14.1 The Spiral Pattern in Interplanetary Space 

14.2 Diagram. The I-Ching Superimposed upon Curved Space   Magazine: Scientific American Mar. 1988, pg. 48 (1/2 toroid only)

(Note: This diagram is an integration of the space curvature of the theory of general relativity, superimposed upon by Ben Franklins 8 x 8 Magic Square matrix (Magic Squares, 511. An 27 sub.2), commonly known as the I-Ching or Ye-King. The reasons for doing this is based upon sciences postulates that space must have an intrinsic order and the universe / sun / earth interactions must be based upon this same order. The I-Ching, being a 13 x 20 grid should also reflect the toroidal shape of the vector equilibrium-13 ball-this side / other side-4D-gravity spheres.)

Copyright. Robert Grace. 1999.

14.3 Magic Squares and Space 

A quote from the end of the Chapter: "In the spirit of the great master whom we have just quoted we may compare the physical universe to an immense magic square. Isolated investigators in different areas have discovered here and there a few seemingly restricted laws, and paying no regard to the territory beyond their confines, are as yet oblivious of the great pervading and unifying Bond which connects the scattered parts and binds them into one harmonious system".

(Note: This is the gist of the following numbers and the whole of universe):

..."The number 729",

14.4 Numbers 3, 5, 9,13, 27, 35, 81,and 243 

..."is found to be of great importance all through the Pythagorean system. Plutarch states that this was the number belonging to the sun, just as 243 was ascribed to Venus, 81 to Mercury, 27 to the moon, 9 to the earth, and 3 to Antichthon (the earth opposite to ours). These and many similar numbers were derived from one of the progressions of the Tetractys,- 1 : 2 :: 4 : 8 and 1 : 3 :: 9 : 27. The figures of the above proportions were combined by Plato into one series, 1(apex), 2, 3, 4, 9, 8, 27...Plutarch in his 'Procreation of the Soul', which is simply a commentary upon Plato's "Timaeus", has represented the numbers in the form of a triangle; the interior numbers 5 (between 2 and 3), 13 (between 4 and 9) and 35 (between 8 and 27) , representing the sums of the opposite pairs, were also of great importance":



..."Numbers which expressed some astronomical fact also held high places of honor, as may be seen from a statement of Plutarch... in reference to the Tetractys. "Now the final member of the series, which is 27, has this peculiarity, that it is equal to the sum of the preceding numbers (1+2+4+9+8); it also represents the periodical number of days in which the moon completes her monthly course; the Pythagoreans have made it the tone of all their harmonic intervals".

14.6 Diagram. The 27 x 27 Magic Square Book: Magic Squares

"This passage indicates sufficiently the supreme importance of the number 27. If we construct a magic square 27 x 27 upon the plan of a checker-board- arranging the numbers 1 to 729 first in numerical order, then shifting the 9 largest squares (9 x 9) into the positions indicated in the familiar 3 x 3 square, repeating the process with the subdivisions of the 9 x 9 squares and so on down- we will arrive at the following combination. It will be noted that we have 365 white squares or days and 365 dark squares or nights- a veritable "checker-board of nights and days". The number 365, the days of a solar year, very appropriately occupies the centre of the system. The columns, horizontals, and diagonals of the central square 3 x 3 foot up 1095, or the days of a 3 year period, those of the larger center square 9 x 9 foot up 3285 the days of a 9 year period, while those of the entire combination 27 x 27 foot up 9855, the days of a 27 year period, in other words, periods of years corresponding to the Tetractys 1, 3, 9, 27"...

Footnote on number 9855: "Not only the perpendiculars, horizontals, and diagonals of this large square foot up 9855, but there are an almost indefinite number of zig-zag lines, which give the same footing".

14.7 The Solution to a Greek Mathematical Problem :

"By taking a hint from our magic square and starting with the number 27, I, (the text author whose Greek text is omitted), believe we may arrive at a good solution of the problem as any that I have seen suggested. The following interpretation of the Greek terms is offered":

Interpretation: "the square of the number times its root" . Mathematics: 27^2 x 3sq.rt27 = 2187


"increased by thrice the first terms (of the Tetractys). Mathematics: (1+2+3+4+9) x 3 = 57

"and four times the whole series". Mathematics (1+2+3+4+9+8+27) x 4 = 216

"of number unlike yet bearing the same ratio whether increasing or decreasing". Mathematics: descending figures of the triangle 8, 4, 2, 1, 3, 9, 27).

"makes the sum commensurable and expressible in all its parts". Mathematics: sum = 2460 (i.e 2460 is easily divisible by 1, 2, 3, 4, 5, 6, 10, 12, etc).

"this sum increased by 1/3"

"and adding 5", "is multiplied by 3". Mathematics: 2460 x 1 1/3 = 3280, 3280 + 5 = 3285, 3285 x 3 = 9855".

"This solution of the problem, 9855, it will be noted, brings us again but by a different route to the magic number of our large square. The second part of the passage contains a description of the number by which the above calculation may be verified":

"(the number) yields two harmonic parts",

"one of which is a square", Mathematics: 3 x 3 = 9

"multiplied by 100" Mathematics: 9 x 100 = 900

"the other has one side equal to the square" Mathematics: 3

"and the other oblong" Mathematics: 3 x 2985 = 8955, Sum = 9855

"The remainder of the passage describes the length of the oblong which we have shown above to be 2985":

"(the oblong) is 100 times the side of a rectangle having diagonals of 5" Mathematics: 100 x 3 = 300

(i.e having sides of 3 and 4).

"less of one each of the expressible parts, i.e., 4 and 5"

"and 2 of the inexpressible" Mathematics: 300-(5+4+3+3) = 285

"plus 100 times the cube of 3" Mathematics: (3)^3 x 100 = 2700 Sum = 2985

"In a treatise by Timaeus the Locrian upon the 'Soul of the World and Nature'...he..made 384 the first of unities...and the double and triple..all their terms, with their compliments and eights must amount to 114,695".

"Plato's account of the combination of the soul is very similar to the above, though he seems to have selected 192, (384 / 2) for the first number. Plutarch in his commentary makes no mention of Timaeus, but states that Crantor was the first to select 384, for the reason that it represented the product of 8^2 x 6, and is the lowest number which can be taken for the increase by eights without leaving fractions. Another very possible reason, which I have not seen mentioned, is that 384 is the harmonic of 27^2 / 2 or 364.5, a number which expresses very closely the days of the year":

243 : 256 :: 364.5 : 384


Quote: "A periodicity in the cycle of eclipses was noticed by ancient Greek astronomers. Its duration is 6585.32 days (or 18 years and 10.3 days)...

(Note: (6561), not 6563 happens to be the numerator of the fraction of the hydrogen atom, which, when divided by exactly 18 = 364.5, the number of days in the year. This numerator 6563 (6561) is also a Mayan Super-number orbital frequency in the Balmer Series of orbitals. It is also found in the File "26 Keely"

"The proportion 243 : 256 (3^5 : 4^4) was employed by the Pythagoreans to mark the ratio which two unequal semitones of the harmonic scale bear to one another.

Batteaux has calculated the 36 terms of the Pythagorean scale starting with 384 and his series must be considered correct, for it fulfills the conditions specified in Timaeus, the numbers all footing up 114,695.

See File, "72 Proportion"

A few of the numbers of this harmonic scale marking the 'first unity' and several of the semitones will be given.



Divisions of 36
1st Octave












2nd Octave






3rd Octave

B flat



B flat


4th Octave




By referring to our magic square, it will be noted that the first of unities, 384, constitutes the magic number of the small 3 x 3 square beginning with the number 100. If we arrange the magic numbers of the 81 squares (3 x 3) in the order of their magnitudes we find that they fall into 9 series of 9 number, each series beginning as follows:



















The intervals between these series are worthy of note.

Between I and II 243, the first member of ratio 243 : 256.
Between I and III 486, C of the 1st octave.
Between I and IV 729, F of the 1st octave.
Between I and V 972, C of the 2nd octave.
Between I and VII 1458, F of the 2nd octave.
Between I and IX 1944, C of the 3rd octave.

If we arrange the magic number of the large squares (9 x 9) in the same way, it will be found that they fall into 3 series of 3 numbers, each series beginning:


Interval between I and II = 2187, B-flat of the 3rd octave.
Interval between I and III = 4374, B-flat of the 4th octave.
(See 2187 (3rd) and 4374 (4th octave) above).

And, (the author finishes), "as Plato once was supposed to have said about all the other sciences and how they should be studied in their "mutual relationships that we may learn the nature of the bond which unites them". "For only then", he states, "will a pursuit of them have a value for our object, and the labor, which otherwise might prove fruitless, be well bestowed".

Magic Squares
511. An 27 sub. 2


Update- 3/21/02: Evidence: The Sun as a 27 x 27 Magic Square, courtesy of Sharon (Wdestiny44@aol.com)

Solar Logos and Helioseismology Depicted in Crop Circle Formations By Kris Sherwood

Fig. 3 - 'Solar Logos' Crop Circle Formation, Etchilhampton, Wiltshire, UK 1990

"The part of the1997 Etchilhampton formation that consisted of a gridded square inscribed by a circle can also can be read as a Magic Square of the Sun. The classic 'Magic Square of 729' is a square divided into a 27x27 cube, contains numbered squares that amazingly add up to 365 in any horizontal, vertical, or diagonal line across the square. (365 also happens to be the numeric equivalent of the name Mithras.) (Ref. 4) In another remarkable synchronicity of numbers, the Sun fully rotates once every 27 days! The Etchilhampton Sun Square had a 'two-over' number present in its geometry, which reminded me of the use of 'coda's, or pairs of extra circles similar to musical repeat marks, that I also observed in the geometry of the Julia Set and Windmill Hill formations of 1996 (Ref. 5). The two 'extra' small circles in the symmetry seeming like an intended irregularity pointing to possibly an unusual aspect, or indicating a 'repeat' of a sequence. This 'extra circle' feature has also been seen in other formations as well, such as the 'Strange Attractor' of 1997, the 1997 Snowflake fractals, etc. The '729 Sun Square' is depicted as a square of 27x27, equaling 729 individual squares that comprise the 729 days and nights of a 365 day solar year (each two squares representing a 24 hour day and night) (Ref. 6). The Etchilhampton Magic Square of the Sun is irregular in a number of ways. It is divided into a grid of squares of 26x29 (not including tramlines), which seems to imply it is not a usual year it refers to. In a curious contortion of numbers, the additional 25 squares that total the formation's 754 squares can be seen to indicate 12 1/2 days in addition to the 365 day year of a typical Magic Square of The Sun year. The formation was first discovered on the 30th of July: projected one year and 12 &1/2 days ahead from that date would indicate August 11, 1998. A coincidental 'pre-anniversary' indicating, with a pre-date by one year, to the date of August 11, 1999, and the Great Total Solar Eclipse across Southern England and Europe? Stretching this a bit further to include the 'repeat' indication in its numbers, one could infer it was even pointing ahead another year to the actual date of the Eclipse. (The fantastic formations that appeared in 1999 had a lot to do with the Millennium ending Eclipse as well, but that's for another couple articles Ed and I have yet to release.)"

14.14 The Mayan Tzolkin As Space Structure

This study comes from Jose Arguelles book, The Mayan Factor, and develops into a toroidal close-packed structure of space as follows:

We know that light comes from the sun into earth. We know this light has life properties, it sustains life. We also know that gravity is what the sun, only, is the source of. Light and gravity are what earth uses to live. The question is this:

How does the binary wave of light and life traverse the Tzolkin Calendar of the Mayans, the Life being the I-Ching, The Code of Life, embedded into the Tzolkin, which is the Code of Light.

14.15 Diagram. The 2 Mayan Tzolkin Spiral Paths

In this diagram of the Tzolkin we see the opposing direction of the 2 paths. One path is called "Past to Future" and the other is called "Future to Past", opposite and inverted.. The 2 dots (.) not only indicate the binary nature of nature but also shows the binary twisting path it takes through the Tzolkin. 8 has an equal and opposite 8, but both 8's have different magic square values. We, at present, happen to be exiting the very last bactun, lower right 8, on the spiraling curve called "Past to Future". This means that we perceive history from past to future, of course. The question, now is, what direction does the arrow of past to future point, as we exit this Tzolkin and , either, enter it again elsewhere, or, enter another Tzolkin space pattern adjoining this present one?

If we place 4 new Tzolkins around this present one, theorizing that space is a tapestry of Tzolkin shapes, possibly in the form of toroidal spheres making up the fabric of space, which we are influenced by, we find in all arrangement, that the "Past to Future history line changes into an opposite arrow indicating the opposite or "Future to Past" Arguelles calls this, not history, but christory.

A 2D flat view of 4 Tzolkins is illustrated in the following Diagram.

The 2 dots (.) also indicate the approximate position of at least 2 spiraling waves coming from and traveling to, the Sun (imagine the Sun behind the Diagram) and into the earth (imagine the earth being just in front of your eyes). These waves order our Past to Future reality and the Future to Past reality now superimposing upon our time perceptions we are used to, give us visions of future flying technology, strange beings, strange phenomena and all the rest... I believe the future is imposing upon this dimension already. More over, we should ask the question:

Does this wave move from 1 to 2, within the same Tzolkin, or 1 to 4 of another Tzolkin adjoining?

14.16 Diagram. 4 Tzolkins representing the Fabric of Space

Diagram edges can be connected top to bottom, each one, and side to side by distorting the square (1 of 4) until it finally looks like a sphere or toroid because of the Tzolkin 7th column with represents the toroidal center or hole, and mirrors the 6 columns on each side therefore the sphere becomes a torus. Therefore the Tzolkin between the Sun and earth is time-in-space in the shape of a torus.

This is what 4 torus shapes might look like in space, in a square arrangement, but they don't have the closest-packing characteristics of like spheres:

14.17 Diagram. A Square Group of 4 Toroidal Shapes

Lets rearrange the toroidal shapes and add more to show the closest-packing of Buckminster Fuller:

14.18 Diagram. Close-packed Toroidal Space

Now there is every other toroid of like motion and polarity, that is, matters electrodynamics of live, energy / consciousness, is traveling up through the center or down through the center of the toroid, (relatively speaking) in opposite spiral paths, according to Rodin's explanations, alternately indicated by + or -. Since any adjacent toroid is moving opposite its neighbor, (as space is said to be... expanding), there is repulsion from that neighboring toroid, which keeps each one intact. This implies a vortexural space.

Whether space has a curved flat-like Tzolkin between earth and Sun, Sun and Galaxy Core or space-Tzolkin shapes are toroidal spheres making up space is a question to be studied. The point is this:

Space is not an empty medium. Space is a hidden order that perpetuates life. This toroidal structure is why space is curved intrinsically which means space is not curved by gravity. How can gravity curve space when there is no gravity in space to curve it?

The following Diagram is a big picture of the possible hidden order of space:

14.19 Diagram. Metagalaxy. Possible Hidden Order of Space

This Diagram described in words is as follows: One-half of a Metagalactic spiral is shown to contain a Megagalactic core trillions of miles from the Metagalactic core. Farther out, we arrive at our Galactic core, and further still we arrive at Sun, earth and several concentric circles representing the human inner psyche and outer 'brain mind', the end of the line in the connections. Upon this huge structure is imposed Magic Squares of various size. These Magic Squares curve through space, following the intrinsic curve of toroidal space, through each core center and out into space again. There is an Incoming From Source (Metagalaxy) side of various Magic Squares, beginning at Meta and traveling to 'human brain', and there is a Return to Source side of various Magic Squares, beginning from the 'human brain' and traveling to the Metagalaxy core. There are two interweaving sinewaves curving from Metagalaxy down through each core into 'human brain'. This represents the harmonics concerning the musical universe.

Notes in the Diagram are as follows:

    Tzolkin = fractal = inversion = the mirror = the wave function (the mental side of the electron) = the division between time and space.

    All Tzolkins are curved upon distorted space.

    The "cosmic eye or lens" is the centers of the sun and galaxies within even larger galaxies.

    The universe we can detect is a mere tiny circle within this unfathomably huge structure far beyond our ability to see it.

14.20 The Magic Square order Incoming From Source: This pertains to I-Ching only, not the Tzolkins in which they are embedded.

This ordering implies that universe was an extremely simple beginning, hence, the 2 x 2 magic square. This ordering may be the Involutionary side of life (the descent of Spirit to matter).

2 x 2 Magic Square, 2^1 I-Ching- Metagalaxy
4 x 4 magic Square, 2^2 I-Ching- Megagalaxy
8 x 8 Magic Square, 2^3 I-Ching- Galaxy. (This I-Ching we know of within a Tzolkin of 260 Magic Squares).
16 x 16 Magic Square, 2^4 I-Ching- The Sun. (This I-Ching, I theorize, is within a Tzolkin of 1040 Magic Squares).
32 x 32 magic Square, 2^5 I-Ching- The Earth
64 x 64 Magic Square, 2^6 I-Ching- Inner Human Psyche.
128 x 128 Magic Square, 2^7 I-Ching- Outer Human Brain.

This ordering is added to imply the inverse of the descent of Spirit (largest Magic Square) to matter. Matter feels it is connected to something "higher". This ordering may be the Evolutionary side of life (the rise of matter to Spirit).

14.21 The Magic Square Order Returning To Source :

2 x 2 Magic Square, 2^1 I-Ching- Outer Human Brain.
4 x 4 Magic Square, 2^2 I-Ching- Inner Human Psyche.
8 x 8 Magic Square, 2^3 I-Ching- The Earth.
16 x 16 Magic Square, 2^4 I-Ching- The Sun.
32 x 32 Magic Square, 2^5 I-Ching- Galaxy.
64 x 64 Magic Square, 2^6 I-Ching- Megagalaxy.
128 x 128 Magic Square, 2^7 I-Ching- Metagalaxy.

14.22 Trinary Logic: The Cube.

If you can't find answers in the Binary logic of planar 2D grids as above lets scrap it and move to the Trinary logic of the Torah codes. The following is a short quote from:

Torah Codes by Manuel Colunga-Hernandez.

"first cubing the number: 304,805.

It doesn't cube into a single entity, it cubes into five cubes with a minimal of three remaindered letters. Rather than going large to small I went from the lst three letters to the largest cube. How this came to me to do it this way, was purely inspiration and coincidental. I met a friend one night while in town we discussed my work with the codes. She asked if I had seen the movie "Contact" I replied I had not. She then told me about how the characters had uncovered a message from a radio signal that was found to be three dimensional... and said, "Manny you should see if you can't find something in three dimensional form!" I then told her it had been on me for about a week to do so,.. I then began. With the help of my wife and a VRML program I was able to plot out a visual set of cubes, along with hard copy versions in sheet form. I am working on converting the first three cubes into their numerical forms at this time...

The cubes work out as follows:

The lst three letters followed by a cube of 27 letters (3^3) a cube of 125 letters (5^3) a cube of 512 letters (8^3) a cube of 3375 letters (15^3) and finally a cube of 300,763 letters (67^3). The '8' cube is a curiosity in and of itself... more on this later. The cubes follow the textual rendering. And go from remainder on the right to largest on the left in the fashion of written Hebrew".

(Note: Is creations progression, not a binary 2, 4, 8, 16, 32, 64 but a 3D solid (Magic Cube) progression of 27, 125, 512, 3375 and 300,763? Or is this arrangement telling us that the progression is a cubic progression of 3, 5, 8, 15 (actually 13) of the Fibonacci Series?).

More on Trinary logic in The New Universal Consciousness by D. G. Leahy pertaining to the mathematics of universe, Hebrew letters and quantum physics. This information is also found in the 93 Over All Picture file.

Impossible Correspondence Index

Copyright. Robert Grace. 1999