|
An
overview, as well as theoretical approach to different ancient number practices from around the world.
The Original Magic Square
| Order 3 Magic Square |
|
|
| 4000 years old |
This numerical pattern appeared on a turtle shell from China
thats been dated to over 4000 years old. Its the oldest known record of a magic square and is also the only pattern you can
create using these nine numbers to square. The added sums of each row, column and diagonal is 15. This is the smallest
magic square possible (and the Order 3 magic cube is the smallest possible) and sets the tone for a numerical anomaly
that has been pondered for millenia by mathematicians world wide.
The applications still escape modern number experts of all kinds.
Higher Order Magic Squares
| Order 5 Magic Square |
|
|
| Most Harmonic |
This is the order 5 magic square and is patterned after the
Lo Shu (or universal) sequence for squaring prime numbers. The center number of the count always lands center of the square,
with the beginning and end numbers located at either end of the same row/column (direction of construction of the square is
relative).
In this square, the magic number is 65 (13x5). This is
a fully pandiagonal sequence containing holographic sequences, as well (pandiagonal meaning, if the diagonal bleeds off
the square, the number count is picked up on the other side). The numbers 1 through 25 are all used without repetition or
omission. If you take any number in the square, you will find that it and any four symmetrically adjacent numbers will
sum to 65 (on the diagonals or rows/columns). Also if you create a space between and continue the sequence, the sums remain
65. E.g.: 13 is surrounded by the numbers 7, 19, 21, 5. All five of those digits sum to 65. Also, the 13 has the pairs 2 &
24, 20 & 6, which with 13, sum to 65. Go out to the second numbers away from 13 symmetrically to find the same concept.
This happens with all of the numbers in the construct.
This is the 1 through 64 enumeration of the I-Ching square pictured
below, easier to read than I-Ching and contains most all of the nuances of the Ben Franklin square and then some. Its
magic number is 260 along the rows and columns. Jose Arguelles is my first reference for the connections of the Maya numerics
and the I-Ching into magic square format from his book The Mayan Factor, but this is the first magic square I've
seen set to the I-Ching binary codice and arranged in such an orderly way. All rows and columns summing to 252 in this case.
This square is fully pandiagonal in enumeration. So in the
I-Ching version, the trigrams become arranged along the rows and columns. The top trigrams of each hexagram along the horizontal
rows are all accounted for. The bottom trigrams along each vertical column is accounted for. Patterns emerge along the diagonals
and pandiagonals as well. Consequently, 1+64 = 65, 2+63 = 65, 3+62 = 65, 4+61 = 65, etc. on in to center at
32+33 = 65. Each of these 32 pairs mirror each other in hexagram format. You can use this square to help find these pairings
in the I-Ching version below. In this the 1 through 64 count, each pair adds to 65 and can be found easliy grouped together
in horizontal and concentric pairings across the vertical (e.g.:1 & 64, 50 & 15, 12 & 53, 59 & 6,...).
The conversion from I-Ching 0 through 63 count and modern 1
through 64 count is simply 1 digit up for each placement.
| Fully Pandiagonal Magic 13 x 13 Square |
|
|
| * Utilizes universal method for creating magic squares from prime numbers. |
This is a fully pandiagonal order 13 magic square (also
of the universal construction). All rows, columns, diagonals and pandiagonals add to the same total of 1105
(85x13). It was built using the same pattern as the Lo Shu 3x3 magic square. There are actually multiple ways to
perform this square with symmetrical results.
The Tzolkin
| The Maya Tzolkin |
|
|
| 13 x 20 Sacred Day Count |
The Mayan enumeration process is, fundamentally, a
simple one. They used a horizontal dot system to denote numbers up to 5. One dot for 1, two dots for 2, 3 dots for 3 and 4
dots for 4. At 5, and multiples of 5 therein, they would use dashes. All numbers in between would receive the extra dots as
needed while always stacking the 5's on the bottom of the number. Ultimately you gain a vertical number with each tier adding
to 5 at most.
The Maya Tzolkin, or Day Count, is comprised of a
20 day heiroglyphic system and a 1 through 13 enumeration process starting in the upper left hand corner and descending
vertically along each column to create a 13 x 20 rectangle. It is essentially a graphing process 20 tall and 13 wide. With
this process you actually count out the numbers 1 through 13, 20 times. It starts on 1 at the upper left hand corner and ends
on 13 at the opposing corner to the right. You gain 7's on each of the other opposing corners as well as a convergence of
13 and 1 at the center of the rectangle. (When counting out the numbers 1 through 13, you will notice that 7 is the center
number of the sequence: 1-6 = 6 digits, 8 - 13 = 6 digits, leaving 7 at center.) If you add numbers that are complete opposites
on the chart, they add to 14. (1 + 13, 2 + 12, 3 + 11, 4 + 10, 5 + 9, 6 + 8, 7 + 7) What also happens is the placement of
each number 1 through 13 along each row, column and pandiagonal on the 13 square. Performing a vesica pisces of perfect Order
13 Magic Latin Squares. Each row and pandiagonal add to 91 (7 x 13), each column of the rectangle averages out to 140 (though
only the central column truly adds to 140.), and is consistent with the universal constant that says, and is provable mathematically,
that magic rectangles can only be performed if both dimensions are even or odd. It is not possible to create a magic
rectangle that has an even length and an odd length.
Also to be found within the Tzolkin is this curious
highlighted area of points performing a helical looking cross shape. They have termed these, "Portal Dates", and I
am still trying to understand why this particular pattern. It contains 52 points that, when added, total 364. It can be divided
into 4 equal "Y" shapes, and opposing "Y" shapes, when paired on the diagonal, total to 182 apiece. These "Y" shapes
are also holographic. As long as all 4 are moved equidistantly from one another and in exact opposite motion from
their partner, they will continue to add to 364.
There are numerous web pages developed to define
the astronomical concepts contained in the numbers, so I won't spend much time with those. What has become interesting to
me, is the interconnections of other ancient numerical practices amongst one another, as well as, a growing connection within
our DNA numerics.
Vesica Piscses
| Vesica Pisces of 13 x 13 Magic Squares |
|
|
| *13 x 20 Rectangle is created. |
This is a vesica pisces of the same magic 13 square. It creates
a 13 digit sequence in descending fashion that mimics the Mayan Tzolkin arrangement, only this time using the numbers 1 through
169. Each number is separated by counts of 13 and 14 with a few exceptions.
A vesica pisces is traditionally made by attaching two equilateral
triangles base to base and then interlocking circles which can only touch 3 of the 4 sides of the diamond shape
that's been created. This makes it 13x19.497 in dimensions.
- 6.5x2 = 13
- 6.5x3 = 19.5
A second vesica pisces can be seen horizontally across the Tzolkin
as well. Though its size proportions out to 20x33. If you create basic shapes to interlock within each circle of
the vesica pisces (the 20x33 version), like a square, hexagon, or octagon,it starts to geometrically validate the
reason for the portal dates.
These interlocking circles are actually a cross-section of a
spindle toroid.
I feel this has relevance not only because of the numerical
structure, but also the fact that a chromatide of DNA is actually an interlocking pair of rings spun together.
I-Ching
| Chinese I-Ching set to Magic 8 x 8 Square |
|
|
| Binary Endcoded 0 Through 63 Count (note:trigrams) |
This is I-Ching and has been set to the fully pandiagonal
magic order 8 square above. It was developed thousands of years ago in China and the fundamental principles revolve around
the patterning and structuring of negatives and positives amongst one another. When stacking a pair of negatives and positives,
you obtain only 4 possible solutions: -/- , -/+, +/-, and +/+. Or 00, 01, 10, 11 in binary. The binary codice is actually
counting out 0 through 3. (00 = 0, 01 = 1, 10 = 2, 11 = 3).
With the I-Ching, they had decided to stack 3 negatives and positives atop
one another. Thus giving us the solutions: 000, 001, 010, 011, 100, 101, 110, 111 and actually counts out the numbers 0 through
7 in an octal format. They then stacked 2 of these "trigrams" as they call them, to perform a "hexagram", and there are
64 possible hexagrams to be found in the I-Ching.
Here is where our DNA numerics come into play. We have 4 primary bases in
our DNA. The bases pair off with the same partners every time and are counted in triplicate form. Cytosine with Guanine, Adenine
with Thymine. Each base is comprised of 4 basic elements: hydrogen, carbon, nitrogen and oxygen. (Except for Adenine, which
only contains 3 of the 4, no oxygen.) Each pairing ultimately holds 28 individual elements. 13 atoms in Cytosine. 15 atoms
in Guanine. 13 in Adenine and 15 in Thymine. I consider the AT base pairing as the negative pair because of
this nuance and the missing oxygen.
So, if each negative and positive in the I-Ching were to actually
represent a base pairing, and the base pairings are combined in triplicate within our DNA, then it is plausible to graph DNA
in such a way as is described in the I-Ching.
Consequently, a hexagram is a 6-bit system using the number
set: 0/1, 2, 4, 8, 16, 32. Over the course of 64 digits, you will have counted out the numbers 0 through 63. 64 hexagrams in
total incorporating 192 negatives and 192 positives in the entire structure. 1 pure negative hexagram, 1 pure positive
hexagram, 6 with 5 negatives and 1 positive, 6 with 1 negative and 5 positives, 15 with 4 negatives and 2 positives,
15 with 2 negatives and 4 positives, and the remaining 20 have 3 of each. This happens to be the sequence of numbers in the
6th line of Pascal's Triangle: 1, 6, 15, 20, 15, 6, 1 = 64 hexagrams.
Pascal's Triangle
| Pascal's Triangle |
|
|
| Binary codice and powers of 11 |
This is Pascal's triangle. It is constructed by first starting
with 1. It represents the totality of everything that is. The next row down is given two 1's, which represents the inherit
duality within totality. Negative and positive polarities permeate through everything living and non-living. And so, you see
1's running down either side of the triangle. One side represents the negative, the other side represents the positive. After
this you begin to add horizontal pairings and placing the product between them at the next row down.
As you develop more rows to add to the pyramid, a pattern
comes into view. Each row, when added, mimics the doubling process found in the binary sequence by summing to those successive
numbers.The first row represents a one bit system. 1 = negative and positive.
The second row, 1, 1 = negative or positive. The third row down gives you the polarities of a two
bit system which has four possible combinations. 1 pure positive, 2 with a negative and a positive, and 1 pure negative =
1, 2, 1. On the fourth row you are given the sequence: 1, 3, 3, 1. In a three bit system, you have eight potential combinations:
1 pure positive, 3 with two positives and a negative, 3 with two negatives and a positive, and 1 pure negative.
In a four bit system, the sequence, 1, 4, 6, 4, 1 occurs. 1 pure positive, 4 with three positives and a negative, 6 with two
of each, 4 with three negatives and a positive, and 1 pure negative. And so the sequence progresses.
A note to be made in regards to the binary sequencing, every
other row can be put to square and only squares contain neutral bytes.
Another curious structuring that occurs is powers of 11. The
second row is literally 11, the third row is 11 squared (121), the fourth row is 11 cubed (1331), and the fifth row is 11
to the fourth power (14641). After this the math becomes entangled and I have yet to secure some relevance to this sequencing.
|
