted based on the finding that it is close to 2.618/360 = 1/137.508, where the Compton wavelength for hydrogen is a distance equivalent to an arc length on the circumference (given by the de Broglie wavelength) of a circle with the Bohr radius and 2.618 is the square of the Golden ratio, which was recently shown to divide the Bohr radius into two Golden sections at the point of electrical neutrality. From the data for the electron (e) and proton (p) g-factors, it is found that (137.508 - 137.036)= 0.472 = [g(p) - g(e)]/[g(p) + g(e)] (= 2/cube of the Golden ratio), and that (2.627 - 2.618)/360 = (small part of the Compton wavelength corresponding to the intrinsic radii of e and p/de Broglie wavelength) = 0.009/360 = (1- gamma)/gamma, the factor for the advance of perihilion in Sommerfeld's theory of the hydrogen atom, where gamma is the relativity factor.
I wonder how the pure electron mass 1/1728 plays into this.
By the way,
pi/Phi^2 = 1.1999816... which is why I think the ancients picked 12 as the cyclic numbering base.
Reciprocal Geometry
I think this has profound consequences from the RS point of view...
Enter ANY number into a calculator, then repeat this 2-step cycle just a few times...
1. Hit 1/x (reciprocal) button
2. add 1, hit enter.
Go back to step 1.
See how many cycles it takes to get Phi/phi to 4 decimal places.
Enter ANY number into a calculator, then repeat this 2-step cycle just a few times...
1. Hit 1/x (reciprocal) button
2. add 1, hit enter.
Go back to step 1.
See how many cycles it takes to get Phi/phi to 4 decimal places.
Reciprocal Geometry
From http://cat.inist.fr/?aModele=afficheN&cpsidt=16641452...
Quote:
http://www.electrochem.org/dl/ma/206/pdfs/0551.pdf . .and. .
from http://adsabs.harvard.edu/abs/2005AIPC..795R.205H...
Quote:
*See Aug.6 post above
Jeez, I wish I would've just STARTED my research with search terms of "bohr radius" and "golden"!
Quote:
Also, look at...
This work arose from the author's finding that the ratio of the radius of hydrogen, estimated recently (C.H. Suresh, N. Koga, J. Phys. Chem. A, 105, 5940 (2001)) by density functional methods, to the ground state Bohr radius is the Golden ratio, which operates in a variety of natural phenomena. It is found that the Golden ratio indeed plays a quantitative role in atomic physics. The interesting results are (1) that it arises in atomic dimensions due to the electrostatic forces between negative and positive charges; (2) that the energy of atomic hydrogen is actually equivalent to the energy of the simplest atomic condenser with the Golden mean capacity; (3) that the origin of two terms in the Rydberg equation for absorption and emission is in fact in the ground state term; (4) that all atoms can be assigned definite values of cationic and anionic radii based on the Golden ratio and covalent radii; (5) that these radii are additive and explain quantitatively bond lengths like those of alkali halides, of hydrides of many elements and of many other bonds, whether covalent or ionic or both; and (6) that the work functions of alkali metals can be evaluated using the bond lengths.
http://www.electrochem.org/dl/ma/206/pdfs/0551.pdf . .and. .
from http://adsabs.harvard.edu/abs/2005AIPC..795R.205H...
Quote:
Recently, the ground state Bohr radius (aB) of hydrogen was shown to be divided into two Golden sections, aB,p = aB/ø2 and aB,e = aB/ø at the point of electrical neutrality, where ø = 1.618 is the Golden ratio (R. Heyrovska, Molecular Physics 103: 877-882, and the literature cited therein). The origin of the difference of two energy terms in the Rydberg equation was thus shown to be in the ground state energy itself, as shown below: EH = (1/2)e2/(κaB) = (1/2)(e2/κ) [(1/aB,p - (1/aB,e)] (1).
This work brings some new results that 1) a unit charge in vacuum has a magnetic moment, 2) (e2/2κ) in eq. (1) is an electromagnetic condenser constant, 3) the de Broglie wavelengths of the proton and electron correspond to the Golden arcs of a circle with the Bohr radius, 4) the fine structure constant (α) is the ratio of the Planck's constants without and with the interaction of light with matter,* 5) the g-factors of the electron and proton, ge/2 and gp/2 divide the Bohr radius at the magnetic center and 6) the ``mysterious'' value (137.036) of α -1 = (360/ø2) - (2/ø3), where (2/ø3) arises from the difference, (gp - ge).
*See Aug.6 post above
Jeez, I wish I would've just STARTED my research with search terms of "bohr radius" and "golden"!
Reciprocal Geometry
Ok, I've got a new premise I'm working on; that alpha has to do with "cyclic numbering"...
1/7=0.14285714285714285714285714285714
12^3=1728; 1/1728=0.0005787037037037...
9^3=729; 1/729=0.0013717421124828532235939643347051
729/1728=0.421875 the cyclic numerals
1/.421875=2.37037037037...
1/137.035999679=0.007297352537599
If this seems like unjustified numerology, just do a search on the amazing properties of the "cyclic numbers".
1/7=0.14285714285714285714285714285714
12^3=1728; 1/1728=0.0005787037037037...
9^3=729; 1/729=0.0013717421124828532235939643347051
729/1728=0.421875 the cyclic numerals
1/.421875=2.37037037037...
1/137.035999679=0.007297352537599
If this seems like unjustified numerology, just do a search on the amazing properties of the "cyclic numbers".
Re: Reciprocal Geometry
davelook wrote:
sqrt(n) = n / sqrt(n)
Where you set n=10. It is valid for any number, but simply amounts to shifting the decimal point when you use powers of 10, because n = sqrt(n) x sqrt(n), so it ends up being n = n in the final analysis. I agree that it does not seem to be applicable to the s/t relationship.
Still looking at the Phi ratio. It is interesting that they call it a "divine proportion" since it is based on FIVE -- historically, the "number of man."
From a symbolic perspective, Phi is associated with the anima, the "soul" or what makes things "animate"--biologic. According to Larson in Beyond Space and Time, the life unit requires a linkage between a material AND cosmic structure. The nature of that linkage appears to be related to Phi, where both the material and cosmic motions are modified in such a way to express themselves (as a projection) using the divine proportion.
Geometrically, Phi represents an infinite recursion. Recursive systems are indicative of Chaos Theory, being based in strange attractors. These attractors, in the RS, are influences from the Cosmic sector, such as particles, atoms and mass. They are "strange" from the perspective of space, but are quite ordinary motion from the perspective of time.
So my question to you is... have you run across any harmonic numbers or numeric coincidences that are associated with the life unit, the cell, or anything biological?
I figured this one out... it works for all powers of 10. Why... it reduces to this formula:Well, since Larson says space and time are reciprocal, I tried sqrt(10) as space and 1/sqrt(10) as time, since 3.162... and .3162 are perfect reciprocals of each other.
No real dice that I could see.
sqrt(n) = n / sqrt(n)
Where you set n=10. It is valid for any number, but simply amounts to shifting the decimal point when you use powers of 10, because n = sqrt(n) x sqrt(n), so it ends up being n = n in the final analysis. I agree that it does not seem to be applicable to the s/t relationship.
Still looking at the Phi ratio. It is interesting that they call it a "divine proportion" since it is based on FIVE -- historically, the "number of man."
From a symbolic perspective, Phi is associated with the anima, the "soul" or what makes things "animate"--biologic. According to Larson in Beyond Space and Time, the life unit requires a linkage between a material AND cosmic structure. The nature of that linkage appears to be related to Phi, where both the material and cosmic motions are modified in such a way to express themselves (as a projection) using the divine proportion.
Geometrically, Phi represents an infinite recursion. Recursive systems are indicative of Chaos Theory, being based in strange attractors. These attractors, in the RS, are influences from the Cosmic sector, such as particles, atoms and mass. They are "strange" from the perspective of space, but are quite ordinary motion from the perspective of time.
So my question to you is... have you run across any harmonic numbers or numeric coincidences that are associated with the life unit, the cell, or anything biological?
Every dogma has its day...
Re: Reciprocal Geometry
bperet wrote:
What numbers should I have an eye out for?
So my question to you is... have you run across any harmonic numbers or numeric coincidences that are associated with the life unit, the cell, or anything biological?
Re: Reciprocal Geometry
davelook wrote:
If we are right about the polar influence of the cosmic sector upon the material, when a life unit is created one of the first things we should see is rotation... something curving or forming a spiral, as the rectangular, Euclidean geometry of space is affected indirectly by the polar, counterspatial geometry of time. This interaction should be harmonic, and may be at the root of the Phi spiral that is seen in many of the lower organisms.
The simpler the "life unit", the easier it will be to detect the influence. I'm thinking perhaps proteins and some of the building blocks of life would be the first to exhibit this. I'll admit that biology has never been my strong point, but I'd be willing to bet that there are certain biological "constants" that will build upon things like the Fibonacci sequences.
If I knew that, I wouldn't be asking!bperet wrote:What numbers should I have an eye out for?So my question to you is... have you run across any harmonic numbers or numeric coincidences that are associated with the life unit, the cell, or anything biological?
If we are right about the polar influence of the cosmic sector upon the material, when a life unit is created one of the first things we should see is rotation... something curving or forming a spiral, as the rectangular, Euclidean geometry of space is affected indirectly by the polar, counterspatial geometry of time. This interaction should be harmonic, and may be at the root of the Phi spiral that is seen in many of the lower organisms.
The simpler the "life unit", the easier it will be to detect the influence. I'm thinking perhaps proteins and some of the building blocks of life would be the first to exhibit this. I'll admit that biology has never been my strong point, but I'd be willing to bet that there are certain biological "constants" that will build upon things like the Fibonacci sequences.
Every dogma has its day...