The Pillars of the Holy Cross

The Pillars of the Holy Cross are found at the Finial Circle of the Spiral of Life. They are 77, 88, 89, 101 and 113. I will discuss their relation to the Lagrange Points and to Pi; I will examine their horizontal proclivity and the role of 888 in this as well as in bringing about the six-fold symmetry of snowflakes.

 

The layout of the pillars resembles a bow with her arrow nocked and drawn.

 

The four bow intervals are: the lower nock, 77; the grip, 88; the arrow rest , 89; and the upper nock, 101. The grip is defined as the arrow rest (the centered bow interval) minus one.

 

The Serving midway along the bowstring is 113.

 

The Sum of the 4 Bow Intervals / The Serving = Pi

 

This shape brings into view five intervals of interest - four along the bow and one - the server - centered along the bowstring. The Pillars of the Holy Cross correspond nicely with the cross numbers of The Spiral of Life. As a result the bow shape maintains the Pi ratio with rotation along successive cross numbers.

 

Cross numbers are intervals which appear at each quarter rotation of Spiral 935 creating a column of primes and a crossbar of composite intervals. The formula x + y + 1 = z defines the spiral's start and progression from center along her eastbound arm. Following this basic rule creates arms in each of the other compass directions matching the same formula albeit with different values. (See the Spiral of Life in this photoset.)

 

From 77 to 125 a ring known as the Finial Circle emerges as a consequence of a slight counter-clockwise shift in distribution among the cross numbers. This shift is essentially a merger of competing forces and can be measured at the juncture of the crossbar and Finial Circle by means of a formula of averages called the Pythagoras Localization. The resultiing cross values are 77, 89, 101, and 113. 88 marks the location where the localization in the spiral shifts the crossbar's juncture with the finial circle one interval from 88 to 89 and from 112 to 113. These five values - 77, 88, 89, 101 and 113 - constitute the Pillars of the Holy Cross and from them we can derive Pi to great accuracy.

 

The formula of averages is named the Pythagoras Localization because even though the formula is applied uniformly from deep within the spiral, two Pythagorean triples on the cross survive with the final one oriented horizontally and marked by intervals 33, 42, 54 and 69.

 

The beauty of Spiral 935's architecture is her simplicity. At first glance we see a cross. We see quadrants. Yet on closer inspection we find something mysterious about this cross: it is shaped by a crossbar of composite intervals and a column of primes save for 7 and 9.

 

If we multiply all spiral values by three, a perfect six-fold symmetry emerges. What natural phenomena implies multiples of three?

 

The snowflake is made up of water, whose molecules possess three atoms. Since we must think in increments of three atoms in terms of the growth of Kepler's snowflake, it is helpful to magnify the spiral by three to get a clearer picture of how the replicating waves of the freezing three atoms create the six fractal arms of the snowflake.

 

Multiplying by three brings into view 12 radial arms of 5 whole numbers apiece. The radial arms end at the Finial Circle with the last radial interval value being 223. The circumference at the Finial Circle of this 12-armed model is 12 squared. Each and every sequence of five radial values stays true to the formula 1x + 1y + 1 = 1z where 1 reflects 3 constituent parts. Just as in the four-arm model, the twelve arms in the magnified spiral alternate between arms of exclusively odd and sixty percent even sequences and in so doing they neatly separate the 12 arms into two sets. Of the total 18 even values (three of five per alternating arm) 10 of them are super-even - that is, as each value is a multiple of 4 they divide into two equivalent even values. TheIr sum is 888.

 

Both sets - the even set of 8 whose sum is 588 and the super-even set of 10 summing to 888 demonstrate mirror symmetry about the crossbar. As a result we find the horizontal orientation - in which Pi emerges at 99.99999% in the bow values of the Finial Circle - is foreshadowed if not determined by the horizontal symmetry of the even radii intervals of which 888 is the premier group.

 

Orientation of an atom or molecule is critical in predicting the outcome of a collision. Conditions such as temperature or magnetic forces may affect whether or not a reaction takes place. Reactions that are affected by orientation include those of enzymes within the human body. In fact enzymes themselves are known to facilitate reactions. Therefore, at a molecular level, understanding how the supereven set of 888 affects the orientation of atoms may help develop strategies to maximize or minimize the reactions of enzymes.

 

Two things become clear when putting pen to paper and sketching this out; one is that the spiral's formula x + y + 1 = z is true for every direction on a plane and at a right angle from center; the other is that the four-fold symmetry of the cross can produce the six-cornered snowflakes which fascinated Johannes Kepler in 1611 and will likely continue to intrigue us for centuries to come.

 

Exactly how the snowflake's fractal arms emerge symmetrically can be explored further in the image Spiral 935; it has to do with the two most important properties of the Spiral of Life- scalability and a location-based model of alignment and structural recreation. From tiny electrons to a planet's orbit around the sun, the laws of gravity and electromagnetism remain intact but they are not simply some arrows pointing in one direction or another. They are full of curves, close collisions, twists and turns yet are remarkably symmetrical and as steady as a nuclear clock.

 

The idea for this spiral came during high school after an unsuccessful attempt to create - from the inside out - an all-positive-integer alternate to the Cartesian coordinate model.

 

Success came through experimentation when I revisited the challenge without worrying about the start. As the other images in the set demonstrate I noticed primes occurring along the column and symmetry in the outer rungs which I sought to maintain as I worked my way back to the center.

 

When considering the bow shape among the cross numbers of the Spiral of Life (irrespective of starting point) we may divide the sum of the four bow intervals by the server to obtain a result of Pi with an average of 98 percent accuracy.

 

However when considering the Pythagorean Localization at the Finial Circle as described in the Spiral of Life, that accuracy leaps to 99.99999% since (77 + 88 + 89 + 101) / 113 equals 355/113 or 3.14159292.

 

In the Spiral of Life, the path to Pi begins as the measure of a point and is equal to one. Within the second rotation she reaches Pi +/- 2%. Yet at the point of regeneration along the Finial Circle she reaches the matured and accurate Pi we have all come to know and love.

 

Pi is of course well-known as the circumference divided by the diameter of a circle - geometric formula which suggests little in the way of motion. While the Pi I describe here shares the same value it appears to be measuring a different beast altogether. And yet they are related. The Pi of the Spiral of LIfe demonstrates that like Cupid - Pi enjoys constant motion and when reached in all its fullness at the Finial Circle brings with it new possibilities..

 

Lagrange Points and the Pillars of Pi

 

An excellent correlation between Pi, the Lagrange points and the Spiral of Life has been uncovered. If one could imagine a tiny Earth in rotation at interval 89 on the Spiral of Life we would find her five Lagrange points also forming a bow and arrow shape (minus the grip) at the following intervals:

 

L1 = 33; L2 = 144; L3 = 113 L4 = 95 L5 = 83

 

L2, at 144, is located due East of 89, forming a horizontal line with L1 and L3. (In moving beyond the Pythagorean Shift between 77 - 125 we shall continue with the Cross formula taking into account the shifted finials of 89 and 113 such that 54 + 89 ( not 88) + 1 = 144.) L4 and L5 mark the bow's upper and lower arms. One of the surprising discoveries (made on Pi Day 2015) is that the location of the five Lagrange points matches intervals along the Spiral of Life which form a Pi relationship.

 

(33 + 144 + 95 + 83) / 113 = 355 / 113 = Pi

 

Lagrange points are also called libration points, or magic points, because their location is permanently fixed to a rotating body in spite of the relatively great distance between them and such body. They are gravitationally significant because smaller objects lying on the points will tend to stay there. The most stable of these spots are L4 and L5 which pull objects into their vicinity as if it were a valley surrounded by hills. However, objects near collinear points L1, L2, and L3 will stray from them unless they've been placed in orbit around their respective Lagrange points - an orbit which must be maintained with occasional adjustments.

 

Comparing the Pillars of the Holy Cross with the Lagrange points yields the following results:

 

L1 (33) + L2 (144) = P1 (88) + P2 (89)

--------------L3 (113) = P3 (113)--------------

L4 (95) + L5 (83) = P4 (101) + P5 (77)

 

 

7/8 : How the Finials relate to the Core of Spiral 935

 

The basic structure of Spiral 935 consists of an inner core of 4 intervals. Intervals 1 and 3 belong to the column; 2 and 4 belong to the crossbar.

 

Beyond the core are the radial arms comprised of 5 interval arcs for each arm. Capping them off are the 4 Finials: 77, 89, 101, and 113.

 

The sum of the 2 arms comprising the column (less the core) is 252. The sum of the 2 arms comprising the crossbar (less the core) is 288. Their ratio is 7/8.

 

Summing the column finials 77 and 101 with the column core values 1 and 3 yields 182. Summing the crossbar finials 89 and 113 with the crossbar core intervals 2 and 4 results in 208. Their ratio is 7/8.

 

As a result, the ratio between the sum of the 14 column intervals and the sum of the 14 crossbar intervals is also 7/8.

 

The precision in this finding strengthens the case for the structure of Spiral 935 from her 4-interval core and her radial arms to Pi and the Pythagoras Localization at the Finial Circle.

 

Furthermore, adding up the values immediately after each crossbar value including her associated core and finial values forms the Fibonacci 505. By shifting the spiral clockwise one interval we can visualize this crossbar whose sequence follows the Fibonacci pattern and matches the localized finial values of 89 and 113 at the horizontal ends of the Finial Circle. Spiral 935 is a model of moving parts, of shifting interval paths that helps explain the mathematical forces inherent in gravity and spin. The Pythagoran Localization can be describe d as a single interval path shift along the crossbar which emerges at the core through the Golden Egg sequence and ends at the finials with the Fibonacci 505.

 

In Roman Numbers 505 is DV. Strictly for entertainment value I point out that the alphabet letters DV could also be a shorthand code for Da Vinci.

 

505 is also the sum value of the four Finials 77, 89, 101, and 113 plus the overlapping "Fifth Finial" 125. It is it at this precise interval and location where a new spiral emerges from almost nothingness, but more accurately, from the event of spin coming full circle.

 

By comparing the Lagrange Pointis to the Pillars of the Holy Cross to Pi we can begin to see Pi in a new light - as a place of alignment that once reached begins the process of reaching towards it all over again. Likewise, by considering the interplay between the Spiral's Golden Egg crossbar and her Fibonacci sequence only one interval off we are able see through Pythagoras how two formulas may converge at the Finial Circle creating the symmetry of the circle common to all life.

 

Why is the Holy Grail Spiral of Life also called Spiral 935?

 

My wife and I owned a language school in Japan. We were visiting my hometown and we passed by Houston Fire Station #93 located at 911 FM 1959 between Ellington Field and the Gulf Fwy. The large numbers stood out prominently. I was in the habit of translating things I read into Japanese so I read it as kyu and mi instead of kyu-ju san, the correct way to say the number 93 in Japanese. Mi, pronounced mee, also means three in Japanese. I pointed to the firehouse and said to her, "Look. That's your number." She liked the comparison and began using both 93 and 935 to sign her artwork. The final 5 of 935 is pronounced 'go' and is a soundalike of the final syllable of her name - 'Ku-mi-ko'. After discovering the spiral model, the centered column intervals stood out - 9 - 3 - 5 - I knew it was a fitting name for the model.

 

The spiral regenerates after every 124 intervals at 90 degree increments such that 4 spirals are needed to create one wave motion. In many cases it is useful to think of the spiral as ending at 123 intervals with 0 being the demarcation, or capstone interval. The total interval count is 496 for one wave. Interestingly, the sum of the cross bar intervals including both finials and associated core values is also 496. The corresponding sum of the column values is 434; the ratio of column to crossbar is 7/8ths. The sum total of all the cross vales, both column and crossbar, associated finials and core values is 930. 9 and 3 also stand out at the spiral's center - the juncture where the column's core meets the north radial arm.

 

A Rare Trinity of Composiite Odds

 

Prior to 363, 93 marks the first and only occurrence of the centered number of the sole trinity of composite odds. They are 91, 93, 95 and are nested within prime numbers 89 and 97; these prime numbers mark the only occurrence of gap 8 primes until 359 and 367.

 

© Prince Blake

 

 

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