N=50 V=6
Circular Pi
Stonehenge Mandalog,
by Iona Miller, 1981, Aion Magazine
Rational pi makes the perimeter of the circle an integral number of the times the length of the radii.
Rational pi is involved in the essential structure of number.
Precession 2012 * Stonehenge * Book of the Law * Ancient Metrology * Number Dynamics
by Iona Miller, 1981, Aion Magazine
Rational pi makes the perimeter of the circle an integral number of the times the length of the radii.
Rational pi is involved in the essential structure of number.
Precession 2012 * Stonehenge * Book of the Law * Ancient Metrology * Number Dynamics
Stonehenge & Cosmic Order
METROLOGY - Megalithic Number Canon: Stonehenge represents the womb of Nuit (56), the Ouroborous Serpent of the Milky Way with the constellation Draco and the Celestial Pole at the center of the inner circle. Stonehenge is an example of ancient measurement and fractional integration, including a solar-lunar calculator marking Dragon's Head & Tail, 56-year cycle of eclipses and Solstice points. The movement of stones once each year from an initial fixed position allows accurate prediction of every important lunar event for hundreds of years. This computer would need resetting about once every 300 years by advancing the stones by one space.
METROLOGY - Megalithic Number Canon: Stonehenge represents the womb of Nuit (56), the Ouroborous Serpent of the Milky Way with the constellation Draco and the Celestial Pole at the center of the inner circle. Stonehenge is an example of ancient measurement and fractional integration, including a solar-lunar calculator marking Dragon's Head & Tail, 56-year cycle of eclipses and Solstice points. The movement of stones once each year from an initial fixed position allows accurate prediction of every important lunar event for hundreds of years. This computer would need resetting about once every 300 years by advancing the stones by one space.
Cosmic Cycles of Creation & Destruction
Ancient metrology is linked to measurement of the matrix of Creation and time with "sacred" numbers: periodicity, geographical measurement (surveying), lunar orbital cycles, the solar year, planetary cycles, and the ages-long cycle of Precession through the Zodiac that changes the celestial pole over vast periods of time. It is the lost science of measuring the Earth and the right-angled Lunation Triangle (ratio 3:2).
There is a missing link between geometry and metrology. Twenty-eight is the minimal number of circular markers used to describe the related cycles of sun and moon. Doubled to 56 it is a minimalistic system that can be used to predict eclipses and the 12-13 new moons of the solar year. This ancient astronomical wisdom based on pure number ratios and hidden properties of numbers is over 5000 years old. For example, multiples of 108 form the basis of Indian time measurement, the Yugas and Ages.
Cosmology, horizon-based astronomy, astrology, architecture, navigation, geography, geometry, mathematics, timekeeping, writing, proportion in art, and musical notation were all related to numerical canon . The ancients encoded their knowledge of the world in their sacred monuments and texts as an esoteric code of numbers, formulas, and proportion.
Ancient state temples may have functioned as permanent repositories of standards of measures. Gods, (to whom the temples were dedicated) had characteristic numbers, from which they were indistinguishable. (In our example, 108, the Universe is also the god Brahma.) Numbers expressed qualities, not just quantities.
In the old beliefs, this code, (whose true source is lost in prehistoric antiquity), is always alleged to have a divine origin, from the gods or a god-like man. Lore relating to sacred words or phrases arose, because letters and numbers were interchangeable or alphanumeric. The code arises naturally from the inherent structure of arithmetic. This code emphasized certain key numbers, which were seized upon by different cultures.
Prime numbers figure prominently in the measuring and numerical canons of ancient and modern times. Ancient metrology is the science whose evidence is encoded in the sacred dimensions of such cosmic image models as the Pyramids and Stonehenge, earthly monuments oriented to the heavens. The numerical code lies behind the layouts of temples and cities and systems of measuring time.
In fact, metrology was the basis for development of both philosophic and scientific attitudes. The divine order of the universe was the central idea of the ancient world, and all belief-systems were enmeshed with it. Metrology provided the foundation of the systematic rational vision of the world. Cosmic order embodied in metrology was the fundamental aspect of ancient thought. Number mysticism was the essential basis of most of their knowledge.
Of course, information about the Universe has always been there, but its availability is limited to those prepared to receive or decode it. Ancient cosmologies were not only models of the physical universe, but representations of a universal mathematical archetype. The numerical canon revealed correspondences between different orders of natural phenomena. Metrology included sacred units for measuring the Universe, units of time, space, weight, and mass (or volume).
In ancient times, the Universe meant the observable Universe. For Pythagorean and Platonist thinkers, the patterns of numerical relationships which occur in the processes of arithmetic and geometry were considered the formative influences behind all of nature's phenomena. Numerical patterns were detected in the manifestations and dynamics of nature. Behind this is a philosophy of numbers which express universal relationships.
Although usually superseded by practical arithmetic, there is much to learn from the study of the relationship of number and form. The essence of all matter is dynamic relationships. Number is the 'first paradigm,' the basic ordering principle of nature.
Many so-called "key numbers of the Solar System" are involved, because key numbers have always stood out for their unique properties. The ancients discovered them through aeons of empirical observations of cosmic cycles. They were capable of observing long-term effects, (such as the precessional cycle), with horizon-based astronomy. Their observations of the divine order were central to the core of their civilizations.
Ancient metrology does provide a clue to what numbers might be interesting to investigate. Syndex II follows the clues by using direct observation, rather than interpretation of what is there to be seen. It requires no ancient, alien, or mystical source, no occult doctrine or arcane secret, no ideology. It predicts no "end time." It is simply a graphically revealed "truth."
In Syndex, numbers do not have values according to historical significance or preconceived ideas. Rather, numbers speak for themselves since numerical progressions are often related by geometry and can graphically display their own qualities. The synergetic aspect of Syndex is showing how the first perfect number six interacts with the prime numbers, and how numbers relate to one another in discrete systems, which have relationships to one another. More: http://syndex2.iwarp.com/whats_new.html
Ancient metrology is linked to measurement of the matrix of Creation and time with "sacred" numbers: periodicity, geographical measurement (surveying), lunar orbital cycles, the solar year, planetary cycles, and the ages-long cycle of Precession through the Zodiac that changes the celestial pole over vast periods of time. It is the lost science of measuring the Earth and the right-angled Lunation Triangle (ratio 3:2).
There is a missing link between geometry and metrology. Twenty-eight is the minimal number of circular markers used to describe the related cycles of sun and moon. Doubled to 56 it is a minimalistic system that can be used to predict eclipses and the 12-13 new moons of the solar year. This ancient astronomical wisdom based on pure number ratios and hidden properties of numbers is over 5000 years old. For example, multiples of 108 form the basis of Indian time measurement, the Yugas and Ages.
Cosmology, horizon-based astronomy, astrology, architecture, navigation, geography, geometry, mathematics, timekeeping, writing, proportion in art, and musical notation were all related to numerical canon . The ancients encoded their knowledge of the world in their sacred monuments and texts as an esoteric code of numbers, formulas, and proportion.
Ancient state temples may have functioned as permanent repositories of standards of measures. Gods, (to whom the temples were dedicated) had characteristic numbers, from which they were indistinguishable. (In our example, 108, the Universe is also the god Brahma.) Numbers expressed qualities, not just quantities.
In the old beliefs, this code, (whose true source is lost in prehistoric antiquity), is always alleged to have a divine origin, from the gods or a god-like man. Lore relating to sacred words or phrases arose, because letters and numbers were interchangeable or alphanumeric. The code arises naturally from the inherent structure of arithmetic. This code emphasized certain key numbers, which were seized upon by different cultures.
Prime numbers figure prominently in the measuring and numerical canons of ancient and modern times. Ancient metrology is the science whose evidence is encoded in the sacred dimensions of such cosmic image models as the Pyramids and Stonehenge, earthly monuments oriented to the heavens. The numerical code lies behind the layouts of temples and cities and systems of measuring time.
In fact, metrology was the basis for development of both philosophic and scientific attitudes. The divine order of the universe was the central idea of the ancient world, and all belief-systems were enmeshed with it. Metrology provided the foundation of the systematic rational vision of the world. Cosmic order embodied in metrology was the fundamental aspect of ancient thought. Number mysticism was the essential basis of most of their knowledge.
Of course, information about the Universe has always been there, but its availability is limited to those prepared to receive or decode it. Ancient cosmologies were not only models of the physical universe, but representations of a universal mathematical archetype. The numerical canon revealed correspondences between different orders of natural phenomena. Metrology included sacred units for measuring the Universe, units of time, space, weight, and mass (or volume).
In ancient times, the Universe meant the observable Universe. For Pythagorean and Platonist thinkers, the patterns of numerical relationships which occur in the processes of arithmetic and geometry were considered the formative influences behind all of nature's phenomena. Numerical patterns were detected in the manifestations and dynamics of nature. Behind this is a philosophy of numbers which express universal relationships.
Although usually superseded by practical arithmetic, there is much to learn from the study of the relationship of number and form. The essence of all matter is dynamic relationships. Number is the 'first paradigm,' the basic ordering principle of nature.
Many so-called "key numbers of the Solar System" are involved, because key numbers have always stood out for their unique properties. The ancients discovered them through aeons of empirical observations of cosmic cycles. They were capable of observing long-term effects, (such as the precessional cycle), with horizon-based astronomy. Their observations of the divine order were central to the core of their civilizations.
Ancient metrology does provide a clue to what numbers might be interesting to investigate. Syndex II follows the clues by using direct observation, rather than interpretation of what is there to be seen. It requires no ancient, alien, or mystical source, no occult doctrine or arcane secret, no ideology. It predicts no "end time." It is simply a graphically revealed "truth."
In Syndex, numbers do not have values according to historical significance or preconceived ideas. Rather, numbers speak for themselves since numerical progressions are often related by geometry and can graphically display their own qualities. The synergetic aspect of Syndex is showing how the first perfect number six interacts with the prime numbers, and how numbers relate to one another in discrete systems, which have relationships to one another. More: http://syndex2.iwarp.com/whats_new.html
N=50 V=6
N=50 V=6
by Iona Miller, (c)1981
24. I am Nuit, and my word is six and fifty.
25. Divide, add, multiply, and understand.
--Crowley, from The Book of the Law
“Most importantly we have learned that from here on it is success for all or none, for it is experimentally proven by physics that "unity is plural and at minimum two" - the complementary but not mirror-imaged proton and neutron. You and I are inherently different and complimentary. Together we average as zero - that is, as eternity.” --R. Buckminster Fuller, Synergetics
CIRCULAR UNITY
Aleister Crowley, in Liber NV, proceeded to divide, add, multiply and understand, disclosing relationships of 50 and 6 to one another:
1
“4. Consider of six and fifty that 50 divided 6 = 0.12
0 the circumference, Nuit.
. the center, Hadit.
2 the world of illusion.
Nuit thus comprehends All in None.
Also 50x6= 56 = 5+6=11. the key of all Rituals.
And 50x6=300, the Spirit of the Child within.”
In the Commentaries of Al, Crowley corresponds Nuit with matter and Hadit with motion “in their full physical sense “. If we purse this correspondence in Physics, Nuit and Hadit may be seen to disclose the relationship of a field to a form of radiant wave propagation. Wave mechanics is an important fundamental from cosmological levels (Cult of the Infinite Without) to sub-atomic levels (Cult of the Implicate Within).
Matter is usually described as varying states of fluidity, going from a particle state to a wave, and then back again. David Bohm, in his recent book Wholeness and the Implicate Order, states that “Every physical situation is now characterized by wave function”. Since motion can be described as a complex wave interaction (or interference pattern), an understanding of wave phenomena in a field is fundamental for a contemporary view of the Universe.
This understanding is critical for establishing one's world view, or connection of “things-as-they-are”, and remaining consistent with current scientific research. Toward this end, we may examine the natural number sequence (integers) as a qualitative field, not merely as a quantitative series.
Nuit, as the number 56, has a relationship with all numbers:
“Nuit comprehends ALL....”
Further amplification of this relationship may be graphically represented by a spiral array of numbers along 56 radii to form the mandala shown on page 1. Joining the 56 equidistant points on the circumference yields a 56 facet circularity.
1. This is obviously a typographical error in Equinox VII; p.14, Liber XI or Liber NV. It should read 6 divided 50 = 0.12.
6. Meditate upon Nuit as the Continuous One resolved into None and Two as the phases of her being.
This quote from Liber XI (“Continuous One”); “Two could be connected to an emergent reflection sequence where the halves of the circle mirror one another.
Had is self defined as motion by the statement, “...for it is I that go.” Had is all pervasive in the number field.
Mass is neither a wave or particle in that it is continually moving from one state into the other. Hadit, then, should be symbolized as a static point (Crowley), but rather as a dynamic, Motion. This viewpoint is more consistent with current models of Quantum Mechanics.
Hadit should not be visualized as a “point” in space because how can one pin down in space something which, by definition, occupies no space. Therefore, Crowley`s attribution of the decimal point to Hadit as the center is somewhat antiquated.
Hadit and Nuit are inseparable. Nuit is the underlying field through which Hadit moves. If the field potential were non-existent, Hadit could not move. There would be no matrix.
Examination of the process described from The Book of the Law yields several important relationships between numbers, which may be seen as forming a “living body” of Nuit:
I. “Divide” : Divide a circle into 56 equal parts, the 56 radii of the proposed mandala. The reciprocal operation divides;
56 divide 360 = 0.31111111
A circle with 56 equal units to its faceted circumference has a diameter of 18 equal units, yielding rational pi ;
56 divide 18 = 3.1111111 = “rational pi”
Rational pi makes the perimeter of the circle an integral number of the times the length of the radii. Rational pi is involved in the essential structure of number.
3.1111111 divide 2520 = 0.001234567
II. “Add”: Adding the sum of the first nine multiples of 56 yields the first number divisible by all base digits: 2520.
56
112
168
224
280
336
392
448
504
2520
The equation 7 x 360 = 2520 shows an important relationship of seven to the circumference of a circle and to the inherent structure of number. There are numbers with interesting properties which may be found by adding columns from the table of sevens.
1 07 014 028 056 112
2 14 028 056 112 224
3 21 042 084 168 336
4 28 056 112 224 448
5 35 070 140 280 560
6 42 084 168 336 672
7 49 098 196 392 784
8 56 112 224 448 896
9 63 126 252 504 1008
315 630 1260 2520 5040
513 036 0621 0252 0405 Added to their reversal
828 666 1881 2772 5445 from reflective numbers
These products, which read the same forward and backward, are part of the binomial reflection sequence. That these numbers have peculiar qualities has been know since ancient times. Buckminster Fuller refers to them as Scheherezade numbers as they figured prominently in the 1001 tales of the Arabian Nights.
These mathematical operations demonstrate certain rhythmical configurations inherent in the natural number sequence. Movement through them may be viewed as a wave or pulse. The reflective numbers themselves may be seen as a particle phase as the wave/particle moves in quantum leaps.
Examination of the numbers show interesting integers recurrent in QBL. These numbers are considered significant in many of the worlds philosophical systems. As the universes of philosophy and mathematics coincide, one begins to perceive the field underlying them, a pattern is becoming recognizable.
III. “Multiply”: The binomial reflection sequence is also shown by multiples of 56. This reflection sequence is bounded by the number 2520. When numbers, spiraled along 56 radii, are graphically represented, they form a visual example of the Formula of Nuit, 0=2. The coded pattern reverses itself at the midpoint, 1260, and forms its perfect reciprocal reflection. The graphic design mirrors itself precisely ( see Fig. 2 Synchrograph A ).
1
Binomial Reflection Sequence
1 9 x 56 = 0504 909
2 18 x 56 = 1008 9009
3 27 x 56 = 1512 3663
4 36 x 56 = 2016 8118
5 45 x 56 = 2520 2772
6 54 x 56 = 3024 7227
7 63 x 56 = 3528 11791
8 72 x 56 = 4032 6336
9 81 x 56 = 4536 10890
10 90 x 56 = 5040 5445
11 99 x 56 = 5544 9999
66130
03166
69296 = 32
We may examine NV = 56 by the equation 7 x 8 = 56 . This equation is important in the magickal tradition because:
(a). Connecting every 7th radii forms the 8- pointed Star of Regeneration, a symbol of the unity of the Spirit. It also forms an octagon, the symbol for yhr central shrine of the transformed self.
(b). Connecting every 8th radii forms the 7 pointed star, whose interlacing lines generate the Seal of Babalon in its center.
45 degrees of the arc x 56 = 2520 divided by 7 = 360
IV. “And understand”: This archetypal order show by the reflection sequence has been the object of philosophical speculation since the time of Plato. Plato spoke of the number 5040 (2520 x 2 ) in his last work, Critias. In fact, this number comes at the end of a passage long considered to be a fragment of unfinished work. It may be viewed, however, as a cryptic insight which left room for one to discover “understanding”. Five times in the Book of Revelations, 1260 ( 2520 divide by 2 ) is allude to cabalistically. It also figured prominently in the works of Ptolemy and Hipparchus.
Commenting on the Eastern philosophical systems in The Myth of Invariance, Ernest McClain states:
2 2
1260 =2 x 3 x 5 x 7 shows a musical theorist how the sacred number 7 generates along with the ‘human’ 5 and the ‘divine’ 3; thus it reveals a basic lesson in mathematical harmonics suppressed in the Reg Veda except by allusion, yet essential to the understanding of ‘Tenness’ in all ancient cosmology.
1. Synergetics, Buckminster Fuller
The ten spheres of the Tree of Life show QBL as a base-10 system. Remember also that Had (h = 4, a = 1, d = 5) = 10.
2520, the “omnisychronistic module”, is the number that accommodates or synchronizes the maximum possible amount of consecutive numbers from 1 onwards. There are larger numbers, but none with as high degree a factor of divisibility.
Crowley was presented this concept in a very abstruse, symbolic form. It is clear that the passage from The Book or the Law, requires from us is a process of deciphering. This offers the possibility of understanding the symbolic on the conceptual level, and taking up a relationship to it.
V. The Auric Key: Current work in graphic representation of this ancient understanding of relationships is being researched under the name SYNDEX by Robert Marshall, et al. The first concern of “sychrographics” is “maximum information expressed via minimal graphic elements.” As QBL, CORRESPONDENCES, such as those between numbers and colors, form an integral part of the system.
Graphic representation with a 56-facet mandala discloses ordered matrices inherent in the relationships among rational numbers. For instance, the 12 “synchrostats” , (numbers divisible by 5, 6, and 7), fall into perfect quadric symmetry along the axes of the circle. This division of the circle into four parts is analogous to four parts is analogous to the four directional orientation of the Banishing Ritual. The “sychrostats” are multiples of 210 and correspond to the 12 zodiacal signs: 12 x 210 = 2520
210 = Aries
420 = Taurus
ect. through
2520 = Pisces, completing the zodiacal circle.
Thus we see that the ‘mandala of Nuit, the 56-facet circularity discloses and encloses the profound patterns of relationship inherent in the natural number sequence. It gives us feeling for “number as Field.” Numbers have a frequency of modulation, and a type of pervading wave phenomena. We could visualize this mandala as a ‘philosophical eye’. Or alternatively, we might view it as a matrix, the all containing ‘womb of Nuit’. A mandala is the empirical equivalent of the alchemical concept of the Unus Mundus (“One World”). The Unus Mundus is one of the many ways of referring to the experience of unification of body/soul/spirit also know as attainment of the Philosopher's Stone.
Sychronistic phenomena are the parapsychological equivalent of the Stone. Jungian psychologist, Mare Von Franz recounts in Number and Time how “...attempts have been made in the past to combine these equivalents into a unitary reality” and construct mandalas, which via synchronicity, would yield parapsychological “knowledge”. This mandala, used as a magical tool, creates the possibility of an altered state of consciousness know as an “access state”. Zosimos and Bruno, Hermetic magicians, used mandala as tools for magically acquiring “information” about the rationally unknowable. By means of this tool, the individual confronts the continuum to produce qualitative experience, from an otherwise latent potentiality.
Number essentially pertains to the behavior of archetypal dynamics, or “ordered sequences”. The 56-radii spiral arrangement to 2520 is the minimum necessary to disclose patterns of relationship in the qualitative field. Total archetypal order of the Unus Mundus and all its contents may be represented this way as there is an equation between archetypal images or ideas, and numbers. This is the foundation of the QBL correspondence system. All patterns are mathematically ordered and there is rhythm in the natural numbers sequence.
Buckminster Fuller refers to this rhythm in Synergetics, when he speaks of the pulsative octave. He states that the interaction of all numbers other than 9 creates wave phenomena, i.e. “self inevitable, self inside-outside octave increasing and decreasing pulsatively, fourfoldly, and tetrahedronally IS ALL THAT EVER HAPPENS!” This is Fuller`s peculiar geometric lingo for speaking of carrier wave order phenomena.
While this concept is fairly simple to grasp mathematically or graphically, it is difficult to express in words. Consequently, the importance of fields and wave phenomena have been understood by only a few. This is why the graphic mandala is such an important tool. It is a visual aid for understanding the relationship formed between field (Nuit) and carrier wave order (Hadit).
In the field or manifold of psychic contents, the nucleus of field is its most imperceptible aspect-this is the circle, Naught. The preconscious aspect of natural numbers points to the idea of a numerical field in which individual numbers figure as energetic phenomena or rhythmical configurations. This “field”, which we take to represent the structural outlines of the collective unconscious, is organized around the central archetype of the Self or Transcendent Function. This function is represented in Magick as the Holy Guardian Angel, another analogy for the experience of the Philosopher's Stone.
A very literal example of “number as field” may be found on a meadow in England at Stonehenge. Here we find a most striking example of Stonehenge is a remarkable verification from the historical past and magical tradition which reiterates the importance of this arrangement.
To make the perimeter of the circle an integral number of times the length of the radii, the Stonehenge programmer used the array of 56 equidistant points. The remnants of these points are termed ‘Aubrey Holes’ in literature about Stonehenge. That a realization of the essence of ‘circular unity’ was necessary to decode the massage of Stonehenge is shown by certain key features.
1. There are 56 Aubrey Holes in the circumference of Stonehenge.
2. Joining every 7th Aubrey Hole generates the outer diameter of the circle of Saren stones. 7 x 8 = 8- pointed star.
3. Joining every 8th hole generates the 7-pointed star and the Star of Babalon, and determines the thickness of the Sarcen stones.
4. Joining every 6th holes equals an equilateral triangle whose apex touches the center of the Sarcen stones.
Bob Marshall refers to these properties of Stonehenge as the “Mandalog” or “Mandalameter.” In all these operations, 56 or 5 + 6 = 11 is indeed the Key to decoding the Rituals.
...to Nuit
For more on ancient number dynamics, see SYNDEX
http://syndex.weebly.com/
2520 Holotome
