Clarity,
PO BOX 255,
Witney,
Oxfordshire,
OX29 6WH,
United Kingdom
Phone/ Voicemail:
+44 (0)20 3287 3053 (UK)
+1 (561) 459-4758 (US).
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.
Hi Luis and Charly,
If one looks at the actual "language of numbers" section of this source: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.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.
Regards,
Frank
I Ching hexagram meaning from line structure
and King Wen Sequence Explained: www.stars-n-dice.com/fluxtome.html
Learn astrology meaning of signs, houses, planets from just the dot-number patterns on the dice cube:http://www.stars-n-dice.com/learnastrology.html
New Yi Oracle Perspective:http://www.stars-n-dice.com/vaginaliching.html
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
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
I Ching hexagram meaning from line structure
and King Wen Sequence Explained: www.stars-n-dice.com/fluxtome.html
Learn astrology meaning of signs, houses, planets from just the dot-number patterns on the dice cube:http://www.stars-n-dice.com/learnastrology.html
New Yi Oracle Perspective:http://www.stars-n-dice.com/vaginaliching.html
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
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
I Ching hexagram meaning from line structure
and King Wen Sequence Explained: www.stars-n-dice.com/fluxtome.html
Learn astrology meaning of signs, houses, planets from just the dot-number patterns on the dice cube:http://www.stars-n-dice.com/learnastrology.html
New Yi Oracle Perspective:http://www.stars-n-dice.com/vaginaliching.html
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
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
I Ching hexagram meaning from line structure
and King Wen Sequence Explained: www.stars-n-dice.com/fluxtome.html
Learn astrology meaning of signs, houses, planets from just the dot-number patterns on the dice cube:http://www.stars-n-dice.com/learnastrology.html
New Yi Oracle Perspective:http://www.stars-n-dice.com/vaginaliching.html
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
Clarity,
PO BOX 255,
Witney,
Oxfordshire,
OX29 6WH,
United Kingdom
Phone/ Voicemail:
+44 (0)20 3287 3053 (UK)
+1 (561) 459-4758 (US).
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