Reciprocal Gnosis

Therein lies esoteric gnosis of the inner-workings of reality through analyzing the first principle of the Quadrivium, Number.  The reciprocals of the natural numbers reveal patterns that are visible only when we put on our goggles of decimal expansion and peer deep into the realms of numeric possibilities.

The reciprocal of a number is simply one divided by that number. The reciprocal of 5 is .2 because 1/5 = .2  Conversely, the reciprocal of 2 is 5, because 1/5 = .2

This resembles patterns that arise is what is known as vortex based math. 

The reciprocals of certain numbers reveal patterns that are easily recognizable at first, but then disintegrate into the apparent randomness. But it’s not random. There exists intelligence in the way nature operates.  With this reciprocal gnosis we can analyze the quality of Number itself and reveal order from ostensible chaos.

49 Octave of Light

The reciprocal of 49 (1/49) reveals binary numbers, (2,4,8,16, etc) in its decimal expansion.  We start at 2 and go up an octave to 4, then up another octave to 8, and so on.  49 encodes cellular mitosis, binary, and the doubling pattern in Vortex Based Mathematics.  Perhaps this is why 49 is such a highly venerated number.

“Many Buddhists believe, as written in the Tibetan Book of the Dead, that the soul takes 49 days between death and rebirth in the reincarnation process. The book contains 49 days worth of specific passages for friends and family to read aloud to assist the deceased in their transition. Traditional Chinese funerals also last 49 days. Amazingly, it is also exactly 49 days after conception when an unborn human embryo undergoes major changes to become a fetus. At 49 days, two very important things happen: (1) the newly formed pineal gland produces a giant spurt of DMT and (2) the gender of the baby is decided! Could this be the moment of reincarnation? Rene Descartes and many others believed the pineal gland, the eye in the pyramid, to be the seat of the soul, where the immaterial soul connects with the material body. 49 days after Easter is Pentecost, the day when “tongues of fire” came into the temple and rested upon the heads of the elders. Symbolically this could mean their crown chakras were illuminated, pineal glands functioning, and the spirit came down unto them, just as literally 49 days after conception, the fetal pineal gland begins functioning, the gender is determined, and the new soul enters!…” -unknown

49 is born from 7 since 7 x 7 = 49

49 octaves light

The 49th octave of light is the only octave the human eye can perceive.

“Just as there are 7 Divisions on the Physical Plane and the Rainbow has 7 Colors, the Energy known as Sound has 7 notes in Music and the same note recurs on the eighth key, only it has a higher or lower Pitch according to which side of the Scale is reckoned. Each complete Scale of Notes is called “Saptaka” or Septave, meaning the Scale of Seven. Actual measurement shows that going from the low to the high, each eighth note has a vibration rate of double the number; thus, each Octave from low to high has double the vibration frequency in the high as in its neighboring low and to find the Octave Frequencies means a question of simple arithmetic …

“On the Forty-Ninth, as the Oscillatory Frequency per Second jumps to the high mark of 562,949,953,421,- 312, the middle of the Spectrum of Colors has come into existence, the first Visible Light starting around 318 Trillion Oscillations per Second, with a faint Red Color. While the range of the ear for hearing is from the Fourth to the Fifteenth Octave, a span of 11 or 12 Octaves, the eye can sense only 1 Octave—the Forty-Ninth. As soon as the Fiftieth is reached, with its 1,125,899,906,842,624 Oscillations, the faint Violet of the Spectrum vanishes and for Seven more Octaves, the potent, but invisible Ultra-Violet Range of Radiations is entered. Before going further, we shall look into some of the properties of Oscillatory Frequencies and the conversion of one Energy into another.” 

from “Spectro-Chrome Metry Encyclopaedia”, Ch. 11 by Dinshah Ghadiali 

Let go up an octave from 49 to 98

98 Reciprocal
Adding up increasingly expanding binary numbers in this manner generates the reciprocal of 98 (1/98)

The same information is encoded into the reciprocal of 98, only the pattern starts with one instead of two.  After taking the digital root of each number it charts the loop in the diagram on the left.

Lets reverse 98 and take a look at 89.

Fibonacci and 89

The 11th number of the Fibonacci sequence is 89.  89 is 11 less than 100.  The decimal expansion of 1/89 is the Fibonacci series, added together in this manner.  Cody Birsner figured this out working on his Fibonacci term paper at the University of Oklahoma in 1994.   One divided by the eleventh number in the sequence creates the sequence itself through self-similar decimal expansion.  Numbers are holographic.  Each piece contains the whole.

Mass of Earth and Moon 1:81

The reciprocal of 81 reveals all numbers in existence.  This is because we live in a decimal based reality and the decimal system is made of 9 numbers. (Zero doesn’t technically count) 9 x 9 = 81.  Peter Plichta found there are exactly 81 stable elements.  Earth is 81 times more massive than our moon.  The dielectric value of pure water (which the moon so heavily influences) is 81, and is therefore 81 times more effective as a charge separator than the vacuum.

81 = 9 x 9 = 3 x 3 x 3 x 3

The Decimal System
The decimal system: How reality is organized

These binary numbers are found in computer science as well as biology.  Every cell in our body has gone through this doubling process.

Cellular Mitosis and 49
49 and Cellular Mitosis

The reciprocal of 7 is .142857142857…  This pattern (which is missing the 3,6,and 9 Tesla spoke so highly of) can be laid upon the Ennead.  G. I. Gurdjieff cherished this diagram and labeled it the law of seven.

The symmetry is realized when we place this decimal pattern in rows of three and add them together to get nine.


Seven is special.  The Pythagoreans considered it the middle ground among the decad (the numbers 1 through 10).

1x2x3x4x5x6x7 = 7x8x9x10 = 5040(Plato’s favorite number)

Enneagram seven
The division of seven within the Enneagram

We exist in a fractal and self organizing matrix of number and geometry based on phi ratios, the divine proportion.  Reality can’t “operate” without this fundamental principle in place.  Without it we are lost.  With this gnosis and understanding we traverse the mountains of self exploration, diving deep down the rabbit whole of the numerical holographic universe.

“Pythagoras was one of the first teachers to establish a community wherein all the members were of mutual assistance to one another in the common attainment of the higher sciences. He also introduced the discipline of retrospection as essential to the development of the spiritual mind. Pythagoreanism may be summarized as a system of metaphysical speculation concerning the relationships between numbers and the causal agencies of existence.” -Manly P. Hall

“God built the universe on numbers.” – Pythagoras

Subscribe to Blog via Email

Enter your email address to subscribe to this blog and receive notifications of new posts by email.

Join 361 other subscribers

7 comments on Reciprocal Gnosis

  1. Hi there 🙂

    Been some time since I let my mind wander in this direction of digital root/mod9 ponderings… now travelling in south east asia and somehow its leaking back knto my thoughts, meeting ppl interested to know what I am interested in has helped 🙂
    Found this post today… and I cant figure out how you took the reciprocal and massaged it to spot the ninary system lile you did in the first image! Its brilliant! Would like to apply the thinking to other decimals/reciprocals. Very fascinating… A new perspective indeed, good job and thank you for sharing. Images coupled with text is a nice and efficient way of communicating the data you find… nice to see how someone does it differentyl 😉

    1. Thanks Christ Ian, The digital root/mod 9 is a fascinating subject. Vortex Based Mathematics led me to discover this gem. What is most interesting to me is the way the FIbonacci series creates a 24 long pattern of digital roots that reveal the importance of nine, as well as the way it encodes the doubling pattern in VBM (1,2,4,8,7,5). 89 also blew my mind as it actually has every fib number hidden it’s reciprocal. Thanks for your insight and happy travels! 🙂

  2. Get this book ->
    And also imagine yourself playing the pi-ano with 2x phi’ve fingers. One hand goes up from key 1 (A0) to key 88 (C8). The other hand goes down from key 88 (C8) to key 1 (A0). At the far extremities you have 2 fingers (one on each hand) playing keys 1+88=89 or 88+1=89 depending on your preferred bias. If you play each note inwardly until the hands cannot move any further without crossing you end up playing key 44 (E3) and key 45 (F3) or key 45 (F3) and key 44 (E3). Once again you have a total of 89. The piano when played with BOTH hands winks at 89 though it’s ever so slightly hush hush… shhh. In fact every mirrored position is exactly 89. Ponder upon the 52 sacred books J.S.Bach had in his occult library… One per white key…
    Here are some visual chlooS ->
    And an app ->

    1. That was a good book, and I’m glad I read it so I don’t have to replicate his work, it’s all laid out for you right there..

      I play the piano a little myself. I’ve got the first part of Karma Police down. 🙂

  3. your example 1/49=0,02040816326530610000…
    the pattern appears in 50^n (578421…) and in 1/50^n (248751…) and by addition the result (in modulo 9 operations of addition are equivalent to operations in modulo 10…)




    and so and on…

    1/(x-1)=1/x+1/x^2+1x^3…1x^n? n not precisely defined but it’s a mathematic formula…make me think about approximation…

What do you think?

%d bloggers like this: