Archive for the ‘Art’ Category

## Hidden Universal Symmetry

For millennia philosophers, mathematicians, architects, artists and mystics have been interested in the divine proportion, but its understanding has been highly fragmented. My recent work attempts to show how the divine proportion is a hidden universal symmetry worthy of comprehensive study and understanding.

Euclid’s book Elements (300 BCE) contains the first known written definition of the divine proportion, something he called the mean and extreme ratio:

“A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.”

Euclid’s mean and extreme ratio is better known today as the golden mean, golden ratio or divine proportion. These names refer to the act of cutting a line at one uniquely important point. Point C cuts the line AB at the divine proportion if and only if the whole line (α+β) is in proportion to the longer segment (α) in exactly the same proportion as the longer segment (α) is to the shorter segment (β).

The Greek letter Ф (phi) is used to denote the divine proportion. Ф is an irrational number whose decimal approximation continues forever without repeating. In fact, the divine proportion turns out to be “the most irrational number” of all. [1]

“Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold, the second we may name a precious jewel.” -Johannes Kepler (1571-1630)

Scientists are just recently starting to catch on to the divine proportion’s role in patterning the universe.

In 2010 an international team of scientists discovered the divine proportion in the quantum world. Researchers created a chain, one atom wide, of linked magnetic atoms and tuned the system to the “Schrödinger’s cat state” of quantum uncertainty [2].

They discovered that in that state the frequencies of the atoms’ spins resonated in the golden ratio. The team’s leader Dr. Radu Coldea said, “It reflects a beautiful property of the quantum system—a hidden symmetry.” The story about their discovery was the most-visited story in 2010 on EurekAlert, the global source for science news. I will save my speculations about why this was so until a bit later in this article.

In 2015, by combining advanced knowledge of mathematics and physics, Tamar Friedmann and C. R. Hagen discovered that the energy levels of a hydrogen atom are based on π, the ratio of a circle’s circumference to its diameter. [3] They showed that the modern quantum-mechanical description of hydrogen’s atomic energy levels is mathematically equivalent to John Wallis’ historic mathematical formula for π (published in 1656).

My opinion of the age old debate is that mathematics appears to be discovered rather than invented.

The Wallis formula is an infinite product equivalent to the area of a square compared to the area of an inscribed circle (4/π￼). I find it especially interesting that 4/π￼ is 99.8% equal to the square root of the golden ratio. Matter and energy are thus divinely proportioned.

From my book The Divine Proportion: [4]

A two-dimensional representation is the most effective way to perceive the divine proportion’s essential quality of self-similarity. The golden rectangle is just such a two-dimensional figure (the golden triangle is another) where the ratio of the longer side to the shorter side is equal to Ф divided by 1, which reduces to Ф.

On the right side of the figure, the shorter side is subdivided again such that what was formerly the smaller part is now the larger, namely the side with the length of 1. The ratio of the new larger segment (1) to the next smallest segment equals 1 divided by 1/Ф, which also reduces to Ф. The subdivision continues in this way, always reducing to Ф.

The golden rectangle implies a spiral, composed of circular arc segments centered on the corner of each square. The smallest rectangle at the end of the spiral is also a golden rectangle, so the process of divine subdivision can continue infinitely inward. The divine proportion is always the same and does not depend on the length of the line being divided.

“Like God, the Divine Proportion is always similar to itself.” –Luca Pacioli (1447–1517)

Spiral galaxies and cyclones (hurricanes) naturally approximate the form of golden spirals.

Images from The Divine Proportion

The fact that the same form appears at such vastly different scales and contexts reveals a universal pattern. I think the reason we see this pattern is that it is built from a simple “recurrence relation”—an equation that recursively defines a sequence. Once one or more initial terms are given, each further term of the sequence is defined as a function of the preceding terms.

The Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, 34, …) is an example of a recurrence relation where each subsequent number is the sum of the previous two. You can create arbitrary recurrence relations like the Fibonacci sequence from any two initial terms. Taking the ratio of any two adjacent terms approximates the golden ratio: the higher the value of the terms, the better the approximation.

I recently created a geometric recurrence relation with the 3:4:5 Pythagorean right triangle. I made this image by simply iterating the triangle and the squares made from its edges. It’s amazing that it has a natural, fractal quality and that the spirals form discrete approximations of golden spirals.

Fractal 3:4:5 triangle and squares

I suspect that a cyclone is formed by a recurrence relation of air pressures. A simple mathematical sequence that builds on itself results in this form. The same is likely to be true of stars in spiral galaxies in terms of solar wind pressures.

The divine proportion turns up at the stellar scale. In 2015 a team of astrophysicists discovered that “the brightness of some stars pulsates at primary and secondary frequencies whose ratios are near the golden mean.” [5]

How could it be that the quantum effect mentioned with “Schrödinger’s cat state” atoms appears also at a cosmological scale? Read on to understand that the divine proportion patterns matter at all scales.

I discovered that the divine proportion shows up on the planetary scale.

From my book Secrets In Plain Sight: Leonardo da Vinci: [6]

The combined polar diameters of Earth and Moon (16185.6 km) divided by the equatorial diameter of the Earth (12756.2 km) is 99.8% equal to √Ф. The size of our planet and its natural satellite fit this elegantly simple geometry.

“Simplicity is the ultimate sophistication.” –Leonardo da Vinci

The circumference of the circle is equal to Ф x π and the perimeter of the square is equal to 4 x √Ф. Therefore, the circumference is 99.9% equal to the perimeter. It is impossible to exactly square the circle because one can never quite rationalize π.

“It is the mark of an instructed mind to rest satisfied with the degree of precision which the nature of the subject admits and not to seek exactness when only an approximation of the truth is possible.”
-Aristotle

At the scale of cities, a few architects mysteriously encode the divine proportion in the their culturally significant structures without publicizing that knowledge.

The CN Tower in Toronto is the tallest structure in the Western hemisphere at 553.33 meters in height and was the tallest structure in the world when built in 1976. The glass floor and outdoor observation deck in the Main Pod are 341.99 meters (1122 feet) in height. 553.33 / 341.99 ≈ Φ (99.99%).

Le Corbusier, the lead architect of the United Nations Secretariat building, previously developed a proportional system used for building design called the Modulor, which was based on human measurements, the divine proportion, and Fibonacci numbers. [7]

“Mathematics is the majestic structure conceived by man to grant him comprehension of the universe.” -Le Corbusier

At the molecular scale, the code of life itself is divinely proportioned.

The view at the top of the illustration shows that the structure’s axis is arranged as a decagon, with 1 as the radius and Ф dimensioned across the molecule. The double helix’s relationship of major to minor grooves is also divinely proportioned. The overall pitch of the spiral compared to its diameter is likewise an expression of Ф (99.9%).

DNA is organized into nucleotide triplets, called codons. Geneticist Jean-Claude Perez discovered that the frequency in which codons appear in the human genome are strongly linked to Ф. [8]

The code of life is a multidimensional embodiment of the divine proportion.

Leonardo da Vinci showed how the human body is structured by the divine proportion.

In the book I explore whether the mass appeal of Da Vinci’s art could be due to his practice of encoding the divine proportion into his works. After all, his dozen or so paintings are the most visited, most discussed and most expensive art in the world.

Leonardo depicted a man in both a circle and a square, based on the ancient canon of proportion found in the writings of Vitruvius…The primary divisions in the golden rectangles point to the navel and heart. The navel is the center of the physical body…The heart is the center of the energetic body, with three chakras above and three below…The golden rectangle anchored on the page itself points to the idealized man’s third eye.

In a recent study, plastic surgeons surveyed 1682 people to discover their aesthetic preferences for navel position on the human abdomen. “When comparing navel position on the same body, the majority of participants choose the one with the navel relocated according to the golden ratio (i.e., 1.618).” [9]

It appears that people prefer the proportions of the idealized body that Da Vinci depicted over 500 years ago. I assume this is because the human body is structured using the divine proportion.

In Da Vinci’s painting “St. John the Baptist” (c.1513), he uses the golden rectangle to point out the prophet’s third eye and his finger pointing to heaven…The spiral convergences on the prophet’s third eye. On the right image, the secondary vertical division locates the upward pointing index finger and dramatically verifies the analysis.

The thesis of my book on Da Vinci is that he consistently pointed with the divine proportion’s divisions to physical and illuminated third-eyes.

“Adrian Bejan, professor of mechanical engineering at Duke’s Pratt School of Engineering, thinks he knows why the golden ratio pops up everywhere: the eyes scan an image the fastest when it is shaped as a golden-ratio rectangle.” [10]

The divine proportion must therefore be built into our visual cortex.

The pineal gland is the physical manifestation of the third-eye chakra. A fascinating article from ConceptualRevolutions.com states the following:

In 2004, Dr. David Klein, Chief of the Section on Neuroendocrinology at the NIH, discovered that the interior of the pineal gland has retinal tissue composed of rods and cones (photoreceptors)…just like the eye, and is even wired into the visual cortex of the brain. He also noted that it even has vitreous fluid in it. Within this context, it would seem that the scientific community may need more courage to follow this evidence wherever it may lead in the pursuit of scientific truth, especially where it concerns the pineal gland’s role as a human sensory organ, and to forego old and outdated theories.

“The photoreceptors of the retina strongly resemble the cells of the pineal gland.” -Dr. David Klein [11]

Albrecht Durer may have learned perspective and the divine proportion from Da Vinci or Luca Pacioli, who at one time lived with Da Vinci. After all, Pacioli and Da Vinci published a book together called De Divina Proportione (1509). Here is what Pacioli wrote in the book’s Introduction:

“A work necessary for all the clear-sighted and inquiring human minds, in which everyone who loves to study philosophy, perspective, painting, sculpture, architecture, music and other mathematical disciplines will find a very delicate, subtle and admirable teaching and will delight in diverse questions touching on a very secret science.” [italics by the author]

The science of the divine proportion had to be secret in their day because these Renaissance luminaries could have easily been burned at the stake for the implications of this science. I believe Da Vinci saw the divine not just in a transcendent heaven (following the church dogma), but through this science saw the divine immanently in the human body and in the world. If this is really true, then one doesn’t need the church hierarchy to “see God”—only the mind’s eye is required.

More ink has been spilled on Albrecht Durer’s “Melancholia I” than any other engraving. [12] Inspired by Franz Deckwitz’s study (1979), I found related but different geometry in my geometric analysis:

Albrecht Durer’s Melancholia I

I see the eyes of the melancholy genius staring directly at the third-eye of the cherub, who is surrounded by a “magical” pentagram. The pentagram traces the angle of the ladder and the horizon and is grounded by the square that it sits on. Again we are directed to a third-eye, this time of a divine cherub.

Pentagrams resonate with the divine proportion. Perhaps that is their magic?

Michelangelo also encoded the divine proportion in the world’s second most famous work of art after Da Vinci’s Mona Lisa, which also encodes it (shown in my book).

In a 2015 paper entitled “More than a neuroanatomical representation in The Creation of Adam by Michelangelo Buonarroti, a representation of the Golden Ratio,” [13] the co-authors build on Dr. Frank Lynn Meshberger’s 1990 discovery that, “The Creation of Adam represented in the Sistine Chapel shows God surrounded by a drape that has the shape of what he believed to be the sagittal section of a human brain.” [14]

The co-authors demonstrate that the gap where Adam receives the divine spark is precisely and fittingly pointed to using the divine proportion.

From Secrets In Plain Sight: Leonardo da Vinci:

With this geometry you can see that Adam’s body gracefully follows the arc and the primary horizontal division in both golden rectangles share the same datum line. This datum line leads from Adam’s eye straight into the heart of God, which is the pineal gland, or third eye, according to Michelangelo’s neuroanatomical representation [revealed by Meshberger]. The divine proportion and the third eye are literally the bridge to the infinite, or “divine realm.”

Michelangelo could have easily been burned at the stake for suggesting that the route to God is within, rather than through the official social hierarchy of God-representatives…Once you see its structure you begin to understand why it is so powerful and sense Michelangelo’s humanistic intent of encoding such a secret in plain sight.

“The noblest pleasure is the joy of understanding.” – Leonardo da Vinci

I believe that the divine proportion works on us because it is part of our bodies, our DNA, and even our atoms, as this article has outlined. For this reason, we tend to resonate with—and preferentially choose—just about anything that is proportioned with the golden ratio, even if we are not conscious of it.

In the macrocosm, the divine proportion structures cyclones in the atmosphere, governs the proportions of the Earth-Moon system, patterns the pulsing of stars, and continuously orders spiral galaxies (my book The Divine Proportion has many more examples).

This hidden universal symmetry operates at all scales.

The charge radius of the proton is 8.775 x 10-16 m, which is 16 orders of magnitude smaller than our human scale. The entire universe has a radius of approximately 14 billion parsecs (4.3 x 1026 m), which is 26 orders of magnitude larger than the human scale. The full gamut of scale is thus 16 + 26, or 42 orders of magnitude from a proton to the entire universe. Amazingly, 42 / 26 is 99.8% equal to Ф, so it logically follows that the human scale is the divine measure of all things!

I see a rebirth of this ancient knowledge—a New Renaissance—starting to happen right now. However, it is going to require a major conceptual revolution. The time is ripe to scientifically understand this profound hidden universal symmetry and apprehend the fundamental mathematical reality of the universe. The “substance” of the universe is number—geometry—music, the universal language.

Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these one is wandering in a dark labyrinth. —Galileo Galilei (1623)

What use is language to anything but consciousness?

“I regard consciousness as fundamental. I regard matter as derivative from consciousness. We cannot get behind consciousness. Everything we talk about, everything that we regard as existing, postulates consciousness.” -Max Planck (1931), who was awarded the Nobel prize for his discovery of energy quanta.

Scott Onstott

Endnotes:

## Recent Articles

I’ve recently written a few articles outside this site that you might enjoy. I was Graham Hancock’s author of the month back in September 2014 and I wrote “Measuring the Mystery” for that occasion, which features several images from my book Quantification that hint at many intriguing mysteries.

Ancient Origins published an article I wrote in November 2014 entitled, “Mathematical Encoding in the Great Pyramid” which goes into the multi-layered encoding in the pyramid, exposing the mathematical nature of reality.

I was pleased to be included in a select group of writers included in Ancient Origin’s second year anniversary edition ebook, Unraveling the Mysteries of Ancient Artifacts, where I wrote an article entitled, “The Mystery of Obelisks.” You can download this fascinating ebook by subscribing for free. The mystery in the title refers to the obelisks’ precise positions on the Earth.

I wrote a step-by-step tutorial entitled, “Drawing in Photoshop” in Photoshop User Magazine explaining how to draw the following image, which I discovered encodes the sacred geometry of the Sphinx and the Pyramid. I have been writing a column called “Beyond Photoshop” in this print magazine since 2007, but this is one of my rare articles that crosses over into SIPS territory.

I also discussed how this image came about in Macrocosmic Harmony. This image got the most traction of any I’ve ever posted on my Facebook wall, with over 500 shares to date. I think that is because the image shows the simple beauty of how sacred geometry is the basis of form.

As above, so below.

## Update

In no particular order, here are some new images I’ve created recently. I posted these on my Facebook wall but they quickly got lost in the ephemeral feed. This blog is a much better repository for this research. This post is a grab bag of things I’ve noticed that haven’t made their way yet into other blog posts.

It turns out that the following 6:5 relationship in the Pyramid of Khafre is 99.9% accurate. The discovery was made by Peter Casperson in his book Den Matematiska Nyckeln Till Guds Namn (which translates from Swedish as “The Mathmatical Key to God’s Name”) published in 2004. The illustration is my own. The 6:5 relationship ties in with what I’ve written before in Taking Measure, the Snowflake and the Flower, and Cubits, among other blog posts.

The Pyramid of Khafre encodes 6:5 proportions

The outer perimeter of the egg’s cross-section is 33,333 feet assuming the eggshell has thickness of ~5 feet at the scale of the Great Pyramid. I made a similar oval image a few years ago called The Megalithic Egg but it was based on the 3:4:5 triangle instead.

The egg formed by the elevation of the Great Pyramid has a circumference of 33333 feet

I made a round image (with Photoshop’s polar filter) of moai on Easter Island looking into the center, and then felt inspired to have them look at the Orion nebula. The 15 moai fit the stages of the alchemical process and I took the stage names from a fantastic novel by Katherine Neville called The Eight that I was re-reading. The philosopher’s stone naturally fits in the center as the final goal of al-kemi. I was playing with the swirling colors as seen above in the nebula or below in the chemicals of the alchemist’s cauldron. Are we looking into the heavens or deep within? They end up in the same place: awareness.

The Great Work

Is this the basis of the Fahrenheit scale, why water boils at 212°? A circle with a diameter of 212 has a circumference approximately equal to 666. It’s interesting also that 33°F = .55555…°C

Here’s a discovery I made some time ago but don’t think I’ve posted it in the blog before. The Governor’s mansion at the top of Victoria Peak overlooking Hong Kong is 3333.3 km from Borobudur. Amazing distance between city mountains: sacred and mundane!

It’s interesting that the two main fortresses of England and Scotland are 333 miles apart. I’m sure that wasn’t planned by humans, but one must not rule out the gods.

The Brandaris connection was discovered by Shannon van den Heuvel. These two monuments are exactly 3333333 meters apart.

The traditional Buddhist retreat lasts for 3 years, 3 months and 3 days. Make sense?

Heliopolis is 3333 miles from Mt Everest and 3333 km from the equator. Both metric and imperial units are based on the dimensions of the Earth. The Sun is 333000 times more massive than the Earth.

There are actually minimum and maximum temperatures. Absolute zero is the coldest possible temperature where there is absolutely no movement. The temperature of the big bang has been calculated as 33 orders of magnitude hotter than absolute zero, as measured in degrees Kelvin. At this maximum temperature all four forces (gravity, electromagnetism, strong and weak) merge into one force and the fabric of spacetime itself is thought to dissolve into nothingness.

Quantum foam (also referred to as space-time foam) is a concept in quantum mechanics devised by John Wheeler in 1955. The foam is supposed to be conceptualized as the foundation of the fabric of the universe. This “foam” is the smallest measurable length, representing the granularity of spacetime itself. The human eye is 33 orders of magnitude larger than the quantum foam.

Here are some of my favorite quotes:

Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these one is wandering in a dark labyrinth.
—Galileo Galilei, The Assayer, 1623

“The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and…there is no rational explanation for it.” -Eugene Wigner, nobel laureate

“How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?” -Albert Einstein

“The most beautiful system of the sun, planets and comets could only proceed from the counsel and dominion of an intelligent and powerful Being.” -Introduction to the Principia by Isaac Newton

“Everything we call real is made of things that cannot be regarded as real.” -Niels Bohr

“Let no one ignorant of geometry enter.” -Engraved on the door of Plato’s Academy

The humble papyrus plant that was processed for writing was echoed in the architecture of hypostyle halls, and in the shape of the Nile, as seen from space.

The distance from Abu Simbel to Heliopolis is 864 km.

Mile End in London resembles the Eye of Horus. Was this intentional?

The Marine Corps war memorial in DC resembles the human eye in cross section. Was that intentional?

My analysis of the Great Pyramid shows very precise encodings of mathematical constants, some which the ancient Egyptians did not know. Were gods the architects and Egyptians the builders?

Miles, furlongs, feet, yards and inches are based on the Earth.

The geometry of the Nile delta implies a pyramid that extends into space.

The Amun oracle is π x 10 million inches from the entrance to the ancient temple dedicated to Amun.

Growth (interior and exterior) resonates with the divine spiral.

Growth

Peter Stanbury discovered the following relationships of the proton to electron mass ratio and the fine structure constant’s relationships to pi. I added the neutron to electron mass ratio and the boxed equation. Taken together, we see how pi, phi and mathematical ratio are fundamental to matter. All is number.

The molecular weight, specific heat capacity and temperature of air control how fast sound waves propagate through the atmosphere. At 3.3°C the speed of sound in air is 333.3 m/s and if the wavelength is 1/3 of a meter, the resulting frequency is exactly 1000 cycles per second, the center of human hearing. The meter, the second, base 10, and the qualities of our atmosphere conspire to produce this metrological sonic harmony.

The average male + female human height is 3.30 meters. These drawings were included on the Pioneer spacecrafts so that aliens can see what we look like naked!

Our planet is 3.3% the distance to the outermost planet in our system. This is true regardless of units.

## Tripolis

The ancient Egyptian Temple of Debod was moved to Madrid, and is aligned with St. Peter’s Basilica in Rome.

The Vatican axis continues eastward to Istanbul, which was once capital of the Eastern Roman Empire. Back then Istanbul went by the name Constantinople. The city went by the name Byzantium even before that, from 660 BCE to 330 AD. There are many layers and chapters to history.

Kevin McMahon wondered if he measured a line all the way from the Temple of Debod in Madrid to the ancient Egyptian obelisk of Theodosius in Istanbul, where would it cross Rome, exactly?

He discovered that the answer is the Lateran Palace, ancient Roman palace which was also the residence of Popes for a thousand years. Immediately outside the Lateran Palace is the largest obelisk in Rome—originally from Karnak, Egypt.

Rome is almost perfectly (99.7%) at the midpoint of this alignment between Madrid and Istanbul. Madrid was also originally a Roman settlement. Isn’t it interesting how this alignment of three cities is both Roman on one layer and Egyptian on another?

While I was pondering this tri-city alignment I noticed that Tripoli is due south of Rome. That’s curious on multiple levels. Lines connecting Tripoli to the tri-polis form a trident shape. Tripoli’s Arabic name literally means Bride of the Sea, which is a perfect moniker for a city resonating with Neptune’s trident.

Madrid, Rome, Tripoli are all their respective nation’s capitals. Istanbul was the capital of four successive empires in the past, although Ankara is the current capital of Turkey. That’s nobody’s business but the Turks. 🙂

We get the word capital, from the Latin caput, meaning head. The Capitoline Hill’s Temple of Jupiter was the head-quarters of the ancient Roman empire. It’s also what we connect to when we CAPITALIZE. This has unusual repercussions in the Roman law we are still subject to today.

The Temple of Jupiter has been a long time gone. Now the statue of Marcus Aurelius adorns the top of the Capitoline Hill. The Italian Kilometer Zero is literally the statue of Marcus Aurelius. Kilometer Zero is the point from which all distances in a nation are measured. All roads lead not only to Rome but to this point.

The distance from the Statue of Marcus Aurelius in Rome to the Arch of Marcus Aurelius in Tripoli is exactly 1000.0 km. It almost seems like it was surveyed to be that distance although we know that level of precision was impossible for the Romans, not to mention that the meter was invented two millennia later. And yet, there it is.

“Because a thing seems difficult for you, do not think it is impossible for anyone to accomplish.” -Marcus Aurelius

Marcus Aurelius’ Meditations is still revered as a literary monument to Stoic philosophy. Meditations takes the form of quotations varying in length from one sentence to long paragraphs. US President Clinton said Meditations is his favorite book.

I’m reading wisdom encoded in the landscape, a little like augurs of ancient Rome interpreted the will of the gods. However, instead of studying the flights of birds, I use Google Earth to take the auspices from the ley of the land.

“Who does not know that this city [Rome] was founded only after taking the auspices, that everything in war and in peace, at home and abroad, was done only after taking the auspices?” -Roman historian Livy

On the spine of the Hippodrome of Constantinople, a Serpentine Column stands immediately adjacent to the obelisk of Theodosius. Quite auspicious, don’t you think?

It’s funny but this obelisk’s twin was once erected on the spine of the Circus Maximus in Rome. In the Renaissance, Pope Sixtus V had it moved across Rome to the Lateran Palace (yes, it is the one in the Tri-polis alignment). Both obelisks were originally the same height and stood together in the Temple of Karnak in Egypt.

The Lateran obelisk replaced the statue of Marcus Aurelius that had been there since antiquity so Marcus and his bronze horse were moved to the top of the Capitoline Hill.

The Serpentine Column has an even more amazing history.

“The Serpentine Column has one of the longest literary histories of any object surviving from Greek and Roman antiquity — its provenance is not in doubt and it is at least 2,491 years old.” –Source

This broken column was one of three legs that together once formed the Delphic Tripod. It is located on the spine of the Hippodrome because Emperor Theodosius took it as a spoil when he closed the Oracle of Delphi in 395 CE and ordered all pagan temples to cease operation. Theodosius himself received the last oracle reading ever made at Delphi. I wonder what the priestess told him?

The Pythia, as every priestess of the Oracle of Delphi was known, sat on the Delphic Tripod. This was where the goddess speaking through the priestess voiced enigmatic answers to questions that so often proved prophetic.

Themistoclea, priestess of Delphi, was one of Pythagoras’ teachers. The name he chose for himself, Pythagoras, and Pythia are from the same branch of a linguistic tree. It is hard to overestimate the importance of the Oracle of Delphi in the ancient world.

Ancient Greek pottery c.330 BCE in British Museum – Delphic Tripod and the Pythia

For example, consider the Oedipus myth. It bears summarizing here.

Oedipus learned from the Pythia, like his father had before him, that he was destined to murder the King and marry his mother. In response to the prophesy his father, King Laius, left Oedipus to die of exposure as an infant and believed he had perished. However, Oedipus was rescued and raised by a poor shepherd.

After growing up Oedipus went to have his auspices foretold by the Pythia. Learning his terrible destiny Oedipus chose not to return home from Delphi but to travel all the way to Thebes, Greece instead and start a new life for himself.

En route he had an altercation with an old man at an intersection where three roads crossed each other. The old man wanted to go first and tried to run Oedipus down. In self-defense, Oedipus killed him. Unbeknownced to Oedipus, the old man of course turned out to be his father, the King of Thebes.

Later on the road outside the city, Oedipus encountered a Sphinx that had been terrorizing the locals with deadly riddles. He ended up answering the famous riddle (answer: a Man) and the Sphinx inexplicably but conveniently killed herself (she is traditionally depicted with two exposed breasts as shown here). When he arrived at his destination he was told the happy news that he had been made King because anyone who killed the Sphinx would be given the throne and have the recently widowed Queen’s hand in marriage. He didn’t find out until much later that the Queen was indeed his mother.

Oedipus and the Sphinx by Francois Xavier Fabre (1808)

According to William Broad in The Oracle: Ancient Delphi and the Science Behind its Lost Secrets, “The Pythia of Delphi was arguably the most powerful woman of the ancient world.”

The Pythia was the last vestige of the ancient Goddess tradition. Here is a snake goddess from Crete more than a thousand years earlier. See any similarities to the Pythia or the Sphinx? They were holders of Serpent Wisdom.

Photo credit Chris 73 CC BY-SA 3.0

The distance from the actual location where Pythia sat on the Delphic Tripod to the Sphinx of Egypt is 666 nautical miles. Note the uraeus on the Sphinx’s third eye chakra. Mark of the beast?

Snakes and 6’s have long gone together. Consider the Star of Life symbol. The snake climbing the pole is at an intersection where three roads cross each other. Sound familiar?

The Star of Life is the symbol of emergency medicine

The King’s Son/Sun got together with his Mother/Moon and it ended in tragedy. Oedipus put out his own eyes in despair. When the Moon eclipses the Sun there is darkness.

Total solar eclipse, photo by Luc Viatour CC BY-SA 3.0

Apollo killed the Python and stashed its body in a crevasse under Delphi. Its rotting corpse was said to release the vapors which gave the priestesses of Delphi their visions.

Apollo slaying the Python

The scientific explanation is that these vapors were naturally occurring ethylene gas.

“Anesthesiologist Isabella Herb found that a dose of 20% ethylene gas administered to a subject was a threshold. A dosage higher than 20% caused unconsciousness. With less than 20% a trance was induced where the subject could sit up, hear questions and answer them logically, although the tone of their voice might be altered, their speech pattern could be changed, and they may have lost some awareness of their hands and feet, (with some it was possible to have poked a pin or pricked them with a knife and they would not feel it). When patients were removed from the area where the gas accumulated they had no recollection of what had happened, or what they had said. With a dosage of more than 20% the patient lost control over the movement of their limbs and may thrash wildly, groaning in strange voices, losing balance and frequently repeatedly falling. All of these symptoms match the experience of the Pythia in action, as related by Plutarch, who witnessed many prophecies.” –Source

There is nothing new under the Sun. In ancient Egypt, the Sun god Ra killed the serpent Apophis, personification of all that was evil.

“It was even thought that sometimes Apophis actually managed to swallow Ra during the day, causing a solar eclipse, but since Ra’s defenders quickly cut him free, the eclipse always ended within a few minutes. On the occasions when Apophis was said to have been killed, he was able to return each night (since he lived in the world of the dead already). However, in other myths, it was the cat goddess Bast, daughter of Ra, who slew Aphophis in her cat form one night, hunting him down with her all seeing eye.” –Source

The sun god Ra, in the form of a Great Cat, slays the snake Apophis

These myths were echoed most recently in the medieval story of St. George and the Dragon.

Saint George and the Dragon by Gustave Moreau 1889

The distance from the Church of St. George, in Lalibela Ethiopia to Temple Bar in Paternoster Square in the City of London is 3033.33 nautical miles.

“The Church of St. George has been referred to as the Eighth Wonder of the World. Lalibela, King of Ethiopia, sought to recreate Jerusalem, and structured the churches’ landscape and religious sites in such a way as to achieve such a feat.” –Source

The built landscape encodes uncanny messages, secrets in plain sight. Pater Noster means “our father.” The flaming golden “pineapple” atop Paternoster Square Column is quite solar. Thanks to Urban Asplund for inspiring this discovery.

Sir Christopher Wren’s Temple Bar provides pedestrian access between St. Paul’s Cathedral (also designed by Wren) and Paternoster Square. However, Temple Bar was relocated from its original position outside Temple Church. A dragon has marked that spot since 1880 in the form of the Charles Bell Birch’s sculpture.

Temple Bar Marker Dragon – Photo by Tony Hisgett CC BY 2.0

I think these myths are all about the Sun triumphing over the Moon, a telling his-tory of men’s domination of women. We are killing ourselves with this tragic meme. We need a new outlook.

The alchemists saw the Sun and the Moon differently—as equal partners.

After all, the Sun and Moon discs share the same size, between 32 and 33 minutes of arc, in our skies. This is truly miraculous!

The opposition between man and woman, day and night, up and down, in and out, need not be externalized into a literal battle. The real battle is internal in all of us and exists within all forms of duality.

“He who lives in harmony with himself lives in harmony with the universe.” -Marcus Aurelius

I would like to rephrase that: “Whoever lives in harmony within themself lives in harmony with the universe.”

The sages of India understood all of this long ago. Lord Shiva’s attributes include a snake around his neck (Serpent Wisdom), a crescent Moon, and a trident called a Trisul.

Photo by Arjuna Filips CC BY-SA 3.0

Shiva’s Trisul represents a variety of trinities including past, present, and future or creation, destruction and preservation. In the human body, the Trishul represents the three main nadis, or subtle energy channels. Pingala is solar, Ida is lunar and the central Shusumna channel circulates kundalini energy up the spine when awakened by balancing your Ida and Pingala energies.

The landscape seems to be echoing the Trisul in the alignments connecting to Tripoli. It is 55555 arc seconds from Tripoli to Madrid, and 1666.66 km from the Arch of Marcus Aurelius in Tripoli to the Hagia Sophia in Istanbul.

Hagia Sophia means Holy Wisdom and Sophia is honored as a goddess of wisdom by Gnostics, as well as by some Neopagan, New Age, and feminist-inspired Goddess spirituality groups. In Orthodox and Roman Catholic Christianity, Sophia, or rather Hagia Sophia (Holy Wisdom), is an expression of understanding for the second person of the Holy Trinity. –Source

The distance from Madrid’s Puerta del Sol, which is also Spain’s Kilometer Zero, to the Hagia Sophia is 3003333 yards. There is a crescent moon at the top of the spire on the dome of the Hagia Sophia. The Muslim calendar is lunar after all. Threes all the way between Moon and Sun.

All that is without is also within. Your body is the true temple, a hologram of the whole. Three subtle channels of energy twist within and around your physical spine, from the first chakra at its base up 33 bones to the head-quarters between your temples.

Screen capture from The Fountain (film) – superimposed graphics my own

Speaking of your head, a third element is needed to transcend and integrate shiva (masculine energy) and shakti (feminine energy). The three nadis join back together in the 6th chakra (third eye). Trinity is always required to transcend duality.

Elemental charge is triple by nature. The third rail is electrified.

Elementary, my dear Watson

Thanks to Clive Hetherington who sent me the link to Peter Stanbury’s discovery of the proton to electron mass ratio and the fine structure constant’s relationships to π. I deduced the other symmetries.

The electron has a charge of one e (not to be confused with Euler’s constant e). The neutron has one up quark and two down quarks, whose charges cancel out making it electrically neutral. The proton has two up quarks and one down quark, netting a charge of one e, polarized oppositely compared with the electron. The fine structure constant is a measure of the strength of the interaction between charged particles.

I think it is vital to understand that there are trinities in the substructure of every thing (i.e. quarks) and that all is number, ratio, proportion, symmetry, geometry, beauty, and harmony. Everything is made of love. Admittedly, it usually looks upside down and bass ackwards, but that dualistic tension is exactly what generates the great mystery. Romae (Latin for Rome) is the first chakra, survival. Where we go from there is up to us. That’s amore (Italian for love)! Let us get the balance right this time.

Bonus: Thanks to Jordi’s comments on this post I measured the distances for another tri-polis, this time all within Spain.

The visual style of this illustration reminded me—back in April, I found another set of correspondences between three ancient cities in Mexico, and only now recognize it as a “tri-polis.” I am continually amazed at how these things come together in my own personal life but even more so about what it reveals about the impersonal world out there. They are connected as any microcosm is to the macrocosm.

## Pilgrimage

Back in 2012 I wrote a post on Burning Man, a post-modern pilgrimage where 50,000 people converge on Black Rock City in the Nevada desert every summer. This cathartic festival culminates in the ritual burning of a giant man in effigy.

Julius Caesar wrote in his Commentary on the Gallic War that the Gauls sacrificed men by burning them inside wicker effigies but it appears that this might have been disinformation designed to demonize the druids.

Wicker Man

Black Rock City is the name of the temporary encampment recreated every year in the Nevada desert. Designed by a now-deceased architect, Black Rock City occupies 66.6% of a circle inscribed within a pentagon. Kevin McMahon realized that the azimuth from the center to one of the points is 333.3° true north. I bring this up now because the axis of Black Rock City points to Santiago de Compostela, a traditional pilgrimage site in northwestern Spain.

Legend holds that St. James’s remains were carried by boat from Jerusalem to Galicia Spain where he was buried in what is now the Cathedral of Santiago de Compostela. The Way of St. James, or the Camino as is is known in Spanish, was one of the most important Christian pilgrimages during medieval times, together with pilgrimages to Rome and Jerusalem.

Counter to what you might expect, the number of pilgrims is growing today. Over 200,000 people made the walk last year. Shirley Maclaine chronicled her transformative physical and spiritual journey in her book The Camino.

People going on the Camino come from all over the world but I wondered if there is a symbolic start point for this pilgrimage?

The axis of the Cathedral of Santiago de Compostela in Spain points directly to the Basilica of Saint Mary of the Angels in Assisi, Italy. I wrote about St. Francis of Assisi (1181-1226), founder of his namesake Franciscan order, in Secrets of San Francisco.

Francis was a wealthy young man when he had an ecstatic vision of nature mysticism.

St. Francis in Ecstasy by Giovanni Bellini (c. 1475)

After going on a pilgrimage to Rome, Francis gave up his riches and possessions and begged with the beggars outside the doors of St. Peter’s. While homeless he had another vision where Jesus said to him three times, “Go and repair my house that is falling into ruin.” He returned to Assisi and circa 1211 rebuilt the tiny Porziuncola, a stone chapel that he lived outside of in a primitive hut. Francis later founded the Order of Poor Clares for women and became known as the patron saint of animals and the environment.

The Porziuncola inside the Basilica of Saint Mary of the Angels – Georges Jansoone CC BY-SA 2.5

Francis died in his hut, not fifteen yards from the chapel, at sunset on Saturday, 3 October 1226. Shortly after 1290 the tiny stone chapel became entirely inadequate to accommodate the throngs of pilgrims visiting the site. The Basilica of Saint Mary of the Angels was built around the Porziuncola to protect it and control the flow of pilgrims.

I took a pilgrimage there with my family (see Trip to Italy and France) and my wife was affected by its palpable sense of sacredness.

Basilica of Santa Maria degli Angeli, Assisi

The prayer of Saint Francis, whether or not it was really written by him, affects me emotionally. It is a work of goodness and humility and thus resonates with St. Francis.

Make me an instrument of peace;
Where there is hatred, let me sow love;
Where there is injury, pardon;
Where there is discord, harmony;
Where there is error, truth;
Where there is doubt, faith;
Where there is despair, hope;
Where there is darkness, light;
And where there is sadness, joy.
Grant that I may not so much seek
To be consoled as to console;
To be understood as to understand;
To be loved as to love.
For it is in giving that we receive;
It is in pardoning that we are pardoned.

Francis of Assisi himself completed the pilgrimage to Santiago de Compostela. The distance from the rond-point of the Cathedral of Santiago de Compostela to the Round Fountain in the Tuileries Gardens of Paris is 666.66 miles. Urban Asplund discovered this geo-metric gem.

Note the orbs in the photo inside the Cathedral of Santiago de Compostela, possibly attesting to the sacredness of that space.

Asplund notes that the distance from the same Round Fountain in the Tuileries to Bugarach Peak overlooking Rennes le Chateau is 666.66 km. Furthermore it is due south. Bugarach Peak is located at 42°51’52.30″N, 2°22’45.21″E.

Bugarach Peak has been a New Age pilgrimage site since the 1960s.

For decades, there has been a belief that Pic de Bugarach, which, at 1,230 metres, is the highest in the Corbières mountain range, possesses an eerie power. Often called the “upside-down mountain” – geologists think that it exploded after its formation and the top landed the wrong way up – it is thought to have inspired Jules Verne’s Journey to the Centre of the Earth and Steven Spielberg’s Close Encounters of the Third Kind. Since the 1960s, it has attracted New Agers, who insist that it emits special magnetic waves.

Further, rumours persist that the country’s late president François Mitterrand was transported by helicopter onto the peak, while the Nazis, and later, Israel’s Mossad, performed mysterious digs there. Now the nearby village is awash with New Agers, who have boosted the local economy, though their naked group climbs up to the peak have raised concerns as well as eyebrows. –Source

The distance from Cleopatra’s Needle in New York City to Bugarach Peak is 3303.33 Nautical Miles.

Twenty kilometers east of Paris is a commune in the historic province of Brie called Champs-sur-Marne. In 2005, a new rond-point was built in the Pyramid district (so-called because of a housing complex of the same name built in the 70s) featuring a scale model of the three pyramids of Giza, complete with Sphinx. The Nile is represented by purple flowers. The distance from the center of this rond-point to the purple peak of Bugarach is 666066 meters. Wikipedia lists the population density of Champs-sur-Marne as 3333 persons per square kilometer. I can’t believe it, but there it is!

The distance from the Round Fountain to the Luxor Obelisk in La Place de la Concorde is 666 meters.

The distance from the Arc de Triomphe de l’Étoile to the Louvre Pyramid is 3333 meters.

In SIPS Volume 1 I profiled the sacred geometry of Jerusalem…

…and showed how it was replicated in the Tuileries Gardens of Paris:

The Round Fountain in the Tuileries correlates with Solomon’s Temple. That’s interesting because Solomon is all about 666’s. Consider this bible quote:

Now the weight of gold that came to Solomon in one year was six hundred threescore and six talents of gold [666]. -1 Kings 10:14

This makes me wonder which man was referred to in Revelation. Might the beast actually be none other than wise Solomon?

Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six [666]. -Revelation 13:18

The Seal of Solomon is the same as his father David’s famous Star, which is on the flag of Israel today. The Star of David has a resonance with 666.

In SIPS Volume 2, I connected Solomon with Sol Amon, names for the Sun and ancient Egyptian Sun God…

…and observed that the grand total of the magic square of the Sun is 666.

Solomon’s Temple (today’s Dome of the Rock/Western Wall/Farthest Mosque) is 666.6 nautical miles from the Kaaba in Mecca. What is it about sacred sites that draws pilgrims? They attract non-physical spirits and spirits-having-a-human-experience with a kind of magnetic action-at-a-distance.

The magnetism of the Kaaba

Today my wife asked me what I was up to and I said I’m writing a blog post on Pilgrimage. She said, “Have you checked out Lourdes?” No I hadn’t. Following her suggestion and this synchronicity, here is what to my utter amazement appears:

In SIPS Volume 1, I analyzed the Louvre Pyramid and showed how it is composed of 666 rhombi. Its height is also 21.6 meters. 6 x 6 x 6 = 216. The Louvre is the world’s most visited museum and the Louvre pyramid is its entrance. I too entered there on my pilgrimage to Paris last year.

The Sanctuary of Our Lady of Lourdes is built over a grotto where beginning on 11 February 1858, a 14-year-old peasant girl named Bernadette Soubirous claimed to have experienced a series of apparitions of a girl dressed in white and with a blue belt around her waist, who eventually introduced herself as the Immaculate Conception, a name by which the Virgin Mary was known. Among the instructions from ‘the Virgin’ were “Go and drink from the spring”, “Go and tell the priests to build a chapel here”, and “Have the people come here in procession”. These 3 instructions in particular were to prove pivotal in the development of Lourdes as a pilgrimage site.

Pope John Paul II at Lourdes grotto and spring – Ireneed CC BY-SA 3.0

Sick pilgrims are reputed to be miraculously healed by Lourdes water. Each year about 350,000 pilgrims bathe in Lourdes water. Kind of makes me wonder about the qualities of the water from the Round Fountain up in Pharia-Isis.

Fittingly, pop star Madonna named her daughter Lourdes.

The Louvre Pyramid is a stone’s throw from the Round Fountain in the Tuileries. Speaking of stones, I put this diagram together two nights ago. The diameters of the planets are given in miles and the diagram is drawn to scale.

Philosopher’s Stones

It builds on the work of renaissance alchemist Michael de’ Maier (1566 – 1622), and contemporary alchemists Bert Janssen, Randall Carlson, and Gary Osborn.

All the rocky planets in our solar system loosely fit the diagram. You are looking at Earth, Venus, Mars, Mercury and the Moon, coordinated by sacred geometry. I submit that the rocky planets are literally the philosopher’s stones. Note that the angle of the triangle is 66° and that Mercury’s diameter is 3033 miles.

The angle between Earth’s North pole and the ecliptic is 66.6°. The ecliptic is the plane in which we travel around the Sun. Spaceship Earth’s average orbital velocity is 66600 miles/hour.

The 3-4-5 triangle encodes the Earth’s obliquity

Asplund noticed that if you draw a line from Santiago de Compostela through Bugarach Peak it goes directly to the City of Rome. More precisely, it is 33003300 inches from Bugarach peak to center of the Spanish steps, just below the obelisk at Trinita dei Monti. I was there last year on my Roman pilgrimage and made this photo-painting which shows the view from that exact point. I especially liked the sundials. Funny how the Spanish steps connect us back to Santiago de Compostela in Spain.

Trinita dei Monti in Rome

If you add up the Roman numerals DCLXVI (500+100+50+10+5+1), they sum to 666. However, Rome is certainly the inversion of everything that St. Francis of Assisi stood for.

Amor backwards is Roma.

Consider the Roma style of Burning Man, for example. The ‘Supreme Sacred Congregation of the Roman and Universal Inquisition’ burned the brilliant Giordano Bruno at a stake in Campo de’Fiore in 1600 for nothing more than holding opinions contrary to the Catholic faith, believing in reincarnation, and the existence of a plurality of worlds.

This statue was erected on the very spot in the 19th century by Italian Masons.

Giordano Bruno in Campo de’Fiore – Sputnikcccp CC BY-SA 3.0

I’ve pointed out before that the distance from the Campidoglio in Rome (considered the Roman kilometer zero) is 1111.11 km from the Arc de Triomphe in Paris. Both are centers of 12 pointed stars, or zodiacs.

Here is the Great Pyramid of Pilgrimage. Its template appears to be a pair of 3-4-5 triangles put together, more or less.

Great Pyramid of Pilgrimage

Asplund also noticed that the distance from Stonehenge to the Louvre Pyramid is 1293100 feet at a bearing angle of 129.31° (the same numbers). Also, Stonehenge is 3456000 feet from the rond-point of the Cathedral of Santiago de Compostela. 3456 is a term in the Cosmic Sequence.

Perhaps not surprisingly, Stonehenge is also part of the matrix. It too was as much a pilgrimage site in ancient times as it is today. I find Bruce Bedlam’s theory that Stonehenge was a building has a lot of merit:

“You have seen the evidence. Evaluate and decide.”