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The Luo Shu - the language of numbers

Sparhawk

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Chris Lofting posted this link in FB. It looks like an interesting book and the price of the e-version is very reasonable.

The Luo Shu - the language of numbers

I don't think it reaches the level of Lars Berglund's dissertation but perhaps interesting for some.
 

charly

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Chris Lofting posted this link in FB. It looks like an interesting book and the price of the e-version is very reasonable.

The Luo Shu - the language of numbers

I don't think it reaches the level of Lars Berglund's dissertation but perhaps interesting for some.
Thanks very much, Luis.

I've stopped working with numbers long ago but it seems very interesting, well designed a clearly exposed.

Abrazo,

Charly
 

fkegan

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Hi Luis and Charly,

If one looks at the actual "language of numbers" section of this source:
The arrangement of numbers into a Magic Square reveals a language in terms of practical math that the ancient Chinese found useful and was part of a revered system of faith that was referred to as the Yi Jing. The Pythagorean Theorem exists within every Magic Square in the Luo Shu format and teaches the fundamentals of algebra which in turn could give man the tools to measure distances.

This math is the basis for land surveying as well as for charting the stars. The Chinese believed that the movement of the stars and celestial events such as eclipses greatly influenced life on earth. This use of numbers would help man to establish some order over the apparent chaos of the heavens; the Chinese believed that numbers (or math) contained a higher intelligence and if used properly could have a positive effect on the yin yang balance. The objective of the Yi Jing is for man to be at one with Heaven and earth and this math was used to help achieve this end.

Shows a bias in favor of modern math and a lack of understanding about Pythagorean math other than the detail of the Pythagorean theorem (Euclid I.47). The rest of the conclusions follow from the errors quoted above.

Regards,

Frank
 

robertluoshu

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The Luo Shu - the language of numbers Reply to Thread

The web site: The Luo Shu - the language of numbers is a synopsis of the book: Number, Time, and Archetype. It is meant as an interpretation of the Luo Shu by the ancient Chinese using the progression of higher order magic squares in the Luo Shu format.

This work definetly does not rise to the dissertation of Lars Berglund, that is one special book and very few books can touch it.

The book does help explain the cosmo-magical symbolism and the Chinese reverence for the Luo Shu by examining the math of the gnomon and the Pythagorean Theorem. It also gives an explanation as to why the Luo Shu is a model that helps to explain the concepts of Time and Space.

The higher order Magic Squares in the Luo Shu format are related to the Yi Jing and played an integral role in prognostication as well as calendar making.

Robert Dickter, author of Number, Time, and Archetype and web master of www.luo-shu.com
 

fkegan

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Hi Robert Dickter,

It's a long way from the single detail of the number triples that yield right triangles to Pythagorean mathematics or philosophy, especially when you start with modern algebra and numbers beginning with zero. Ancient geometry is a very, very different science of magnitudes and units. Ancient arithmetic, called number theory nowadays, is about the essential meaning embodied in each number, not just their place upon a number line. The best introduction to Pythagorean number today is the dot-number patterns upon the dice cube or Pythagorean computer.

The assumption that any mathematical system can be claimed to explain mathematically the I Ching is just modern superstition, as is the 27 x 27 magic square which centers upon the number 365 which is of no use to any one really. Modern solar year calendars use 365.25 days (requiring leap year every four years) and ancient systems use the common denominator of the numbers 1 to 10 (except 7) which is 360.

Your web site and magic square makes much use of the number seven, though without any explanation of why this special number (the perfect number 1+2+3= 1*2*3 rendered prime by adding 1) is of such importance in forming the giant magic square. There are no traditional mathematical proofs or any indications of how any of this work relates to Chinese philosophy in general or the Chou Yi (I Ching in the King Wen Sequence) in particular.

However, it is a lovely giant magic square with many algebra and arithmetic calculations to entertain and amaze the reader.

Best Regards,
Frank
 

robertluoshu

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To the respectable Frank Kegan (only),

Number triplets that form Pythagorean Triads in Luo Shu magic squares represent a significant discovery. No one in four thousand years has made this association that is known. It is a short walk from here to Chinese philosophy and numerology. The primary purpose of numbers and math is for measurement. Math represents the only truth, everything else is illusion.

The best introduction to Pythagorean mathematics today is to examine its root origin, which is Chinese.

If I am to be criticized, please quote me correctly. I never said that my mathematical system could explain the Yi Jing. I said in the above paragraph that higher order magic squares are related to the Yi Jing and play a role in prognostication and calendar making. This is a far cry from claiming that I have all the answers.

My work may be of no use to you, but in the short time my research has been publicly posted a mathematical proof has been written and published, and ground breaking progress has been made on “retention” Magic Squares in the Luo Shu format.

I do not have to explain why the number seven is so significant, it is enough to demonstrate how the number seven plays a significant role in understanding the “language of numbers”.

Other people can explain why this, or philosophize about that. That is the point of research, to open the minds of people and stimulate thought as well as to interact with one another. And if were lucky, we evolve. There is no evolution with judgements and criticisms.

This work represents the beginning of much more research and insight into Magic Squares in the Luo Shu format. This is not for everybody, it is for people with open minds who seek knowledge or entertainment. It is good, innocent fun and a great way to use the mind.

Persistence, confidence, and hard work will triumph in the end.

Robert Dickter, author, Number, Time, and Archetype webmaster of www.luo-shu.com
 

fkegan

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Hi Robert,

Perhaps if you were clearer in your claims and your proofs it would be easier for others to find your work commendable.

I don't know if Pythagoras arose from Chinese philosophy, though I agree they do explain one another. However, I do not find any "measurement" involved in fundamental Pythagorean number symbolism or in Chinese philosophy. Nor any greater truth in Math than in anything else. Ultimately, all is maya. Though as the master who ran from a charging elephant with his student, noted to his student who asked, Master, do you not teach that the elephant is but maya, illusion?"
"Yes, but my running is illusion (Maya) too."

OK, so what is the relationship you see between your magic squares numbers and the I Ching? You don't make any clear statements beyond your magic squares are based upon Pythagorean triples. OK, how does that relate to anything?

I commend your attitude of hard work. Keep at it. Criticism is not contingent upon others knowing your work better. It arises from your not explaining yourself clearly.
Each of us must face criticism, deserved or not in our own eyes, but only further effort and more clarity of expression is of any use to anyone.

Your work has many 7's in it for reasons you do not know. OK those who like 7's will be intrigued. The rest of the universe will wonder what is so important about a magic square no matter how big it is. Answering that question, not just to me, but in general will be important. Finding great meaning in a magic square of vast extent derived from an algebra equation seems more the work of an earlier era. Do you truly claim no one else worked out the formula for deriving and developing magic squares?

Though, again, your work is extensive, entertaining and filled with interesting numbers. Congratulations, again.

Frank
 

robertluoshu

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The Luo Shu - the language of numbers Reply to Thread

Hello honorable Frank,

My math is a rediscovery of the Math the ancient Chinese used concerning magic squares in the Luo Shu format. This math has been rediscovered thousands of times of the the last four thousand years. Plato, Socrates, Pythagoras, Lucas Pacioli, Leonardo da Vinci, Albrecht Durer, Raymond Llully, Giardano Bruno, Al Buni are just some examples of people who were aware of this math. Actually, if I can rediscover it, I am sure it is not too difficult, my last math class was 35 years ago and I never made it past algebra.

Can I prove the above statements? No. But neither can you prove that anyone has worked out the formula for generating Magic Squares in the Luo Shu format. What is clear is there is no publication in existence that has a set of higher order magic squares in the Luo Shu format (prior to my publicaton), nor is there any publication that has the formula, nor is there any publication that makes the connection to the Pythagorean Triads that occur in the middle of each and every Magic Square in the Luo Shu format.

Frank, if you know of any publications, please, share with us. If you know about the number seven, share it. I do not know why the number seven, I only know how it is (sometimes) used in Magic Squares (in the Luo Shu format).

I am just the messenger.

Actually, the formula has been published now by Aale de Winkel. So one of my earlier statements is actually out of date. But Aale just published his article only two weeks ago, with my influence.

I am often asked, "What is the point", and my standard reply is, "there is no point".

For those who are interested, the ancient Chinese revered the Luo Shu as a cosmo-magical symbol that was a model that helped explain Time and Space.
Space as in the Pythagorean Theorem, and Time as in the calendar.

A pleasure once again,

Robert Dickter, author of Number, Time, and Archetype webmaster of www.luo-shu.com
 

fkegan

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Hi Robert,

Things are always better when folks are clear in their statements. Though others might be as bewildered as I was about the progression of claims finally winding down to this ultimate statement of what you see your work to be.

As a formula for the generation of magic squares in the Luo Shu format I am convinced your work is excellent. And to your statement that there is no point to this exercise in pure math; I agree and that is also excellent.

I would quibble only with the notion that Socrates was a discoverer of mathematical wonders. I am firmly convinced his only contribution to anything was to inspire Plato's dramatic dialogues and other works attempting to resolve Socrates' PTSD nightmares from the catastrophic Athenian defeat in the Battle of Delium. However, what is an extra name in a list of luminaries?

Time and Space are very slippery notions. Your definition of them as Euclid I.47 and "the calendar" is a nice clarification.

Good Luck with your work.

Frank
 

erime

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Robert Dickter,

Hi - really nice website you have made. I enjoyed looking through many of the pages.

I was wondering whether you would be interested in how the Lo Shu has been used as one of the calibration devices when creating the Former and Later Heaven trigram sequences from the arrangements of the visible celestial bodies around a Taiji symbol?

My thread here explains the procedure, and the Lo Shu comes in to play in post #8. Maybe you would have some additional insight, being so much more familiar with the Lo Shu than me?

Thank you for putting all that information online.

All the best,

Erime
 

fkegan

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I was wondering whether you would be interested in how the Lo Shu has been used as one of the calibration devices when creating the Former and Later Heaven trigram sequences from the arrangements of the visible celestial bodies around a Taiji symbol?

Hi Erime and Robert,

I thought you two were doing similar work. Nice to see you connected with one another. There is another fellow working on relating the Taiji symbol to astronomical data, I don't at the moment remember his name or thread, but others may well.

There is the minor quibble that the Taiji and all of the notions of Yang and Yin are not fundamental or original to the Yi and particularly the King Wen Sequence. However, that is only important to those who care about historical accuracy or philosophical implications of ancient geometry.

I hope you are able to help each other in your mutual projects to make algebraic calculations to be applied to current notions of I Ching.

Regards,
Frank
 

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Hello Erime,

An important discovery was made last night concerning magic squares. I refer you to the new section of my web site titled "Outside Contributions" and the 7x7 Retention Magic Square that generates the number 365.

Notice the color and resulting shape of the numbers referred to as water retention cells. This is known as the Ya - shape, an important symbol to the ancient Chinese. For a better explanation of the use of this symbol, please read Chapter Nine, especially the subchapters Temple Design and TLV Bronze Mirrors and the Ming Tang.

This now means there are two 7x7 Magic Squares of importance that you might consider using in your system:

1. The Magic Square in the Luo Shu format that generates the central number 25.
2. The Retention Magic Square that generates a central symmetrical lake of retention numbers in the shape of a cruciform with a water retention value of 365.

Each Magic Square will generate a set of important numbers.

I thought you might find this interesting,

Dr. Robert Dickter, author, Number, Time, and Archetype owner, www.luo-shu.com
 
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erime

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Thanks Robert. I am not sure how 7x7 magic squares would help me - the Iching is 8x8 in format. I will check it out anyway, when time permits.

Regards.

Erime
 

frank_r

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The magic squire with the number 6 in the middle

Some time ago I found a magic squire with the number 6 in the middle.Does anybody from you know this one to.
And if you do you know how they use it in China?

Frank
 

robertluoshu

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The Luo Shu - the language of numbers Reply to Thread

To Frank R.,

I need some more information such as what is the size (order) of the square? For example, is it a 3x3 Magic Square, a 5x5 Magic Square?

If you saw a number in the center of the square, by definition it must be an odd magic square. The problem is there are several hundred thousand arrangements of numbers for the 5x5 Magic Square, and over a million differnt arrangements for the 7x7 Magic Square!

Also, where did you see this magic square? Do you have a reference?

Robert Dickter, author of Number, Time, and Archetype and web master of www.luo-shu.com
 

frank_r

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To Frank R.,

I need some more information such as what is the size (order) of the square? For example, is it a 3x3 Magic Square, a 5x5 Magic Square?

If you saw a number in the center of the square, by definition it must be an odd magic square. The problem is there are several hundred thousand arrangements of numbers for the 5x5 Magic Square, and over a million differnt arrangements for the 7x7 Magic Square!

Also, where did you see this magic square? Do you have a reference?

Robert Dickter, author of Number, Time, and Archetype and web master of www.luo-shu.com

Hello Robert,

This squire I found in a article about magic squires. The Luo Shu is the most used common one but this one they allso used with the Chinese Calender.
This one counts up to 18(9). And together all the nummbers are 11 all together 99 the number of the cosmos.
With this you have the time calculation of the calender.
5 is the number of earth and 6 the number of Heaven.

The Luo shu is used to explain the meridians(I'm a acupuncturist), but I try to understand how I can use the second one to explain some acupuncturist insights.
So that was my question, do you know how you can use this magic squire? What is the 6 about in your personal way of thinking.

The references I have are from an article from Willem Venerius a Dutchman that wrote about it, and the book from Marcel Granet, Das Chinesische Denken. A whole chapter is about this squire in combination with the common Luo Shu.

Frank

6inmiddden.jpg
 
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robertluoshu

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Wonderful square! I have not seen this before and the wonderful references you name are not available in English (if they are please let me know), although Marcet Granet is one of the great originals!!

The ten has replaced the one of the conventional Luo Shu. Here the square reflects a predominance of even numbers which form a cruciform shape with six as the center, while the odd numbers occupy the four quadrates. In Shang Chinese cosmology, the even numbers represent Earth so this particular square is the "Earth" and the Luo Shu, with its cruciform shape of odd numbers and five as the center is the "Heaven" square.

This square shows a Pythagorean triad of 6, 8, and 10. This is pretty good news!!

Perhaps the six symbolizing heaven is because it is the center of the square, the center also representing the non-being or wu state. And the five represents Earth because it is in the quadrate of the square and not the cruciform.

Five and six are used in Chinese numerology but some one else would have to weigh in.

The cruciform shape was of high significance to the Shang Chinese and was represented by the Ya character, it means the center or centrality. The ya shape was the ground plan for royal tombs and the Ming Tang temple. The symbol is incorporated into the TLV Bonze mirrors and the Jade Bi disc, as well.

The constant of the above square is 18, while the total sum of the square is 54, or the product of the size of the square and the constant. The calendar correspondences you offer I do not understand.

Do you think an eleven replacing the two would generate yet another magic square, this one with a cruciform shape of odd numbers and the even numbers in the four quadrates?

Robert Dickter, author Number, Time, and Archetype and webmaster of www.luo-shu.com
 
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frank_r

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Wonderful square! I have not seen this before and the wonderful references you name are not available in English (if they are please let me know), although Marcet Granet is one of the great originals!!

The ten has replaced the one of the conventional Luo Shu. Here the square reflects a predominance of even numbers which form a cruciform shape with six as the center, while the odd numbers occupy the four quadrates. In Shang Chinese cosmology, the even numbers represent Earth so this particular square is the "Earth" and the Luo Shu, with its cruciform shape of odd numbers and five as the center is the "Heaven" square.

This square shows a Pythagorean triad of 6, 8, and 10. This is pretty good news!!

Perhaps the six symbolizing heaven is because it is the center of the square, the center also representing the non-being or wu state. And the five represents Earth because it is in the quadrate of the square and not the cruciform. [/url]

Granet is writing on page 147: "... mag auf den ersten Blick überraschen, geht es doch um die Erklärung, daß die (ungerade) 5 zur Erde (die yin ist) und die (gerade) 6 zum Himmel (der yang ist) gehört. Sie bringt nur dann eine Erklärung, wenn man implizit begreift, daß bei ihrer Vereinigung Himmel und Erde ihre Attribute vertauschen."
Translated in Englisch: " … may this at first sight surprise, goes it nevertheless around the explanation that (odd) the 5 to the earth (yin ) and (even) the 6 to the Heaven (yang ) belongs. It brings an explanation only if one understands implicitly that when the combination Heaven and Earth come together they change places.


The cruciform shape was of high significance to the Shang Chinese and was represented by the Ya character, it means the center or centrality. The ya shape was the ground plan for royal tombs and the Ming Tang temple. The symbol is incorporated into the TLV Bonze mirrors and the Jade Bi disc, as well.

The constant of the above square is 18, while the total sum of the square is 54, or the product of the size of the square and the constant. The calendar correspondences you offer I do not understand. [/url]
Granet is writing that these squires together explained the calender. 94+61=72+83;72+105=94+83. They are both in balance. But they also express both 360. They average between 354 and 366. 94+61+72+83 =2X155+310+50=360. The other figur makes 72+105+94+83=2x177+354+6=360 If we count twice 6(zenith and nadir which are surrounded by the four wind directions) to 354 we get 366 the Sun year.

Do you think an eleven replacing the two would generate yet another magic square, this one with a cruciform shape of odd numbers and the even numbers in the four quadrates? [/url]

As far as I know there is no magic squire of 11. But 11 is the holy wedding between Heaven and Earth. The victory over the duality Mind-Nature through the adept or Yogi. Maybe that's why there are also 11 meridians in acupuncture and not 12, what most people think.

Frank
 
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robertluoshu

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attachment.php



Here would be the next two squares, with 7 and 8 as the center cells, and the cruciform alternating with odd and even numbers.

This is a pattern which coud be written in mathematical terms and published.

Robert Dickter, author Number, Time, and Archetype and web master of www.luo-shu.com
 

frank_r

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attachment.php



Here would be the next two squares, with 7 and 8 as the center cells, and the cruciform alternating with odd and even numbers.

This is a pattern which coud be written in mathematical terms and published.

Robert Dickter, author Number, Time, and Archetype and web master of www.luo-shu.com

Nice work, Robert.

Yes, I see these squares can go on and on. The sum is always 3X the centre.


All the best Frank
 

robertluoshu

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Frank,

Here is a set of six 3x3 magic squares, three with a cruciform of odd numbers and three with a cruciform of even numbers. My feeling is these magic squares fall into these two groups, and as you observed, they go on and on.

My favorite is the one with "nine" as the center number and the constant is 27 and the sum total is 81. I am unclear how they are used for the calendar, but thank-you for bringing the first square with 6 in the center to my attention.

It is always nice to read Marcel Granet's interpretations in English. One problem is that he is one of the few who write on this subject so there do not exist too many published writings on this topic.

Another interpretation, the five and six come together in the 11x11 Magic Square, and this is the first appearance of the number 91 (which is also the product of the seventh number and the seventh odd number). 91 represents the number of days in a season, a most important number to the agriculturally minded Chinese.

See the link for the 11x11 Lo Shu Magic Square for a fuller explanation:

http://luo-shu.com/book/part_two/order11_examples

Robert Dickter, author of Number, Time, and Archetype and webmaster of www.luo-shu.com
 
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Sparhawk

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Hi Robert,

Wonderful square! I have not seen this before and the wonderful references you name are not available in English (if they are please let me know), although Marcet Granet is one of the great originals!!

I believe that you most likely have seen this square, and the one by Marolleau (which is rotated 180deg, with 05 on the upper left corner), but forgot the reference. It is in Lars Berglund's "The Secret of Luo Shu," pg 39 and goes on for a few pages. Do you still have it? If you don't, I can send you copies of those pages.
 
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fkegan

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Hi Robert,

Glad to see you are enjoying more magic squares. They are an early form of appreciating equalities. Personally, I found 1+2+3 = 1*2*3 enough for me.

Frank
 

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Hello Luis, Frank R., and Frank K.,

Thank-you Luis for pointing out the reference in Berglund's book The Secret of the Luo Shu.

Berglund maintains that using both squares, one with the five and one with the six in the center, was a theory of Granet's and there is no evidence that the early Chinese used the "6" square.

It is interesting to note that the two squares combined generate an 11 in each cell and the square adds up to 99, a so called cosmo-magical number. Each pair of subsequent squares, the next pair with 7 and 8 in the center, will generate the same number when added together, supporting Dr. Kegan's observation that the pair of squares is about appreciating equalities, balance, yin and yang, male and female, Heaven and Earth.

Exploring the square with the six in the center led to a new pattern of squares and the realization that any nine consecutive numbers can be arranged in a 3x3 Magic Square, while maintaining the cruciform shape. My thanks to Frank R. for sharing this great square.

Here is an interesting square:
3x3with81-1.jpg


Robert Luoshu at www.luo-shu.com
 

fkegan

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Hi Robert,

Glad to have been useful for your work.

Frank
 

robertluoshu

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Understanding 3 - 6 - 9

Hello Frank R.!

Nice to speak with you again. I have heard this quote before,

"Understand the 3, 6, and 9 and you will understand the universe."

I do not know what that means, any help out there?

Does it have something to do with balanced ternary notation????

robertluoshu at www.luo-shu.com
 

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Hello Frank R.!

Nice to speak with you again. I have heard this quote before,

"Understand the 3, 6, and 9 and you will understand the universe."

I do not know what that means, any help out there?

robertluoshu at www.luo-shu.com

Hello Robert,

I studied the ennegrams for a while, and looking at the diagram of the enneagram you see that 3,6 and 9 is the central triade. Here there is a synthesis between the other numbers. It is hexagram 1 and 2(being the triade) and 63 and 64 that are trying to find the triade. Ouspensky wrote some interesting things about the ennegram and the 3-6-9 triade. http://www.endlesssearch.co.uk/philo_enneagram1.htm
Also when you looking to numerology when you count the numbers the only numbers you get that way is 3,6,9 and 10(the centre of the triade).

Does it have something to do with balanced ternary notation????]

Never heard of that term so I had a look what it meant. 3,6,9,27,81,243, 729. If I understood it correct. 3,6,9 where we now speaking of. 27, the hexagram of the jaw,( the Temporo-mandibular joint). and 81 the central point of your last squire.

Frank
 

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Hexagram 27 and Magic Squares

Hello Comrade Frank,

I am a little slow at his hexagram / enneagram stuff. Don't know much about it at all.

But I have been studying the TMJ (the Temporo-mandibular joint) for over half my life and treat people with TMDs (Temporo Mandibular Disorders). You have peeked my interest.......

Are you saying that some magic squares, when translated by balanced ternary notation, make anatomical correspondences with the hexagrams????

The center of the body some feel is the TMJ, tell me more about the 27 hexagram and its centering qualities.

Nice to hear from you,

robertluoshu
 

frank_r

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Hello Comrade Frank,

I am a little slow at his hexagram / enneagram stuff. Don't know much about it at all.

Hello Robert,

I think it is interesting that when you divide 1 through 7( the number of emotions and openings in the head) you get the enneagram diagram(without the triade 3,6,9) the numbers 1,2 4, 5, 7 and 8 in the enneagram order. When you take the numbers and put these in the Tai Qi symbol you get a little bit of a Lo Shu diagram.
For the rest there is a lot more to say about connections between the enneagram numbers and the hexagrams but that's another subject.
ennegram.jpg

FuShinumbers.jpg
[/QUOTE]

But I have been studying the TMJ (the Temporo-mandibular joint) for over half my life and treat people with TMDs (Temporo Mandibular Disorders). You have peeked my interest.......

Are you saying that some magic squares, when translated by balanced ternary notation, make anatomical correspondences with the hexagrams???

The center of the body some feel is the TMJ, tell me more about the 27 hexagram and its centering qualities. ????

Nice to hear from you,

robertluoshu

Yes, that would be interesting but that is a bridge too far. But when I saw the numbers and the conversation we had on the TMJ I had to think about hexagram 27, for instance Karcher/LiSe translate this hexagram with Jaws.(http://www.yijing.nl/i_ching/hex_17-32/27-28.htm)

It is also the hexagram of life(in contrast with 28 what is death). And in that way it is very much connected with the stomach and the spleen. When you have a better look at the line text then you see they are speaking in almost all lines about the jaw. And Carinn Dunne is writing in her book Yijing wondering and wandering(a beautifull and very spiritual book)" What is perhaps most encouraging is that the core lines of Yi(27) and Da Guo(28) intertwine in the form of the figure 8. Rejecting the lower jaw(27.3) leads to a preoccupation with appearance over reality(22), which results in exhaustion(47). But exhaustion forces us to dig deep(48), where we come upon our essence(21), which alone can sate the tiger(27.4), who replaced the magic tortoise, and who is the tortoise(correlation between line 1 and 4) in another guis. The tight bond of the figure 8 seems to say that if life requires a death, death also brings forth new life." (page 231)
27.4--21 - 22 --27.3

28.3--47 - 48 --28.4

For me this quote says everything about the stomach and the spleen, what the element earth is in the 5(4+1) elements. And it that way also the TMJ in the jaw. Not only food but also the eartly senses/expressions of the head.

Frank
 
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