New Website

In the course of identifying patterns in art, architecture, urban design & the cosmos through the lens of Secrets in Plain Sight, what I find always seems to boil down to sacred geometry.

What is Sacred Geometry?

There is no American geometry, no Russian geometry, no Chinese geometry because geometry is universal. There is only one geometry.

One quickly realizes that simplicity and geometry are the language of timelessness and universality. -Paul Rand (1914-1996)

Ancient sages and modern physicists say that the universe is pure geometry. Sacred geometry is the practice of creating microcosms of universal geometry. As such, sacred geometry is a mysterious mirror reflecting the exterior universe in your interior universe.

Experiencing geometry in this way naturally feels sacred. It is not religious or something to over-intellectualize, but the sacredness of geometry is definitely something to experience.

Sphinx Geometry

As an example of sacred geometry, for millennia geometers have been trying to reconcile the square and the circle, by length or area, trying to bring these two penultimate symbols of straight and curved, rational and transcendental, known and unknowable together.

Even though it was proven that “squaring the circle” exactly is impossible, it didn’t stop geometers from trying to find approximations because the drive to square the circle is part of the human soul. It is the desire to reconcile opposites, to find balance within duality and bring order from chaos.

Squaring the circle

How does Sacred Geometry differ from the Geometry you learned in School?

The geometry you may have learned in school is concerned with axioms, theorems, proofs, tests, grades and so on. This approach to geometry has been a particularly effective means to stimulate rational thinking for more than two thousand years.

“Almost from the time of its writing and lasting almost to the present, Euclid’s ‘The Elements’ has exerted a continuous and major influence on human affairs. It was the primary source of geometric reasoning, theorems, and methods at least until the advent of non-Euclidean geometry in the 19th century. It is sometimes said that, next to the Bible, The Elements may be the most translated, published, and studied of all the books produced in the Western world.” -Bartel Leendert van der Waerden, 1903-1996

Tip: See khanacademy.org for a 21st century approach to learning Euclidean geometry.

sacred geometry diagram

Sacred geometry has entirely different foci—the experiential and philosophical aspects of geometry. I find it amazing that we can explore the universe within using a pencil, paper, straightedge and compass. Why are these same tools so effective in exploring and creating in the world, and what does this say about the nature of reality? Where do the universe-within and the universe-without meet?

Sacred geometry is a particularly effective means of stimulating trans-rational thinking—the phenomenological world beyond rationality. Trans-rational thinkers retain their left hemisphere’s capacity to analyze, yet simultaneously treasure their right hemisphere’s capacity to synthesize and see interconnections between microcosm and macrocosm.

Creativity is just connecting things. When you ask creative people how they did something, they feel a little guilty because they didn’t really do it, they just saw something. It seemed obvious to them after a while. That’s because they were able to connect experiences they’ve had and synthesize new things. -Steve Jobs, 1955-2011

Sacred geometry hasn’t been taught much in the last two thousand years, perhaps because its practical value isn’t obvious. However, there is more to reality—and more to living life to its fullest—beyond obvious practical considerations. Geometry is an elegant vehicle that has the potential to move you to experience the exquisite sacredness of existence, which can be powerfully healing and transformative.

Do I have to remember anything I learned in School to explore Sacred Geometry?

The short answer is not really. Of course there is a basic language of points, lines, circles, angles, etc. that is helpful to recall. Prior knowledge of classroom geometry only enhances the experience but is by no means necessary. What you need to know about the mechanics of drawing sacred geometry can be learned in 15 minutes—it’s very simple and anyone can do it. There are no tests, grades, theorems or proofs. The purpose of drawing with the traditional instruments is to lead you to an experience, an experience shaped by the perfection inherent in the geometry, guided by your own higher wisdom.

New Website

Metatron's cube

I built a new website called Sacred Geometry Academy (http://sacredgeometry.academy) to initiate small groups in the universal language of sacred geometry in the course of intensive weekend workshops. This is the most effective way that I have found to ground the message of Secrets in Plain Sight in one’s own life. Personally experiencing sacred geometry in a small group can be a most powerful and transformative experience. The first such workshop was a great success and you can read what the participants wrote about their experiences here.

If your budget allows I invite you to make time to attend one of these events:

  • Access extraordinary states of mind simply by drawing with pencil, straightedge & compass and adorning what you’ve drawn with natural materials.
  • Move beyond talk into life-changing transpersonal experiences in a safe space where you can connect with your own inner-healing intelligence.
  • See how everything around you is in a very real way interconnected by perceiving all-pervasive patterns of geometric order surrounding our lives.
  • Learn to properly draw with compass and straightedge even if you have never drawn before. Everyone can do it!
  • Enjoy a deeply rewarding sensation of satisfied completion with every drawing.
  • Use the traditional tools of the Tibetan Masters—chak-purs.
  • Interact with the archetypal forces operating just below the psyche’s surface.
  • Harness the power of mandala to move beyond the thought stream of the mind.
  • Feel group connectedness when co-creating a large mandala.
  • Honour the impermanence of all things through a letting go / gratitude session.
  • Give yourself time, space and permission to set aside the outside world for one weekend and explore geometry in a way that can facilitate a reconnection with your essential centre.

I’ve had to close comments on this site due to increasing wordpress comment-spam. If you have any questions or comments please feel free to contact me directly.

Trip to UK & Ireland

I recently returned from a three-week exploration of England, Scotland and Ireland. It was gratifying to finally see some of the locations in my films in person and explore many others I haven’t yet covered in my work. My wife and son made the trip with me, and we three are still digesting the experience and feeling spaced out with jet lag.

We drove close to two thousand miles and I did all the driving. This was my first time driving from the right seat of the car down the left side of the carriageway and by the end it felt natural. However it took a while for me to retrain my reflexes so driving became autonomic. I kept wanting to get into the car on the wrong side in the parking lot and to follow the lane marker on the left (wrong). The process made me aware that driving is largely a subconscious activity.

I had to watch myself when I returned to Canada that I didn’t continue using my mirrored mental pathways. Sure enough, when I got in my car at the airport and drove off, my body/mind wanted to drive on the left and I had to fight it for a moment until the pathways flipped back. My driving experience reminds me of a less extreme version of the Backwards Brain Bicycle.

It was a bit frightening picking up a car in central London with everything reversed compared to what I was used to. Thank God the pedals aren’t also reversed or I would have been completely lost. I jumped right into the urban frying pan at rush hour and thankfully didn’t get burned.

I wish we had more roundabouts in North America. Roundabouts mean you usually don’t have to stop at intersections, just slow and time your entry right. How cool it that? I have collectively wasted years of my life at red lights in North America.

Larger traffic circles with multiple lanes require that you to pick the correct entry lane depending on which exit you plan to leave the circle. In the UK and Ireland, stay right if you want to leave the circle at the second or third exit. Some very large traffic circles have exits written on the ground in your lane—this makes conflict-free interchanging easy. Not sure where to exit? Just go around again.

How did we ever get around without smartphones? I sure remember using fold out paper maps—and Thomas Bros spiral bound maps to get around California—but it’s amazing how much GPS (read “location-based services”) has changed our lives in helpful, practical ways.

20th century map

20th century map

Google maps knows just when you will arrive, even with all the traffic—it is a bit spooky. Apple/Google/Big Brother tracks your every move and knows when and where you made it. Location based services are helpful and terrifying at the same time, putting any thinking person into a state of cognitive dissonance.

21st century map — from blog post by Elizabeth Flux

21st century map — from post by Elizabeth Flux

The same GPS data by which we are constantly tracked has enabled much of my work on Secrets In Plain Sight by providing us all with tools such as Google Earth that I have used to uncover accurate long distance patterns in a way that is impossible with paper maps. For example:

Giza is the golden location on the longest possible distance on land

Giza is the golden location on the longest possible distance on land

London is expensive. Partly it’s the fact that about 2 Canadian dollars = 1 pound Sterling. London was affordable only if I forgot to double the price of everything. We had 25 pounds in two old bills from 15 years ago that Temple Church wouldn’t accept as payment for entry, except they said the Bank of England would exchange it. I guess the “Mother of all Banks” is bound to accept legal tender no matter how old it is. I had the same problem with Lira in Italy in 1997 but couldn’t get into the bank in Rome because the revolving door was also a locking metal detector and my legs are made of titanium, but that’s another story.

So we went to the ground zero of fractional reserve banking in the City of London, the old financial capital of the world. A solicitor we met on the tube said that most all the banks moved to Canary Wharf about 10-15 years ago (clustered around One Canada Square). He was kind enough to walk us to St. Paul’s from the tube station where we got our bearings on the City.

I had to show my old currency to gain entry to the Bank. Trading in old bills was the only thing people seemed to be doing at the Bank of England—some Russians had piles of money they were upgrading. You have to return old money magic to the gnomes at its source who upgrade it into the current magic, the “currency.” I was amazed to discover that the pavement in the main lobby of the Bank of England is emblazoned with the following hermetic diagram of the human energy system.

Main lobby floor in Bank of England, City of London

Main lobby floor in Bank of England, City of London

At the friendly solicitor’s suggestion we had lunch in Leadenhall Market, which my wife discovered later was the Harry Potter film location for Diagon Alley.

Leadenhall Market

Leadenhall Market

Leadenhall is immediately adjacent to architect Richard Rogers’ famous inside-out Lloyd’s Building I remember from studying architecture at the University of California. Historic England says Lloyd’s is, “Universally recognised as one of the key buildings of the modern epoch.” I watched people going up and down in the glass elevator while eating a burrito in Diagon Alley. Interesting mythic/modern contrast, paralleling two of Jean Gebser’s structures of consciousness (he called them mythic and mental; Ken Wilber later rebranded them mythic and modern).

The Inside Out building

The Inside Out building

Here is what the Mother of all Banks at the top of the London street pyramid looks like from the outside. It’s quite the temple of money magic.

The mother of all banks

The mother of all banks

The base of the City’s street pyramid rests on the London Stone, the Umbilicus Londinium set in place by the Romans about 2 millennia ago.

LondonStone

The next day we went to Westminster Abbey, and by sheer luck we were there when the Queen was opening parliament with her speech / bizarre ritual. I managed to step in the Queen’s horse’s excrement (yes, that’s as close as one can get) while crossing Parliament Street because I was looking at all the soldiers with bayonets in front of the Cenotaph, wondering what the heck was going on. I was able to snap the above photo in 2 secs before a policewoman told me to move along. The sidewalks were packed with people.

Parliament Street looking towards Cenotaph

Parliament Street looking towards Cenotaph

The Sun shines right down Parliament Street at 11:11 am on 11/11 (Remembrance Day), matching the perspective in the above photo (see my Anthology p598). Thanks to Tina Silver for that discovery.

I stuck my hand through the Parliament’s gate and snapped this on my smartphone:

Eye and Benben

Eye and Benben

It was amazing standing at the base of Cleopatra’s needle, 3333.33 km from where it stood in Alexandria for 2 millennia. Deep planning indeed!

Scott Onstott at Cleopatra's Needle London

Scott Onstott at Cleopatra’s Needle London – photo by Jenn Nelson

This post is already getting long and I’ve only covered highlights of the first two days! Here are some of the major locations of my trip in pictures. There is a story about each one. Maybe I will integrate some of these in another book or video someday, but first I must get over jet lag and digest the rich experiences of this trip.

Temple Church London

Temple Church London

Paternoster Square

Paternoster Square

That’s the Shard on the right, tallest building in Europe right now.

View from the Millennium Bridge

View from the Millennium Bridge

The Shard is 66.66 nautical miles or 123454.321 meters from Silbury Hill, tallest prehistoric mound in Europe.

Silbury Hill

Silbury Hill

Stonehenge

Stonehenge – photo by Jenn Nelson

Glastonbury Tor

Glastonbury Tor – photo by Jenn Nelson

Chalice Well

Chalice Well, Glastonbury

"The Avenue" of standing stones near Avebury

“The Avenue” of standing stones near Avebury

Avebury

Avebury ring and its ancient standing stones

The Circus of Bath

The Georgian Circus of Bath

View from Edinburgh Castle

View from Edinburgh Castle

Rosslyn Chapel - from interview by Paul Troy

Rosslyn Chapel – photo from interview by Paul Troy

Scottish Highlands

Scottish Highlands – photo by Jenn Nelson

Urquhart Castle on Loch Ness

Urquhart Castle on Loch Ness

Sueno

Pictish Sueno’s Stone near Findhorn, Scotland – photo by Jenn Nelson

Uisneach, Ireland

Uisneach, the sacred centre of Ireland

The Catstone of Uisneach, aka Umbilicus Hibernia

The Catstone of Uisneach, aka Umbilicus Hibernia

Forgotten dolmen on peat mountain overlooking Lough Derg, Ireland

Forgotten dolmen at sunset on peat mountain overlooking Lough Derg, Ireland

The Cliffs of Moher on the west coast of Ireland

The Cliffs of Moher on the west coast of Ireland

Newgrange, Ireland

Newgrange, Ireland – photo by Jenn Nelson

Sphere within Sphere at Trinity College, Dublin

Sphere within Sphere sculpture by Arnoldo Pomodoro reflecting my family at Trinity College – photo by Jenn Nelson

Many thanks to Tina Silver, Mark Golding and Helena Skoog, Peter and Nikki Garrett, Paul Troy, Jantien Vandenberg and her partner Mark, and Geoff Fitzpatrick, each of whom we spent time with on location. You enhanced our experiences of England, Scotland and Ireland in many untold ways.

The Metre

The metre (spelled meter in United States) was introduced by the First French Republic in 1799. It was originally defined to be one ten millionth of the distance (10,000 km) between the North Pole and the Equator through Paris.

Kilometre_definition555

Since then the metre has been defined variously as the length of certain prototype objects, the wavelength of a specified light spectra, and since 1983 in terms of the speed of light, which is itself defined by the metre and the second.

The first metre, Paris; Image Ken Eckert CC BY-SA 4.0

The first metre, Paris; Image Ken Eckert CC BY-SA 4.0

I discovered that the metre exposes something amazing about the absolute size of the Earth and the Moon. The Earth’s polar diameter is 10,000 times the square root of the divine proportion (aka golden ratio, approximately 1.618033989) in kilometres. The combined polar diameters of Earth and Moon are 10,000 times the divine proportion in kilometres. My book The Divine Proportion delves deeply into this amazing ratio which is symbolized by the Greek letter Ф.

Earth-metre

The reason the above correlations are only 99.97% accurate is because when GPS satellites became operational in the 1990’s we learned that one ten millionth of the distance between the North Pole and the Equator is not exactly 1 m as extrapolated at the end of the 18th century, but is actually 1.000197 m.

In 1973, John Michell published in The View Over Atlantis that the Great Pyramid’s slope of 51°51′ encodes the proportions of the Earth and Moon. The base of the pyramid in the following diagram corresponds with the Earth’s equator. The apex of the pyramid coincides with the center of the Moon when the Moon is drawn tangent to the Earth as shown. The sole surviving ancient wonder of the world therefore encodes the proportions of Earth and Moon in its aeons-old architecture.

Earth-GP555

I discovered that the Great Pyramid’s location on our planet is divinely proportioned with respect to the longest possible distance on land, based on the global sea level since the last ice age.

Published in The Divine Proportion in miles

Published in The Divine Proportion in miles

In my Secrets In Plain Sight Volume 1 film, I pointed out Webb’s discovery that the Great Pyramid’s latitude (29.979245.8°N) precisely encodes the speed of light (299792458 metres per second).

The Great Pyramid's latitude encodes the speed of light

The Great Pyramid’s latitude encodes the speed of light

The metre is officially defined as, “the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second,” and the latitude 29.979245.8°N makes me wonder if the pyramid was originally designed as a shining mountain of metrology? The metre might have merely been rediscovered in relatively recent times (circa 1799) as an obvious method of rationalizing the circumference of the Earth.

The fact that the light speed latitude and the Ф point along the longest distance on land should coincide is nothing short of miraculous.

Author Gary Osborn discovered that the location of the so-called granite “coffer” within the “King’s Chamber” inside the Great Pyramid is the focus of a golden spiral (based on the divine proportion). This explains why the King’s Chamber is offset with respect to the centerline of the pyramid. Read on to see how this supports the notion that the coffer may have been used as an resonation chamber for the human body.

Gary Osborn ©2005

Gary Osborn ©2005

I speculate that they put salt water in the coffer and the ancient initiate floated in the warm dark like people do in modern isolation tanks. It would be the ultimate place for the human body to resonate with the pyramid mountain, the Earth’s landmass and the Earth-Moon system.

Consider also that the human body is divinely proportioned with respect to the scale of all things. We are literally the bridge between macrocosm and microcosm.

Flinders Petrie meticulously surveyed the Great Pyramid in the 19th century. See page 27 of The Pyramids and Temples of Gizeh for Petrie’s measurements of the King’s Chamber. Petrie measured everything in inches but if we convert to metres, something amazing pops out—the King’s Chamber encodes divine proportions directly in metres.

The dimensions of the King's Chamber encode the divine proportion in metres

The dimensions of the King’s Chamber encode the divine proportion in metres

The base circumference of the King’s Chamber is (2 x 5.24) + (2 x 10.47) = 31.42 m. 10π is approximately 31.42. Thanks to Leo Nolette for spotting this connection. So the King’s Chamber encodes the ratio of a circle’s circumference to its diameter in metres and of course base 10.

I have created numerous illustrations of the Great Pyramid’s mysteries over the years and published many of them in my books. This one shows how the pyramid “squares the circle” and how the mathematical constant e (Euler’s number) is encoded by comparing the pyramid with an inscribed equilateral triangle.

This one shows how the human body resonates with the divine proportion and the pyramid form.

PyramidHuman555

This one shows how the Sphinx was located in proximity to the G2 pyramid (neighboring the Great Pyramid) to purposefully encode a single geometric template based on the vesica piscis and the divine proportion. This setup creates a sympathetic resonance as above, so below.

“Through the phenomenon of cosmocization…the human becomes microcosm of the house or temple, just as the house or temple becomes microcosm of the cosmos. The inverse is true as well: the cosmos is macrocosm to the house, the house is macrocosm to the human, and the human is, therefore, in profound interrelationship with the cosmos.” -Beverly White Spicer

Cosmocization is what I referred to in the cover of my most recent book, Tripartite.

Tripartite-3D-Book-Cover555v2

In 1999, Osborn showed the correspondence between what I’m now calling the Cosmocization Chamber (aka King’s) and the third eye at the center of the human brain.

Gary Osborn ©1999

Gary Osborn ©1999

Osborn later connected the physiology of the third eye to the ancient Eye of Horus symbol, which he called the Gate of God.

Brain-Eye

The third eye is the mind’s eye, the Gate of God, the locus of enlightenment. This reminds me of a quote from my essay on Light.

“If we consider the word light as a euphemism for the word knowledge, our definition of the word light is then clarified. We then find that light is knowledge and we are all on the path of true knowledge.

Now, knowledge as listed in the dictionary comes from the French root word knowen, to know; (1) having understanding gained by actual experience, or practical experience; (2) the state of being aware of something or of having information; (3) the act of understanding: clear perception of truth; (4) something learned and kept in mind.

If we interchange the word knowledge for the word light we have the true Rosicrucian meaning…If light is knowledge, and knowledge is born intuitively, then the “Path of True Light” is not outward but inward.” –Ronald Cannata (1971)

The Great Pyramid elegantly encodes great truth using the universal language of proportion and metrology. The way that it does so on multiple simultaneous levels is truly illuminating. We still have much to learn from this secret in plain sight.

Light

What is Light?

Light_dispersion_conceptual_waves350px

“A photon is an elementary particle, the quantum of light and all other forms of electromagnetic radiation. It is the force carrier for the electromagnetic force.” -Wikipedia Photon article

Photons have no size and are detected as zero-dimensional mathematical points. However they are also simultaneously waves that extend arbitrarily, possibly infinitely, across the entire universe.

Photons travel at the speed of light—the Universe’s maximum speed—and because of this they experience no time. Photons are therefore eternal. Photons are also massless, which means they are literally immaterial—the stuff of mind, ideal.

“The massless photon mediates the electromagnetic interaction.“ -Wikipedia Elementary_particle article

This means that when one electron scatters off another, a “virtual” photon is emitted from one electron and is then immediately absorbed by the other. The virtual photon transfers momentum and carries the force from one particle to the other. Light is therefore what gives matter the quality of solidity. Material is everywhere mediated by eternal immaterial light.

Light mediates electromagnetic interaction

Feynman diagram showing photon as the force carrier between interacting electrons

Light mediates the electromagnetic force which drives chemistry and ultimately life.

The electromagnetic force [and thus, light] plays a major role in determining the internal properties of most objects encountered in daily life. Ordinary matter takes its form as a result of intermolecular forces between individual molecules in matter. Electrons are bound by electromagnetic wave mechanics into orbitals around atomic nuclei to form atoms, which are the building blocks of molecules. This governs the processes involved in chemistry, which arise from interactions between the electrons of neighboring atoms, which are in turn determined by the interaction between electromagnetic force and the momentum of the electrons. -Wikipedia Electromagnetism article

Last year scientists discovered a way to turn light into matter.

“The collider experiment that the scientists have proposed involves two key steps. First, the scientists would use an extremely powerful high-intensity laser to speed up electrons to just below the speed of light. They would then fire these electrons into a slab of gold to create a beam of photons a billion times more energetic than visible light.

The next stage of the experiment involves a tiny gold can called a hohlraum (German for ‘empty room’). Scientists would fire a high-energy laser at the inner surface of this gold can, to create a thermal radiation field, generating light similar to the light emitted by stars.

They would then direct the photon beam from the first stage of the experiment through the centre of the can, causing the photons from the two sources to collide and form electrons and positrons. It would then be possible to detect the formation of the electrons and positrons when they exited the can.” –Source

Hohlraum or golden room of light

The golden hohlraum where light can be transmuted into matter in a laboratory

It is fitting that an empty golden room is the crucible where light can be transmuted into matter. The word chemistry comes from alchemy after all.

Einstein’s famous equation E=mc^2, rewritten E/c^2 = m says light’s intensity divided by its velocity squared is what we call mass, the basis of matter. Matter is literally made of an immaterial, dimensionless, chargeless substance—light. Matter is light turned inward. Materialism is seen through when you realize that all matter is actually made of, and continually mediated by, immaterial light.

Energy-Mass555

“Light as the element with atomic number 0 is entirely compatible with the Big Bang Singularity. Hydrogen as the element with atomic number 1 is not. It’s self-evident that Big Bang theory implies that material, extended atoms come from immaterial, unextended atoms (i.e. atoms of light). Unextended, dimensionless, massless light atoms can constitute a Singularity, the necessary condition for a Big Bang. Extended, dimensional atoms with mass cannot be consistent with a Big Bang Singularity. They can be produced by a Singularity event (a Big Bang), but they cannot be part of the Singularity, whereas “zero” atoms (photonic atoms) emphatically can.

The introduction of light atoms (zero atoms) into science makes complete sense of the Big Bang at a stroke, and renders it an analytic, scientific and mathematical event and not some miraculous, random explosion of existence from non-existence, as science irrationally claims.

One simple change to the head of the periodic table can alter humanity’s entire conception of reality – because that change takes science away from empiricism, materialism and physical (dimensional) mathematics, to rationalism idealism, and ontological (dimensional AND dimensionless) mathematics.” –Causation and the Principle of Sufficient Reason by Mike Hockney

By putting light with atomic number 0 together with the full-width periodic table (that doesn’t breakout the Lanthanides and Actinides to save space as is usually depicted), we see the symmetry that light stands alone as the 33rd column—the fountainhead of all matter.

The Home of The Supreme Council, 33° has 33 outer columns which are each 33' high.

The Home of The Supreme Council, 33° has 33 outer columns which are each 33′ high.

“If we consider the word light as a euphemism for the word knowledge, our definition of the word light is then clarified. We then find that light is knowledge and we are all on the path of true knowledge.

Now, knowledge as listed in the dictionary comes from the French root word knowen, to know; (1) having understanding gained by actual experience, or practical experience; (2) the state of being aware of something or of having information; (3) the act of understanding: clear perception of truth; (4) something learned and kept in mind.

If we interchange the word knowledge for the word light we have the true Rosicrucian meaning…If light is knowledge, and knowledge is born intuitively, then the “Path of True Light” is not outward but inward.

Light is Knowledge! Knowledge is Truth! Truth is Light!” –Ronald Cannata (1971)

Light: as above so below

Light: as above so below

Light may have a role beyond mediating the electromagnetic force in biology in terms of biophotons. It’s controversial but plant and animal cells appear to communicate with light. I think we will understand this better once people develop optical computers.

“How do I know where creation comes from? I look inside myself and see it.” -Lao Tzu

Excuse me if I make light of enlightenment:

Ontological Math 3.3

Ontological Math 3.3

“There was a young fellow from Trinity
Who took √∞.
But the number of digits
Gave him the fidgets;
He dropped Math and took up Divinity.” -George Gamow

Symmetry 33

Symmetry 33

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.

FinsStructureConstant-detail2

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

Pi-approximation2

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

Phi-ve-math2

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.” –PhysOrg.com

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

Pyramid-Ontology2

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

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