This material may be of interest to your study, Robert.

In and Outside the Square: The Sky and the Power of Belief in Ancient China
http://www.onlineclarity.co.uk/friends/showthread.php?p=108694#post108694

The Enneagram and the Lo Shu

Greetings pantherpanther,

I appreciate your insightful comments on the Enneagram, thank-you for the discussion.

I don't know what organic, practical experience they related to the magic squares.

The practical, organic experience ancient humankind may have experienced from magic squares is rooted in the merging of their cosmological belief system with everyday life, which was considered a practical and traditional way to live.

The Kabbalists used magic squares as amulets or talismans to offer protection or promote good fortune by invoking the spirits of the appropriate planet (Budge, Amulets and Talismans).

The Gnostics and Christians had used magic squares on covers of their illuminated manuscripts (example: the Lindau Gospels); it seemed practical to use sacred math (magic squares) as a designation of a sacred text.

And of course, the Shang Chinese incorporated the Luo Shu in their city planning and temple design just as the Han dynasty Chinese incorporated the Luo Shu into ceremonial artifacts such as the bi disc and TLV Bronze mirror (Cammann, Berglund, Schinz). Examples

The numerology and cosmology of the Luo Shu was also incorporated into the language of the Chinese in order to establish political authority and influence (Mark Lewis, Writing and Authority in Early China and Lars Berglund, The Secret of the Luo Shu). Examples

The Magic Squares gained more popularity in the west with the publication of Agrippa’s de Occulta Philosophia in 1533 as it was explained how to use the squares in Magic and Alchemy. Whether this was practical is open to question but it was popular at the time.

With the Enneagram, the numbers may relate, but the diagram is a partial representation of different levels of energy (it contains three octaves and a process in which they can relate in different ways) which is not really shown in the 2D drawing- rather, it is indicated.

Considering the Enneagram as a partial representation of different levels of energy is an approach that offers some intriguing possibilities. The 27x27 Magic Square may offer some insight as the numbers of the Enneagram (147/174; 258/285; 369/396) are to be found in pattern and linked to one another.

This website refers to these “enneagram” numbers as the Solfeggio frequencies:

http://theleeburton.blogspot.com/2009/03/so-here-we-go.html

I strongly believe there is a connection with the 27x27 Magic Square and music, or the three octaves. The correspondences of Magic Squares, Pythagorean Triplets, the Enneagram, the Pythagorean philosophy concerning the “music of the spheres” as well as the Pythagorean Comma seem connected and may come together in the 27x27 Magic Square.

If we may take liberties to identify the Enneagram numbers as they appear in the 27x27 Magic Square, one can consider this a three dimensional model derived from a two dimensional magic square because any Magic Square in the Luo Shu format defines a three dimensional torus or doughnut shape.

Therefore, the 27x27 Magic Square can be represented as a 3-D torus and the numbers will have a different relationship to one another than when arranged in a two dimensional matrix.

If the enneagam numbers can be treated as frequencies and the numbers have a synergistic three dimensional toric relationship then perhaps a certain tonal or musical energy can be generated from the 27x27 torus.

A true mathematical model may be there or perhaps only a part of one (and this may be intentional).To practice the Movements, as the multiplication 142857 etc., engages one in the process the E describes.

The movements are attributed to Gurdjieff, who is responsible for bringing the Enneagram to the attention of the “West”. Gurdjieff may have had special insight into the Enneagram, but I am interested to know if his was a personal interpretation or are his movements a rediscovery of an ancient tradition?

I propose the Ennegram was originally a purely mathematical (musical, energy…) relationship that later evolved into a popular westernized version that involved movements, transcendence, as well as psychological analysis.

This Enneagram on the front piece of Athanasius Kircher’s Arithmologia (1655) is numerical (but not solely) and includes three triangles but I believe Kircher has the incorrect order of the triangles so as not to give away too much “secret knowledge”.

In this art piece, Kircher makes a connection with the Luo Shu, the enneagram, the Pythagorean Theorem, and the tetractys. Note the Luo Shu is held by an angel in Heaven (consistent with Chinese mythology that the Luo Shu was presented to humankind from Heaven). The enneagram corresponds to the third eye and illumination while the Pythagorean Theorem rests on the terrestrial earth.

Arithmologia is a text written in Latin concerning the first nine magic squares and alchemy (illumination), hence the connection with the Enneagram, the Luo Shu, and the Pythagorean Theorem.

That can reveal an experience of Time and Space and laws which is verifiable but not expressible in words or the figure of the Enneagram. It couldn't be otherwise with any objective work of art, for example. A statue of a Buddha that was made by those who had conscious knowledge and placed that it, can raise the consciousness of an observer (as well as touch the being of all people, whatever their knowledge or development). A sacred Mass can do the same. Perhaps the Enneagram is not on the level of some sacred symbols, but was created as a bridge to the sacred for those who needed assistance in that direction.

The Pythagoreans and the Chinese believed that number (the language gifted from the Gods) could explain everything and lead to evolution and prosperity. Magic square “cerebral exercises” can lead to many mathematically useful revelations that can serve to raise the consciousness of a practitioner just as a mandala, a statue of Buddha, or a sacred mass can raise/alter the consciousness.

Perhaps Math was used as a bridge for “purposeful” transcendence and the vehicles were useful matrixes of numbers which were endless but none the less could serve as a guide for the evolution of humankind.

What I am suggesting is it is not "complete" and was not intended to be. It was to be a guide, so to speak. I have at moments seen the symbol of the E as "alive," which leaves me in question as to its "completeness'." Is it sacred or objective? I don't know.

Can Number (the Math of the Luo Shu and the Enneagram) not be sacred as well as objective? I believe the early Chinese and the Pythagoreans treated it as such (Marie Louise von Franz, Number and Time).

The western mind may have difficulty understanding the practical use of Magic Squares in society.

However, it is clear that the Magic Square played an integral role in early Chinese cosmology and must have been considered to have a practical use in order for the Luo Shu model to have been incorporated into religious, political, architectural, and linguistic aspects of early Chinese society for thousands of years.

Robert,
Very interesting thoughts and information to ponder

Gurdjieff was perhaps a Master of sacred dance, and he used the figure of the Enneagram in teaching his Movements. G was not a professional musician in terms of Western music, and he composed much of his music for the Movements with de Hartmann who was well-known composer in his own right.

After meetings with pupils G would often play on a simple harmonium. The music was deeply moving. His daughther Dushka Howarth made many recordings, some of which are now available. This was not simple folk music, yet I don't know how it would be analyzed by professionals. G seemed to know certain laws and how to express them to produce different emotions and states.

(I recall once I was on an old London double- decker bus in Tehran. A blind boy, a flute player was seated at the front wall which separated the driver's cab from the passengers. I forgot
where I was and when I woke up I had passed my stop by quite a distance.)

Many Eastern teachings contain a whole teaching in one picture or symbol or work of art. Gurdjieff made it his aim to make Eastern wisdom intelligible to Western minds, and he often used language of western science. He taught many individual ideas separately or sequentially although they all were parts of a whole teaching (or system as Ouspensky called it). Over many years G taught his ideas using different words and images. The Moscow version that Ouspensky recorded in Search contains much that isn't in Beelzebub,which, is the most developed and authoritative version of G's final teaching. Both Search and Beelzebub are true to Gurdjieff's teaching but different expressions. If you compare the Table of Hydrogens, the Ray of Creation the Food Diagram and the Enneagram in Search, they are all about the same essential teaching, yet not exactly related to each other in the same way. And G used different material in Beelzebub.

Hi Robert, et al,

Here are some cool videos about the work of Lee Burton on the Luo Shu. He seems to take upon some of your ideas. Very interesting.

The Luo Shu Fractality

lo shu Magic Square solfege Matrix

Field Lattice Matrix I Ching Fractal 27 Magic square continuum

sparhawk said:

Hi Robert, et al,

Here are some cool videos about the work of Lee Burton on the Luo Shu. He seems to take upon some of your ideas. Very interesting.

The Luo Shu Fractality

lo shu Magic Square solfege Matrix

Field Lattice Matrix I Ching Fractal 27 Magic square continuum

Click to expand...

Thanks for showing these videos Luis very interesting to see, with nice music from Radiohead.But he is talking about the so called No Shu matrix, does anybody know and understand this No Shu diagrams?
Cann anybod explain these to me?

Thanks Frank

Just found the explanation in the book Luis mentioned(http://www.onlineclarity.co.uk/friends/showthread.php?p=109493#post109493) in this book he explains the Well. The No Shu.
But if anybody has more information about the connection between these two, please.

thanks Frank

frank_r said:

But if anybody has more information about the connection between these two, please.

thanks Frank

Click to expand...

Hi Frank,

The "No Shu" name isn't Chinese, other than the Shu part; it is made up. It is a derivation of the Luo Shu, an invention perhaps, of the group of people Lee Burton is part of. Here is some information.

The Nu Shu and No Shu

I received an e- mail correspondence from Lee Burton last night:

I had a glance at the link last night, the no shu and nu shu are just for identifying the families of 9, i read someone wasnt sure.
So ill add it to the video's etc to be clear, sorry its i had to label them in the early work.
as there were 3 sets of 9 = 27 unified.

Also we have a thread on graham hancock.com
http://www.grahamhancock.com/phorum/read.php?f=1&i=272624&t=272624

its pretty long, but loads of questions and answers regarding all the magic squares matrices.
There's also one on the science board in hancock worth a look.

i recommend following the link to Paul Martyn smiths site, i ching math. All the same work.

thanks

lee

Enneagram Talk - G. I. Gurdjieff
http://www.endlesssearch.co.uk/philo_enneagramtalk.htm

The Lo SHu and No Shu and 4 and 5

This is a diagram with the combined Lo Shu and No Shu that is from importance to the so called extra ordinary meridians in acupuncture.
David Twicken has written a book about this subject and he comes with this diagram.
He of course never heard of this No Shu diagram.
The interesting part is that all numbers of the Lo Shu and No Shu have a difference of 5 or 4. The empty space between 4 and 5 in the enneagram, The place to come to the middle to GOD as some writers that are talking about the enneagrams are writing. The world between the Post and Pre heaven.

This extra ordinary meridians make the connection in our body to our DNA and our spiritual world.
Does anybody have some more clues looking at this diagram?



Lo Shu in black and No Shu in red.

Frank

The Lo Shu, No Shu, and the numbers 4 and 5

frank_r said:

The interesting part is that all numbers of the Lo Shu and No Shu have a difference of 5 or 4.

Frank

Click to expand...

When the even or the odd numbers are paired the difference is four. There are five such pairings.

When an odd number is paired with an even number the difference is five. There are four such pairings.

A balance of yin and yang. I think.

The group of paired odd numbers forms a right angle or gnomon.

There are more groups of paired odd numbers than paired even numbers because odd numbers reign supreme over even numbers.

Hi Robert. Firstly I must say sorry for putting an incorrect fig on page 108 of my book, this of course doesn't change the math put forward in anyway as the math is still fully described in the book, and now the correction has been attended too in free PDF, and the forthcoming reprint. This correction should indeed make the math simpler to comprehend without actually having to undo it all for oneself (if one would so wish to).

The quote from Frank appears to have arisen from the original mixture of the work done between Lee Burton and myself, a mixture of Rodin's work and the working's of the I Ching's River Maps. The use of the term No Shu or Nu Shu had been a carry-over from Marko Rodin's explanation of the value's contained within the Torus and its linkage to the Lo Shu, and as these references are confusing they are also indeed now unnecessary.

Through understanding the math of the Image's of Heaven and Earth (the 10 Cyclic Signs) as they are placed into each of the 5 Elements or Direction's of the Ho Tu, the value's of the 3 x 3 Magic Square of The Well appears (as Frank listed) = The Well has a central value of 9, and all opposites across the 8 Spoke Wheel = 9.

This integer pattern is the same in all numbers 1 to 8, as:-
12(3)45(6)78(9), to 87(6)54(3)21(9)
24(6)81(3)57(9), to 75(3)18(6)42(9)
36(9)36(9)36(9), to 63(9)63(9)63(9)
48(3)72(6)15(9), to 51(6)27(3)84(9)

This 1 to 8 leaves the central value of The Well = 0 or empty of any number, so only in the addition's of 1 to 8 etc does 9 appear as an integer sequence in which all values are between 1 to 10.

The Well 3 x 3 Magic Square gives a value to all the Trigrams of the Ba Gua, so in the 3 x 3 and the Octet of the Ba Gua a match between the Binary Images of the Images of Heaven and Earth and their integer value is found in 1 to 8, but also an 8 to 1 Sequence is also given as Earth (K'un) to Heaven (Ch'ien), as in the Directions 1 to 6 and 2 to 7 are reflective opposites of North and South, Fire and Water (Fire/Heaven = odd values, Water = even values).

The 8 Spoke of the Well and Ba Gua gives both binary and integer opposites in 8 Trigrams sequence manufactured by Heaven and Earth = the Trigrams of Ch'ien and K'un, so the addition of the 6 other possible binary combination's of the Children (Eldest = Chen and Sun, Middle = Li and K'an, Youngest = Ken and Tui) through which each Trigram has a value and its correct placement in the order. The simple ordering of the Trigrams starts with the values 1 to 6 in the North or Element of Water (Northern Gate of the Ancestors or the first values of 1 and 6) all progress + 5s and then + 10s that give the Central or 5th Element of 5 to 10.

The Ho Tu's progression is Metric, only the values 1 to 10 are used, so the Ho Tu is giving a means of creating a relationship of values between every 1 to 10 (to infinity), as can be seen in the 9 x 9 Square of the Lo Shu. The Trigram value's are given between 1 and 89 in the Magic Square of the Moon, and each relationship produces 64 Hexagrams 8 x 8.

It's only in the addition of the Metric 1 to 10 that the x 6s, 12s, 24, and then 36 appears in the 8 x 8 Square's of Mercury found in the Ho Tu give a value of 10 = 240, and only in the addition of 5 = 120 does 360 (the extra 1/3rd) appear.

The addition of all the 1 to 8s of The Well expands into the working's of the Lo Shu by the addition of 1 to 8 = 9 + 1 = 10 as a total for all pairings of opposite integers, 1 to 8, 2 to 7, 3 to 6, 4 to 5, but in the finding of the Total = 9s then 1 + 9 gives the Lu Shu's central value of 5 as all value's of 5 are not then included in the Outer 4 Square's of the Ho Tu 8 x 8 as 5 can only make a Trigram Pairing with the total = 10 = 15. The integers count 1,11,21,31,41,51 etc - 81, to 9,19,29,39, 49, 59 to 89 so all opposites = 90, and 90 = 540. This base of x6s become x 7s when the value of the binary is added to its position in the Square, as 1 + 6 = 7, or 45 + 270 = 315, and 540 + 90 = 630.

The No Shu and Nu Shu are no longer needed to explain what the Ho Tu and Lo Shu already provide as a complete package = all the value's in the Torus 1 to 9 and 1 to 89, as the measure of Time and Measure in the Lo Shu or Magic Square of Saturn/Time, as the sequence of 9s always = 9 (18 = 9, 27 = 9, 36 = 9, 45 = 9, 54 = 9, 63 = 9, 72 = 9 etc etc).

As all value's in the 1 to 9 are x 6s, simply found as a pattern common to all integers, all added together 3 times = +6s (1 + 2 + 3 = 6, and so 9 = 54, and 10 = 60 - the count of the Ho Tu is sexatenary (+60s).

My regards - Paul.

The 5th Element or Direction in the Ho Tu.

Thanks very much for your welcome.

In my last posting I should have left you all an URL to just show how the central value's of 5 and 10 produce the 5th Element of Earth.

http://web.mac.com/paulmartynsmith/iWeb/IChingmath/Blog/D6B7C725-F901-4367-807C-93A58AF88D73.html

I hope this simplifies the working's that progress from the Ho Tu to the Lo Shu - Inner to Outer.

My regards - Paul.

I noted this post.
-pp
http://www.onlineclarity.co.uk/friends/showthread.php?t=9919&page=8

Imo and for your reference, I would like to submit the following:

1) How the eight trigrams are formed – Please see the attached sketch 1.
2) How the eight trigrams are integrated and unfolded with Ho Tu – Please see the sketch 2.
3) How the pre-heaven diagram is drawn according to Tai Ji Tu – Please see the sketch 3.


Regards
Tuck
www.iching123.com
Attached Files
File Type: zip Sketch 1.zip (12.2 KB, 7 views)
File Type: zip Sketch 2.zip (59.7 KB, 6 views)
File Type: zip Sketch 3.zip (35.3 KB, 8 views)

Also, a later post:

People usually say: The pre-heaven diagram (i.e. the sequence of earlier heaven) presents the essence of eight trigrams, while the post-heaven diagram (i.e. the squence of later heaven) highlights the application (i.e. the direction and time…) of eight trigrams.
My comprehension of the first sentence of chapter 3: The sky (Qian) and the earth (Kun) are positioned, the mountain (Gen) and the marsh (Dui) exchange breath…….

Regards
Tuck

The undoing of the Integer sequences and the Binary.

Hi Tuck sorry I can't read your work on my machine.

Just to make things clearer - the work between Lee Burton and myself has progressed to the point where it now resolves all problem raised by readers of the 396 and 693 in the combination of the Binary 124875 sequence of 32 light and 32 dark values = 124875. The Binary expansion doesn't include 3s,6s,9s but they manufacture them in their combination's, this gives the link to the integer patterns as inherent within their form. In the Integer sequences such as 5 and 4 the sequence run gives 51(6)27(3)84 to 48(3)72(6)15 - and as in all the sequences the value + to 51 = 6, 27 = 9, 84 = 3 etc. So the pairings that appear in the Binary pairings and as seen in the Fibonacci the values =
124875
578421
--------
693396 But the values of matched to 9s = 396 or 693.
--------
We can take these relationships to the whole structure of the Trigrams and Hexagrams as through them the binary is added to the integer sequences, through which all the Magic Squares generated in the Ho Tu flow into the 1 + 8 + 9 + 1 = 10 gives us all the correct values in the Lo Shu. This math undoes Rodin's Torus as a 8 Spoke or 3 x 3 and not a division of the circle by 9, as 9 is only the product of all pairings in the Torus and Fibonacci which all = 3s and 6s, and then 9s in the additions of 1 to 8, 2 to 7, 4 to 5 or 81,72,54 etc.

As Robe Miller has pointed out this also fits primes, and I had stated various points on this that have now recently been accredited to others, but at least they are shown to work (all good). The first was that all primes are -1/+1 of x 6, that they fit a pattern with the 8 x 8 and the circle or spiral = 1.6.

The values of 3 6 also appear as 30 and 60 degrees in the expansion of hexagons or cubic hexagons, but also the values of the hexagrams that produce the x 6x also gives 7s. This turns the Magic Squares into the x 13s of the Mayan Count, as the addition of the extra 73rd part gives the difference between the 360 Decan or Tun, and the Sothic or Haab counts = 365. One strange point in the binary count being:
1248 +
7512
-----
8760 the Hours in 365 days.
------
Without any more messing about on these side details - the math is now completely undone and it works on all points in the Inner 1 to 10 and the Outer values of The Field Pattern (Flower of Life) as given in the 3 x 3 of The Well, and the Lo Shu as a binary to integer expansion to 9x9x9 - this expansion forms a pattern to infinity in the Metric 1 to 10 from which all the other division in the ascending and descending binary flows are found.

My regards - Paul.

http://web.mac.com/paulmartynsmith/iWeb/IChingmath/Home.html

The Mystery of the 3s, 6s, and 9s.

Hi Robert et al.

I note that there is a long standing problem in the math of the integer and binary runs, as to the generation of the 3s, 6s, and 9s. A set of numbers mentioned by Tesla as being the values that will unravel the universe.

Please note that as with other materials such as the 27 x 27 or 9 x 9 x 9 cubes that has appeared on your site after your previous contact with Lee Burton - this material is given freely and is not to be used for personal gain without permission. We just hope that the I Ching math receives the acclaim due, and to Lee's and my own work also due respect will be given in the future (easy to correct a mistake at this point so 'Why wait a whole day'). Possession or ownership is one of the biggest blocks to be overcome, and this is paramount within the verses of The Law as given in the readings to the Hexagrams by the attributes of the Trigrams. If one speaks the speak then walk the walk and find peace in the mutual understanding of what depths 'The Changes' contains but the rope of values must go all the way down to the source and be drawn up without touching the sides = the central or middle values of the Magic Squares.

The failure of finding the working's of 3,6,9 (3s) and indeed 396 and 639 (6s) has been because the integers haven't previously been matched to the integer pairing of Heaven 1 to Earth 10 as these are the Original Trigrams or the Primal Binary Opposites of Ch'ien and K'un placed as odd and even values. In other words the 3s,6s and 9s are found to be products of Hexagrams that are opposites and also reversals - this whole structure mimics the values of the Solid unbroken and the Broken Line as = 9 and 6 but in 6 the central 1/3rd is empty or clear of value.

The values I can give you on this open forum gives us an Original Trigram match to all the 5 Directions or 5 Elements of the Ho Tu as in placing 1 + 5 = 6 into the northern Gate (of the Ancestors) as this gives a count of 84 between all binary opposites. The symmetrical balanced Magic Square 8 x 8 create between 1 to 6 give a 1 to 8 Trigram count of C'hien = 123 = 6 and K'un = 6,12,18 = 36 so between them the 8 Trigrams give = 6,11,16,21,21,26,31 and 36. In this way we can have a reflective Magic Square produced by either having Upper 12345678 to Lower 12345678, or 12345678 to 87654321 and this latter gives an integer count from the Trigrams into Hexagrams of:

42,47,52,57,57,62,67,72
37,42,47,52,52,57,62,67
32,37,42,47,47,52,57,62
27,32,37,42,42,47,52,57
27,32,37,42,42,47,52,57
22,27,32,37,37,42,47,52
17,22,27,32,32,37,42,47
12,17,22,27,27,32,37,42

In this all Binary Opposites = 42 x 2 = 84 = 12 = 3, and all opposites that are also reversals of each give 3,6,or 9s.

3 to 8 =

66,71,76,81,81,86,91,96
61,66,71,76,76,81,86,91
56.61.66.71,71,76,81,86
51,56,61,66,66,71,76,81
51,56,61,66,66,71,76,81
46,51,56,61,61,66,71,76
41,46,51,56,56,61,66,71
36,41,46,51,51,56,61,66

I'll leave the reader to undo the other Squares, of 2 to 7, and 4 to 9, as these give a reversal from Light to Dark as 2 and 4 are both even or Earth values so their sequences start with K'un not Ch'ien and give 8 to 1 and 1 to 8.

This process is then carried on through all the other Directions of the Outer plus their total value found in 5 to 10 the 5th Central Element of Earth. The Outer values of the 4 Direction are called the seasons or the Quarters and the average value of the 8 x 8 = 2160 or 4320 Light and 4320 Dark.

The other Directions of 2 to 7 = opposites 54 x 2 = 108 = 9, 3 to 8 = 66 x 2 = 132 = 6, and 4 to 9 = 78 x 2 = 156 = 12 = 3. Finally 5 = 30 and 10 = 60 = 90 x 2 = 180 x 2 = 360 = 9. In the 2 Sequences of 1 to 8 and 8 to 1 the total given in the 5 Elements = 360 x 2 = 720, giving 360 Light and 360 Dark.

These values of 1 to 10 thereby give a complete expansion through the matching of binary to integer, and in this the whole construction of the symmetry within the levels are found as a total division of 360 degrees of the circle, and as I have explained the 360 division gives us the the correct relationships between the Sothic, Venus, Earth to Sun etc, and the Tropical, Polar, or Mean Circumferences of the Earth - the scope is vast as to what these value can be applied to.

The binary of the I Ching reveals the secret of the universal code bound to the whole structure of matter as in the Field Pattern or Flower of Life, in the Octave and then the Solfeggio count. The Solfeggio has a 21, 42 or a 63 base, and progresses by 111s as given in the opposite and reversed values of the Lo Shu.

I hope this helps to clear up what you have not understood in this matter so far - Paul.

The 27 x 27.

Hi Robert et al.

The 27 x 27 as is given on your site has little to do with the 27 x 27 put forward within my own or Lee Burton's work, so I give my full apologies for giving any such conception that it might be otherwise than gained from your own investigations. As for the 9 x 9 x 9 cube of the 8 x 8 x 8 in the Ho Tu's 5 Elements, they give up their values by adding the 5th central square of each of the 16 x 16 Outer Squares as in 1 to 8 = 9 and + 1 = 10 + 5, this again doesn't appear within your work, so again my apologies for any misleading statements made.

I repeat my words that whatever does appear in my work is for sharing openly, and is not considered 'Mine' for any personal gain, as in sharing may we hopefully come to mutual understanding of what the math and narrative of The Changes means.

My regards, and I hope your investigations bring much reward - Paul.

Progress on 111 to 999 expansions.

Hi Et Al.

Just to leave an update on progress made since last posting.

The relationships between Central Values of the Magic squares as in The Well and Lo Shu 3 x 3 fits into the values termed as Solfeggio with its 111 expansion.

All the values given are + 6 as they also are in the Trigram values 1 + 2 + 3 = 6, the values given in Solfeggio (a modern concept but ancient working) = + 111 from a 63 base = 174 - so 1 + 6 = 7 + 6 = 13 = 4 (all contracted integers within 1 to 9).

174
285
396
417
528
639
741
852
963
----
174

The Central Values = 7 gives 5s (5555 to infinity). Central 8 = 7777s. C9 = 9999s (as in The Well and Bagua), C1 = 2222s, C2 = 4444s, C3 = 6666s, C4 = 8888s, C5 = 10s = 11110 (as in Lo Shu) and C6 = 33333s.

We can thereby list the values of 12345678(9) = 51627384(9)51627384 (contracted values of 4s and 5s from central 9 of The Well and Bagua all = 9 in opposite binary images and integer value).

123456789
516273849 =
-------------
639639639, so 4s and 5s = 2s and 7s =

516273849 =
753186429 = 369369369.

These values fit all the layers of the binary progression (as now shown in graphics on Lee Burton's Blog) 124875 124875 = the Binary Contraction. We therefore have a complete union between the ancient math and the modern math of Physics (Change).

The inherent contraction of integers placed into the binary images of the Trigram that generate the 8 x 8 Magic Squares of the 5 Elements of the Ho Tu produces the Lo Shu through a Metric Progression, that with the addition of the Outer Elements or Direction all = 10 produces all values needed (and exactly) by the addition of 5 = 15 = 6. This giving a consistent working to the math throughout the whole.

My regards et al - Paul.

Free download of book has been corrected in spelling and grammar and revised in math - please enjoy.

Please note that another typo has been found (I'm very good at such mistakes it appears) on page 105, the texts 'Earth 7 to Heaven 2' should indeed read Earth 2 to Heaven 7. The Yin Sequence always starts with an even integer = Earth, the Trigram K'un. My full apologies (again).

http://files.me.com/paulmartynsmith/18ud0n

Well numbers of the luo shu

WELL NUMBERS OF MAGIC SQUARES IN THE LUO SHU FORMAT​

Well numbers symbolize the center or axis mundi of magic squares. Well numbers of magic squares in the Luo Shu format have an additional significance: they are part of a Pythagorean triad of numbers that help provide the mathematical formula to define space.

At the heart of every Luo Shu magic square lies a Pythagorean triplet.

I thought it interesting to begin the 111 expansion beginning with 36. The numbers that follow would then be:

147 - 3
258 - 6
369 - 9
480 - 3
591 - 6
702 - 9
I am not understanding how the well numbers of the higher order magic squares are used in the 111 expansion and how it relates to the solfeggio frequencies.

I believe pantherpanther had some insight of this. I do not understand binary and tertiary language but indications are this is the key to understanding the relationships of the Luo Shu / He Tu, the trigrams, and music.

The luo shu, the solfeggio scale, and the torus

MAGIC SQAURES AND TORIC RELATIONSHIPS


The 9x9 magic square in the Luo Shu format can be transcribed so all the numbers are reduced to their Pythagorean root number.

For instance, 37 = 3 + 7 = 10 = 1 + 0 = 1

This creates a new magic square using only the numbers one thru nine. There are some interesting features to this new magic square:

1. Five is the center number of the square as five is the center number of the numbers one thru nine. Five is also the center of the 3x3 Magic Square known as the Luo Shu.

2. The diagonals in one direction consists of one integer only, and the diagonals in the opposite direction is always a continuous progression of numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9....

3. The magic square forms a three dimensional torus. That is, the numbers continue in order from one edge to the opposite edge allowing the two dimensional square to be folded once into a tube shape then a second time to form a torus.

4. The numerical pattern in the column, row, and one diagonal direction is: 1, 6, 2, 7, 3, 8, 4, 9, 5, 1…

5. The 9x9 Magic Square and the 27x27 Magic Square in the Luo Shu format can have their numbers transcribed into their Pythagorean root numbers and still maintain a magic square as well as define a torus. The next magic square able to do this would be the 45x45 magic square.

The significance of all this is that the torus shape has important industrial uses.

When the numbers of magic squares are used to construct a torus shape, the numbers have an ideal harmonic balance that may create a synergy that offers the least resistance to electricity.

The harmonics may be related to the solfeggio scale (in red), an ancient musical scale that had powerful implications not understood by present society. There are six frequencies separated by an interval of 111.

Beginning with 63 and doing the “111 expansion” one arrives at:
If we refer to the 27x27 Magic Square in the Luo Shu format (see attachment below) and follow the progression of the above numbers: 63, 174, 285, 396, 507, 618, to finally 729 – the last number of the square – a pattern is established. If we continue the pattern in the 27x27 magic square, we will pick up the other numbers of the solfeggio harmonics (in red):

Furthermore, these numbers, 84 thru 639 are linked on the diagonal to the numbers 111, 222, 333, 444, 555, 666.

And the numbers 174, 285, and 396 are linked on the diagonal to the numbers 147, 258, and 369 – the numbers of the Enneagram.

​

All of these twenty four numbers listed break down to the Pythagorean root number of 3, 6, or 9.

Theory proposal: when the numbers of a large magic square in the Luo Shu format are transcribed into their Pythagorean root numbers a magic square is generated that is in perfect harmonic balance that also (can) describe a torus and this may have powerful toric implications.

Hi Robert,

Apropos Magic Squares, the other day I came across this book in Google Books:

Magic squares and cubes
By William Symes Andrews, Paul Carus, Lorraine Screven Frierson, Charles Albert Browne


Perhaps you've seen it already. Cool stuff in that old book.

Magic Squares and Cubes by WS Andrews

Hey Luis,

Yes, I have the Andrews book, published in 1919. I liked the paperback so much that I wanted to invest in a hardcover version and paid $90 over the internet for a xeroxed copy of the paperback with a hard bookbinding. Copyright law does not apply to books of this era.

On page 150, CA Browne published the first known 27x27 Magic Square. However, his square is not in the Luo Shu format BUT his square does feature 365 as the center number of the square. Browne's article, Magic Squares and Pythagorean Numbers, makes several interesting points:

1. The use of the number 729 in Plato's Republic
2. The importance of the number 729 in the Pythagorean system
3. Odd numbers were superior to even numbers
4. The reference of the 27x27 Magic Square and the calendar
5. Pythagorean harmonics (the octaves and numerical ratios)

Similar to the topics that we have discussed here on this thread. It is impressive that Browne could build such a large square without the aid of a computer, every time he changed a number he would have to re add the row and column affected, 27 numbers in each.

I have included two attachments in my previous post that show:

1. the 27x27 Magic Square in the Luo Shu format with the numbers of the solfeggio frequencies highlighted in a specific pattern
2. the 27x27 Magic Square reduced to its Pythagorean numbers one through nine

Values of Changes in Solfeggio and Torii.

Hi Robert.

Thanks for your mail and question. Yes this does have a lot to do with the work between myself and Lee Burton. The pattern you find of 369369 also has an opposite of 639639 in which all values in The Well and Binary Opposites of the Bagua are found in the values 3 and 6, but in the 1 to 8 of The Well and Bagua the other values given in the contracted integers = 2 to 7 and 4 to 5 as I have already explained in the previous postings.

The central value of the Well = 9 and all expansions in the 8 directions all = 9s and run as follows:

75318642>9<75318642>9< = 2 and 7s
51627384>9<51627384>9< = 4 and 5s
------------------------------
36936936>9<36936936>9
------------------------------

51627384>9<
12345678>9<
---------------
63963963>9< so we have gone full circle as 123456789 + 6s = 2 and 7s.
---------------

The way these values can be tied to what is now termed Solfeggio is in the 111 sequences that start with 63 + 111 =

174
285
396
417
528
639
741
852
963 - but this pattern is also reflected in all + 111 counts as

123
234
345
456 etc, so it's inherent in all integers in the fact that the central value of The Well and Lo Shu give the central value of 5 = 10s (1) and 9 = 9s, but all values can be included =

Central value =
852 = C5 =10
396 = C9 = 9
741 = C4 = 8
285 = C8 = 7
639 = C3 = 6
174 = C7 = 5
528 = C2 = 4
963 = C6 = 3
417 = C1 = 2
852 = C5 = 10 = 1. So the contracted integer runs are total interchangeable with each other, and also the value of C = the value found in all expansions as in the Lo Shu C5 = 11111s in all crossover or reversals of the values, or n the Well C9 = 9999s (this is present in every C = value). This generation of values C = is to infinity but only need be taken to 9 in the values of the Magic Squares that are manufactured in the 9 Stack or which appear in Rodin's Torus.

Lee gives all the values in his work and so both math comply.

It's the value of 4 and 5 that appears in the Ho Tu as 5>162738495>1 gives the 5 directions of 1 to 6, 2 to 7, 3 to 8 4 to 9 and 5 to 10 as the 5 Elements and that each of these relationships found in the Trigrams of Ch'ien and Kun in the value's of Heaven and Earth produce a 1 to 8 in the Trigram sequence that produces the 8 x 8 Magic Squares - as in the reduction all the values that give the values of Time contract back 3, 6 and 9s. The average value of each of the Outer Squares/Directions/Elements = 2160 so a total of 8640 appears = to 240 + 120 = 360 = the values of the 360 day-year = 4320 light and 4320 dark or the values in the 9 x 9 square of the Lo Shu that are said to set the gods and demons in motion, and in the addition of the values 10 + 5 the Great Cycle of 12,960, 25,920, and = 51840 is attained. Interestingly the values of the 9 x 9 give the working's of the Ho Tu in each integer expansion of the Trigrams 1 to 8 = so then 1 can be + 9 = 10 so the expansion is Metric. In the values of the Trigrams all = 6s so 1 = 6 to 89 = 534 = 90 = 540 so 5 or 45 = 270 (same as values found at Angkor Wat and to those that can be applied to the GPs as 540 + 216).

The value of 729 is the main value being mentioned in many recent posting on this by Lee and now some other people's investigations. So please read both my own and Lee's work for the full pic.

I hope this is of assistance - sincerely - Paul.

p mac said:

It's the value of 4 and 5 that appears in the Ho Tu as 5>162738495>1 gives the 5 directions of 1 to 6, 2 to 7, 3 to 8 4 to 9 and 5 to 10 as the 5 Elements and that each of these relationships found in the Trigrams of Ch'ien and Kun in the value's of Heaven and Earth produce a 1 to 8 in the Trigram sequence that produces the 8 x 8 Magic Squares - as in the reduction all the values that give the values of Time contract back 3, 6 and 9s.

Click to expand...

This I like very much. The numeric pattern of 1, 6, 2, 7, 3, 8, 4, 9, 5.... is related to the Ho Tu and the Luo Shu torus.

Question on the 111 expansion beginning with 63:

p mac said:

The way these values can be tied to what is now termed Solfeggio is in the 111 sequences that start with 63 + 111 =

174
285
396
417
528
639
741
852
963​

-

Click to expand...

From 396 to 417 is not 111 but 21. Why is there this interruption then a continuance of an expansion of 111?

I find it interesting that even with this numerical interruption above, there is no interruption of this pattern in the 27x27 Magic Square in the Luo Shu format.

robertluoshu said:

Beginning with 63 and doing the “111 expansion” one arrives at:

174
285
396
507
618
729 = 27x27
84
195
306
417
528
639​

Click to expand...

Indeed this was my first question.

Hi Robert indeed when first seeing the Solfeggio site this question as to why 21 appeared between 396 and 417 was my own first question ???? The working's given in the Book of Changes only follows sequences with center 1 = 417 so all values to infinity from central 1 = 222 etc in the cross-over of the Magic Square as +

963
417
852 so all are 1627384951 as in the Ho Tu, in which all the Squares 8 x 8 in the 5 Elements generate the values of Time and the Measure of the Cycles of Change.

The way you now laid out the math concurs with my own working's and with Lee's, as each central value produces a set value as C1 = 2s, C2 = 4s, C3 = 6s and so on as already described in previous postings and in The Sum of Things.

The only part that that I would question as a base is in the workings of the 8 Spoke wheel and not a division of 9 being the base as 9s is the product or the central value of The Well. If you are dealing with the Binary Trigrams 1 to 8, and all other values within the Trigram Pairings then as also pointed out the integer relationships are 1(9)8 or 8(9)1, 2(9)7 and 7(9)2, 3(9)6 and 6(9)3, 4(9)5 and 5(9)4. In the listing of the Ho Tu it gives 4 to 5 as 1627384951 which already seem to have now looked at. You are not only dealing with integers but also their link to the binary structure of the Changes, but it's all now so close to a mutual math that I see no problems in them coming together.

The well has a central of 9 and gives 999s in all directions of cross-over integers within the squares to infinity, and the Lo Shu from central 5 gives 1111s as 10s to infinity. But in the Torus or Torii every value produces 9 from 1 to 8, and only in finding the values of 1 to 8, and all the Opposite Binary pairings = 9 are the Central relationships confirmed as each C value gives sequences from 111 to 999. Lee's work will also confirm this for you in respect of the contract values, but you must undo the Trigrams and Hexagrams to also gain the expanded.

I feel we now close enough in the math to say that the work is understood and that in the values of the addition of the extra 73rd part of 120 hours to 360 in the division of 8640/72 the value of 8760 is found in the 365.

So indeed Robert I leave all this with you and look toward a future in which the math of The Changes is now being revealed. My regards and all the best - Paul.

More on the ancient workings that fit modern physics.

Hi Robert.

Shame this thread was left in limbo as we were getting so close to a mutual on these workings.

I can now add that Scot C Nelson who has worked with Marko Rodin on the math of the Torus appears to be putting forth the same math, a change in what they term Vortex math to now become I Ching Math. The only difference between us all is the 8 Spoke with a central 9 that manufactures the all values linked between The Well and Ba gua - thereby giving us a integer to binary interchange in the 1 to 8 = 9s. Scot has used the contracted integers as I put forward and seen the manufacture of the Central Value to the cross-overs or reversals in the Magic Squares of 111, 222 333 to 999 expanded to infinity as a balanced perfect Magic Square in both number and binary.

I noticed you also used the 9 division whereas myself and Lee would only see 1 to 9 as a product of 1 to 8 in both integer and binary images of trigrams. The 1 to 9 appearing in the product of the Ho Tu's values as they create the Lo Shu. I give this in the Outer Direction's or Element's as 1234 to 6789 with 5 pairing to 10 in the 9 x 9 Magic Square that in turn gives us the value of 10s and 15 (all generated from the 8 x 8 Magic Squares or circle of 64 Hexagrams in each Quarter plus the Central 5th Element). The Ho Tu using 1627384951 which is linked to the obvious expansion of the contracted integers 5 and 4 = 516273849-51etc also to infinity.

All this math is so close, and so I hope we can continue this thread to gain a mutuality on how everything works. More has been added to Lee Burton's site and to my own book's new edition of 'The Sum of Things' now available from ABE Books. So as Rodin is now considering the same workings I hope we can bring our math to a conclusion and allow the old to meet the new.

My sincere regards - Paul.

Question for all

Hello mi name is Romina and i live in Uruguay. Sorry! my english is horrible! I am maths teacher. I am studyin the King Wen sequence. I know that there is an extensive work that made R.S. Cook but my observations are about the simmetry and sums. I would like to discuss with someone interesting in this work. Thanks. Romina.
P.D. Si contestan en español mejor!!! Gracias.

Qué tal, Romina,

Bienvenida. Gracias por escribir y preguntar. Te cuento que también soy de Uruguay, aunque transplantado hace 25 años a los EEUU. Hay otro uruguayo por acá, Sergio, y tenemos a Charly que es de Argentina.

Si querés saber más sobre el trabajo de Cook, digerido y en español, no tenés más que ir a lo del amigo Raúl Jurovietzky y el sitio Saiching de Argentina y empezá por acá:

http://www.saiching.org/novedades.htm#junio2008

Saludos,

Gracias

Gracias por su respuesta. Me alegro de encontrar uruguayos por acá. Tal vez no me expresé bien pero mi idea no es discutir el trabajo de Cook, sino discutir un trabajo que yo elaboré sobre la disposición de hexagramas del Rey Wen. En el trabajo que he elaborado he realizado observaciones sobre simetría y sumas que me han sorprendido muchísimo. Quería saber si en esta comunidad hay alguien interesado en discutir eso. He visitado la página de la sociedad argentina de i ching y fue a partir de un artículo de Raúl Jurovietzky que comencé a realizar el trabajo. También me he comunicado con él y le he mandado el trabajo, estoy esperando su respuesta. Pero tal vez encontraba por aquí a otras personas interesadas en esto. Gracias nuevamente. Saludos. Romina.