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The King Wen Sequence and Magic Squares (Soduko)

Qiaozhi Yeats

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It sums to pi or phi in all directions;?; I am told on good authority there are two hexagrams missing.
 
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svenrus

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Hmmm, that sounds tricky to me: Two hexagrams missing ???
 

Qiaozhi Yeats

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Hmmm, that sounds tricky to me: Two hexagrams missing ???
The person who told me this is a Chinese convert to Christianity, she based it on the fact that there are sixty six books in the Bible (at least that's what she told me, I have never read it or checked). Perhaps such comparisons are facile, after all there are said to be lots of books missing from the Bible as well. I was slightly mad when I wrote the original post (I am diagnosed as a schizophrenic for my sins) however I do think there is something in the idea of the King Wen sequence being a magic square (the mathematical name of matrices like those that appear in Soduko) that approximates some significant constant, but this might be wishful thinking, much like the two hexagrams missing comparison.
 
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svenrus

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Hi, and thanks for reply.

Here - is a reason for why there are exactly 64 hexagrams as seen in my opinion.

And I've also seen the series of Fibonaccinumbers in maybe a odd way: Here

But as You can see it's my own playing with it and phantasy sometimes can get unreined can't it.....
 

Qiaozhi Yeats

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It seems to me that the very simple reason we have 64 six-line figures (hexagrams), is because that's the maximum number of unique combinations of solid or broken lines you can have within a 6-line figure.

It's sort of like a 3x3 soduko cube: if you have one number in each space, you'll always have 9 numbers to work with, not 10, or 7, or 23. And the same is true for the 64 hexgrams.

And I don't see how it serves us to complicate this fact, though some may seek to find additional means in the bible or fibinocci numbers, or the easter bunny, or alien abductions ... and so forth.

Best, D.
It seems to me that the very simple reason we have 64 six-line figures (hexagrams), is because that's the maximum number of unique combinations of solid or broken lines you can have within a 6-line figure.

It's sort of like a 3x3 soduko cube: if you have one number in each space, you'll always have 9 numbers to work with, not 10, or 7, or 23. And the same is true for the 64 hexgrams.

And I don't see how it serves us to complicate this fact, though some may seek to find additional means in the bible or fibinocci numbers, or the easter bunny, or alien abductions ... and so forth.

Best, D.
I have often said that maths is like looking in the clouds, and with numerology you can often see anything you want. So on one level, I agree, why complicate things. On the other hand the golden mean (ratio) known as phi in mathematics crops up in many commentaries on the Yi Jing and this is related to the Fibonacci sequence that Swen mentions. However the Lo Shu doesn't contain the number ten to my knowledge, so I don't quite see the connection he points out, unless I am mistaken. Thank you.
 
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svenrus

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#6

"...…………...this is related to the Fibonacci sequence that Swen mentions. However the Lo Shu doesn't contain the number ten to my knowledge, so I don't quite see the connection he points out, unless I am mistaken……………..."

I Ching and the Fibonaccinumbers.jpg

Qiaozhi Yeats : Yes, it's Numerology in it's extreem I admit. But if You take it as an observation You'll see that the highest number ie 1+2+3+4+5+6+7+8+9+10 (=55) only occur ONE time where it fit's that same number in the Fibonacci-series.
Again: take it for an Observation. Nothing more are in it but inspiration for further thinking so to speak.
 
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svenrus

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#9
Freeda,

No, if You mean the Chart it's something I puzzled with years ago.

Joseph Adler has translated Chu Hsi's book about what I will call Numerology concerning this subject here, and if You ask me ? Well, judge for yourself. Quote from this book:

"......What we call Heaven is the light purity of yang, which positions itself upward. What we call Earth is the heavy turbidity of yin, which positions itself downward. The yang numbers are odd. Thus 1, 3, 5, 7 and 9 are all classified as Heavenly. This is what is meant by the "five numbers of Heaven." The yin numbers are even; thus 2, 4, 6, 8 and 10 are all classified as Earthly. This is what is meant by the "five numbers of Earth." The Heavenly numbers and Earthly numbers each according to their kind attract each other. This is what is meant by the statement, "The five positions match each other." Heaven from 1 gives rise to water, and Earth with 6 completes it. Earth from 2 gives rise to fire, and Heaven with 7 completes it. Heaven from 3 gives rise to wood, and Earth with 8 completes it. Earth from 4 gives rise to metal, and Heaven with 9 completes it. Heaven from 5 gives rise to soil, and Earth with 10 completes it. This is the meaning of "Each has its mate." Summing up the five odds we get 25; summing up the five evens we get 30. Together these two make 55. This is the complete number of the River Chart, according to both the ideas of Confucius and the discourses of all the scholars. ..... "
[Introduction to the Study of the Classic of Change, Chu Hsi, translated by Joseph Adler, Global Scholarly Publications, Utah 2002. Page 7, this ed.]
 
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svenrus

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I don't think You are reading what I'm writing.

You ask (#9) Where does this come from? A book?
I answer ( #10) No, if You mean the Chart it's something I puzzled with years ago.
No means off course that it didn't came from a book, but was something I puzzled with years ago.

And there are basically two River diagrams: the Yellow river map and the Writing from the river Lo, and it is from the river Lo Map that the number 55 are found. See Wilhelm/Baynes edition, The great treatise, Chapter IX 'On the oracle', page 310 in the 1968 edition.

Or haven't I understood what You are writing ?

Freedda #11 writes: "......... All well and good, but there are two issues here: first, there are two Lo River images that are referred to in the Ta Chaun................ "

So, I don't understand You because You tells me that there are two Lo River images ???

When You get angry Freedda do it with sense, Please.

- and that counts for me too.
 
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svenrus

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Oh Yeah it counts for me too. I'll take some of my harsh and stupid formulaions above back and express myself this way:

You ask (#9) Where does this come from? A book?
I answer ( #10) No, if You mean the Chart it's something I puzzled with years ago.
No means off course that it didn't came from a book, but was something I puzzled with years ago.

And there are basically two River diagrams: the Yellow river map and the Writing from the river Lo, and it is from the river Lo Map that the number 55 are found. See Wilhelm/Baynes edition, The great treatise, Chapter IX 'On the oracle', page 310 in the 1968 edition.

Apoligize - I got upset, sorry
 
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svenrus

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On #8 here I tried to answer Qiaozhi Yeats question concerning the Lo river map and the Fibonacci series but I also warned him that this is numerology in it's extreme.

On #4 I gave him my opinion why there are 64 hexagrams - but that's not a prove I know, just my take on it. And that can be discussed.

And yes, I can be short on head/taking things obvious to me for granted that it is also obvious to others. It is as a matter of fact a quality needed in this hurrying times where one often can take things for guaranted that someone (like You) sort of asks into it and makes critisism/pointing at possible mistakes, and personally I know that if I ignore such "wake-up" calls it will hurt me in the end. So: Thank You for that Freedda, and keep on with it.

On whether my answers are useful to Qiaozhi Yeats I can only hope.
 
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svenrus

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..... talking about Numerology to it's extreme:

Sum of the digits and the six lines in the Hexagram.jpg
Thanks to the arabs we got the Zero and if I do not remember wrong our system of numbers we got from India ? (Correct me if I'm wrong). The zero means that we can go beyond number Nine and continue with 1 and 0, 1 and 1, 1 and 2, 1 and 3 (10, 11, 12... ) etc. With Sum of the Digits we do keep the numbers within the frame of ten where number 32 to example are number 5 (3+2) within this frame.
Now, the above are without doubt an extreme explanation to why there are six lines in a Hexagram giving 64 hexagrams - and not seven, eight etc. lines in this system.
------------------
At the 15' level, with the variation of lines giving 32768, the Sum of digits should be eight instead of one
 
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svenrus

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Don't worry, it's a possible reason to the old question: Why six lines, why not seven, eight etc. or even four lines ???
- But I don't think that king Wen saw it that way.
 

Qiaozhi Yeats

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The idea that we get our concept of zero from India is subject to interpretation. It is not true that the Greeks didn't have a concept of zero, they simply didn't consider it a number like the rest. But in fact they didn't consider one to be a number either. In other words, zero and one were more akin to the Chinese concepts of yin and yang, than counting numbers, from which they are derived. The similarity should be clear. Numbers begin with the first prime number, two. What comes from India is the expression of numbers in terms of combinations of zero and one to base ten. The Yi Jing is written as expressions of numbers in terms of zero and one to base two, which became called binary in the West after it reached the philosopher, mathematician and diplomat, Gottfried Leibniz in the seventeenth century. Leibniz is said to be the first Westerner whose name was recorded, to study the Yi Jing. Greek numbers were written in base one as combinations of one only, with no written zeros, not because they did not have a concept of zero but because they did not use it to write numbers. In fact this is not strictly true, as zero, the void, was expressed when grouping the numbers together algebraically, so in fact, it could be said that the Greeks did not use a base at all, i.e. the hierarchy was fluid, perhaps the origin of democracy philosophically. As a side note, algebra, an Arabic word, again only refers to the mode of expression, with the Arabs introducing a syntax for algebra, as opposed to actually inventing the algebra itself. The Greeks carried out algebra using words. I know I am placing a lot of emphasis here on Greek mathematics, I am of Greek heritage, so biased, but all cultures do mathematics, and despite ideas of so called ethno-mathematics being popular in certain anthropological circles, I believe mathematics to be universal, it is simply, counting, shuffling and drawing. Numerology is a branch of mathematics, just as astrology is a branch of science. Divination is a combination of the two, and these aspects of divination go back as far as has been recorded, though their expressions have changed. Thank you.
 
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svenrus

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As a note, in earlier time what we do now know as astronomers (to measure the Sky) were the assistants of the astrologers (to understand the Sky/the logic) and today the astronomers has taken their role - but leaving behind the Holism that the astrologers saw ie that the Sky are not only to be measured but that it has effect on us in a spiritual way. The assistants to the "magee's" has taken over their place.
 
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svenrus

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Well, how far back in time I can't know if it were so (assistants measuring the positions of planets and stars) but as Kepler and Tycho in our time had assistants to make the practical observations (and Tycho & Kepler and many others also did that themselves) which they used then for their astrological ptognostications it would be strange that this weren't a tradition they had from former times.
Freedda: " nor did they ever leave behind any sort of 'wholistic' outlook or wisdom. "
- No ?
 
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svenrus

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I know nearly nothing about Chinese astronomy or astrology but I do know out of what's been written that astrology in the Western ancient World were the leading approach to the study of the phenomena in the Sky. The astrologers of the ancient time were those who used the knowledge of that time concerning these phenomena in the Sky to prognosticate for kings and other rulers and I must confess, when You ask for prove as whether they had assistents to do the measuring and astronomical tables, that I don't know for sure.
But they, the astrologers in ancient Babylonia, were the authorities concerning study of the Sky and they may have had students, disciples, assistants who helped them to do the measuring in the field. It should be unlike that they hadn't.
Again: thank You for asking in to a claim I made ! I do not have the time or material at hand to make a deeper prove, so: let your critisism be the guide for now.
 
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svenrus

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Hi again Freedda, First: I'm not a scholar but since I was very young I were caught by the interest in astronomy - as surely did You too - and second: my claim here (#22) are based on reading books on the subject, and especially in my later years about the History behind our knowledge concerning this. My claim is a synthesis from what I remember out of these readings, so: as usual, be critical as my memory sometimes play games with me. In the earliest time the study of the Stars served the purpurse to read Omens, good or ill, out of the positions of the Stars and the Planets. Those who progronisticated those Omens out of the positions, the Magee's, were very high ranked like Priests and close they were to the Powers ruling. According to my clame they interpreted, but they did not do the work concerning figuring out, measuring these Star Constellations - to do that there were people specialized in that who noticed their observations and handed these tabels over to their Masters. At some point this knowhow in measuring rather than interpreting the Signs from these Gods on the Sky took over probably as the Church banned the old practice: Astrology.
I'll stop here, both because I think this is common knowledge but also because a proof on this clame needs more, like sources. One thou, concerning the observations made in ancient times are: the Dutchman B.L. van der Waerdens work "Die anfänge der Astronomie, P. Noordhoff Ltd, Groningen, 1966".
And besides that I have been working out Horoscopes but not in a commercial way, rather as a practice in calculating Time and Space etc.
Finally I think we should not underestimate the insight of those ancients, most of it gone lost but therefore not to be counted as unserious.
 
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svenrus

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#27
"...……….. and handed these tabels over to their Masters"
Tables, sorry.
But shouldn't we drop my Note here (#22), also because it's misplaced as Freedda correctly pointed out ?

- and whether there are two hexagrams missing (#3) or there are four hexagrams too many (my note) I find it interesting to search for connections between the Greek math, like You points out in the beginning of this thread Qiaozhi Yeats, and the hexagrams.
One of the things that first draw my attention when reading the handling with Numbers in the Commentaries to the I Ching, or the Ten Wings, were it's vast difference to handling with Numbers I've learned in school; it has nearly nothing to do with mathematic in "the Western sense".
But, important it is, because it's not Math in the way people in the West works with it I think there are a lot of interest to be discovered here. I haven't yet found a logic in the Numerology giving sense... I mean, no practical sollutions can be drawn out of this Numerology as can with Mathematics used as this is in all kinds of things (technical projects etc.) - but this doesn't mean that it should not get value for to solve other kinds of sollutions, sollutions yet unfamiliar with our materialistic approach to the World.
 
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