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Number Theory: Infinite Scope of Phi, the Golden Ratio
Not only are there infinitely many sets of golden ratios solving the roots of higher order polynomials in a single unknown, but there are also another system of ratios engulfing the silver ratio of one plus the square root of two. Some of these systems of ratios each form the basis for a planet's anthropology involving not only aesthetics determining how we perceive and respond to harmony through our senses, but also the structure of: astrology, Sanskrit, the major and minor chakras, and oceanic salts and blood salt on any particular planet wherein life can evolve.
The idea is that life is more than about politically correct science or consumer-based technology; it's also about art, or how do we perceive our experiences. It's not always the same on various planets.
https://web.archive.org/web/20010304...planets0.shtml
For example, take the music of Richard Wagner for instance. He sometimes makes use of 11th and 13th chords spanning beyond the mere perfect 8th that we've become accustomed to. This suggests, to me, a chromatic scale of sixteen notes spanning a frequency of relationship between the tonic of neighboring chromatic scales of a major tenth (a perfect eighth plus a major third), exhibiting a frequency ratio of 1 to 5/2, rather than 1 to 2.
Furthermore, we've been able to destroy a planet between Mars and Jupiter, and blow off the atmosphere of the moon, before coming here to Earth.
And the Earth is foreign to this solar system having been brought from the Pleiades along with its resident Cetaceans on board. This is partly analyzable by examining what little we know about: the Sun (as a planet), Venus, Mars, the Earth, and the works of Carlos Castaneda. In all of these examples, except the Earth, a world predominated by sulphur, not chloride, salts are in evidence. Or else, in the case of the Sun, the ratio of the atomic weights of its iron and calcium silicate surface, also yields the same silver ratio derived from the Pell series of numbers, 1, 2, 5, 12, 29, 70, ... as do the other compounds of sulphur (Mars and the Asteroid belt as a remnant planet), or phosphate (Venus), predominating on these few exampled planets in our solar system.
The surface of the Sun:* The sun has a rigid iron surface located under the photosphere that is revealed by satellite imagery.* The solar surface sits beneath the sun's visible photosphere and is electrically active.
All we have to do is look at the U.S. dollar bill and measure its length versus its height to get the silver ratio of 2.414, and then whip out our credit card and measure its proportions to see that it's the golden ratio of 1.618. And then regard the historical record of the Masters of the Arts, during the Renaissance, freely making use of both the golden and the silver ratios as if they had the strong inclination not to divorce themselves from either ratio. Just because this planet's native population of young souls harbors an inclination to use merely the golden ratio doesn't mean the smaller segment of the population of older souls - many of whom have reincarnated from somewhere else - can't use both, and do. Such as, the garden apartment complexes in the coastal town of Ostia, Italy, built by the Romans during the first and second century AD for their vacationers whose floor plans are predicated on something called the 'sacred cut' -- a derivation of the silver ratio using nothing other than a straight edge and compass.
Watts, Donald J. and Carol M.; A Roman Apartment Complex; Sci. Am., Vol. 255, no.6, 132-140, Dec. 1986
http://mimoza.marmara.edu.tr/~maeyler/CONNECTIONS.pdf - description begins on PDF pg. 45, text pg. 28.
Carol Martin Watts and Donald J. Watts, “Geometrical Ordering of the Garden Houses at Ostia,” Journal of the Society of Architectural Historians, vol. 46, no. 3 (Sep., 1987), pp. 265-276. {cited in...}
https://www.khanacademy.org/humaniti...tecture-insula
Humpback whales sing in a diatonic scale. Who taught them to do that? And if you speed up a recording of their song at just the right speed, it will sound exactly like bird song! Nature designs their sense for harmony and pitch just like Nature designs our sensibilities -as well- by all of us being born and raised on the same planet invoking the same proportional ratio of aesthetic appreciation approximated by the atomic weight of chlorine (~35.453) divided by the atomic weight of sodium (~22.9898), or: ~1.54 (1.54212).
BTW, in aesthetic theory, unlike science, it's not about speed - nor is it about accuracy - to achieve approximations of irrational ratios, because whenever we perceive something and register it in our mind as an image or a sensation, it is our mind which will interpret the impression our senses bring to us as a recognition of a pattern -- in this case, a pattern of aesthetics based on the golden ratio which is commonplace to our planet. So, don't be perturbed if my approximations are not exactly the same as whatever I am comparing them with.
Aesthetic recognition of an ingrained pattern can also be about how, or in what style, do we approximate it. Which implies we can go really, really slowly by deviating from the norm in various formats.
Take, what I call, the Ptah series I found mentioned in a book about ancient Egyptian pyramids....
https://web.archive.org/web/19990831.../pyramids.html
Like the Lucas series,
The Lucas Numbers
...which is a deviation from the Fibonacci series, the Ptah series is also offset from the Fibonacci but by a different amount exhibiting properties so uncanny as to suggest that the ancient Egyptians may have been capable of computing PI - Π, and the 48 divisions of a circle in radians, to four decimal accuracy and thus possibly fake trigonometric survey - which would have come in handy when building the pyramids at Giza.
I did this research back between the years of 1994 and 1997. I put some of my findings up on the internet for several years only to suffer a lapse. Now, I've managed to renew my interest in sharing this mathematical knowledge along with its hypothetical conclusions. I'm using one of my websites to post the math at...
http://vinyasi.info/Infinite%20Range...lden%20Ratios/
There's a lot of material, all of it technical, to revive which will probably take some time to recall and, if I'm lucky, dig up from storage on an old computer. So, this is just a general announcement of a start.
The conclusions may seem far fetched, I admit, to the casual mind. But I won't hold back by making value judgments of what I think is acceptable by common sense standards. I'll just present all of it as I know it to be...
The idea is that life is more than about politically correct science or consumer-based technology; it's also about art, or how do we perceive our experiences. It's not always the same on various planets.
https://web.archive.org/web/20010304...planets0.shtml
For example, take the music of Richard Wagner for instance. He sometimes makes use of 11th and 13th chords spanning beyond the mere perfect 8th that we've become accustomed to. This suggests, to me, a chromatic scale of sixteen notes spanning a frequency of relationship between the tonic of neighboring chromatic scales of a major tenth (a perfect eighth plus a major third), exhibiting a frequency ratio of 1 to 5/2, rather than 1 to 2.
Furthermore, we've been able to destroy a planet between Mars and Jupiter, and blow off the atmosphere of the moon, before coming here to Earth.
And the Earth is foreign to this solar system having been brought from the Pleiades along with its resident Cetaceans on board. This is partly analyzable by examining what little we know about: the Sun (as a planet), Venus, Mars, the Earth, and the works of Carlos Castaneda. In all of these examples, except the Earth, a world predominated by sulphur, not chloride, salts are in evidence. Or else, in the case of the Sun, the ratio of the atomic weights of its iron and calcium silicate surface, also yields the same silver ratio derived from the Pell series of numbers, 1, 2, 5, 12, 29, 70, ... as do the other compounds of sulphur (Mars and the Asteroid belt as a remnant planet), or phosphate (Venus), predominating on these few exampled planets in our solar system.
The surface of the Sun:* The sun has a rigid iron surface located under the photosphere that is revealed by satellite imagery.* The solar surface sits beneath the sun's visible photosphere and is electrically active.
All we have to do is look at the U.S. dollar bill and measure its length versus its height to get the silver ratio of 2.414, and then whip out our credit card and measure its proportions to see that it's the golden ratio of 1.618. And then regard the historical record of the Masters of the Arts, during the Renaissance, freely making use of both the golden and the silver ratios as if they had the strong inclination not to divorce themselves from either ratio. Just because this planet's native population of young souls harbors an inclination to use merely the golden ratio doesn't mean the smaller segment of the population of older souls - many of whom have reincarnated from somewhere else - can't use both, and do. Such as, the garden apartment complexes in the coastal town of Ostia, Italy, built by the Romans during the first and second century AD for their vacationers whose floor plans are predicated on something called the 'sacred cut' -- a derivation of the silver ratio using nothing other than a straight edge and compass.
Watts, Donald J. and Carol M.; A Roman Apartment Complex; Sci. Am., Vol. 255, no.6, 132-140, Dec. 1986
http://mimoza.marmara.edu.tr/~maeyler/CONNECTIONS.pdf - description begins on PDF pg. 45, text pg. 28.
Carol Martin Watts and Donald J. Watts, “Geometrical Ordering of the Garden Houses at Ostia,” Journal of the Society of Architectural Historians, vol. 46, no. 3 (Sep., 1987), pp. 265-276. {cited in...}
https://www.khanacademy.org/humaniti...tecture-insula
Humpback whales sing in a diatonic scale. Who taught them to do that? And if you speed up a recording of their song at just the right speed, it will sound exactly like bird song! Nature designs their sense for harmony and pitch just like Nature designs our sensibilities -as well- by all of us being born and raised on the same planet invoking the same proportional ratio of aesthetic appreciation approximated by the atomic weight of chlorine (~35.453) divided by the atomic weight of sodium (~22.9898), or: ~1.54 (1.54212).
BTW, in aesthetic theory, unlike science, it's not about speed - nor is it about accuracy - to achieve approximations of irrational ratios, because whenever we perceive something and register it in our mind as an image or a sensation, it is our mind which will interpret the impression our senses bring to us as a recognition of a pattern -- in this case, a pattern of aesthetics based on the golden ratio which is commonplace to our planet. So, don't be perturbed if my approximations are not exactly the same as whatever I am comparing them with.
Aesthetic recognition of an ingrained pattern can also be about how, or in what style, do we approximate it. Which implies we can go really, really slowly by deviating from the norm in various formats.
Take, what I call, the Ptah series I found mentioned in a book about ancient Egyptian pyramids....
https://web.archive.org/web/19990831.../pyramids.html
Like the Lucas series,
The Lucas Numbers
...which is a deviation from the Fibonacci series, the Ptah series is also offset from the Fibonacci but by a different amount exhibiting properties so uncanny as to suggest that the ancient Egyptians may have been capable of computing PI - Π, and the 48 divisions of a circle in radians, to four decimal accuracy and thus possibly fake trigonometric survey - which would have come in handy when building the pyramids at Giza.
I did this research back between the years of 1994 and 1997. I put some of my findings up on the internet for several years only to suffer a lapse. Now, I've managed to renew my interest in sharing this mathematical knowledge along with its hypothetical conclusions. I'm using one of my websites to post the math at...
http://vinyasi.info/Infinite%20Range...lden%20Ratios/
There's a lot of material, all of it technical, to revive which will probably take some time to recall and, if I'm lucky, dig up from storage on an old computer. So, this is just a general announcement of a start.
The conclusions may seem far fetched, I admit, to the casual mind. But I won't hold back by making value judgments of what I think is acceptable by common sense standards. I'll just present all of it as I know it to be...
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