Clarity,
Office 17622,
PO Box 6945,
London.
W1A 6US
United Kingdom
Phone/ Voicemail:
+44 (0)20 3287 3053 (UK)
+1 (561) 459-4758 (US).
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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.
Last edited by robertluoshu; March 27th, 2010 at 05:11 PM.
frank_r (March 29th, 2010)
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.
frank_r (April 7th, 2010), robertluoshu (April 5th, 2010)
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/i...58AF88D73.html
I hope this simplifies the working's that progress from the Ho Tu to the Lo Shu - Inner to Outer.
My regards - Paul.
frank_r (April 9th, 2010)
I noted this post.
-pp
http://www.onlineclarity.co.uk/frien...?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
Last edited by pantherpanther; April 12th, 2010 at 08:45 AM.
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/i...math/Home.html
robertluoshu (May 18th, 2010)
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.
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.
robertluoshu (May 23rd, 2010)
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.
sparhawk (August 20th, 2010)
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
sparhawk (August 25th, 2010)
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.
Clarity,
Office 17622,
PO Box 6945,
London.
W1A 6US
United Kingdom
Phone/ Voicemail:
+44 (0)20 3287 3053 (UK)
+1 (561) 459-4758 (US).
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