Archive for the ‘Number’ Category

Why 137?

“Why 137?” was the question Nobel Prize winning physicist Wolfgang Pauli (1900-1958) was preoccupied with throughout his life. You see the fine structure constant, a dimensionless fundamental constant of physics, has a value nearly equal to 1/137. Here’s an overview:

In his Nobel lecture delivered in Stockholm on 13 December 1946, Pauli expressed his goal was to establish a theory “which will determine the value of the fine-structure constant and will thus explain the atomistic structure of electricity, which is such an essential quality of all atomic sources of electric fields actually occurring in nature.”

The charge of an electron is equal to the square root of (fine structure constant x 4π) in natural units.

Pauli famously quipped, “When I die my first question to the Devil will be: What is the meaning of the fine structure constant?” Unfortunately Pauli died without accomplishing his goal in the Red Cross Hospital of Zurich in Room 137—and he was aware of that synchronistic irony before he died.

The great psychotherapist Carl Jung helped Pauli in his quest to find a mathematical basis for the fine structure constant by interpreting more than 400 of Pauli’s dreams, published in Jung’s Psychology and Alchemy. Jung believed that Pauli unconsciously comprehended “some grand cosmic order.” Arthur Miller wrote a book about their collaboration entitled, 137: Jung, Pauli, and the Pursuit of a Scientific Obsession.

The brilliant Nobel Prize winning physicist Richard Feynman had this to say about the fine structure constant:

“It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it. Immediately you would like to know where this number for a coupling comes from: is it related to π or perhaps to the base of natural logarithms [known as e]? Nobody knows. It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the ‘hand of God’ wrote that number, and ‘we don’t know how He pushed his pencil.’ We know what kind of a dance to do experimentally to measure this number very accurately, but we don’t know what kind of dance to do on the computer to make this number come out, without putting it in secretly!” -Richard Feynman QED: The Strange Theory of Light and Matter (1985)

Belshazzar's Feast by Rembrandt (1635) — slightly altered by the author

Belshazzar’s Feast by Rembrandt (1635) — slightly altered by the author

Curiously, the Hebrew word קבלה, meaning Kabbalah, takes a Gematria value of 137. The Bible says Ishmael lived to the age of 137. The Koran says Ishmael is buried next to the Kaaba in Mecca.

Symbolically, this is the threshold between the physical dimension and the utterly spiritual dimension. In other words, at the boundary line of the physical world, the number 137 emerges…

Physicist Leon M. Lederman numbered his home near Fermilab 137 based on the significance of the number to those in his profession. Lederman expounded on the significance of the number in his book The God Particle: If the Universe Is the Answer, What Is the Question?, noting that not only was it the inverse of the fine-structure constant, but was also related to the probability that an electron will emit or absorb a photon. He added that it also, “contains the crux of electromagnetism (the electron), relativity (the velocity of light), and quantum theory (Planck’s constant). It would be less unsettling if the relationship between all these important concepts turned out to be 1 or 3 or maybe a multiple of π. But 137?”

-Wikipedia article on 137 (number)

Cosmologist Robert L. Oldershaw reasons that 137 is the relationship of the strength of the unit electromagnetic interaction compared with the strength of the unit gravitational interaction. That sounds pretty fundamental to me.

Strangely, approximately 137 x 10,000,000 years have elapsed since the Big Bang.

In the Bohr atomic model, the innermost electron of a hypothetical atom with atomic number 137 would be orbiting just below the speed of light, and the next heaviest element would be impossible because its electron would have to exceed c. Atoms close to the theoretical limit of 137 are unstable and not found in the universe.

The fact is, the fine structure constant is not exactly 1/137. The currently accepted value is 1/137.035999074 (CODATA 2010). The denominator of the constant is called α (alpha) and it is slightly larger than 137.

In order of increasing accuracy, here are various thinkers’ attempts to discover the math behind 1/α.

The quest for a mathematical basis of 1/α

The quest for a mathematical basis of 1/α

I learned about most of these discoveries from an outstanding paper called Dimensionless Physical Constant Mysteries by Ke Xiao.

My illustration of the golden angle below is coincidentally exactly equal to Bohr’s formulation of alpha, 360/(Ф^2). The golden angle controls plant patterning of repeated biological units (called phyllotaxis) and governs the geometrical optics of rainbows. More info on these subjects is available in The Divine Proportion. It is worth pondering whether phyllotaxis and/or rainbows are ultimately governed by the golden angle or alpha? They are 99.7% equivalent.

The golden angle, from The Divine Proportion

The golden angle, from The Divine Proportion

The equation by D. Beere (1973) above is actually from his book USP-A: Physics for Flying Saucers. I had to work out the math to find the hidden formula for alpha and it turns out to be an elegant one, which comes out of comparing electrical inductance in a loop with the fluid mechanics of a vortex. It is fascinating that putting the math together from these two different but analogous phenomena (magnetic vortex vs. material vortex) yields an approximation of alpha. This might be an avenue for more research.

W. A. Harrington contacted me a few days ago because of my work on the Divine Proportion and shared some of his complex equations related to the fine structure constant (one of his is shown above). What little I understand of them inspired me to dig deeper and attempt to answer Pauli’s question myself, “Why 137?” and this blog post (and my fortuitous formulation of 1/α) is the result.

W. R. Mellen’s equation is elegant because it is simply the hypotenuse of a Pythagorean triangle. However, it doesn’t tell us anything about where 137 comes from.

The hypotenuse is α

The hypotenuse is α

In my final formulation of 1/α (revised Jan 2016), the repetition of digits was the key and it resonates with the fact that 137 is the 33rd prime. I was able to figure it out because one of W. A. Harrington’s formulas for 1/α has a value of 137.037037037… and I recognized that repeating pattern.

When I cracked Jules Verne’s code in Quantification (20,000 Leagues Under the Sea was a journey of 111,111 km), I realized that 33.333…^3 = 37037.037037037… and this led to the following equation, with error in parts per million. The bars above 3 of the digits indicate eternally repeating digits.


An approximation of the ratio of a circle’s circumference to its diameter can be expressed in terms of alpha and repeating threes.


The way I exactly expressed Ф and its reciprocal in The Divine Proportion was another repetition of digits.


Feynman called Euler’s Identity “our jewel” and “the most remarkable formula in mathematics.” It normally takes the form you can read about on Wikipedia but I came across an alternate formulation of Euler’s Identity in Xiao’s paper that I think is even more beautiful because it relates e, i (√-1), π, Ф, and ϕ, fundamental constants others have used to express α:

The most beautiful equation in mathematics

The most beautiful equation in mathematics

The above equation is a kind of mathematical poetry connecting 4 of the most important constants. The poetry is beautiful because of this elegant interconnection. Having 1 and 0 in the standard formulation is better than -1 but I think that the most pleasing formulation includes the golden ratio Ф (≈1.618) and its reciprocal ϕ (≈0.618) because this expresses the unique nature of the divine proportion whilst simultaneously forming a elegant relationship with e, i and π.

Astrophysicists measured variations in the fine structure constant in 2011. WTF!

“While the data from just one telescope seemed to suggest that alpha varies in time, data from the two telescopes show that alpha also seems to vary in space. Such a discovery could have major implications, starting with shattering the basic assumption that physical laws are the same everywhere in the universe. The results also violate the Einstein Equivalence Principle, and suggest that the universe may be much larger than currently thought – or even infinite in size.

If alpha were just 4% bigger or smaller than it is, stars wouldn’t be able to make carbon and oxygen, which would have made it impossible for life as we know it to exist.

One intriguing possible implication is that the fine-structure constant is continuously varying in space, and seems fine-tuned for life in our neighborhood of the universe.” –

Fortunately for us the amount of variation is 4.1σ – 4.2σ, which means we only have confidence in α to 99.99%.

The mystery about α is actually a double mystery. The first mystery – the origin of its numerical value α ≈ 1/137 has been recognized and discussed for decades. The second mystery – the range of its domain – is generally unrecognized. —Malcolm H. Mac Gregor, The Power of Alpha (2007)

It will be harder to elicit the true math behind the fine structure constant until we understand precisely how such a fundamental constant changes.

“There is no need to suppose that all the laws of nature sprang into being fully formed at the moment of the Big Bang, like a kind of cosmic Napoleonic code, or that they exist in a metaphysical realm beyond time and space…If we want to stick to the idea of natural laws, we could say that as nature itself evolves, the laws of nature also evolve, just as human laws evolve over time. But then how would natural laws be remembered or enforced? The law metaphor is embarrassingly anthropomorphic. Habits are less human-centred. Many kinds of organisms have habits, but only humans have laws.” –Rupert Sheldrake

The reason 137 has obsessed so many thinkers to try and find the math behind it is
clear. Einstein wrote, “In a reasonable theory there are no numbers whose values are only empirically determinable.”

“It is impossible for human minds to construct something as infinitely rich as mathematics, that so successfully describes our universe down to the finest detail. Given that it is impossible for anything else to describe our world so accurately, it is also impossible to conclude that the universe is not mathematical.

It’s often said that the whole of biology is explained by chemistry, the whole of chemistry by physics and the whole of physics by mathematics, the queen of the sciences. If all physics is contained within mathematics, it has the most radical consequences. Advocates of the Multiverse seek to argue that life in our universe is an accident, an outcome of a random version of physics that applies to our universe. If, however, there’s only one physics, defined entirely by ontological mathematics (which is a single, interlocked edifice) then the fact that there is life in our universe is no accident at all. It implies nothing less than that our universe is alive. It is designed for life because it IS life.

The fundamental constants of physics are finely tuned for life precisely because they are manifestations of a living system. [emphasis my own]

A living universe is a universe of mind. The ideology of scientific materialism is thereby refuted. Many scientists are so blindly wedded to materialism that they would rather invoke infinite universes and infinite versions of physics and infinite sets of varying fundamental constants than embrace mind and life. Yet infinity does not help them. How can infinity convert the inanimate into the animate? How can consciousness come from mindless atoms? These are impossibilities, pure and simple. EVERYTHING makes sense as soon as it’s accepted that the universe, in its most basic aspect, is living not dead, and minded not mindless.” –Mike Hockney


Yours is the eye perceiving atop the pyramid, the answer to the question, “Why 137?”

Location, Location, Location

It has long been known that the three most important factors determining real estate value are: location, location, location. I notice that this aphorism is true not only for residential and commercial properties, but also somewhat unexpectedly for sites having great symbolic and/or spiritual significance.

My research reveals a previously unknown system of non-monetary valuation transcending any particular culture, tradition, or time period that takes the entire Earth and the built environment into account.

Repdigits and transcendental mathematical constants are the keys to locating sites in this system. For example, consider the fact that the Western Wall in Jerusalem is 666.6 nautical miles from the Kaaba in Mecca. These two are the most sacred sites in Judaism and Islam.

'Sacred Stones' from Quantification

‘Sacred Stones’ from Quantification

Why nautical miles? There are 6x6x600 nautical miles in the meridian circumference of the Earth, revealing more repdigits in the unit used to do the encoding.

The nautical mile was originally defined as one arc minute and the metric system was originally defined by dividing the arc length from the pole to the equator into 10 million parts called metres. So one degree is 10,000,000 m / 90° = 111,111.111… m and one arc minute is 111,111.111… / 60′ = 1851.85185… m.

The nautical mile was defined as exactly 1852 m by international convention, so they rounded it off to the nearest meter. This obfuscates two very interesting patterns. The repeating numbers use the same digits of the Great Pyramid’s slope angle of 51.85° (51°51′) and the following:

1851.85185… yards = 5555.555… feet = 66,666.666… inches.

There is also an unusual link between nautical miles and meters:

666.6 nautical miles = 1234543.2 meters
6666.6 nautical miles = 123456543.2 meters

The black stone in the Kaaba is 5055005 yards from the Mahabodhi Temple in India, the location of the original tree under which the Buddha became enlightened.

'Sages' from Quantification

‘Sages’ from Quantification

The Buddha apparently died 333,333 feet from the place where he was born.


The distance between the center of the world’s largest Buddhist meditation center (capacity 1 million meditators) and the third eye of the world’s largest Buddha statue is exactly e million (2,718,282) yards. The transcendental constant e is Euler’s number, used in finance, engineering and many scientific disciplines.

300,000 Buddha statues adorn the Dhammakaya Center and the yard is a unit equal to 3 feet. The ‘Great Retreat’ in Buddhism correspondingly lasts 3 years, 3 months and 3 days.


According to the Bible, Jesus lived 33.3 years and performed 33 miracles. Did King David, father of Solomon, really rule for 33 years and did Jacob really have 33 children or are these repdigits actually codes?

The Kaaba, the stone cut temple of Ellora in India and the largest religious complex in the world at Angkor Wat not only form a great circle alignment but the distances between them also encode 33° and π.


Long ago, the Western Wall in Jerusalem formed the foundation of Solomon’s Temple. Solomon’s Temple was 33.33° from Stonehenge.


The Dome of the Rock stands on the site of Solomon’s Temple and is 3333.33 km from the center of the symbolic Place de la Nation of Paris.


In the 19th century, one of Cleopatra’s Needles was moved exactly 3333.33 km from the harbor wall in Alexandria to where it now stands in London. Likewise the Ishtar Gate of Babylon was moved 3333 km to the Pergamon Museum in Berlin.


The Eiffel Tower stands 3033.33 km from the site of the former Lighthouse of Alexandria, Egypt. In turn the Lighthouse was 3333.33 km from the standing stones of Carnac, France. The oldest standing obelisk in the world, in Heliopolis Egypt, is in a great circle alignment with the Lighthouse of Alexandria, Egypt and the replica Lighthouse of Alexandria, Virginia (333 feet high), officially titled, “The George Washington Masonic National Memorial.”


The center of the Eiffel Tower is exactly e million (2,718,282) feet from the center of the Cathedral of La Sagrada Familia in Barcelona, which is topped by solar discs. The Sun disc’s circumference is e million miles (99.99%).


The world’s tallest building is currently the Burj Khalifa in Dubai. It is e thousand feet high and 1633333 meters from the Kaaba. The total land area of the League of Arab States equals 13333333 square kilometers (99.9997% accurate).

'Arabic Connections' from Quantification

‘Arabic Connections’ from Quantification

A higher structure known as the Kingdom Tower is currently under construction in Jeddah, Saudi Arabia. It will be 3303 feet high when completed. Funding was just secured to complete the tower, probably by 2020.

The Kingdom Tower will be 33.3° from the Golden Temple in India, which the most sacred shrine in Sikhism.


The center of the Kingdom Tower of Jeddah is 3,333,333 inches from the word Allah (in Arabic calligraphy) atop the world’s highest and largest clock tower in Mecca, steps from the Kaaba. The Kingdom Tower is also oriented so one leg points at the Kaaba and the Abraj Al-Bait Tower.


The vector connecting the word Allah on the clock tower terminates at the center of the equilateral triangular void within the Kingdom Tower, symbolizing the Eye of Providence, or Allah in this case.

Eye of Providence from Jewish cemetery - Image Aw58 CC BY-SA 3.0

Eye of Providence from Jewish cemetery – Image Aw58 CC BY-SA 3.0

Sometimes important sites are related by repdigits within cities. For example, consider Tehran, Iran. The Tower of Freedom is 55,555.5 feet from the center of the Mausoleum of the Ayatollah Khomeini. Interestingly, this distance is also equal to 666,666 inches and both complexes ironically have similar plans. The Tower was built in 1971 to honor the Shah and later renamed Azadi, meaning Freedom, after the Revolution of 1979 that ousted the Shah. The architect of the tower was a Baha’i who was driven out of the country when religious pluralism was rescinded in the Revolution of 1979, led by the Ayatollah Khomeini. It is therefore highly unlikely that there was a conspiracy to locate the Mausoleum of the Ayatollah in a repdigit relation with the Shah’s tower. The encoding transcends culture and religion, a secret in plain sight.


I have thus presented you with many such secrets in plain sight, many of which hinge on different units of measure. These units of measure are ultimately based on, and have surprising resonances with the dimensions of the Earth and the Moon. For example, the Imperial system of inches, feet, yards, furlongs and miles has clear resonances that are far from accidental. There are 63360 inches in a mile (5280 feet/mile x 12 inches/foot). There are 63360 furlongs in the Earth’s diameter. The circumference of a circle encompassing the Earth and the Moon measures 63360 miles.


John Michell discovered that the combined Moon & Earth radii measure 1x2x3x4x5x6x7 miles. The arc length around one-quarter of the circle circumscribing the Earth and Moon is 8x9x10x11 miles, which is also curiously equal to the Earth’s diameter.

Read the essay “Yards” in my Anthology for more info on the resonances of that particular unit.

The Imperial system is not unique in having resonances with the Earth and the Moon. The Metric system does also. The combined diameters of the Earth and the Moon are equal to 10,000 times Ф km (99.97% accurate). The symbol Ф represents the Divine Proportion. The Earth’s polar diameter is 10,000 times the square root of Ф km. The Earth and Moon are divinely proportioned with respect to each other as shown by the triangle and the diagram showing two intersecting golden rectangles tangent to the Earth below.


In fact the Imperial and Metric systems are related by the divine proportion, or nearly so (see the tiny half percent gap on the upper right).


So our systems of units resonate in multiple fascinating ways with the structure of our planet and its natural satellite. Here are some surprising repdigit patterns in our units, revealed by a hexagon inscribed within the Earth.


I do not believe the Moon was made by aliens or is made of cheese, nor do I believe the Earth is flat or that sea-monsters patrol its edges. Please read David Mathisen’s well-written article, “The Invisible Kraken: Evidence that the Earth is not Flat” and think about it if you are a “Flat Earth Truther.” Do not contact me with flat earth theories or conspiracies about NASA or scientists in general, or about people suppressing flat earth theories or the theorists themselves.

“Belief is the death of intelligence.” -Robert Anton Wilson

So what do I ascribe to the meaning of location, location, location? Although you might initially think that these structures were sited according to a grand human conspiracy, the great antiquity of many of these examples stretches this theory well beyond its rational breaking point. The standard materialist view would have physical agents coordinating all of this, so aliens are the next most likely suspects. However, consider their motives.

If aliens encoded repdigits and transcendental mathematical constants both in our units of measure and in the locations of many significant structures, they must have had for thousands of years, and continue to have up to the present time, intimate knowledge about what our species considers significant. If we could put aside our primate/primal fear of people who aren’t from around here—aliens—we might consider that these agents know us very well, so well perhaps, that they must not be alien at all. They might know us better than we know ourselves.

Why would anyone bother to encode all of this—what could they possibly hope to accomplish with such a massive effort? Clearly the encoding transcends any particular culture, ethnic group, religion or belief system, spans a great deal of time, and reveals a high level of intelligence. As such it appears to be a universal message to humanity, one that has been there in plain sight all along, waiting for discovery. This has only been possible for about a decade, since GPS satellite data has been publicly accessible through computer interfaces such as Google Earth. Now that the genie is out of the bottle, what does it mean?

Encoding messages in the locations of significant structures is a non-destructive, gentle approach that reminds me of the low-impact of crop circles. Information is conveyed but it remains entirely up to us to assign meaning, if and when we are able to do so and curious enough to do it.

I think we have to work this out backwards, in other words, “by their fruits we shall know them.” The fruits have to be knowledge and perhaps human enlightenment. So who would want to educate and enlighten us?

We can rule out God, unless you define God as a being who transcends religion. We can rule out aliens too, unless they aren’t actually alien and have transcended their own selfish agendas.

More likely are higher selves and/or spiritual beings, but that requires one to consider trans-material reality—things beyond that which we can readily weigh and measure.

It’s amazing to me, but scientific materialists who believe that everything is made of atoms tend to see no contradiction that everything came from nothing in the Big Bang. Scientific materialists also believe in dark matter and dark energy. Neither dark matter nor dark energy has ever or probably can ever be detected, and yet we are supposed to believe these substances are 96% the mass of the universe, because that figure makes the math in the standard model of physics work out. That is like saying invisible pink unicorns are 96% the mass of the Universe, an unfalsifiable (you can’t ever prove that it is false) and therefore unscientific premise. Time to rethink the standard model?

“According to the standard Big Bang narrative, space and time did not exist prior to the Big Bang. Therefore, the “cause” of the Big Bang could not have existed within space and time. In that case, it existed outside space and time, hence was dimensionless, hence was immaterial, hence was mental! The very thing that scientific materialism claims cannot exist — independent, causal mind — is the only possible, plausible candidate for explaining the Big Bang.” –Hyperreason by Mike Hockney

In addition, we can rule out dark matter and dark energy as immaterial encoders (assuming they even exist) because these universal forces or fields presumably don’t “know” anything, including what is significant to our particular species.

The encoders are minds possibly imagined by a singular mind (the Universe itself) with an intelligence that chooses to encode repdigits and transcendental mathematics in the locations of our significant sites for some teleological purpose. I suspect that this purpose is to teach us eventually who we are.

Information processing networks

Information processing networks

“Let us pretend that there was a machine, which was constructed in such a way as to give rise to thinking, sensing and having perceptions. You could imagine it expanded in size (while retaining the same proportions) so that you could go inside it, like going into a mill. On this assumption, your tour inside it would show you the working parts pushing each other, but never anything which would explain a perception.” -Gottfried Wilhelm von Leibnitz

Perhaps the first thing to realize is that more is going on here than just atoms. Quantum physicists have known for a century that atoms are really 99.9999999999% empty space, but we have yet to come to terms with that information.

99.9999999999…% = 100%.

The only possible descriptions of sub-atomic particles are mathematical descriptions because that is precisely what they are: mathematics.

Our Pater & Mater (Latin: Father & Mother) are Pattern and Matter

Our Pater & Mater (Latin: Father & Mother) are Pattern and Matter

“If you only knew the magnificence of the 3, 6 and 9, then you would have the key to the universe.” -Nicola Tesla

This is the key: the universe is 100% mathematics, the universal language. There is no objective “substance” out there. However, if all is number, then who are you?



Saturn's Patterns

Saturn’s Patterns

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

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

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.”

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

From The Divine Proportion:

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.

From The Divine Proportion:

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.

From Secrets In Plain Sight: Leonardo da Vinci:

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.

From Secrets In Plain Sight: Leonardo da Vinci:

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 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

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

This article also appears on



Cosmic Lottery

Physicist Max Tegmark has identified 32 dimensionless ratios that are basic properties of reality in his though-provoking book, Our Mathematical Universe: My Quest for the Ultimate Nature of Reality. These are 32 pure numbers from which every other fundamental constant of nature can be theoretically derived.

In this illustration I depicted these parameters and added the missing on/off switch, bringing the grand total of controls needed to mathematically define a universe up to the magic 33.

33 controls must be tuned to create our universe

33 controls must be tuned to create our universe

These knobs must be so incredibly finely-tuned to create a universe, let alone a universe capable of supporting life, that we have truly won the cosmic lottery. Tegmark explains:

“How far could you rotate the dark-energy knob before the “Oops!” moment? The current setting of the knob, corresponding to the dark-energy density we’ve actually measured, is about 10−27 kilograms per cubic meter, which is almost ridiculously close to zero compared to the available range: the natural maximum value for the dial is a dark-energy density around 1097 kilograms per cubic meter, which is when the quantum fluctuations fill space with tiny black holes, and the minimum value is the same with a minus sign in front. If rotating the dark-energy knob…by a full turn would vary the density across the full range, then the actual knob setting for our Universe is about 10−123 of a turn away from the halfway point. That means that if you want to tune the knob to allow galaxies to form, you have to get the angle by which you rotate it right to 123 decimal places!

That’s interesting also because of the parallel with the game of Chess. Louis Victor Allis, a Dutch computer scientist working in the artificial intelligence field, has calculated that there are at least 10^123 games of Chess that can possibly be played. That means that the probability that our universe contains galaxies is akin to exactly 1 game of chess in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 games. Unlikely doesn’t even begin to describe these odds. There are “only” 10^81 atoms in the observable universe, after all.


Tegmark continues:

…if the electromagnetic force were weakened by a mere 4%, then the Sun would immediately explode as its hydrogen fused into so-called diprotons, an otherwise nonexistent kind of neutron-free helium. If it were significantly strengthened, previously stable atoms such as carbon and oxygen would radioactively decay away.

If the so-called weak nuclear force were substantially weaker, there would be no hydrogen around, since it would all have been converted to helium shortly after our Big Bang. If it were either much stronger or much weaker, the neutrinos from a supernova explosion would fail to blow away the outer parts of the star, and it’s doubtful whether life-supporting heavier elements such as iron would ever be able to leave the stars where they were produced and end up in planets such as Earth.

If electrons were much lighter, there could be no stable stars, and if they were much heavier, there could be no ordered structures such as crystals and DNA molecules. If protons were 0.2% heavier, they’d decay into neutrons unable to hold on to electrons, so there would be no atoms. If they were instead much lighter, then neutrons inside of atoms would decay into protons, so there would be no stable atoms except for hydrogen. Indeed, the proton mass depends on another knob that has a very wide range of variation and needs to be fine-tuned to thirty-three decimal places to get any stable atoms other than hydrogen.

Many of these fine-tuning examples were discovered in the seventies and eighties by Paul Davies, Brandon Carter, Bernard Carr, Martin Rees, John Barrow, Frank Tipler, Steven Weinberg and other physicists. And more examples just kept turning up.”

The Moon and the Sun constitute further proof we passengers on spaceship Earth are winners. There is nothing in physics that says the Moon and Sun must appear the same size in our skies. In fact our Moon is the only satellite in our system that even comes close to doing this. It is truly amazing that the Moon and Sun discs match up—and they won’t forever as the Moon is slowly moving away from the Earth. We won the cosmic lottery again!

A look at any total solar eclipse is proof of the astronomically unlikely situation that the Sun is 400 times larger than the Moon and 400 times father away from Earth than the Moon.

Luc Viatour / CC-BY-SA-3.0

Luc Viatour / CC-BY-SA-3.0

I discovered another such symmetry in the orbital dynamics of Moon and Earth.

During one orbit around the Sun, Earth actually rotates about its own axis 366.3 times. The Moon orbits the Earth in 27.3 days. Of course a day is one Earth rotation on its own axis.

366.3 x 27.3 = 9999.99

At the same time, the Earth is 366.3% the diameter of the Moon and the Moon is 27.3% the diameter of Earth.

366.3% x 27.3% = .999999



To better understand why the Earth rotates more times than there are days in the year, watch this clear explanation:

How can it be that the Earth and Moon are in a reciprocal mathematical relationship in terms of number of rotations and in the pure ratios of diameters? Nothing in physics says this need be so. It is far too perfect and we won the cosmic lottery yet again!


The following equation also reveals something about the unexpected perfection of the Earth-Moon system:


The combined diameter of all the planets in our solar system is 10 times greater than the Earth’s circumference. This has astonishingly high accuracy at 99.99%. As we don’t know the combined diameters of all the planets with more than 99.99% accuracy this relationship might in fact be exact. It is a powerful argument for the primacy of base 10.

“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


We won the cosmic lottery yet again, against astronomical odds! What are we not understanding?

God, Aliens, Conspiracy, Randomness and/or Triviality are unsatisfying explanations to me. These major secrets placed so obviously in plain sight make me feel like humanity is destined to understand the deeper implications.

Many more such symmetries and wonderment are in my most recent book, The Divine Proportion.

Macrocosmic Harmony

The best temples serve as bridges between human scale and the macrocosm. When Beverly Spicer sent me the following image, something clicked and I understood the human body, the Sphinx and the Pyramids in a new way. I’m not sure which book this black-and-white geometric analysis of Pharaoh Rameses II was scanned from—it appears to be mirrored all over the Internet.


The nemes headcloth has distinctive, straight-edged folds, which imply an intersection point above the head. Nested equilateral triangles locate the pharaoh’s third eye appropriately as an all-seeing-eye in the center of the triangle (like the eye of providence on the dollar bill).

That reminds me of an image I made recently. Here is essentially what I wrote about it on Facebook:

Beauty is experienced in the world, love in the body, and truth in the mind. The eye of horus in the center symbolizes the view of any observer. The transcendentals are ontologically one and thus they are convertible: e.g., where there is truth, there is beauty and love also. The transcendentals are irreducible qualities of awareness. The circle represents the seeming boundary between your interior sensations, thoughts, and perceptions and your exterior body, mind, and world.


Just as the transcendental qualities of awareness (love, beauty, truth) are ontologically one, so too are the trinity of data types you experience. How far from your awareness are your sensations, perceptions or thoughts? Examine your experience and you will see that there is no distance.

Do the thoughts running through your mind take place in a fundamentally different place than the sensations of your body or your perceptions of the world? They are all convertible because all this data is experienced by awareness and yet we have no trouble identifying which channel the information flows through. There is a fundamental and irreducible trinity to awareness.

I now see this ontological trinity as the fountainhead of relationships such as Isis/Horus/Osiris, Mary/Jesus/Holy-Spirit, and even Neutron/Proton/Electron.

Following a hunch I wanted to see if the Sphinx’s nemes followed the same pattern. I discovered that the pattern is similar but is also subtly different. The Sphinx’s nemes doesn’t imply nested triangles but the uraeus symbolizing the pharaoh’s pineal gland is located in the center of the vesica piscis as indicated by the crossed red lines. Incidentally, I described how to draw this image step-by-step in the latest installment of my Photoshop User Magazine column, Beyond Photoshop.


Zooming out, the G2 pyramid also appears to fit the pattern.


It clicked for me when I realized that the geometric template for the Sphinx is the same as the geometric template for the Great Pyramid that I published in my book Quantification. The edge of the inscribed equilateral triangle measures 555.5 feet in the Great Pyramid.


In this way the House of the Temple (it was never a tomb) is a macrocosm of the Body carved on the Sphinx. Zooming out once again, the Engraved Hourglass Nebula is a macrocosm of that House. As above, so below.


The above image wonderfully illustrates Mircea Eliade’s homology, Body—House—Cosmos, from his book “The Sacred and the Profane” (1959).

A big synchronicity for me is that I learned about this three-level holographic homology not from reading Eliade but from reading Beverly Spicer’s excellent book and PhD thesis from the School of Architecture at the University of Texas called, “The Ka’bah: Rhythms of Culture, Faith and Physiology,” which she was kind enough to send me. Remember Beverly was the person who sent me the black-and-white Rameses II image? That whole sequence of events was quite illuminating!

Speaking of illumination, did you know that the human eye is most sensitive to a wavelength of 5555 Ångströms, which forms the center point of our visual perception? At other frequencies, more radiant intensity is required to achieve the same luminous intensity.

See how the colors are strongest in the middle of the color ramp and fade away as they approach the infrared and ultraviolet ends of the spectrum? 5555Å is the central wavelength.

5555 Ångströms

5555 Ångströms

The peak luminous intensity of sunlight also has a wavelength of 555.5 nanometers (5555 Ångströms). This should be no surprise because our eyes evolved, or perhaps were designed to view the light of our particular Sun. The beauty of repeating 5’s harmonizing our visual perception, 5 symbolizing life, is not lost on me.

After reading a stimulating article Joe Dubs linked on Facebook entitled, “The Pythagorean Relationship Between Pi, e, and Phi” by Peter Felicetti, I realized I already knew the content, but I hadn’t considered the following geometry algebraically before. One can arrange Phi, Pi and e as an almost perfect Pythagorean triangle, but there is a tiny gap that I labeled “The Mystery” at the end of my article on Graham Hancock’s site.

This mystery is drawn to scale

This mystery is drawn to scale

When I saw it algebraically, a few more puzzle pieces fit together and it is no longer a mystery to me but a harmonious work of rational design from a very high level.

Tech note: I realize that some of my detailed graphics might be hard to see. I recommend pressing Command+ on the Mac or Ctrl+ on Windows several times to enlarge the content displayed in your browser. Use Command/Ctrl- to make it smaller later on.

The Quadrivium

The Quadrivium

The same gap that we hear between twelve just perfect fifths and seven octaves (known as the Cycle of Fifths or the Pythagorean comma), the relationship of transcendental constants arranged in a Pythagorean triangle, and the orbital mechanics of our planet are all related because we are living in a mathematical construct. This was known long ago.

“All is number.” -Pythagoras

The above image expresses the quadrivium: number, geometry, music, and astronomy. In other words, number in itself, number in space, number in time, and number in spacetime.

I knew the Solar Year also factors in the Earth’s equatorial circumference—the following equation was published by John Michell and Robin Heath in The Lost Science of Measuring the Earth. I made this illustration commemorating this important relationship, one that essentially defines the foot.


Speaking of Michell and Heath, they were the authors who deciphered the 5:12:13 triangle and its connection with the lunar cycle. When I was researching extending the Pythagorean theorem into three dimensions, I came across a diagram connecting the 5:12:13 and 3:4:5 triangles. That, and studying Gary Osborn’s work, inspired me to put together this image showing how dynamics related to the Earth, Moon and Sun emerge from something as fundamental to geometry as the first two Pythagorean triples.

Number in space and spacetime

Number in space and spacetime

Earth’s orbital circumference has certain clear resonances with our measurement systems.


Bringing together what I wrote about in Cubits, in my book Taking Measure: Explorations in Number, Architecture and Consciousness, and from my recent experience participating in Graham Hancock’s forums when I was author of the month, these pieces now fit together with greater clarity.



Michael Kuser wrote something on my wall that inspired the following image. The first part shows the combined diagonals of the cubes bounding Earth and Moon compared to their average distance from the Sun are proportioned as the foot is to the mile (99.3%).

Lawrence Edlund discovered that the average distance of the Earth to the Sun compared to the distance light travels in one revolution of the Earth around the Sun are proportioned as the inch is to the mile (99.9%).

I put two and two together and graphically show how our units of measure resonate with our local macrocosm.


In “Rotations” you see more proof that our system is a product of base-10 design. The Moon’s orbital period with respect to the fixed stars is 27.3 Earth days. Earth actually rotates 366.3 times per year relative to the stars because the orbital motion of the Earth around the Sun causes roughly one additional rotation of the planet on its own axis. Here is what Knight and Butler had to say about this phenomenon in Before the Pyramids (p240), where they describe how the megalithic system is based on the division of a circle into 366 units:

“In a solar year the Sun rises 365 times but, during the same time, a star will have risen 366 times. It sounds odd but it’s true. Each day according to the rising of a star (a sidereal day), is 23 hours 56 minutes 4 seconds in length, whereas a mean solar day is 24 hours in length. That leaves a discrepancy of 236 seconds, which over the course of a year amounts to another 24 hours. It is part of the clockwork mechanism of our solar system that there are different sorts of years, dependent on what one is observing. Our megalithic and pre-megalithic ancestors in Britain focused on the number of times a star rose in a year, and the result was 366 times [366.3 with one more digit of accuracy].”



Tonight I realized that the product of these rotations, 27.3 x 366.3 = 9999.99. What are the chances? I can’t begin to calculate the astronomical odds against such a numeric symmetry if our planet and its natural satellite were formed by random processes. Note that this product is independent of units and calculated solely on number of Earth rotations relative to our Moon and Sun.

Peter Plichta’s book God’s Secret Formula: Deciphering the Riddle of the Universe and the Prime Number Code taught me that 1/27.3 ≈ 0.03663 and 1/366.3 ≈ 0.00273, which you can easily verify with a calculator.

The ratio of the polar diameter of the Earth to the polar diameter of the Moon is 3.663 and vice-versa, the reciprocal ratio is 0.273 with more than 99.9% accuracy. This means the Earth and Moon system’s rotations and sizes are related in a reciprocal mathematical relationship.

Of course this is another example of what I have called “The Mystery of 273,” in this page out of Quantification.

The Mystery of 273 (update)

The Mystery of 273 (update)

Is what we call “conscious thought” incredibly rare in the grand scheme of things, relegated as it is to 2-3mm of neocortex on the surface of our brains?

We and all other organisms on this planet live in a thin biospherical shell 2-3 miles thick. The Earth orbits the Sun in the sweet spot where oceans are kept liquid and the planet retains a transparent atmosphere so perfect for astronomy and our survival. A planetary magnetic field and ozone layer shields us from the charged particles continually pouring out of the Sun, along with many variables conductive to life being fortuitously fine-tuned.

Our system orbits the center of the Milky Way galaxy in another sweet spot, a circular band where products of stellar fusion such as elements heavier than helium are plentiful enough, but star formation isn’t still so active that we are bombarded out of existence. In this light, consciousness appears to be a gossamer membrane, a rare and exquisite miracle in all the cold vastness of space. This membrane/shell structure is another Body—House—Cosmos homology if you think about it.


The following comparison highlights another possibility. The neuronal structures within our brains, roads (which evolved organically around Paris rather than through city planning as in much of North America), and the large-scale structure of the universe (simulated on the Max Planck supercomputer) all exhibit the same specific branching, filamentous pattern. Come to think of it, so too do mushroom mycelial mats, and maps of the entire Internet. What these disparate phenomena have in common is that they are all information processing networks.



If we view Paris from the level of cars, then roads don’t seem to be self-aware. If we view the large-scale structure of the universe from the vantage point of supercomputer simulations computed on Earth, it doesn’t seem self-aware. If we were able to view a neural structure from the point of view of electrons it probably wouldn’t seem self aware to them either, just a kind of electrical network.

However, when we use our own neural structure to introspect, then awareness is self-evident. It’s really a question of which way you are looking. If the universe looked inward, then it presumably would be self-evident that it is self-aware, including all its in-formation including suns, planets, cities, roads, people, neurons, electrons, etc.

The amazing thing is we experience this same self-awareness at our level. We are a microcosm of larger wholes and have microcosms within. Perhaps cells are also self-aware, coordinating the activities at their tiny scale. The organism of which they are a part wouldn’t seem to be self-aware to them at all. Talk about all that would seem like mere philosophy.


This is yet another example of the Body—House—Cosmos homology. The human built environment accessed by roads, our “House,” is a macrocosm of the neurons in our Body, and the large-scale Cosmos is a macrocosm of our House. It is the same form, harmonizing and coordinating information at vastly different scales.

The universe itself looks like it might literally be “the mind of God,” a self-aware matrix in the process of creating complex in-formation. Awareness is not rare, but the ground of being. There has only ever been, is, or ever will be awareness being aware of itself.

“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 in The Observer (1931).

That said, our limited manifestation of consciousness might be rare and in a way, precious. We live at a golden scale in the macrocosm.



However, our awareness doesn’t require human minds anymore than the Sun requires a candle for illumination.


Everything is sacred, everything is precious.

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