Quantum Gravity Research (QGR) is a research organization which states its mission as:

“QGR’s mission is to discover the geometric first-principles unification of space, time, matter, energy, information and consciousness. Our team of physicists, mathematicians and chemists are hard at work on what we call “emergence theory,” a new quantum gravity theory (or “Theory of Everything”) that unifies space, time, energy, matter, information and consciousness.“

QGR produced a 2017 YouTube Video titled “What is Reality?” that explains how the golden ratio plays a significant part in this.

At the 20:42 mark of the video, this is explained, saying:

The golden ratio may be the fundamental constant of nature. It is a ratio that is fundamental to circumscribed equilateral triangles and it’s weirdly ubiquitous, appearing everywhere from quantum to celestial scales. Ever so interestingly, it appears in black holes.“

The golden ratio is the precise point where a black hole’s modified specific heat changes from positive to negative:“

M⁴ / J² = Φ

It is part of the equation for the lower bound on black hole entropy:“

8πSl^2P / ekA = Φ

The golden ratio even relates the loop quantum gravity parameter to black hole entropy:”

2^πγ = Φ

Why does this support the claim that the golden ratio is the fundamental constant of nature? Because a theory of everything must unite general relativity with quantum mechanics, and a black hole is where these two theories converge at their limits.”

In matrix mathematics, the highest probability non-trivial eigenvalues that show up in binary matrices are Φ and -1/Φ!“

So we now see a deep root between black holes and quantum mechanics because the golden ratio appears deeply in both black hole physics and in quantum mechanics.”

The golden ratio appears to startling accuracies in many other ways throughout the universe in scales both large and small. It is so prevalent that its existence simply cannot be looked at as coincidental.”

In the past the appearance of this ratio has usually been ignored by scientists because they had no way to explain it, so interest in it was considered the stuff of amateur scientists. But now, for the first time, a rigorous quantum gravity is being developed which predicts the golden ratio’s existence is literally everywhere.”

As someone who has researched and written about the golden ratio for decades, I have to say that this is more than even I expected. As this site at www.goldennumber.net has grown, my research and articles have shown it to appear in the following areas:

• Life, from the proportions of the DNA spiral to those that define the human face.
• Beauty, including human perceptions of beauty in the human face and in the aesthetics of harmony and innate natural appeal in any of the design arts, from ancient architecture to modern day logos.
• Mathematics, including many ways that it can be derived.
• Geometry, including many fascinating ways that it is found in a variety of geometric constructions.
• Cosmology and physics, including appearances in the solar system and even in the relative proportions of the Earth and Moon.
• Financial market price and timing trends, and gaming strategy.

The proposition by QGR that it is “so prevalent that its existence simply cannot be looked at as coincidental” is not surprising, but is certainly fascinating and validating.

This perhaps explains why it has captivated some of the greatest minds and best artists in history, including Plato, Euclid, Leonardo da Vinci, Michelangelo, Johannes Kepler, Georges Seurat, Le Corbusier and more.

I’d like to thank QGR for their work and discoveries in this area, and recognize and thank Scott Beach, an independent researcher and long time contributor to this site, for bringing the video by QGR to my attention.

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A research article called “Strange Nonchaotic Stars” published at the American Physical Society reported the discovery of a class of white-blue variable stars that pulsate in a fractal pattern at frequencies close to the golden ratio. Download the paper in PDF format here: strange-nonchaotic-stars-pulsate-golden-ratio-1501.01747v2

Pulsations described as “strange nonchaotic behavior.”

The discovery was reported by John F. Lindner, Vivek Kohar, Behnam Kia, Michael Hippke, John G. Learned, and William L. Ditto. The analysis was perfomed by John Lindner at the University of Hawaii and his colleagues. The stars may be the first example in nature of what chaos theorists call a “strange nonchaotic attractor,” a system that has fractal structure, but not the sensitivity to initial conditions of a chaotic system like the weather.” The fractal pattern was described as “strange.” “Nonchaotic” means the pattern is orderly rather than random. Most fractal patterns in nature, such as weather, are chaotic, so these characteristics of the variable stars was unexpected.

“Golden variables” have frequencies in a ratio close to the Golden Ratio

Researchers from the University of Hawaii at Mānoa have been studying a specific kind of stars called Golden RR Lyrae variables. Dr. Lindner said, “We call these stars ‘golden’ because the ratio of two of their frequency components is near the golden mean, which is an irrational number famous in art, architecture, and mathematics.”

They used data collected by the Kepler Space Telescope to plot the brightness of a particular star, known as KIC 5520878, at roughly 30-minute intervals over a four-year span. Variable stars dim and glow for a variety of reasons, and sometimes at more than one frequency. Two of this star’s frequencies, at a 4.05-hour and a 6.41-hour cycle, respectively, exhibited a ratio of 1.58, which is close to the golden ratio. Frequencies that are based on multiples of irrational numbers can be signatures of strange nonchaotic dynamics.

Fractal patterns also appeared within the frequencies

To show this was the case in KIC 5520878, and other stars they studied, the Lindner team performed a fractal analysis of their plots at different magnifications. This was done by converting their plots to frequency spectra. They then counted the number of spikes in the converted plots whose heights surpassed a certain threshold, with a power law dependence on the threshold that was a sign of fractal behavior. The pulsating frequencies conformed to fractal patterns, and when the oscillations were separated into parts, additional weaker frequencies were identified. Researchers described the weaker frequencies as following a pattern similar to how shorelines appear jagged at any distance from which they are viewed. The authors believe that this fractal pulsation may carry information about characteristics of the star’s surface, such as changes in opacity. They offered this as evidence of the first observations outside the laboratory of strange nonchaotic dynamics in nature. Their findings could bring improvements to the classification and modeling of variable stars. While the sample of stars in this study was very small, the researchers noticed an intriguing pattern among the four stars with pulsation frequencies close to the golden ratio. These stars all exhibited fractal behavior—never-ending patterns that repeat on continuously smaller scales—whereas the two non–golden ratio stars did not. “That suggests there might be a pattern,” Linder says. “What we need is more data.”

The Golden Ratio or Divine Proportion when used in plots creates a Fractal Pattern.  For at least the last 14 years, meta-physicians and modern physicians have been advancing the proposition studying fractal patterns may lead to a greater understanding of the Universe, as well as a Unified Field within it that may be a factor in the structure the Universe.

The meaning or connection to the golden ratio is uncertain, but could reveal new insights

RR Lyrae variable stars are at least 10 billion years old, and their brightness can vary by 200 percent in as little as 12 hours. This makes their observation challenging due to the Earth’s day-night cycle. The researchers also observed five other pulsating stars. Three of these showed pulsating frequencies close to the golden ratio and evidences of fractal patterns while the other two displayed neither. It is thus still not clear whether or not the stars’ fractal pattern behavior happens for a reason. If it does, then there are other clues regarding the physics of stars awaiting discovery. If not, then the discovery of the golden ratio in pulsating frequencies is a mere coincidence. The researchers have hope that it could provide information about the dynamics of these variable stars.

Linder commented, “If you look in the literature, you see lots of examples of strange chaotic behavior. I think our paper is going to bring this overlooked type of dynamics to the foreground.”

As the author of this site, I prefer to see claims of golden ratio relationships that represent 1.618 with a higher degree of accuracy than the observation of 1.58 presented in this research. It is unusual though to find relationships in nature as the one they’ve found, so perhaps additional research will indeed show that it is not coincidence and another of the many manifestations of the golden ratio in nature.

References:

http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.114.054101

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.054101

http://phys.org/news/2015-02-evidence-fractal-behavior-pulsating-stars.html

http://www.scientificamerican.com/article/strange-stars-pulsate-according-to-the-golden-ratio/

http://www.smithsonianmag.com/smart-news/pulsing-stars-flicker-pattern-close-golden-ratio-180954195/

http://en.wikipedia.org/wiki/RR_Lyrae_variable

https://edocs.uis.edu/jmart5/www/rrlyrae/rrlyrex.htm

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The illustration shows the relative sizes of the Earth and the Moon to scale.

• Draw a radius of the Earth (1).
• Draw a line from the center point of the Earth to the center point of the Moon (square root of Phi).
• Draw a line to connect the two lines to form a Golden Triangle (Phi).

Using dimensions from Wikipedia and geometry’s classic Pythagorean Theorem, this is expressed mathematically as follows:

Source:  Hidden Nature by Alick Bartholomew.  Thanks to Sathimantha Malalasekera for bringing this to my attention.

Certain solar system orbital periods are closely related to phi

Certain planets of our solar system seem to exhibit a relationship to phi, as shown by the following table of the time it takes to orbit around the Sun:

Saturn reveals a golden ratio phi relationship in several of its dimensions

The diameter of Saturn is very close to a phi relationship with the diameter of its rings, as illustrated by the green lines. The inner ring division is in a relationship that is very close to phi with the diameter of the rings outside the sphere of the planet, as illustrated by the blue lines.The Cassini division in the rings of Saturn falls at the Golden Section of the width of the lighter outside section of the rings.

Note: Phi grid showing Golden Ratio lines provided by PhiMatrix software.

A closer look at Saturn’s rings reveals a darker inner ring which exhibits the same golden section proportion as the brighter outer ring.

Venus and Earth reveal a golden ratio phi relationship

Venus and the Earth are linked in an unusual relationship involving phi.  Start by letting Mercury represent the basic unit of orbital distance and period in the solar system:

Curiously enough we find:

Ö Period of Venus * Phi = Distance of the Earth

Ö 2.5490 * 1.6180339 = 1.5966 * 1.6180339 = 2.5833

In addition, Venus orbits the Sun in 224.695 days while Earth orbits the Sun in 365.242 days, creating a ratio of 8/13 (both Fibonacci numbers) or 0.615 (roughly phi.)  Thus 5 conjunctions of Earth and Venus occur every 8 orbits of the Earth around the Sun and every 13 orbits of Venus.

Mercury, on the other hand, orbits the Sun in 87.968 Earth days, creating a conjunction with the Earth every 115.88 days.  Thus there are 365.24/115.88 conjunctions in a year, or 22 conjunctions in 7 years, which is very close to Pi!

See more relationships at the Solar Geometry site.

Relative planetary distances average to Phi

The average of the mean orbital distances of each successive planet in relation to the one before it approximates phi:

Note:  We sometimes forget about the asteroids when thinking of the planets in our solar system.  Ceres, the largest asteroid, is nearly spherical, comprises over one-third the total mass of all the asteroids and is thus the best of these minor planets to represent the asteroid belt.  (Insight on mean orbital distances contributed by Robert Bartlett.)

2005 unveiled the discovery of a 10th planet called 2003UB313.  It was found at a distance of 97 times that of the Earth from the Sun.  Its ratio to Pluto would thus be 2.47224, much higher than any previous planet to planet orbital distance ratio.  Could it be that this is actually the 11th planet and the 10th planet will be found at an orbit whose ratio is 1.52793 times that of Pluto, preserving the phi average?  Time will only tell, but if it happens remember that you heard it here first.

The shape of the Universe itself is a dodecahedron based on Phi

New findings in 2003 based on the study of data from NASA’s Wilkinson Microwave Anisotropy Probe (WMAP) on cosmic background radiation reveal that the universe is finite and shaped like a dodecahedron, a geometric shape based on pentagons, which are based on phi.   See the Universe page for more.

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From the distances between the planets, to the structure of Saturn’s rings to the shape of the Universe itself, phi is found again and again in different manifestations.

New findings reveal that the universe itself is in the shape of a dodecahedron, a twelve-sided geometric solid with pentagon faces, all based on phi.

Saturn’s magnificent rings show a division at a golden section of the width of the rings.

Curiously, even the relative distances of the ten planets and the largest asteroid average to phi.

There’s even an unusual energy source at the frequency of phi that is found in the universe.

Explore these appearances in more detail in this section.

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ELFRAD (Extremely Low Frequency Research And Development), a self-funded research organization which tracks radiation on Earth through an array of antennas, has found an extremely low frequency signal at phi, or 1.618033 Hertz, or cycles per second.  Their site says the following:

“This chart indicates the detection of signal bursts with a frequency of 1.618033 hertz. This frequency, sometimes called the Golden Ratio. These signals appear with no clear relationship with any known source. They are not related to solar anomalies or any known weather pattern. They do vary in amplitude or intensity and are irregular with their timing. We will continue to monitor this frequency and will display the result. These signals have been detected on a global scale and are of extreme interest.”

“The universe is composed of an infinite number of frequencies. Some macroscopically large and some microscopically small. All exist in uncountable phase relationships with one another.  The colors of light, the sound of music, the smell of flowers, the touch of velvet, all are made of combined frequencies. Some are in phase and adding to, some are out of phase and cancel from, a multitude of vibrations.  Our five senses are capable of interpreting these particular waves and making them tangible to our perception.  Acoustic, seismic, and electromagnetic signals, both natural and artificial, surround us and are a part of our environment. The source of these signals, both terrestrial and extra-terrestrial, and their content is of extreme interest to our research.”

Source: http://elfradgroup.com/elfinfo.htm

While certainly of interest, it must be kept in mind that “seconds” are a manmade measure, so even 1.618 cycles per second is not completely in the realm of nature.  As phi is first and foremost a relationship of proportion, receiving two unusual waves whose cycles are in phi proportion would be of greater interest yet.

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In January 2010 Science Daily and Physics World announced the discovery of a hidden Phi symmetry in solid state matter.  As explained in the Science Daily article:

“On the atomic scale particles do not behave as we know it in the macro-atomic world. New properties emerge which are the result of an effect known as the Heisenberg’s Uncertainty Principle. In order to study these nanoscale quantum effects the researchers have focused on the magnetic material cobalt niobate. It consists of linked magnetic atoms, which form chains just like a very thin bar magnet, but only one atom wide and are a useful model for describing ferromagnetism on the nanoscale in solid state matter.

When applying a magnetic field at right angles to an aligned spin the magnetic chain will transform into a new state called quantum critical, which can be thought of as a quantum version of a fractal pattern. Prof. Alan Tennant, the leader of the Berlin group, explains “The system reaches a quantum uncertain — or a Schrödinger cat state. This is what we did in our experiments with cobalt niobate. We have tuned the system exactly in order to turn it quantum critical.”

By tuning the system and artificially introducing more quantum uncertainty the researchers observed that the chain of atoms acts like a nanoscale guitar string. Dr. Radu Coldea from Oxford University, who is the principal author of the paper and drove the international project from its inception a decade ago until the present, explains: “Here the tension comes from the interaction between spins causing them to magnetically resonate. For these interactions we found a series (scale) of resonant notes: The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618…, which is the golden ratio famous from art and architecture.” Radu Coldea is convinced that this is no coincidence. “It reflects a beautiful property of the quantum system — a hidden symmetry. Actually quite a special one called E8 by mathematicians, and this is its first observation in a material,” he explains.”

The E8 structure itself has relationships to Phi (1.618).

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The g factor of the electron is defined as the ratio of its magnetic moment to its spin angular momentum.  The electron g-factor is due to the stretching of space-time as the electron spins at the speed of light.

Mathematically, the electron g-factor is approximately:

gfactore = -2 / sin (Ø)

and the proton g-factor is approximately:

gfactorp = 2Ø / sin (1/Ø)

 Thus it appears that the Golden Ratio, or Phi, is a constant produced by time.

The National Institute of Standards and Technology (NIST) states these gfactor constants as per the table below.

While the phi-based approach is not exactly equal to the NIST constant, with quantum level constants, there will always be a difference between theoretical work and empirical work.  This can be due to the irregularities in the metal of the test equipment, stray background radiations, or a host of other minute causes. The results of any empirical measurement always show some degree of statistical spread as a consequence.

Such constants are adjusted as new measuring techniques and better materials become available. So any theoretical value that is within one part in a thousand has scientific value.  Even if the degree of accuracy of a constant is believed to be accurate to within one part in a billion this is true. The accuracy of one part in a billion could mean that a stable condition for a specific experiment configuration has been achieved, but that particular configuration could still be influencing the measurement to a small degree.

Insights on this page were contributed by David W. Thomson of the Quantum AetherDynamics Institute and are explored in more depth at his page athttp://www.16pi2.com/gfactor.htm.

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In October 2001, NASA began collecting data with the Wilkinson Microwave Anisotropy Probe (WMAP) on cosmic background radiation.  Like visible light from distant stars and galaxies, cosmic background radiation allows scientists to peer into the past to the time when the universe was in its infancy.  Density fluctuations in this radiation can also tell scientists much about the physical nature of space.

NASA released the first WMAP cosmic background radiation data in February of 2003.  In October 2003, a team including French cosmologists and Jeffrey Weeks, a freelance mathematician and recipient of a MacArthur Fellowship or “genius award,” used this data to develop a model for the shape of the universe.

The study analyzed a variety of different models for the universe, including finite vs. infinite, flat, negatively curved (saddle-shaped), positively curved (spherical) space and a torus (cylindric).  The study revealed that the math adds up if the universe is finite and shaped like a dodecahedron, as in the illustration below provided by Weeks:

 

The connection to Phi is found in the Pentagons that form the faces of the Dodecahedron.

A shown on the Geometry page, A dodecahedron consists of twelve pentagons.  Take a pentagon and connect all the points to form a 5-pointed star.  The ratios of the lengths of the resulting line segments are all based on phi, , or 1.618!

See the Five and Phi and Penrose Tiling pages for other relationships of the number 5 and pentagons to phi.

This is still a theory, but supported by data that can be tested.

Weeks cautioned that his team’s model of a finite, dodecahedral-shaped universe, while promising, is hardly a proven theory. He said, “There’s more work to be done. It could be affirmed, or it could be refuted.  What makes it exciting now is it’s not a matter of idle speculation.  There’s real data to look at and the possibility of getting a definite answer.”  If proven by further evidence and scrutiny, the model would represent a major discovery about the nature of the cosmos.

A description of their research appears in the science journal Nature and at National Geographic, below and HERE.

http://physicsworld.com/cws/article/news/2003/oct/08/is-the-universe-a-dodecahedron

A 2015 update by Luminet can be found here:

http://www.scholarpedia.org/article/Cosmic_Topology

Thanks go to J.D. Ahmanson for first bringing this finding to my attention.

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Is there a Golden Ratio point of the Earth?

It has been claimed that the Golden Ratio of the Earth is in Mecca.  (See archived website or the 2009 video “Holy Mysteries” by Erdem Cetinkaya on  Vimeo or YouTube. See also his updated 2023 “Holy Mysteries” video with English subtitles and related article on Kaaba and Arafat.  Is this true?

Latitude

January 6, 2021: When I wrote this article in March 2010, I wrote the following on Mecca’s latitude:

Let’s first look at latitudes.  Phi to 15 places is 1.6180339887499.  There are 180 degrees between the North Pole and the South Pole, so 180 divided by Phi is 111.246….  As latitudes are expressed in degrees and distance from the Equator, we subtract 90 degrees and convert this to a latitude of 21.246… degrees, or 21 degrees, 14 minutes and 46.02 seconds, North or South.

The latitude of Mecca, according to Google Earth, is 21 degrees, 25 minutes and 38.56 seconds.  This puts it only 10 minutes and 52.54 seconds north of the exact northern golden ratio latitude of the Earth.  This is a variance of less about 1/10 of a percent, about 12 miles or 20 kilometers north of the exact golden ratio latitude point.

Update January 6, 2021: With comments provided by site visitors, I am providing this updated information on Mecca’s latitude:

The city of Mecca, however is over 20 kilometers from its northern border to its southern border. As noted above, the exact golden ratio point is 111.246…, or 21.246… degrees from the equator. The latitude of Mecca’s northern most border is 21.592 degrees, and the latitude of Mecca’s southern-most border is 21.278 degrees. That means that the exact golden ratio based on latitudes between the north and south poles still falls just barely south of the city limits of Mecca.

Site visitors did alternate measures based on the miles shown by Google Earth from the North Pole to Mecca to the South Pole, submitting that the golden ratio point falls within the boundaries of Islam’s holy city. They found the North-South distance to be 19980 kilometers, and divided by 1.618034 to arrive at a distance of 7,631.68, which they said was within Mecca’s city limits.

In corroborating this, I found the North-South distance on Google Earth to be 20003.89 kilometers, with a golden ratio point at 7,640.81 from the North Pole. I also found the Mecca’s northern-most border to be at 7,610.91 from the North Pole and its southern most border to be at 7,645.66 kilometers from the North Pole. This approach would then place the golden ratio point of the Earth pole’s within the city limits of Mecca.

It became clear in this process that measures of the Earth’s surface are done by various methods, with factors that make them subject to some variability.

Site visitors also noted that the latitude coordinates of Kaaba is 21 degrees and 25 minutes, and that the first time the word “Kaaba” appears in the Quran is 2:125. Additionally,  the first verse in the Quran that has the word “Makkah” (Mecca) is exactly proportioned according to the golden mean. The word “Bakkah”, has a ratio of 1.618, when the letters of this verse are counted and divided by 1.618. (47/1.618=29; there are 29 letters from the beginning of this verse till the word Makkah). Lastly, the dimensions of Kaaba also embody the golden ratio, with its 21.2 meter length by 13.1 meter width (taking the original Hatim region into account), and 21.2/13.1= 1.618. 

So as to the claim, the golden ratio point of the Earth between the North and South poles does indeed fall within the city limits of Mecca based on the mileage distances shown by Google Earth, and there are interesting references to Kaaba and Mecca in the Quran that relate to its latitude and to the golden ratio.

Longitude

Latitudes have a clear reference point of origin that is determined by the poles defined by the Earth’s axis of rotation.  Selecting the origin point of the longitudes is not as clear as there is no single definitive reference point.  Those who claim Mecca as the Golden Ratio of point of the Earth’s longitudes base this on a Mercator projection of the Earth, to which a Golden Section has been overlaid using the PhiMatrix software available from this site:

One could start from any longitude to get to any location, but using a world projection is a reasonable approach.  The challenge though is that there are hundreds of different renditions of world projections that vary considerably.  Here’s an example of others that produce similar results:

The top image is the familiar Mercator projection.  The bottom  image is a Peters projection which eliminates the bias of the Mercator to highlight the Northern hemisphere.

Rather than use an image subject to interpretation to determine the golden ratio of the latitude, perhaps it is better to use actual longitude measurements.

If you accept the premise that a world projection map that divides East and West is the right foundation, the most accurate starting longitudinal reference point would then be the midpoint between Alaska and Russia at 168 degrees, 52 minutes and 42 seconds found in the satellite photo below.  Using this as a starting point, the Golden Ratio point falls at 31 degrees, 22 minutes and 16.05 seconds, which is 938 km to the west of Mecca, which according to Google Earth is at 39 degrees, 48 minutes and 53.42 second East.  If we use mankind’s own Meridian at 180 degrees as the origin point, the Golden Ratio point is at 42 degrees, 29 minutes and 32.05 seconds, which is 298 km to the east of Mecca.  

The  image below shows the midpoint between Alaska and Russia.

An alternate way to approach this is to start at the longitude of Mecca and move a Golden Ratio of 360 degrees away (222 degrees, 29 minutes and 32.05 seconds) to see where you land.  This point is at 117 degrees, 19 minutes and 21.37 seconds West, which is inside the border of Russia as shown below.  Click on the image to enlarge.

Is Mecca at the Golden Ratio point of the Earth?  The answer is subject to interpretation.  As one who believes in God though, the author says this:

If God exists (and I have unwavering faith He does) and wanted to make His existence known with absolute certainty He could do so in many ways.  The God I have come to know though Jesus Christ gives us a choice to accept Him, out of His love for us.  He gives us all the signs and evidence we need to sense His love and presence but always leaves enough margin for doubt so that we come to Him out of our own choice of faith and love, and not because there is no other alternative but to do so.  He loves us, and desires our love, but true love requires true choice.  He speaks to us in many ways, yet sometimes we decide to not grasp or accept the message, as noted in these scripture passages:

“The heavens declare the glory of God; the skies proclaim the work of his hands.   Day after day they pour forth speech; night after night they display knowledge.  There is no speech or language where their voice is not heard.  Their voice goes out into all the earth, their words to the ends of the world.” Psalms 19:1-4

“Though seeing, they do not see; though hearing, they do not hear or understand.  In them is fulfilled the prophecy of Isaiah:  ‘You will be ever hearing but never understanding; you will be ever seeing but never perceiving.  For this people’s heart has become calloused; they hardly hear with their ears, and they have closed their eyes. Otherwise they might see with their eyes, hear with their ears, understand with their hearts and turn, and I would heal them.’ But blessed are your eyes because they see, and your ears because they hear.”  Words of Jesus Christ in Matthew 13:13-16

So whether it be seeing phi in the beauty of the human form or the location of one’s holy place, may our eyes, ears, heart and mind be open to the message of our Creator and God.  Wherever the golden ratio point of the Earth may lie, these passages point to a deeper meaning yet in finding the place where our God would lead us to worship Him:

“Sir,” the woman said, “I can see that you are a prophet. Our fathers worshiped on this mountain, but you Jews claim that the place where we must worship is in Jerusalem.” Jesus declared, “Believe me, woman, a time is coming when you will worship the Father neither on this mountain nor in Jerusalem. You Samaritans worship what you do not know; we worship what we do know, for salvation is from the Jews. Yet a time is coming and has now come when the true worshipers will worship the Father in spirit and truth, for they are the kind of worshipers the Father seeks. God is spirit, and his worshipers must worship in spirit and in truth.” The woman said, “I know that Messiah” (called Christ) “is coming. When he comes, he will explain everything to us.”  Then Jesus declared, “I who speak to you am he.”  John 4:19-26

Once, having been asked by the Pharisees when the kingdom of God would come, Jesus replied, “The kingdom of God does not come with your careful observation, nor will people say, ‘Here it is,’ or ‘There it is,’ because the kingdom of God is within you.”  Luke 17:20-21

References:

HolyMysteries.com archived website (The site is no longer active.)

Holy Mysteries video on Vimeo or YouTube.

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