zhou wen wang’s development of yijing (book of changes) 64 hexagrams
DESCRIPTION
An exploration of Leibniz' unrequited effort to unlock the 64 Hexagrams binary code. By using binary number theory this paper demonstrates how this can be done and what it means for us now in the West and the East.TRANSCRIPT
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
1
Zhou Wen Wangs Development of Yijing (Book of Changes) 64 Hexagrams AN INDUCTIVE RECREATION OF BINARY EXTRAPOLATIVE OPERATIONS
END OF SHANG DYNASTY, FOUNDING OF ZHOU DYNASTY 12TH/11TH CENTURIES BCE CHINA
By Kevin Mequet 2013
The Master said, Reviewing the old as a means of realizing the new
such a person can be considered a teacher.
Confucius, Analects (2, 11)
Introduction
Gottfried Wilhelm Leibniz (1646 1716) spent a significant amount of his time and creative
intellect upon the subject of China.1 While not the first western sinologistthat singular
distinction went to Li Madou/Matteo Ricci (1552 1610) a century before2he was
certainly an ardent sinophile. Whether in conversations and studies in Western Europe or
extensive correspondences with Roman Catholic missionaries in China, he investigated a
broad range of subjects from natural philosophy, theology, philosophy, politics or as is the
focus of this essay upon mathematics. As the popularizer of a base-2 binary number and
arithmetic applications system in Europe, he was intrigued and transfixed by his vicarious
encounter with the very real possibility of ancient Chinas invention and use of this very
same systemliterally several thousand years before its (re)invention in Western Europe.
Unfortunately Leibniz had two liabilities operating against him. First, unbeknownst to
him, the materials made available to him in Western Europe and the correspondences with
which he prolifically participated were teleological and imprudent by todays standards of
scholarship and academic practice. Second, also unbeknownst to him, the first emperor of
unified China in 221 BCE, Qin Shihuangdi (259 210 BCE), destroyed practically all
mathematical and literary materials in a systematic consolidation of power disrupting a long-
1 Michela Fontana, Matteo Ricci: A Jesuit in the Ming Court, Rowmann & Littlefield Publishers, Inc.,
(2011), p. 290 2 Ibid, p. 264
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
2
lived continuity of rich intellectual provenance.3 The importance of this cannot be overstated
as we will see.
A workable base-2 binary system was extant in Western Europe with which Leibniz was
fascinated and conversant such that Roman Catholic Church Reverend Father Joachim
Bouvet (1656 1730), a Jesuit missionary to the Imperial Capitol in Beijing for most of his
life, corresponded with him about coincident resonances with the 64 Hexagram matrix he
erroneously associated with Fu Xi First of The Three Sovereigns of Ancient China 30th
century BCE.4 The first iteration of the Yijing (Book of Changes) by Wen Wang of Zhou
occurred in late 12th century BCE. The hexagrams they were looking at were Wen Wangs
and not Fu Xis. Due to the loss of continuity precipitated by Qin Shihuangdi an inferior
turn-of-the-eras reconstruction of Wen Wangs Yijing was reformed by Shao Yung (1011
1077 CE) during the great intellectual renaissance of the Song Dynasty.5 The Jin northern
insurrection and Mongol invasion brought the Song dynasty to an end in the Late 13th
century CE. Mongol Khan successors were assimilated and alloyed into Chinese culture
founding the Yuan Dynasty that lasted into the Late 14th century CE. The collapse of the
Yuan gave birth to a golden period of civil society valorizing Confucius and ushering in Neo
Confucianism under the Ming Dynasty that lasted until 1644 CE, two years shy of Leibniz
birth. The venerated Li Madou/Matteo Ricci, a Roman Catholic Church Jesuit missionary,
opened the doors to a broader relationship between China and Western Europe at the
decline of the Ming Dynasty. It is during the advent of the turbulent and truncated
Manchurian insurrection that gave rise to the last dynastic Empire of the Great Qing. By the
3 Ibid, pp. 255 6
4 Daniel J. Cook and Henry Rosemont, Jr., Gottfried Wilhelm Leibniz: Writings on China, Open Court
Publishing Co., Chicago (1994), p. 63 [from Leibniz autograph, On the Civil Cult of Confucius, (1700/1701)] 5 James A. Ryan, Leibniz Binary System and Shao Yongs Yijing, University of Hawaii Philosophy East
& West Volume 46 (1996), pp 67 73
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
3
late 18th century Imperial China had closed its doors to Western European meddling in its
internal affairs of state.6 This was the context that influenced Leibniz sinology.
Fu Xi never formulated nor knew of the 64 Hexagrams in 30th century BCE China. He
formulated the 8 Trigrams of Harmony Between Heaven and Earth. Leibniz worked out a
sufficient documentation of the binary system in his seminal short autograph Explication de
lArithmtique Binaire (1703Published Memoires de lAcademie Royale des Sciences) or Explanation
of Binary Arithmetic, and later recapitulated it in Remarks on Chinese Rites and Religion (1708)by
which he attempted unsuccessfully to translate Fu Xis trigrams into binary numerals.
Leibniz project was to legitimize the superiority of mathematics as the only authoritative
system of reconciliation between the Roman Catholic Church of Europe and the Natural
Philosophy and Theology of China thereby not only positioning himself as a leading
authority in the burgeoning East/West relationship but also forging a durable
accommodation between Reformation Protestantism and the same Roman Catholic Church.
It was perhaps too grand and self-congratulatory. He quite possibly was unaware of this
being Li Madou/Matteo Riccis very same project in China by then in decline and outright
repudiation by Pope Clement XI and eventually long after Leibniz death strident
nonaccommodation was permanently institutionalized as Church policy by Clement XIV.7
Leibniz thesis was that Fu Xis trigrams were binary in another format in the following
way. He took the trigrams three horizontal lines, solid signifying unity or (1) and broken or
gapped signifying aught or (0) giving 2 options for each line position to be 23 = 8 total
unique configurations: 010 (0002), 110 (0012), 210 (0102), 310 (0112), 410 (1002), 510 (1012), 610
(1102), and 710 (1112).
He committed two foundational errors that had Leibniz traveled to China would have
been revealed to him. First, there has never been, nor is there, in traditional Chinese
6 Michela Fontana, Matteo Ricci: A Jesuit in the Ming Court, Rowmann & Littlefield Publishers, Inc.,
(2011), p. 294 7 Ibid, p. 294
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
4
pictography a numeric representation for zero (0), which leads to the second error. The Fu
Xi 8 Trigram Sequence was numeral characters 1 8, and not 0 7. Consequently, Chinese
binary numerology could never be directly reconciled, but only tangentially analogized,
because it followed binary rules using 1, 2, and the doubling principle or 2x. The numeral
character for 1 at the beginning of the sequence as (12) stood symbolically for Harmony and
Heaven, and 10002 ended the series as 8 for Disharmony and Earth. Thus the series should
be represented as 11 = 110 = 12, 21 = 210 = 102, 310 = 112, 2
2 = 410 = 1002, 510 = 1012, 610 =
1102, 710 = 1112, and 23 = 810 = 10002. As we now can see, Leibniz could never make the Fu
Xi Trigrams sequential character line position options obey a doctrinaire adherence to solid
unity for 1 and broken/gapped aught for 0 in the Western representational binary numeral
sequence. The Fu Xi Trigram Sequence follows binary extrapolative rules, is pictographic,
but are not binary numerals in the Western sense, nor are they sequenced as such. We will
return to this line of inquiry below. QED
Why would anyone want to translate Arabic/Hindus numeralslet alone Chinese
pictographic trigrams and hexagramsinto binary in the first place? Because the binary
arithmetic system becomes advantageous in the simplification of handling large number
manipulation and also provides for the elimination of multiplication and division. 0 X 0 = 0,
0 X 1 = 0, 1 X 1 = 1; 0 / 1 = 0, 1 / 1 = 1; therefore, these two operations are rendered void.
Addition and subtraction are the only operations required as long as a durable and reliable
system for conversion from base-10 to base-2 and back is used and one makes no
computational errors. Multiplication and division are accomplished by specialized rules of
addition and subtraction, respectively. This will become important below.
Fu Xi was erroneously associated with the Yijing (Book of Changes)s 64 Hexagrams by the
Roman Catholic Church Jesuit missionaries in the 17th and 18th centuries CE. At the time, it
was impossible for Leibniz to know that Wen Wang of the 12th century BCE invented the 64
hexagrams.
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
5
Leibniz takes up the Fu Xi [Wen Wang] Hexagram Matrix in the fourth section of
Discourse on the Natural Theology of the Chinese (1715/1716) Concerning the Characters of Fohi,
Founder of the Chinese Empire, Used in His Writings, and Binary Arithmetic. There is
some progress made between 1708 and 1716 from his earlier work. Now he attempts to
conform the Fu Xi Trigrams into a systematic method for combining them by stacking two
at time into the Wen Wang Hexagrams. As we will see he came so very tantalizingly close to
solving it. But it seems as though he had given up any attempt at reconciliation.
Unfortunately, while it might be reasonable to extrapolate the remainder of this autograph
from Explanation of Binary Arithmetic (1703), this cant be done because it cannot be
postulated how Leibniz would have reworked it for the missing remainder ending with
than the natural numbers themselves which are their roots The documentation of this
autograph is disrupted, jarringly so, and ends here. Would Leibniz have figured out the Wen
Wang Hexagram Matrix? Would he have made a leap of logic to postulate an ancient
Chinese binary number system?
Posterity records no resolution to this conundrum because sadly Leibniz did not finish
this last work before his death.
1
It is extremely difficult to precisely establish provenances in Before Common Era China,
principally though not exclusively due to the actions taken by Qin Shihuangdi. At some
point in the late 12th century BCE Zhou Wen Wang (1152 1056 BCE), born Ji Chang,
King Wen Wang of Zhou, honored by his son Wu as the founder of the Zhou Dynasty after
the overthrow of the Shang Dynasty, extrapolated the 64 Hexagrams while he was
imprisoned as a rival political dissident by King Zhou of Shang during which he composed
the first iteration of the Yijing (Book of Changes). It is impossible to know with certainty his
was the first iteration. We can only know his was the earliest written iteration that has
survived. Hence forth we will refer to them as the Wen Wang Hexagram Matrix or 64
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
6
Hexagrams. For this essay we will use the traditionally accepted Yijing (Book of Changes) 64
Hexagrams format which we will see is the very matrix created by Wen Wang thirty-one-
hundred years or so ago.
Fig. 1 Credit: Wen Wang 64 Hexagrams Yijing, Late 12th Century BCE
At bottom right we find the Yijing interpretive hexagram for Heaven or the numeral 1
in the beginning position which is interestingly known as the seed position. There is a very
surprising reason why it became known as the Heaven hexagram as we will soon see. In the
top left we find the Yijing interpretive hexagram for Earth or the numeral 64 in the
completion position which is also interestingly known as the exhaustion position. Let us at
this point dispense with the extant methods of divination, its manifold iterations of evolved
prophetic, divine and/or theological interpretations, and proceed only with mathematical
designations. Once we have performed this recreation we will then return to some
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
7
observations on divination. From this point forward each of the 64 pictograms will be
identified with a single base-10 and base-2 numeral. While not the original purpose of the
matrix, it is my contention that it also serves an unexpected ancillary purpose. One that
might very well explain why it was invented in the first place.
The key to deciphering this arrangement requires two postulates. Postulate One: the
pictograms are idiomatic and not numerals as westerners would attempt to read them.
Postulate Two: this arrangement is not a binary number system, but a rudimentary doubling
number system rigorously following binary rules which provides for the ancillary benefit of
functioning as a rudimentary digital binary calculator for the performance of the simple
operations of addition, subtraction, multiplication and division, analogous to the binary
arithmetic system without employing binary numerals.
Each character consists of 6 horizontal lines. Let us now dispense with Leibniz
interpretive symbolic terminology and return to traditional Chinese Yijing interpretive
symbolic terminology. The lines can be either solid symbolizing harmony 1 or
broken/gapped symbolizing disharmony 2. Since there are two options for each position of
a hexagrams 6 lines, this gives us 26 number of combinations totaling 64 individually unique
pictograms. So hence forth we will refer to each hexagram in a specific sequential position 1
64, right to left (left-reading), bottom to top, and its line positions as 1st, 2nd, 3rd, 4th, 5th, and
6th, from bottom to top. All the other characters are extrapolated from the beginning seed
character.
The formatting rules of the matrix are derived from the first hexagrams formatting rules.
It makes no difference at all the manner in which you chose the formatting convention of
the final matrix. There are 8 possibilities; left-reading, up; up-reading, right; right-reading,
down; down-reading, left; left-reading, down; up-reading, left; right-reading, up; and down-
reading, right. Once chosen, one cannot deviate from the chosen convention. One must
apply the rules to the chosen convention until the matrix is completely extrapolated. One
can easily understand why the beginning hexagram is associated with Heaven. It is
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
8
embryonic. It gives full bloom to the final matrix of characters. The following binary
extrapolative rules open the seed hexagrams iterative developmental potential until the
exhaustion hexagram is reached completing the matrix.
The first binary extrapolative rule of the hexagrams is that there are 7 exponent numeral
character hexagrams in 7 specific locations that graphically denote periodic doubling, and
establish the matrixs geometry.
Therefore: 11 =110, 21 = 210, 2
2 = 410, 23 = 810, 2
4 = 1610, 25 = 3210, and 2
6 = 6410. In binary
the following series is true: 12 = 110, 102 = 210, 1002 = 410, 10002 = 810, 100002 = 1610, 1000002
= 3210, and 10000002 = 6410. Now that we have a beginning theoretical series we can
examine the matrix for synchronicity.
810/23/10002 410/2
2/1002 210/21/102 110/1
1/12
Fig. 2 Credit: Wen Wang 64 Hexagrams Yijing, Late 12th Century BCE Row 1 (bottom) Wen Wang Hexagram Matrix
The 1st character at the lower right of the first row bottom is 6 solid 1st, 2nd, 3rd, 4th, 5th &
6th lines depicting the numerals 110 or 12. The 2nd character to the left is 5 solid 1st, 2nd, 3rd, 4th
& 5th lines under 1 broken/gapped disharmony 6th line depicting the numerals 210 or 102. The
4th character to the left is 4 solid harmony 1st, 2nd, 3rd & 4th lines under 2 broken/gapped
disharmony 5th & 6th lines depicting the numerals 410 or 1002. The 8th character to the left end
completing the row 1 bottom is 3 solid harmony 1st, 2nd & 3rd lines under 3 broken/gapped
disharmony 4th, 5th & 6th lines depicting 810 or 10002 [Fig. 2].
1610/24/100002
Fig. 3 Credit: Wen Wang 64 Hexagrams Yijing, Late 12th Century BCE Rows 1 & 2 (from bottom) Wen Wang Hexagram Matrix
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
9
3210/25/1000002
Fig. 4 Wen Wang 64 Hexagrams Yijing, Late 12th Century BCE Rows 1 4 (from bottom) Wen Wang Hexagram Matrix
Now we must move to the second row from the bottom and to the eighth character to
the left end or the 16th character in the numeral series which is 2 solid harmony 1st & 2nd lines
over 4 broken/gapped disharmony 3rd, 4th, 5th & 6th lines depicting 1610 or 100002 [Fig. 3].
Next we go 2 more rows up to the 4th row from the bottom over to the eighth character to
the left end or the 32nd character in the numeral series which is 1 solid harmony 1st line under
5 broken/gapped disharmony 2nd, 3rd, 4th, 5th & 6th lines depicting 3210 or 1000002 [Fig. 4].
Lastly, we now go up another 4 rows to the 8th row to the 8th character to the left end or the
64th character in the numeral series which is no solid harmony lines at all and only 6
broken/gapped disharmony 1st, 2nd, 3rd, 4th, 5th & 6th lines depicting 6410 or 10000002 [Fig. 5].
QED
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
10
6410/26/10000002
Fig. 5 Credit: Wen Wang 64 Hexagrams Yijing, Late 12th Century BCE Rows 1 8 (from bottom) Wen Wang Hexagram Matrix
The doubling periodicity becomes obvious in the graphic design of the Wen Wang
Hexagram Matrix. Row 1 at the right beginning position depicts 11, double it to the left for
21, double it to the left for 22, and double it to the left end of row 1 for 23. Double row 1 to
the left end of row 2 for 24. Double these 2 rows to the left end of row 4 for 25. And finally
double these 4 rows to the left end of row 8 for 26 [Fig. 6]. QED
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
11
26
64 63 62 61 60 59 58 57
1000000 111111 111110 111101 111100 111011 111010 111001
56 55 54 53 52 51 50 49
111000 110111 110110 110101 110100 110011 110010 110001
48 47 46 45 44 43 42 41
110000 101111 101110 101101 101100 101011 101010 101001
40 39 38 37 36 35 34 33
101000 100111 100110 100101 100100 100011 100010 100001
25
32 31 30 29 28 27 26 25
100000 11111 11110 11101 11100 11011 11010 11001
24 23 22 21 20 19 18 17
11000 10111 10110 10101 10100 10011 10010 10001
24
16 15 14 13 12 11 10 9
10000 1111 1110 1101 1100 1011 1010 1001
23
8 7 6 5 23
4 3 21
2 11
1
1000 111 110 101 100 11 10 1 Credit: Kevin Mequet
Fig. 6 Wen Wang Hexagram Matrix by binary number theory First binary extrapolative ruleExponent Numerals
The second binary extrapolative rule of the hexagrams is that there are exactly 32 of the
same feature common to the first 1 32 numerals that must be the exact opposite for the
remaining 32 numerals 33 64, and that this feature must follow the binary principle that all
odd numerals in base-10 will end with 1 in base-2 and all even numerals will end with 0 in
base-2. The only feature common to all the numeral hexagrams 1 32 is that every
characters 1st line is solid harmony denoting 1 in binary base-2 and therefore 1 in Chinese
numerology. We will now denote the first rows 1 4, numerals 1 32 as register 1. The only
exact opposite feature common to all numerals 33 64 is that every character 1st line is
broken/gapped disharmony denoting 10 in binary base-2 and therefore 2 in Chinese
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
12
numerology. We will now denote the second rows 5 8, numerals 33 64 as register 2 [Fig.
7]. QED
26
64 63 62 61 60 59 58 57
1000000 111111 111110 111101 111100 111011 111010 111001
56 55 54 53 52 51 50 49
111000 110111 110110 110101 110100 110011 110010 110001
48 47 46 45 44 43 42 41
110000 101111 101110 101101 101100 101011 101010 101001
40 39 38 37 36 35 34 33
101000 100111 100110 100101 100100 100011 100010 100001
25
32 31 30 29 28 27 26 25
100000 11111 11110 11101 11100 11011 11010 11001
24 23 22 21 20 19 18 17
11000 10111 10110 10101 10100 10011 10010 10001
24
16 15 14 13 12 11 10 9
10000 1111 1110 1101 1100 1011 1010 1001
23
8 7 6 5 23
4 3 21
2 11
1
1000 111 110 101 100 11 10 1 Credit: Kevin Mequet
Fig. 7 Wen Wang Hexagram Matrix by binary number theory Second binary extrapolative ruleRegister Residency
The third binary extrapolative rule of the hexagrams is that there are exactly 32 odd and
32 even hexagram numerals, that the feature common to all odd numerals will follow the
binary principle above, and that the exact opposite feature common to all even numerals will
do the same. All 64 hexagrams 6th line follows this rule. There are 32 alternating 6th line solid
harmony 1 hexagrams in columns 1, 3, 5 & 7. Therefore columns 1, 3, 5 & 7 are odd
hexagram numerals. There are 32 alternating 6th line broken/gapped disharmony 2
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
13
hexagrams in columns 2, 4, 6 & 8. Therefore columns 2, 4, 6 & 8 are even hexagram
numerals [Fig. 8]. QED
26
64 63 62 61 60 59 58 57
1000000 111111 111110 111101 111100 111011 111010 111001
56 55 54 53 52 51 50 49
111000 110111 110110 110101 110100 110011 110010 110001
48 47 46 45 44 43 42 41
110000 101111 101110 101101 101100 101011 101010 101001
40 39 38 37 36 35 34 33
101000 100111 100110 100101 100100 100011 100010 100001
25
32 31 30 29 28 27 26 25
100000 11111 11110 11101 11100 11011 11010 11001
24 23 22 21 20 19 18 17
11000 10111 10110 10101 10100 10011 10010 10001
24
16 15 14 13 12 11 10 9
10000 1111 1110 1101 1100 1011 1010 1001
23
8 7 6 5 23
4 3 21
2 11
1
1000 111 110 101 100 11 10 1 Credit: Kevin Mequet
Fig. 8 Wen Wang Hexagram Matrix by binary number theory Third binary extrapolative ruleOdd/Even Numeral Columns
Now that we understand the overall distribution of the hexagrams we can correctly
interpret the non-exponent numerals. The 1st lines of all the hexagrams denote register
residency 1 or 2. The 6th lines of all the hexagrams denote odd or even numerals. The first
cardinal group of characters is the exponent hexagrams whose unique designs begin with the
first numeral 1 odd character, the remaining 5 are all even characters and self-organized by
the doubling principle into a total of 6 residing in register 1 with 1st lines solid harmony 1,
and 6th lines solid harmony for the first numeral 1 character and broken/gapped
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
14
disharmony 2 for the remainder, and a single numeral character residing in register 2 with
1st & 6th lines broken/gapped disharmony 2. The second ordinal group of hexagrams is
actually comprised of 16 distinct quadragrams sandwiched between 1st line register residency
and 6th line odd or even numeral designation.
The fourth binary extrapolative rule of the hexagrams is that all the numerals have
quadragrams sandwiched between 1st & 6th line positions, thusly: 2nd, 3rd, 4th & 5th lines gives
us 4 line positions to make 24 = 16. That means 16 different quadragrams are possible. There
are 32 hexagrams in a register. There are 16 odd/even pairs, so 1 quadragram can be used
for each odd/even pair. Then we will repeat exactly for register 2 because register 1 is 1st
solid harmony line, and register 2 is 1st broken/gapped disharmony line.
Reusing our previous binary extrapolative rules let us now extrapolate the 16
quadragrams, only now in a 4 by 4 matrix because the exhaustion character is the 16th.
Similarly to the hexagrams the beginning seed quadragram has 4 solid harmony lines. The
end exhaustion character is 4 broken/gapped disharmony lines. The first character in the
series denotes 11 = 1 and the last denotes 24 = 16. Naturally, in a 4 X 4 matrix this must
mean the first binary extrapolative rule of exponent characters makes the second character 3
solid harmony lines under 1 broken/gapped disharmony line or 21 = 2. The fourth character
therefore is 2 solid harmony lines under 2 broken/gapped disharmony lines or 22 = 4. Next
the eighth character will be 1 solid harmony line under 3 broken/gapped disharmony lines.
As we have already seen the exhaustion end character must therefore be 4 broken/gapped
disharmony lines or 24 = 16 [Fig. 9].
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
15
24
16 15 14 13
10000 1111 1110 1101
12 11 10 9
1100 1011 1010 1001
23
8 7 6 5
1000 111 110 101
22
4 3 21
2 11
1
100 11 10 1 Credit: Kevin Mequet
Fig. 9 Wen Wang Quadragram Matrix by binary number theory First binary extrapolative ruleExponent Numerals
The second binary extrapolative rule dictates that characters 1 8 are register 1
characters with bottom line position solid harmony lines. Therefore characters 9 16 are
register 2 characters with bottom line position broken/gapped disharmony lines [Fig. 10].
24
16 15 14 13
10000 1111 1110 1101
12 11 10 9
1100 1011 1010 1001
23
8 7 6 5
1000 111 110 101
22
4 3 21
2 11
1
100 11 10 1 Credit: Kevin Mequet
Fig. 10 Wen Wang Quadragram Matrix by binary number theory Second binary extrapolative ruleRegister Residency
The third binary extrapolative rule dictates that the first and third columns of characters
must have top line position solid harmony lines denoting odd numeral characters. Therefore
the second and fourth columns of characters must have top line position broken/gapped
disharmony lines denoting even numeral characters [Fig. 11].
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
16
24
16 15 14 13
10000 1111 1110 1101
12 11 10 9
1100 1011 1010 1001
23
8 7 6 5
1000 111 110 101
22
4 3 21
2 11
1
100 11 10 1 Credit: Kevin Mequet
Fig. 11 Wen Wang Quadragram Matrix by binary number theory Third binary extrapolative ruleOdd/Even Numeral Columns
Using a variation on the fourth binary extrapolative rule we can complete the
quadragram matrix. The middle two line positions must follow the exponent characters lead
and have one configuration that applies to each odd/even pair of numeral characters, thusly:
numerals 1 & 2 have both middle line positions solid harmony lines, numerals 3 & 4 have 2nd
line position solid harmony lines under 3rd line position broken/gapped disharmony lines,
numerals 5 & 6 have 2nd line position broken/gapped disharmony lines under 3rd line
position solid harmony lines, and numerals 7 & 8 must therefore end the series at exhaustion
both middle lines broken/gapped disharmony line, completing the register 1 numerals 1 8.
Repeat exactly for register 2 numerals 9 16 [Fig. 12].
24
16 15 14 13
10000 1111 1110 1101
12 11 10 9
1100 1011 1010 1001
23
8 7 6 5
1000 111 110 101
22
4 3 21
2 11
1
100 11 10 1 Credit: Kevin Mequet
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
17
Fig. 12 Wen Wang Quadragram Matrix by binary number theory Fourth binary extrapolative rule16 Quadragrams Sandwiched & Completion
Now we can confidently complete the Wen Wang Hexagram Matrix. Insert sequentially
each quadragram between each hexagram bottom and top lines, 1 quadragram for every
odd/even numeral pair to complete the register 1 numerals 1 32; then repeat exactly for
the register 2 numerals 33 64 [Fig. 13].
We have now correctly derived the Wen Wang Hexagram Matrix using binary number
theory.
26
64 63 62 61 60 59 58 57
1000000 111111 111110 111101 111100 111011 111010 111001
56 55 54 53 52 51 50 49
111000 110111 110110 110101 110100 110011 110010 110001
48 47 46 45 44 43 42 41
110000 101111 101110 101101 101100 101011 101010 101001
40 39 38 37 36 35 34 33
101000 100111 100110 100101 100100 100011 100010 100001
25
32 31 30 29 28 27 26 25
100000 11111 11110 11101 11100 11011 11010 11001
24 23 22 21 20 19 18 17
11000 10111 10110 10101 10100 10011 10010 10001
24
16 15 14 13 12 11 10 9
10000 1111 1110 1101 1100 1011 1010 1001
23
8 7 6 5 23
4 3 21
2 11
1
1000 111 110 101 100 11 10 1 Credit: Kevin Mequet
Fig. 13 Wen Wang Hexagram Matrix by binary number theory Fourth binary extrapolative rule16 Quadragrams Sandwiched & Completion
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
18
2
As compelling and beautiful as this recreation of the Wen Wang Hexagram Matrix by
extrapolation from binary number theory is, regretfully, it is not how he devised his matrix
from Fu Xis trigrams. Now using our new eyes developed from extrapolating the matrix
from binary number theory lets recreate what Wen Wang did some thirty-one-hundred or so
years ago.
At the beginning of this essay I said we would return to the Fu Xi Trigram Sequence. Let
us use the same formatting rules and conventions as we did for the Wen Wang Hexagram
Matrix. Therefore, each trigram consists of 3 line positions with 2 line options for each
giving 23 = 8 total distinct characters in this sequence. Using our binary extrapolative rules
we have 4 exponent characters 11 = 1, 21 = 2, 22 = 4 and 23 = 8. So the beginning first
trigram seed character is 3 solid harmony lines, the second trigram character is 2 solid
harmony lines under 1 broken/gapped disharmony line, the fourth character is 1 solid
harmony line under 2 broken/gapped disharmony lines, and the ending final exhaustion
character is 3 broken/gapped disharmony lines. The register 1 characters consist of numerals
1 4 with bottom solid harmony lines, and the register 2 characters consist of the numerals
5 8 with broken/gapped disharmony lines. The odd numeral characters have top solid
harmony lines, and the even numeral characters have broken/gapped disharmony lines.
Therefore, the middle line position binary extrapolative rule must give the third character to
be bottom solid harmony line, middle broken/gapped disharmony line, and top solid
harmony line; the fifth character must be bottom broken/gapped disharmony line, middle
solid harmony line, and top solid harmony line; the sixth character must be bottom
broken/gapped disharmony line, middle solid harmony line, and top broken/gapped
disharmony line; and the seventh character must be bottom broken/gapped disharmony line,
middle broken/gapped disharmony line, and top solid harmony line [Fig. 14]. QED
23
22
21
11
x8 x7 x6 x5 x4 x3 x2 x1 Credit: Kevin Mequet
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
19
Fig. 14 Fu Xi Trigram Sequence by binary number theory First Fourth binary extrapolative rulesComplete Sequence
Wen Wang had this much venerated and valorized sequence to mediate Between Heaven
and Earth in his mind as he worked. Having extrapolated his matrix from binary number
theory we can see how easily he extrapolated from the Fu Xi Trigram Sequence to make a
more compelling matrix matching the complexities of Heaven and Earth that would be the
most rational arrangement of character divination. All he didliterallywas multiply the 8
characters by the 8 characters to make a graphic depiction of that multiplication in an 8 X 8
= 64 character matrix.
This is where Leibniz was truly and tragically blind. Had he eschewed a default
hierarchical Western colonial overlay upon the East he could have seen that the characters
could never give themselves to a Western representationalist binary numeral systembut
were instead, hidden plainly in sight, the pictographic depiction of 8 X 8 = 64. If you take
every character and divide it into a lower and upper trigram then the operation becomes
glaringly obvious. The lower trigram for all 8 characters in the bottom first row is the first
Fu Xi Trigram Sequence character. Then the second character for all 8 characters in the
second row, and so on through the top eighth row [Fig. 15].
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
20
23
23
64 23
63 23
62 23
61 23
60 23
59 23
58 23
57
8x 8x 8x 8x 8x 8x 8x 8x 8x
56 55 54 53 52 51 50 49
7x 7x 7x 7x 7x 7x 7x 7x 7x
48 47 46 45 44 43 42 41
6x 6x 6x 6x 6x 6x 6x 6x 6x
40 39 38 37 36 35 34 33
5x 5x 5x 5x 5x 5x 5x 5x 5x
22
22
32 22
31 22
30 22
29 22
28 22
27 22
26 22
25
4x 4x 4x 4x 4x 4x 4x 4x 4x
24 23 22 21 20 19 18 17
3x 3x 3x 3x 3x 3x 3x 3x 3x
21
21
16 21
15 21
14 21
13 21
12 21
11 21
10 21
9
2x 2x 2x 2x 2x 2x 2x 2x 2x
11
11
8 11
7 11
6 11
5 11
4 11
3 11
2 11
1
1x 1x 1x 1x 1x 1x 1x 1x 1x Credit: Kevin Mequet
Fig. 15 Wen Wang Hexagram Matrix by Fu Xi Trigram Sequence Lower Half of HexagramsTrigram the same for each character in a row
Every single characters upper trigram in all 8 rows is the same Fu Xi Trigram Sequence
character distributed sequentially left-reading [Fig. 16]. Or congruently put another way, each
column of characters has the same upper trigram.
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
21
23
22
21
11
x8 x7 x6 x5 x4 x3 x2 x1
23
64 63 62 61 22
60 59 21
58 11
57
x8 x7 x6 x5 x4 x3 x2 x1
23
56 55 54 53 22
52 51 21
50 11
49
x8 x7 x6 x5 x4 x3 x2 x1
23
48 47 46 45 22
44 43 21
42 11
41
x8 x7 x6 x5 x4 x3 x2 x1
23
40 39 38 37 22
36 35 21
34 11
33
x8 x7 x6 x5 x4 x3 x2 x1
23
32 31 30 29 22
28 27 21
26 11
25
x8 x7 x6 x5 x4 x3 x2 x1
23
24 23 22 21 22
20 19 21
18 17
x8 x7 x6 x5 x4 x3 x2 x1
23
16 15 14 13 22
12 11 21
10 11
9
x8 x7 x6 x5 x4 x3 x2 x1
23
8 7 6 5 22
4 3 21
2 11
1
x8 x7 x6 x5 x4 x3 x2 x1 Credit: Kevin Mequet
Fig. 16 Wen Wang Hexagram Matrix by Fu Xi Trigram Sequence Upper Half of HexagramsTrigram the same for each character in a column
A pictographic depiction of 8 X 8 = 64 [Fig. 17]. QED
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
22
23
22
21
11
x8 x7 x6 x5 x4 x3 x2 x1
23
26
64 63 62 61 60 59 58 57
8x 8x8 8x7 8x6 8x5 8x4 8x3 8x2 8x1
56 55 54 53 52 51 50 49
7x 7x8 7x7 7x6 7x5 7x4 7x3 7x2 7x1
48 47 46 45 44 43 42 41
6x 6x8 6x7 6x6 6x5 6x4 6x3 6x2 6x1
40 39 38 37 36 35 34 33
5x 5x8 5x7 5x6 5x5 5x4 5x3 5x2 5x1
22
25
32 31 30 29 28 27 26 25
4x 4x8 4x7 4x6 4x5 4x4 4x3 4x2 4x1
24 23 22 21 20 19 18 17
3x 3x8 3x7 3x6 3x5 3x4 3x3 3x2 3x1
21
24
16 15 14 13 12 11 10 9
2x 2x8 2x7 2x6 2x5 2x4 2x3 2x2 2x1
11
23
8 7 6 5 23
4 3 21
2 11
1
1x 1x8 1x7 1x6 1x5 1x4 1x3 1x2 1x1 Credit: Kevin Mequet
Fig. 17 Wen Wang Hexagram Matrix by Fu Xi Trigram Sequence Lower Half & Upper Half of HexagramsLower Trigram by Upper Trigram gives 64 unique hexagrams by pictographic depiction
Now anyone can easily extrapolate the Wen Wang 64 Hexagrams Yijing (Book of Changes)
matrix as was done some thirty-one-hundred or so years ago.
3
Did you by any chance notice the characters in the Wen Wang Hexagram Matrix that are red
on the bias from character position 1 through 64? At numerals 1, 10, 19, 28, 37, 46,
55, and 64 [Fig. 1]? As Western sequential numerals they make no sense. But as a
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
23
pictographic depiction of numeral operations they do. Look closely at each character. Notice
anything distinctive? If youre paying attention to this essay it should now stand out for you.
Each character is a graphic depiction of Fu Xi Trigram Sequence numeral character squares
or x2. Each one has a lower and upper trigram that is the same.
This is graphic depiction of Fu Xi Trigram Sequence numerals 1 X 1 = 1 giving a single
hexagram character, the seed hexagram symbolizing Heaven. Fu Xi Trigram Sequence
numerals 2 X 2 = 4 giving a 2 X 2 hexagram matrix comprising 4 characters. Fu Xi Trigram
Sequence numerals 3 X 3 = 9 giving a 3 X 3 hexagram matrix comprising 9 characters. Fu Xi
Trigram Sequence numerals 4 X 4 = 16 giving a 4 X 4 hexagram matrix comprising 16
characters. Fu Xi Trigram Sequence numerals 5 X 5 = 25 giving a 5 X 5 hexagram matrix
comprising 25 characters. Fu Xi Trigram Sequence numerals 6 X 6 = 36 giving a 6 X 6
hexagram matrix comprising 36 characters. Fu Xi Trigram Sequence numerals 7 X 7 = 49
giving a 7 X 7 hexagram matrix comprising 49 characters. And finally, Fu Xi Trigram
Sequence numerals 8 X 8 = 64 giving an 8 X 8 hexagram matrix comprising 64 characters
and the last exhaustion character symbolizing Earth [Fig. 17].
The appropriate convention is to refer to these combinations relationally as lower
trigram by upper trigram, not arithmetically as lower trigram times upper trigram. In the
figure diagrams the convention used is lower trigram 1 8 by upper trigram 1 8. So the
hexagram 3 X 7 = 21 denotes the sequential 23rd hexagram with lower 3rd trigram by the
upper 7th trigram delineating a matrix of 21 characters bounded 3 up by 7 across to the left.
4
To my western eyes this matrix at first looked like a digital binary calculator because I saw
the characters sequentially, not as Wen Wang or his contemporaries would have seen them. I
now understand this was a serendipitous happenstance of its simultaneity with binary
number theory. While not intended as its primary function, because it follows binary number
theory laws, it can be used as a sequential digital binary calculator in the following way.
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
24
If we exchange sequential Arabic/Hindus numerals for the hexagram characters we get 1
64 in an 8 X 8 numeral matrix. Now lets flip and rotate this matrix for western convention
upper left corner start position, right reading top to bottom. You manipulate this manual
calculator digitally using your index finger following binary arithmetic operations [Fig. 18].
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48
49 50 51 52 53 54 55 56
57 58 59 60 61 62 63 64
Credit: Kevin Mequet
Fig. 18 Wen Wang Yijing Digital Binary Calculator (Patent Pending) Interpretive info: right-reading; red, exponent numerals; blue, odd numerals; black, even numerals; yellow, register 1 numerals; and green, register 2 numerals.
Place your finger or a stylus on the character that you wish to begin the calculation, and
then count sequentially to get the result. If adding, count forward to the right from the first
addend numeral the number of the second addend to achieve the sum. If subtracting, count
backward to the left from the first subtractend numeral the number of the second
subtractend to achieve the resultant subtend. If the second subtractend is larger when you
reach numeral 1 tap your figure or stylus again, count once againbecause there is no (0) in
this calculatorand continue counting backward to the left, the resultant subtend is a
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
25
negative number or a deficit. If multiplying, count the multiple forward to the right, such as
4 X 5, start at numeral 1 and count 5 sets of 4 characters till you reach numeral 20. The
answer is 20. You could also correctly count 4 (5s) forward to the left. If dividing, do the
reverse of multiplying, such as 20 / 5, start at the numeral 20 count the divisor 5 backwards
to the left, thats 1 (5), another 5, thats 2 (5s), count another 5, thats 3 (5s), another 5 which
brings us to numeral 1, thats 4 (5s), the answer is 4 with no remainder. If theres a remainder
note it with the resultant dividend.
What happens if your calculation exceeds 64? Start adding or subtracting (64s). Lets
suppose an answer of 103 wants to be obtained. How do you deal with it? You count to 64
and then start from the beginning numeral 1 again and keep going, such as 64 and 39. The
answer is 64 and 39. So running debt or surplus totals would be formatted in multiples of 64
and a remainder under 64, if any. Extraordinarily large numberswith carecan be
manipulated.
Conveniently, the numerals and design tells you what to do; its self-embodied and
complete. By using very simple rules it does the work of addition, subtraction, multiplication
and division very similar to the binary numeral system. But this isnt what Wen Wang
invented his matrix to do in his time. He invent this singular matrix to produce what he said
would become the most rational system of divination.
5
Lets now turn to an important consideration. Why do human beings regardless of disparate
evolutionary cultural development strive to embody existence into systematic mathematical
objects? The posing of this question seems to be at the heart of this essay and might provide
a methodology for finding common ground cross-culturally for promoting profound dialog
and mutually illuminating inquiry.
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
26
Leibniz and Western Europe held the view that mathematics is at the heart of all
creation and human endeavor. It is the perfect unchanging language of G-d in Western
Europe and of the Son of Heaven in China. Through ancient antecedents, both in the
European and East Asian continents, Li Madou reintroduced China to this view
reinvigorated and exhorted by Christopher Clavius, Matteo Riccis mathematics teacher at
university.
As was noted at the beginning of this essay Qin Shihuangdi precipitated a titanic
discontinuity in Chinas intellectual continuum. It was a breach so vast that it could not be
mitigated internally, but awaited a chance encounter from outside her borders in the late 16th
century Ming Dynasty by Li Madou from the Great West. That chance encounter would set
in motion events of unforeseen consequence. Until Li Madou wrote in Mandarin a treatise
on mathematics translating Euclids Elements into Jihe yuanben (1607)literally translated as
the origin of quantity but more-widely known as Elementary Treatise on Geometrya
small rivulet of reconnection could not develop into a flood of reclaimed arithmetic
expertise. Lauded by the Chinese literati as an exemplary homage to Confucius Li Madous
preface quoted from Christopher Clavius translation of Euclids Elements. It was an oversell
of mathematics to the Chinese to bolster a skeptical Chinese Imperium of its value and
virtue. Ironically it was the same oversell as was Clavius preface to bolster a skeptical
Roman Catholic Church of the integral value and virtue of arithmetic in the syllabuses of
their universities. Clavius compared mathematics to a fountain from which the other
branches of science gush; Ricci compared it to a ladder leading up to the peaks of
knowledge.8 After an arithmetic drought of 1,800 years the importance of mathematics to
Chinas well-being and promotion of good societal order fell upon receptive ears.
The downside is that this view falls prey to an overdominant condition, whereby creative
speculation, language and the arts become secondary endeavors. One can so easily mistake
8 Ibid, p. 254
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
27
mathematical objects as interchangeable, even replaceable, with reality. Unfortunately, this is
not so.
We have reached a philosophical and scientific impasse that must be surmounted. The
case is laid out quite clearly and succinctly by Lee Smolin in his latest book, Time Reborn
(2013), where we must accept the reality of time suffusing the universe, events as real in the
moment, time as the passage of successive moments with directionality, novelty and change
in an unbounded, open-ended, evolving Leibnizian Universe of relationality, fundamentally
unpredictable and uncertain, but extravagantly diverse and unique. He says Leibnizian
because he takes as a given two important principles of Leibniz: The Principles of Sufficient
Reason and Identity of the Indiscernibles,9 or Univocity of Singular Uniqueness.10
The problem to be mitigated is summed up quite nicely by Smolin:
Mathematics will continue to be a handmaiden to science, but she can no longer be
the Queen.11
Mathematics and sciencethe same as the arts/humanities and the sciencesmust be
interrelated and interplayed the way Deleuze formatted his two numerical series interacting
in intensity and extensity giving rise to his formulation of the virtual and actual, both/and,
neither preferenced or annihilated, distinguishable but indivisible.12
And so the same must be said of this extrapolation of Wen Wangs Yijing Hexagrams
which culminates Leibniz unrequited inquiry begun three centuries ago.
9 Lee Smolin, Time Reborn, Houghton Mifflin Harcourt Boston, NYC (2103), pp. 114 - 7
10 Gilles Deleuze, Difference & Repetition, Columbia University Press (1968 French, 1994 English), p. 37;
the author is synthesizing Deleuzes thought which he synthesized from Leibniz and Spinoza. 11
Lee Smolin, Time Reborn, Houghton Mifflin Harcourt Boston, NYC (2103), p. 251 12
Clayton Crockett, Deleuze Beyond Badiou, Columbia University Press, NYC (2103), p. 40
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
28
Li Madou had no patience, let alone a spirit of accommodation, with what he termed the
several thousands of charlatans peddling false fortune-telling in the Imperial Capitol.13 He
was undoubtedly referring to Yijing divination. This was an unfortunate colonial
misunderstanding. I would desire correcting it and welcome an open dialog to deepen my
understanding of this long-beloved Chinese tradition in the Confucian ideal:
The Master said, Reviewing the old as a means of realizing the newsuch a
person can be considered a teacher. 14
We seem, regardless of differing evolutionary cultural development, to be extraordinarily
concerned with the avoidance of risk and detriment by attempting to transform unruly,
unpredictable, uncertain existence into orderly, controllable life with the benefit of certainty.
This is at root a zero-sum game. We must eschew this illusory wish for an authentic
relationship with reality that includes time and acclimatizes us to becoming comfortable with
uncertainty. Wishing mathematics to remain the Queen of science in the West is not so
dissimilar with wishing the Yijing to give some certainty in an uncertain world. Mathematical
objects can only approximate processes in time in the world and never perfectly model or
replace them. I could confidently say Heideggers Being the World would fit nicely here. So
like everything else the interpretive project must extend to mathematical objects: useful
handmaidens but never Queens, as is demonstrated in this essay. We must come to a place
where we realize that to live fully we must live joyfully into uncertainty. Perhaps we can
more effectively connect with each other cross-culturally if we share our mutuality in
certainty and together venture beyond it?
Coming full circle, lets reconsider Wen Wangs Hexagrams. If we perform the same
operation upon the 8 X 8 = 64 matrix as we did to produce the Yijing Digital Binary
Calculator we get a relational matrix of Fu Xi trigrams multiplied by themselves [Fig. 19].
13 Michela Fontana, Matteo Ricci: A Jesuit in the Ming Court, Rowmann & Littlefield Publishers, Inc.,
(2011), p. 262 14
Ibid, p. 243; Confucius, Analects (2, 11)
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
29
1x1 1x2 1x3 1x4 1x5 1x6 1x7 1x8
2x1 2x2 2x3 2x4 2x5 2x6 2x7 2x8
3x1 3x2 3x3 3x4 3x5 3x6 3x7 3x8
4x1 4x2 4x3 4x4 4x5 4x6 4x7 7x8
5x1 5x2 5x3 5x4 5x5 5x6 5x7 5x8
6x1 6x2 6x3 6x4 6x5 6x6 6x7 6x8
7x1 7x2 7x3 7x4 7x5 7x6 7x7 7x8
8x1 8x2 8x3 8x4 8x5 8x6 8x7 8x8
Credit: Kevin Mequet Fig. 19 Relational Wen Wang Yijing Hexagrams from Fu Xis Trigrams Interpretive info: right-reading; red, x2 characters; blue, odd column characters; black, even column characters; yellow, register 1 characters; and green, register 2 characters.
We cannot know with certainty how Wen Wang used his Yijing Hexagram Matrix for the
most rational method of divination. It is lost to us now by the actions commanded by Qin
Shihuangdi. But just as we have reconstructed here how the matrix was originally created, it
might be possible to inductively reason how the methodology of divination might have been
conceived by Wen Wang. An idea of Stuart Kaufmanns might help us here. It posits that in
a relational world one must look for what can happen next, or the processes of the world
follow the Principle of the Adjacent Possible.15 In a relational Yijing Hexagram Matrix
devised from multiplying Fu Xis Trigrams by themselves relationally, might we look for
relational operations of divination based upon Kaufmanns Principle of the Adjacent
Possible? I would like very much to investigate this further with Chinese scholars.
15 Lee Smolin, Time Reborn, Houghton Mifflin Harcourt Boston, NYC (2103), p. xvi
-
kevin dobson mequet 605 WATKINS STREET CONWAY, ARKANSAS 72034 501-327-9470 [email protected]
Never doubt that a small group of committed citizens can change the world: indeed its the only thing that ever has. Margaret Mead
30
Copyright 2013 Kevin Dobson Mequet; Zhou Wen Wangs Development of Yijing (Book Of Changes) 64 Hexagrams: An Inductive Recreation of Binary Extrapolative Operations. It is intended for strictly individual personal use. All rights are reserved. It may not be reprinted without obtaining prior written permission from Kevin Mequet. It may not be altered, misquoted, truncated, misattributed or plagiarized. Please adhere strictly to competent academic citation and attribution.