The following essay excerpts are re-printed at the Memorial Website of Jerry Wayne Jeffries
by special permission of the Author, Jonathon Earl Bowser

 

The Perfection of Number

 

The atomic number of carbon - the element of life - is six, and its crystal structure is hexagonal. The bible describes God creating the universe in six days (or rotations of the earth), and resting upon the seventh. This became the model for the western week: six days of activity enclose a passive seventh day in the centre. Such human-made reckonings are a reflection of a simple geometric, or Absolute Truth: six perfect circles (or rotations of a line) arranged side by side in a larger perfect circle, exactly circumscribes a seventh circle of equal size. That is, a sixfold structure surrounds the master seventh component (or creator) in the center.

Why "lucky" seven should have been the number of the Divine in so many ancient belief systems all around the world is an interesting question. There are some important human perceptions that are informed by that number. Light, the most enduring symbol of the creator, is composed of six visible colors: red, orange, yellow, green, blue, and violet (the primary and secondary colors of the rainbow), which when combined make the glorious Seventh - White. All that we will ever see is a combination of these seven colors (black is the absence of light, and not a color). And yet, they are but one octave in a vast scale of different frequencies of light - from radio waves to gamma rays - that we will never see. Fortunately, there are other forms of vibrations, scales of frequencies we experience in a different way, that we can perceive in greater magnitude.

In ancient times, one and two were not considered "real" numbers. One is the origin of all numbers, that divides into two. And from those two derive all things. So three and four are the first "real" numbers. Three (the Trinity) is the number of the spirit, the number of the transcendent, the number of God. Four (the points of the compass, the seasons, the states of matter) is the number of the body, the number of the immanent world. And these two numbers - 3 and 4 - have an interesting relationship. 3 + 4 = 7, and 3 X 4 = 12. This simple 7 - 12 arithmetic relationship is the basis for all musical structure. Within the 12-tone chromatic scale, is the better-known 7-tone diatonic scale: Do Re Mi Fa Sol La Si... The final "Do" - vibrating exactly twice as fast as the first "Do" - begins a new octave. From ancient times this 7 - 12 relationship of music has been regarded as a way for the voice of the divine to penetrate into this existence. Like few other things we will experience in this life, these ordered mathematical ratios - given substance as harmonic inter-relationships between seven musical notes - pass effortlessly through our life-hardened exteriors, and can fill our weary hearts with rapture.

And there are some very unusual, purely mathematical properties of the number 7: 1 x 2 x 3 x 4 x 5 x 6 x 7 and 7 x 8 x 9 x 10 both equal 5040. And 1 x 2 x 3 x 4 x 5 x 6 and 8 x 9 x 10 both equal 720. Whether the number 7 is included or deleted, it acts as the pivot or center of the Dekad (the sacred Tetrakus of the ancient Greeks) - the very foundation of our decimal system of mathematical notation. No other number does this. Of all the polygons in the Dekad (triangle - 3, square - 4, pentagon - 5, etc.), only the heptagon cannot be captured precisely. The angle which specifies its construction is 51.42857142857..., an infinitely repeating decimal that can only be approximated - it does not exist with precision in the real world. (Although the angle of the Great Pyramid is VERY close approximation - off by less than 1 sixth of one degree!) Its place shall only ever be in the Eternal Transcendent realm of the Ideal. In fact, any number (excluding multiples of 7) divided by 7 results in the same infinitely repeating set of six numbers: 1 divided by 7 equals 0.142857142857..., and 279 divided by 7 equals 39.857142857..., etc. Six numbers forever in motion around, but never quite reaching, the elusive, transcendent number they seek to quantify. It is this mysterious, evanescent quality that led the ancients to associate 7 with the Sacred Virgin.

 


 

Music is mathematics made audible, because it consists of precise numerical relationships of frequency (a vibrating string divided exactly one third to two thirds produces the interval called a perfect fifth, etc.). One octave consists of 12 notes (and contains the familiar scale of 7 tones: do re me... etc.). The color-wheel (consisting of primary, secondary, and tertiary hues) has 12 colors. The double helix of Life, DNA, consists of 4 alternating base-pairs (adenine-thymine, and guanine-cytosine) that spiral upward around a vertical axis. In one rotation, there are 12 chemical steps. (But, of course, the ancients could not possibly have known this.)

Against the fixed stars of the heavens, the ancients saw 7 points of light that were not fixed, and appeared to move about the sky in whirling patterns when observed over many successive nights. In Greek, they were called "wanderers" (planetes). Mercury, Venus, Luna, Mars, Sol, Jupiter, and Saturn. 7 Celestial Deities representing 7 celestial spheres revolving through the 12 constellations around the earth (which corresponded nicely with the 7 tone scale within the octave of 12 notes). The supreme Deity in this pantheon of Gods was Jupiter (Latin form of the Greek Zeus). Its orbital duration is 12 solar years.

 

 

Mysterious Number 7

Babylonian Ziggurats had seven steps, as did the Temple of Solomon. The angle of the Great Pyramid is that of a seven-sided polygon. Rome was built on seven hills. The Tree of Life has seven branches, six around one trunk that is the axis of the universe. The ancient symbol of the Trinity, Borromean Rings (three rings which mutually interlock precisely through their centers), has seven sections - six around one in the center. There are seven stars in the celestial crown of the Virgin Mary, like the seven rays of Justice that shine from the head of Liberty. In Persia there were seven gates that lead to Glory of Mithras. Ishtar in Babylon and Isis in Egypt both passed through seven gates in the underworld to effect the resurrections of their slain husband-deities. Buddha seeks salvation for seven years before circling the Bodhi Tree seven times, thereby achieving enlightenment. The world Mountain has seven sides, each one facing one of the seven continents. In Tibet and Japan, the souls of the dead are said to tarry for 7 x 7 days before departing to distant, unknown realms. The constellation Ursa Major (the Big Dipper), by which early navigators found the north star - and thus their way home - consists of seven stars.

The ancients had a different, less-informed view of the structure of our solar-system. Their geocentric view reckoned seven worlds revolving around the earth: Mercury, Venus, Luna, Sol, Mars, Jupiter, an Saturn. We now know of course that they were entirely mistaken - nine planets, revolve around the sun - but this celestial appearance of seven was of enormous significance. From this perception of Seven Celestial Spheres came the idea of Seven Heavens (six outer heavens with the creator God in the center), and our reckoning of the week (six days of work around the Sabbath). Six around One.

North American Indians see the cosmos as consisting of seven domains: up, down, forward, backward, left, right, and the center where one stands. Six around One. This motif is repeated in dice, six-sided structures with an implicit recognition of the seventh: opposing sides always total seven (1 - 6, 2 - 5, 3 - 4). And when rolling two dice, "Lucky Seven" is statistically the most probable of all possible outcomes.

There are Seven Pillars of Wisdom, seven Wonders of the Ancient world, seven circumambulations around the Ka'ba in Mecca, seven Liberal Arts, etc., etc., etc...

This is but a tiny sampling of the available list; surely there is no more venerated number than seven. But what is the origin of our fascination with this number? Is it all a function of the seven day phase of the Moon, or is there something else at work here...something biological?

Numerology and Sacred Geometry are endeavors most arcane. Much of it is quite arbitrary, and therefore not relevant to an investigation into the biology of spiritual insight. Are there genuine examples of religious intuition that have been subsequently validated by scientific inquiry? I believe there are.

For instance: Plato delivers a mind-numbing barrage of numerological data in his brilliant book Timaeus, all of which, he assures us, is derived from far more ancient sources. Among many interesting observations, he claims that odd numbers are masculine, and even numbers are feminine. 2500 years later microbiology determines that, in humans, genetic material is carried by chromosome pairs (one of maternal and the other of paternal origin): 22 pairs of autosomes, and a final two, for a total of 46. In women, these final two chromosomes are a matching pair of x chromosomes (even); in men, these final two chromosomes are a none-matching pair of one x and one y chromosome (odd).

I believe this little co-incidence is a genuine example of what might be called "transcendent vision": the ability to "see" or apprehend some part of a larger, invisible Truth - even though the Truth is not understood in its entirety. You might reasonably think that Plato had a 50/50 chance of getting it right, but 2500 years later, we still think - in every part of the globe - of even numbers as feminine. Every subsequent tradition that could have chosen differently doubles the odds against the right choice. This did not happen: somehow we have always known that even numbers are passive (and therefore feminine), and odd numbers are active (and therefore masculine). I think that is precisely what is at work in the prevalence of the number seven - the first and still most ubiquitous sacred number. To be moved by seven-ness is to apprehend an unknown part of ourselves and our place in the universe.

There are six colors in the spectrum, and in union they generate the master seventh color, white. Six around One. There are seven tones in one octave of the diatonic musical scale (do-re-me...), and when the Pythagorean "spiral of fifths" (a method of dividing a musical string in successive 1/3 - 2/3 steps, by which the musical scale was first discovered) is extended for seven octaves, the full chromatic scale of twelve tones is revealed. We have five senses. And while the taste of a fine Bordeaux, the smell forest meadow, or the touch of a woman's breast may all be sublime, we do not call such expressions of perfection art. It is only through the senses of sight and sound that we experience art. And all the art we shall ever see or hear is a product of these two seven-fold realities: the spectrum of light and the octave of sound.

It is the mathematical and geometric properties of seven that are perhaps the most interesting. The ancients believed there were only 10 numbers (as does our modern decimal system, for that matter); everything else is a mere repetition of the "true" numbers, but at a higher plane. And they knew that polygons of number contained within the "dekad" could be constructed with only three simple geometers tools: stylus, compass, and straightedge. By using the geometry of the Vesica Pisces ( two equal circles which pass through each others' centers), the triangle (angle - 120 degrees), square (angle - 90 degrees), pentagon (angle - 72 degrees), hexagon (angle - 60 degrees), octagon (angle - 45 degrees), nonagon (angle - 40 degrees), and decagon (angle - 36 degrees), could all be drafted with perfect precision without protractor measurement of any kind. The conspicuous exception was the heptagon. The angle that specifies its construction is 51.42857142857... This infinitely repeating decimal means that only an approximation of this polygon is possible; it cannot exist with precision in the real world. Its infinite quality places it external to the world, in the transcendent domain of idea.

The problem here is that we are seeking to divide 360 (the degrees in a circle) by seven, and that simply cannot be done. In fact, any non-whole divisor of seven will yield the same set of six numbers (142857...) in the decimal expression of the remainder; six numbers forever revolving around the transcendent seventh number they seek to quantify. Six around One. Seven is unattainable, immutable, eternal. Its infinitude gives seven an otherworldly purity, hence its universal association with the divine dimensions of being forever beyond the grasp of the known world. (Because seven-sided structures cannot exist with precision, there are no seven-sided crystals - large-scale projections of atomic lacework - in nature. But there are, however, seven "kinds" of crystals: cubic, tetragonal, orthorhombic, monoclinic, triclinic, rhombohedral, and hexagonal.)

You might reasonably suppose that the 360 degrees of a circle is an artifact of human design; this is, of course, correct. If those ancient geometers had reckoned a circle to consist of, say, 210 degrees, we would then be able to draft a perfect 7-sided polygon. But all other polygons not consisting of a number of sides divisible by 7 would then be infinite: we would only be able to measure 7-sided angles! All our buildings would have 7 sides, instead of 4. There would be no cardinal directions, because we could not measure four-ness. Mariners would never find their way home, and without the requisite trade and exchange of ideas, civilization would never begin.

Twelve-based geometry is far more versatile than seven-based geometry, and that is why it was chosen. Seven-ness or Twelve-ness. You can know one or the other, but not both. As with the ratio of a circle's radius to its diameter (the irrational number pi: 3.14...), or of a fundamental particle's position and momentum, we are presented here with an irreconcilable paradox: what very much appears to be a unity in nature is in fact a duality, and one half of this apparent unity does not exist in our universe. If twelve-ness is the proper way to reckon the dimensions of the universe - and it is - then where is seven-ness?

Six around One. This is (as mentioned in my essay "Order and Chaos") a reflection of a simple geometric Truth: six circles of equal size arranged in a perfect circle exactly circumscribe a seventh circle of equal size in the center. The center circle functions like the master template for the six-fold, external domains beyond. The center is simultaneously the circumference, and the circumference is made in the image of the center...

 

The Seven-Year Cycle

It is said that the cycle of events in a human life runs 7 years, in accord with the duration of time nature requires to replace every atomic particle in the human body. (This is apparently true: by the end of a seven year cycle, every electron and proton in your body has been replaced by another particle, and nothing of your former self remains; even the brain is entirely remade, so where is the "me" that lives behind my eyes, if it is not in the material of which I am composed?) Each new 7-year period of life will present different challenges than the preceding one. I'm certain that many lives are not in accord with this mysterious 7-year cycle. But mine is. Exactly.

Age 7 - I am given my first taste of real freedom and adventure: my parents give me a bicycle. Thus begins a 21 year relationship with broken bones and emergency-room nurses...

Age 14 - I enter this year with a boy's body weight of 80 lbs., and leave it - only 12 months later - with a man's body weight of 160 lbs. Now I can do some real damage...

Age 21 - I graduate from Art School, move out of my parents house, venture out into the world, move in with my first love, and I do not have a clue what to do...

Age 28 - I suffer the last of an unfortunate series of serious injuries, and thus ends my relationship with the suture-and-plaster men. Perhaps I am meant to do something more creative...

Age 35 - I leave the city and province where I grew up, to live in a place where "www" means "windswept winter wasteland." And my new life with Elisabeth (a Veterinarian) will take me many other places even farther away before I get back to my mountain home again...

 

A Sixth Sense?

Are such seven-fold reckonings real, or are they manufactured by the mind? Many of the interesting properties of seven would have been well known in Greco-Roman times, but, as I have shown, adoration of seven is older by at least 20,000 years. Paleolithic hunters could not have known any of the mathematically mystical qualities of seven - and yet they did. How? And how could they sense that the regeneration of life was in some way connected to the spiral - the same spiral that was revealed only in my parents lifetime to be the structure of DNA - the six around one molecule that is the regeneration of life?

There are those who will dismiss this extraordinary symphony of meaningful concords as coincidence; perhaps that helps them to sleep at night, untroubled by the bewildering mysteries of life, consciousness, and being. But these concords are not coincidence; the magnitude and symmetry of the alignments is too great to be mere chance. They represent, in fact, what would be a statistically impossible coincidence. There is some other mechanism at work here - a rare and poorly understood mechanism of the mind.

That paleolithic shaman "saw" something; a real-world thing apprehensible by the mind, but invisible to himself, and unknown to everyone else. He didn't have words to explain his vision to his contemporaries, or the benefit of scientific literacy to explain his vision in a language that would make sense in our modern technological world; so he used the only tool of communication available to him: he drew a picture and said, "What I see is like this image I have carved on this rock."

There are modern equivalents to this kind of magical insight: Newton, Maxwell, Einstein, Heisenberg, and many others in the field of science, all had a sudden apprehension of a profound truth about the cosmos. But their "visions" were easily translated into the universal language of mathematics, and thus easily communicated to the many people conversant in that lexicon. The same cannot be said of all visions apparently, and thus we cannot easily confirm their veracity. But surely it is the same mechanism of mind that apprehends these numinous truths? If Einstein could venture out into the dreamscape and retrieve a little morsel of information like "gravity bends space," why couldn't our ancient hunter have done the same? I think he did. And not only did he retrieve that information, he invented a language to communicate it: we call it symbolism.

There are approximately one billion Christians in the world today, most of whom believe - in one form or another - that Christ was resurrected from the dead. This is an audacious claim. No one alive today ever met Christ. The four men who wrote about his life (Matthew, Mark, Luke, and John), never met Christ - the Gospels were written almost one hundred years after his death. These men never even met someone who met Christ. St. Paul - the first Christian missionary, whose efforts literally invented the Church - never met Christ, although he does claim to have met the apostle Peter. (But Paul could be a bit of a crank: he also claimed that women should shave their heads - I Corinthians 11:3-10.) So here we have this spectacular historical event (it is claimed), and no one who saw it wrote it down, or even talked to someone who wrote it down. If we were talking about anything else, the whole claim would be summarily dismissed without further discussion. And yet, one billion people believe this happened. Why?

These special insights into the True nature of things are surpassingly rare. Apparently only very few are capable of this "meta-vision" (literally, to see beyond). But when a True vision is retrieved, it is recognized by many people as a True vision - even if they have not had the vision themselves. A visionary returns to the world from "parts elsewhere", shares the vision, and we accept it. We also "see" something in the symbolic language by which the vision is shared - we too can apprehend the Truth. So this meta-vision is a faculty possessed by most - if not all - of us, but in a latent, dormant form. What if we could utilize that 90% of our brains that neuroscience tells us is not used; what if we could awaken this sleeping part of our consciousness. What Truth would we see, if we could focus our six senses to the contemplation of the Numinous One in the center?

Discovery

1 cubed (1 x 1 x 1) = 1
2 cubed (2 x 2 x 2) = 8
3 cubed (3 x 3 x 3) = 27
4 cubed (4 x 4 x 4) = 64
5 cubed (5 x 5 x 5) = 125
6 cubed (6 x 6 x 6) = 216
7 cubed (7 x 7 x 7) = 343

1 cubed = 1 (1 squared)
1
1 cubed + 2 cubed = 9 (3 squared)
1 + 2 = 3
1 cubed + 2 cubed + 3 cubed = 36 (6 squared)
1 + 2 +3 = 6
1 cubed + 2 cubed + 3 cubed + 4 cubed = 100 (10 squared)
1 + 2 +3 + 4 = 10
1 cubed + 2 cubed + 3 cubed + 4 cubed +5 cubed = 225 (15 squared)
1 + 2 +3 + 4 + 5 = 15
1 cubed + 2 cubed + 3 cubed + 4 cubed +5 cubed + 6 cubed = 441 (21 squared)
1 + 2 +3 + 4 + 5 + 6 = 21
1 cubed + 2 cubed + 3 cubed + 4 cubed +5 cubed + 6 cubed + 7 cubed = 784 (28 squared)
1 + 2 +3 + 4 + 5 + 6 + 7 =
28

And these bold numbers (1, 3, 6, 10, 15, 21, 28) are the series of triangular numbers...

(End Excerpts)


 

 

 

Life is changed, not taken away.
To live in hearts we leave behind is not to die.

 

 


 
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