HÁN
VIỆT
DỊCH
SỬ
LƯỢC
GS
Nguyễn
Hữu
Quang
Nguyên
Giảng Viên Vật Lư Chuyên về Cơ Học Định Đề
(Axiomatic Mechanics, a branch of
Theoretical Physics)
tại Đại Học Khoa Học Sài G̣n trước năm 1975
CHƯƠNG
05
DỊCH TIỀN
ĐỀ
(Tiếp theo Kỳ 49)
FURTHER
READING
Two
_______________________________________________
CONGRUENCE FUHSIWATSONCRICK
生
生
之
謂
易。
Change is
recursive and crossgenetic.
− The Great Appendix, Section I, V/6
The physicist Erwin Schrödinger’s
book What is life? (1944) had a great impact on the
development of molecular biology and stimulated scientists
such as Watson and Crick (E).
The problem of relating digrams to the codons and the
genetic code to the hexagrams was raised by the molecular
biologist Gunther Siegmund Stent (19242008) in his book
The Coming of the Golden Age; a view of the end of progress
(2G)
and, four years later, by Dr. Martin Schonberger in his book
The I Ching and the Genetic code; the Hidden Key to Life
(2F).
The former mistook the minor yin for the minor yang because
of a misinterpretation by Richard Wilhelm himself in his
translation of the original I CHING or Book of Changes (2I
&&
2J)
into the German I Ging. The latter mixed up
everything and his congruence between digrams and triplets
fails the horizontal test of a function. Finally, came Dr.
J. F. Yang with his DNA and the I Ching, the Tao of Life
(2K).
His interpretation conforms to the tradition of the Four
Emblems and agrees with my own.
It is important to notice at once that di, tri and
hexagrams grow upwards like trees when alone and outwards
like trees’ yearly rings when grouped in cyclads. Hence,
when writing down or reading out a hexagram’s binary
representation, we do it from left
Consequently, the readers may notice that the four emblems
are: Old Yang
:,
Lesser Yin
;, Lesser Yang
<, Old
Yin
=,
and not the other way around. Thus, in the Lesser Yin, the
yin line is younger than the yang line because it is in a
higher (later) position than the yang line.
Similarly, in the lesser yang
<, the yang line is younger than the
yin line for it is in a higher position than the latter.
Thus, we have the following table:
Table 2.1 Digrams and their Properties
Digram 
Bin.
Val. 
Dec. 
Parity 
Mantic
Value 
Emblem 
Nucleotide
Base 
Sym 
= 
00 
0 
even 
6 
Old or
Major Yin 
Adenine 
A 
< 
01 
1 
odd 
7 
Young or
Lesser Yang 
Cytosine 
C 
; 
10 
2 
even 
8 
Young or
Lesser Yin 
Thymine
(Uracil) 
T
U 
: 
11 
3 
odd 
9 
Old or
Major Yang 
Guanine 
G 
DNA (deoxyribonucleic acid) is the fundamental substance of
which genes are composed. Chemically, it is a double chain
of linked complementary nucleotides (AT or CG), having
deoxyribose as their sugars.
On the other hand, RNA (ribonucleic acid) is a
singlestranded nucleic acid similar to DNA but having
ribose sugar rather than deoxyribose sugar and uracyl rather
than thymine as one of the bases. The principal function of
RNA is to copy the genetic information from the DNA and then
to transform into proteins. Chemically, RNA differs from DNA
by an additional hydroxyle OH linked to the pentose.
The five nucleotide bases have the following chemical
structures, formulas and molecular weights (mw):
Thymine
Uracil
Adenine Cytosine
Guanine
(2,6 dihydroxy (2,6 dihydroxy (6aminopurine)
(2hydroxy (2amino
5mehtyl pyrimidine)
aminopyrimidine) 6hydroxypurine)
pyrimidine)
C_{5}H_{6}N_{2}O_{2} C_{4}H_{4}N_{2}O_{2} _{ }C_{5}H_{5}N_{5} _{ }C_{4}H_{5}N_{3}O C_{5}H_{5}N_{5}O
mw = 126.12 mw = 111.9 mw = 135.13 mw = 111.10
mw = 151.13
Fig. 2. 2 Structure and
Molecular Masses of the Nucleotide Bases
Cytosine and thymine (uracil) are pyrimidines with two
hydrogenbonds thanks to the nonpaired electrons of the
nitrogen atoms; adenine and guanine are purines with three
Hbonds as shown in the following chemical structures:
Fig. 2.3 Pyrimidines
Structure Fig. 2.4 Purines Structure
The assignement of the 4 nucleotide bases to the 4 digrams
is natural and consistent for several reasons:
1) In Yilogy, the odd numbers are yang and the
even numbers are yin so that the yin/yang property of the
digrams matches that of the enblems. This property
corresponds to the WatsonCrick pairing of A to U (AU) and
of G to C (GC).
2) The purines (A, G) are classified 'major' and the
pyrimidines (C, T/U) 'minor' because the formers are larger
in dimensions and heavier in weights than the latters: G =
151.13 > C = 111.10; A = 135.13 > T = 126.12 and U = 111.9.
3) The WatsonCrick pair AU(T) is yin or even,
with an even number (2) of Hbonds while the pair GC pair
is yang or odd with an odd number (3) of Hbonds. Moreover,
GC pairs are denser than AU pairs and the GC content is
usually estimated by measuring the density of DNA double
helices.
4) Leading zeroes are meaningless; the leading
polyA (0) (polyadenylic acid) do not encode any amino acid;
but once initiated, the codon AAA =
B
(K’un)
encodes lysine. By the way, in the amino acid composition of
proteins, lysine appears very frequently. This suggests that
there is excess of 0s not replaced by 1s. After the
initiation by AUG =
u
(progress) =
methionine (Met), the leftover polyA contribute to the
excess of lysine.
5) Chemically, the codon GGG =
A
(Ch’ien) and its
anticodon CCC =
(Wei Chi) (i.e. the first and the last hexagrams in the King
Wên’s sequencing) form a total of 9 Hbonds. On the other
hand, the codon AAA =
B
(K’un) and its anticodon UUU =
? (TTT) (Chi Chi) (the
second and the antepenultimate hexagrams in the King Wên’s
sequencing) form 6 Hbonds between them. The remained
codonanticodon pairs could possibly have 2 + 2 + 2 = 6,
3 + 2 + 2 = 7, 3 + 3 + 2 = 8 or 3 + 3 + 3 =
9 Hbonds, i.e., one of the very four mantic numbers of
the digrams 6, 7, 8, 9. As a matter of fact, in the 3coin
method of divination, Head (yang) has a value of 3 and tail
(yin) a value of 2, following tightly the syntagma:
“The
number 3 was assigned to Heaven, the number 2 to earth, and
from them came all the other numbers.”
(Discussion of the Trigrams, I/2).
Remember that a protein is a macromolecule of amino acides
chained end to end with a linear string. The general formula
for an amino acid is H_{2}N―CHR―COOH, in which the
lateral chain, or R group, can be anything from a single H
atom (as in glycine Gly) to a complex ring (as in tryptophan
Trp):
Here are the sidechains of some of the remained amino acids
along with their 3letter abbreviations:
There are 20 common amino acids in living organisms (Table
2.1.4), each having a different R group. Amino acids are
linked together in proteins by covalent bonds called peptide
bonds which are formed through a condensation reaction
involving the removal of an H_{2}O molecule:
n other words, the
NH2 group of one amino acid interacts with the COOH of a
A peptide possessed a zigzagging backbone of nitrogene and
carbon analogous to the sugarphosphate backbone of a
polynucleotide with R groups projecting outward in
alternating fashion. A peptide containing many peptides, is
called polypeptide.
Table 2.2 The 20 common Amino Acids in living organisms
The amino acids with
asterisks are hydrophobic; the rest are hydrophilic. To this
list we should add the Stop codon (symbol X) or termination
codons. They are regarded as similar to periods or commas
punctuating the message encoded in the DNA.
There
are mainly four classes of RNA: tRNA = Transfer RNA (it
carries the information contained in a gene to the
ribosome); rRNA = Ribosomal RNA (component of the ribosomes
that serves as a kind of scaffolding for the processes of
polypeptide synthesis); mRNA = Messenger RNA (the mRNA
molecules, which are produced in the DNA template, pass out
through the nuclear pores into the cytoplasm and here the
information in the sequence of the mRNA is translated into
protein), and hetRNA = heterogenous nuclear RNA (found only
in eukaryotes).
If a single nucleotide in an mRNA specifies a
single amino acid in a protein, it would mean that proteins
could contain only four amino acids, whilst in living
organisms they contain 20. Similarly, a doublet code could
only generate 4^{2} = 16 combinations of pairs of
nucleotide bases, still not enough to specify all 20 amino
acids. Therefore, we need 64 triplet codes. 16 < 20 < 64
shows that the code is degenerate, meaning that an amino
acid may be specified by more than one triplet. In fact, as
many as 64 – 20 = 44 of the putative triplets are never
found in natural mRNAs.
Thus we have exactly 64 triplets because each time we can
chose one out of the four letters G, U, C, A; since there
are three choices for the codons, we get, all in all 4 x 4 x
4 = 64, the very cardinality of the set of hexagrams. The
triplet codes of a codon or anticodon correspond to the
three digrams of a hexagram.
When poly AC is synthetized from mixture containing equal
proportions of A and C, eight triplets should occur: AAA,
AAC, ACA, CAA, ACC, CAC, CCA, and CCC. Using poly AC it was
found that six amino acids are incorporated into
polypeptides: asparagine (AAC), glutamine (CAA), histidine
(CAC), lysine (AAA), threonine (ACC & ACA), and proline (CCC
& CCA).
Now it’s about time to establish the congruence between the
WatsonCrick Genetic code and the Fushian biocode through
the following Tables 2.2 and 2.3, in which we adopt the
following conventions:
·
In Table 2.3 The Genetic
Code, the letters are proceeded from left to right as usual;
·
In Table 2.4 The Fuhsian
Biocode, we respect the tradition by sequencing the digrams
from bottom to top: the first digram (Earthdigram) is at
the bottom, the second digram (Mandigram) is in the middle
and the third digram (Heavendigram) ends up at the top.
By the way, it is good to notice the three digrams’
positions in a hexagram reflect the nature of the genetic
DNARNAprotein trio: DNA as Earth (Space), RNA as Heaven
(Time) and protein as Man (Humanity). This kind of triad
abonds:
Biology(DNA) Western Chinese Yiching
Hinduism Modern
Philosophy Philosophy
Science
Codon Mind Heaven
PreHeaven Brahma Information
Pscychon Soul Mankind
InHeaven Vishnu Energy
Somaton Body Earth
PostHeaven Siva Matter
Exercise:
Find the triads corresponding to: Buddhism, Christianism,
NeoConfucianism, Computer Science, and Psychology.
Any
hexagram comprises either 3 digrams (top, median, bottom) or
2 trigrams (upper and lower). Traditionally, it is read top
down. It’s why, in the Fufsian biocode the order is: top,
median, bottom
Table 2.3 The
WatsonCrick Table 2.4
The Fuhsian
Genetic
Code
Holistic Biocode
The table 2.3
reveals several features of the genetic code:
·
The code is seen to be
degenerate: six codons are used to specify a single amino
acid (arginine, leucine or serine);
·
Only two amino acids are
represented by a single codon: tryptophane UGG and
Methionine AUG. The latter specifies the initiation of
translation;
·
The three codons UAG (amber
codon), UGA (opal codon), and UAA (ochre codon) are
often called nonsense because they fail to stimulate
acyltRNA binding and serve only as chainterminators
signals.
Two notable patterns
emerge from this table 2.3:
1.
Certain amino acids can
be brought to the ribosome by several tRNA species having
different anticodons while certain other amino acids are
brought to the ribosome by just one tRNA. This feature of
the code is thought to minimize the consequences of errors
made during translation or of mutagenic base substitutions.
2.
Certain tRNA species can bring their specific amino acids in
response to several codons, not just one, through a sloppy
pairing at one end of the codon and anticodon (wobble).
For instance, all codons starting with AC specify threonine,
all codons starting with CC specify proline, all codons
starting with CG specify arginine, all codons starting with
CU specify leucine, all codons starting with GC specify
alanine, all codons starting with GG specify glycine, all
codons starting with GU specify valine and all codons
starting with UC specify serine. This flexibility in the
nucleotides of a triplet may well help to minimize the
consequences of errors. At the same time, the upper trigram
of the corresponding hexagrams remains the same
(specifically
!ch’ien,
kên,
)sun,
%li,
#tutui,
or
'chên).
Here the names of the trigrams are not capitalized to
differentiate them from the hexagrams having the same names.
I have asked the mathematician Brian Hayes how to calculate
the total number of possible genetic codes. Here is his
answer:
“There are 20 amino acids plus the
"stop" signal, so each of the 64 codons can have any of 21
possible meanings. Thus a first approximation says there are
21^{64} possible genetic codes; this number is equal
to 4.1882719x10^{84}. However, not all of those
codes are legal. We require that every amino acid and the
stop signal have at least one codon assigned to it, and so
we have to exclude all of the codes that do not satisfy this
condition. How many of those illegal codes are there? Well,
if we choose some specific amino acid, say ALA, there are 20^{64}
codes that do not assign any codon to ALA. It's the same for
ASN, ASP, etc. Thus there are 21 x 20^{64} codes
that fail to include at least one amino acid or the stop
signal. Therefore the number of legitimate codes is 21^{64}
 (21x20^{64}), which works out to 3.144556x10^{83}.
Here is the exact number, in case it might amuse you:
314455595548268427310020743752976432915773724299403513508038881183728210190544679681”.
I figured out that
this result is obtained by using the software Derive 6.1. On
the other hand, the exact number of possible genetic codes
is:
4188271851027274266670020743752976432915773724299403513508038881183728210190544679681
@
4.188271851 x 10^{84}.
Table 2.5 King Wên’s Arrangement
N. B.
In the Table 2.5, the octal representation of the King Wên’s
hexagram precedes the period and the binary value of the
Fushi’s hexagram follows it. The name of the corresponding
hexagram is given in Enhanced WadeGiles. Last last row
gives the tricode as well as the singleletter of the
corresponding aminoacid given in Table 2.2.
HEXAGRAMS DERIVATION
An rpermutation a_{nr }(r
b
n) of n things is an ordered arrangement of r of them. In
any book on Combinatorial Mathematics, it is proved that
there are
(n)_{r} =_{ } n(n – 1) (n 2) … (n – r + 1)
rpermutations of nobjects (0 < r
b
n). The symbol (n)_{n} , written n!, read
"nfactorial ", and (n)_{r} is sometimes called the
“falling rfactorial of n”.
It is also be proven that if there are
n = n_{1} + n_{2} + … + n_{k}
objects, of which n_{1 }are of one kind, are
of a second kind, … , n_{k } are of a kth kind, then
the number of permutations of the n objects is
Finally, it is proved that the number of rsubset of a set S
containing n elements is
When there are only two labels we can shorten the notation
and write
Pascal's triangle is a
number triangle with
numbers arranged in staggered rows such that
where
is a
binomial coefficient.
The triangle was studied by the French mathematician,
physicist, philosopher and writer Blaise Pascal (162362),
although it had been described centuries earlier by the
Persian astronomerpoet Omar Khayyám (10481131),
who helped reform the ancient Muslim calendar,
and by the Chinese mathematician Yang Hui楊
輝
Dương
Huy
(c.
1239–98), active in the great flowering of Chinese
mathematics during the Southern Song Dynasty (11271279)
Thus, it is known as the Yang Hui’s triangle in China.
In his book, A New Kind of Science (p. 611), Stephen
Wolfram has presented the Pascal’s triangle as nested
patterns constructed using arithmetic operation. He also
generalized this triangle so that each number is the sum of
the numbers above it and to its left and right on the row
above.
The Pascal’s triangle starts with n = 0:
Fig. 2.5 Yang Hui’s Isoceles
Triangle Fig. 2.6 Fig 2.7
Pascal’s
Rectangle Triangles
N.B.
In Fig. 2.7, the digits A, F and K are successively the
decimals 10_{10}, 15_{10}, and 20_{10}
in a number system of radix 21 (0, 1, 2, 3, 4, 5, 6, 7, 8,
9, A, B, C, D, E, F, G, H, I, J, K). In that case, the
different lines of Fig. 2.4.2 are simply the successive
powers 0, 1, 2, 3, 4, 5, 6 of the number 11_{10}.
Pascal's formula shows
that each subsequent row is obtained by adding the two
entries diagonally above,
For n = 2, the binomial becomes:
(a + b)^{2} = a^{2}
+ 2ab + b^{2}
Replacing a and b by the monograms
?
and
>
meaning
0 and 1, we get
the four forms:
a^{2 }=
=
00 old yin moving
yin Adenine (A)
2ab =
<
01
lesser yang resting yang
Cytosine (C)
=
;
10 lesser yin resting
yin Thymine (T)
b^{2} =
:
11 old
yang moving yang
Guanine (G)
For n= 3,
the binomial becomes:
(a + b)^{3} = a^{3} + 3a^{2}b + 3 ab^{2}
+ b^{3}
Replacing a and b by the monograms
?
and
> meaning
0 and 1, we
get the eight trigrams:
a^{3} =
/
000 0_{8} 0 k’un Ultimate Yin
3a^{2}b =

001 1_{8}
1 kên
Lesser Yang
=
+
010 2_{8 }2
k’an Younger Yang
=
)
011 3_{8 }3 sun Older Yin
3ab^{2} =
'
100 4_{8 }+0 chên Older yang
_{
}=_{
}
%
101 _{ }5_{8} +1
li Younger Yin
=
#
110 6_{8}
+2 tui
Lesser Yin
b^{3} =
!
111 7_{8} +3 ch’ien
Ultimate
yang
N.B. The first number is binary, the second one octal, and
the third one algebraic. The trigrams’ names are not
capitalized in order to distinguish them from the hexagrams
having the same names. In the last column we give the
aliases of the corresponding trigrams in the terminology of
the Pristine Envelop Classic. Here the leading letters are
capitalized in order to distinguish the trigrams from the
digrams having the same nanes.
For n = 6, the binomial becomes:
(a + b)^{6} = a^{6}
+ 6a^{5}b+ 15a^{4}b^{2}+ 20a^{3}b^{3}
+ 15a^{2}b^{4} + 6ab^{5} + b^{6}
In the last column, the mantic value is calculated by the
general formula:
(2n  1) x (5
± 1)
with n = 1..6 (line number)
The "+" sign corresponds to a yang line
>
and the
"" sign to a yin line
?.
Replacing again a and b by the monograms
?
and
>,
we get:
6G bin octal trinucleotide mantic
value =
a^{6} =
B
000000
00 AAA 144
6a^{5}b =
X
100000
40 AAU 146
G
010000 20 AAC 150
O
001000 10 AUA 154
P
000100 04 ACA
158
H
000010 02 UAA 162
W
000001 01 CAA 166
15a^{4}b^{2 }=
S
110000 60 AAG 152
d
101000 50 AUU 156
s1100100
44 ACU 160
C
100010 42 UAU 164
[
100001 41 CAU 168
n
011000 30 AUC 160
h
010100 24 ACC 164
]1010010
22 UAC 168
D1010001
21 CAC 172
~
001100 14 AGA 168
g
001010 12 UUA 172
t
001001 11 CUA 176
m
000110 06 UCA 176
c
000101 05 CCA 180
T
000011 03 GAA 184
20a^{3}b^{3 }=
K
111000
70 AUG 162
v
110100 64 ACG 166
i
110001 61 CAG 174
w1101100
54 AGU 170
101010 52 UUU 174
V
101001 51 CUU 178
Q
100110 46 UCU 178
U
100101 45 CCU 182
j
100011 43 GAU 188
`
011100 34 AGC 174
p
011010 32 UUC 178
R
011001 31 CUC 182
010101 25 CCC 188
{
010011 23 GAC 190
_
001110 16 UGA 186
x
001101 15 CGA 190
u
001011 13 GUA
` 194
L
000111 07 GCA 198
15a^{2}b^{4} =
b
111100 74 AGG 176
E
111010 72 UUG 184
Z
111001 71 CUG 184
z
110110 66 UCG 188
f
110101 65 CCG 178
}
110011 63 GAG 192
q
101110 56 UGU 188
^
101101 55 CGU 192
e
101011 53 GUU 196
Y
100111 47 GCU 200
r
011101 35 CGC 196
y
011011 33 GUC 200
F
010111 27 GCC 204
a
001111 17 GGA 208
6ab^{5} =
k
111110
76 UGG 194
N
111101 75 CGG 198
I
111011
73 GUG 202
J
110111 67 GCG 206
M
101111 57 GGU 210
L
011111 37 GCA 198
b^{6 }=
A
111111 77 GGG 216
Mark White, a
physician and inventor in Bloomington, Indiana, discovered
the genetic code can be represented succinctly on an
icosidodecahedron which is a combination of a dodecahedron
(made up of 12 pentagones) and its dual the icosahedron
(made up of 20 triangles). Each pentagonal face of this
solid is labeled with one of the four nucleotides, each of
which appears thrice. Each encoded amino acid will be found
adjacent to the first base, along the edge leading to the
second base, and inside the triangle formed with the third
base.
Fig. 2.8 Icosidodecahedral Representation of the
genetic code discovered by
Mark White and embodied by him in a GBall (G stands for Genetic
code), a.k.a. Rafiki Map.
For example, in Fig. 2.4, a tour
from A to A to U yields asparagin, a tour from A to G to U
gives serine, and a tour from A to U to G specifies
methionine.
In the following figures, we can identify successively
lysine (AAA), proline (CCC & CCA), glycine (GGG) and
Phenylalanine (UUU).
Fig. 2.9
GBall 1:
Lysine
(AAA)
Fig.
2.10
GBall 2: Proline
(CCC & CCA)
Fig. 2.11
GBall 3: Glycine (GGG) Fig.
2.12
GBall 4: Phenylalanine (UUU)
White notices that
the icosidodecahedral model is closely related to the first
coding scheme of the genetic code, the diamond code,
proposed in 1954, by the physicist George Gamow, the chief
proponent of the Big Bang theory in Cosmology (2D).
This takes us back to square one (Fig. 2.9).
Fig.
2.13 The Diamond Code Fig. 2.14 The 20 classes of the 64
Codons
B«
O
P«
~
02
«
15
16
«
62
D«
R «
r
04
«
18
64
«
50
}«
I J«
A
61
«
09
10
«
01
C«
?
Q«
q
03
«
63
17
«
49
G«
W«
n«
t
07
«
23
«
46
«
52
S«
T«
K«
u
19
«
20
«
11
«
53
X«
H«
d«
g
24
«
08
«
36
«
39
h«
c«
`«
x
40
«
35
«
32
«
56
v«
L«
b«
a
54
«
12
«
34
«
33
s«
m«
w«
_
51
«
45
«
55
«
31
i«
{«
Z«
y
41
«
59
«
26
«
57
[«
]«
V«
p
27
«
29
«
22
«
48
f«
F«
N«
l
38
«
06
«
14
«
44
U«
o«
^«
\
21
«
47
«
30
«
28
j«
«
e«
E
42
«
60
«
37
«
05
Y«
z«
M«
k
25
«
58
«
13
«
43
Fig. 2.15 The 20 classes Fig.
2.16 The King Wên
of 64 hexagrams Perspective
We will see in CHAPTER SIX: THE YI ABSTRACT ALGEBRA that the
set H of hexagrams is a commutative ring under the modulo
operations. Moreover, the congruence between the codons and
the hexagrams confers to the formers a similar algebraic
structure. Thus, in Fig 2.10, the symmetries of the diamond
code sort out the 64 tricodons into 20 classes. All the
codons in each class specify the same amino acid. The 16
palindromic tricodons at the top of the table 2.10 come in
pairs and correspond to the first 16 hexagrams in Fig 2.15;
the remaining tricodons are in groups of four and correspond
to the 48 remaining hexagrams.
Table 2.6 Relationship between Quadrilines and Hexagrams
N.B.
1)
In this table, 1 Chi
極
= 7 yuan
元
= 7 x 3 or 21 chi
紀
= 7 x 3 x 20 or 420 pu
部
= 420 x 4 or 1680 metonic cycles
章=
31920
sui歲;
NOTES
1) The first row contains the the starting Gregorian date
(GD) of the leading tsan of the leading shou in each column.
2) The second row, the bottom row and rightmost column give
the ternary (in bold) and balanced ternary values (in
italics) of the shou situated at their intersection.
3) Notice that the rightmost column contains top down: the
row number starting with 0, the balanced ternary values (in
bold) and the ternary (in italics).
4) Each cell contains successively the details on each of
the 81 shou:
a) its enhanced WadeGiles romanization (in particular, in
the first and the last row of cells, the EWG romanization is
preceded by a column number) ; b) Its Chinese name; c) Its
ordinal number along with its native representation; d) The
ordinal number along with the representation of the
corresponding hexagram.
The interconversion between the ordinal number n of a shou
and its balanced ternary value is proceeded as follows:
Since, n є
[1, 81]1
≤ n ≤ 81.
Dividing n by 9, we obtain a quotient q and a remainder r: n
= 9 x q + r. Its decimal nonal representation is qr with
both q and r in the interval [0, 8]. Now we can uses the
phalanges of the index I, the medium M and the ring finger R
on both hands as cells of two similar tables for this
matter. The two thumbs are pointers.
r 

I 
M 
R 
↓
yx → 

> 
? 
 


1111 
22 
3 
> 
1 
0 
3 
6 
? 
2 
1 
4 
7 
 
3 
2 
5 
8 
q 

I 
M 
R 
↓
yx → 

1> 
? 
 


1111 
22 
3 
> 
1 
0 
3 
6 
? 
2 
1 
4 
7 
 
3 
2 
5 

Left Hand Nonal
left digit q Right hand Nonal right digit
Examples: N44
→
n = 43 = 9 x 4 + 7 = 47_{9} = 2232
=
:+
;
=
;:;
N67
→
n = 66 = 9 x 7 + 3 = 73_{9} = 3221
= <+
3
=
3<.
In examining the systematics of
indices of physicochemical properties of codons and amino
acids across the genetic code, Bashford and Jarvis (2A))
used a simple numerical labelling scheme for nucleic acid
bases, A = (1, 0), C = (0, 1), G = (0, 1), U = (1, 0), to
fit data as low order polynomials of the 6 coordinates in
the 64dimensional codon weight space. Their work shows that
fundamental patterns in the data such as codon
periodicities, and related harmonics and reflection
symmetries are associated with the structure of the set of
basis monomials chosen for fitting.
We will see in Chapter Seven: Triadic Combinatorics and
Abstract Algebra, that a quadriline or Shou is formed by the
superposition of four triadic lines, i.e. each line can take
one of the 3 values  , , and
>
standing for
or 1, 0 and 1 in the balanced
ternary number system (Table 2.6). Since each quadriline has
9 tsan, it may be either embedded in a sextiline or simply
included in the quadriline as superscript. Thus, codons are
labeled either as ordered sextuplets, or by a superscripted
quadriline or sextiline. For example,
CGA = (0, 1, 0, 1, 1, 0) :=
3@
<...
BIBLIOGRAPHY:
2A
Bashford, J. D. & Jarvis, P.D. The Genetic Code as a
Periodic Table: Algebraic Aspects,
submitted to Biosystems, physics/0001066, (http://www.physics.adelaide.edu.au/~jbashfor/).
2B
——.
Systematics of the genetic code and anticode: history,
supersymmetry,
Degeneracy and
periodicity,
physics/9809030, in Proceedings of the XII
International Colloquium on
Group Theoretical Methods in Physics, S.P. Corney, R.
Delbourgo and P.D. Jarvis
(Eds.) (International Press, Boston), 147151.
2C
Hayes, Brian. Ode to the Code, American Scientist, Nov.Dec.
2004, vol. 92, number 6, p. 494.
2D
Gamow, G. "Possible relation between
deoxyribonucleic acid and protein structure", Nature,
vol. 173, p.318, 1954.
2E
Murphy, M. P. & O’Neill, L. A.J., eds. What is Life? The
Next Fifty Years, Speculations on the future of biology,
Cambridge University Press, Cambridge, 1997.
2F
Schonberger, M. Verborgener
Schlüssel zum Leben
(The I Ching and the Genetic code; the
Hidden Key to Life),
ASI Publishers Inc., New York, 1979.
2G
Stent, G.S., The coming of the Golden Age, a view of the end
of progress, the National History Press, Garden City, N.Y.,
1969.
2H
White, Mark. The GBall, a New Icon for Codon Symmetry and
the Genetic Code,
http://www.codefun.com .
2I
Wilhelm, Richard. I Ging, 14.
Auflage, Eugen Diederichs Verlag, München, 1990.
2J
———————.
The I Ching or Book of Changes, rendered into English by
Cary F. Baynes, Third Edition, Bollingen Series XIX,
Princeton University Press, 1967.
2K
Yan Johnson F. DNA and the I Ching: The Tao of Life, North
Atlantic Books, Berkeley, 1991.
Xem Kỳ 51
GS
Nguyễn
Hữu
Quang
Nguyên
Giảng Viên Vật Lư Chuyên về Cơ Học Định Đề
(Axiomatic Mechanics, a branch of
Theoretical Physics)
tại Đại Học Khoa Học Sài G̣n trước năm 1975
www.ninhhoa.com 