The Iching is the ancient fortune telling
book of China. The Iching literature mentions
various methods for casting fortune patterns
of Iching. The various methods include
hot ironing of turtle shells (-t.),
manipulations of yarrow sticks, flipping coins,
throwing shaman bones, and dice.
One analogy from North America
is a shaman throwing or
shuffling stick dice. I made three stick dice for
Iching by cutting a dowel of square cross section
into three sticks.
For the three stick dice, the flat sides are marked or
burned with 2 or 3 holes alternately.
Two sticks are marked
with {3 2 3 2} dots on the sides. One stick is marked
with {3 3 3 2} dots on the sides.
In casting such three dice,
the possible sums are 6,7,8, or 9. Further, the
stick dice are cast six times to obtain whole lines
or broken lines in a pattern or set of six lines.
A set of six Iching lines is called a gua
in the orient or a hexagram in some translations
of the Chinese. In the Iching interpretations, casts of
6 and 8 are broken or yin (female) lines,
while casts of 7 and 9 are whole or yang (male) lines.
The casts are recorded by pencil with the first line
at bottom and marking up the column.
It is possible to record the numbers from the
casts with tally sticks or Chinese counting rods,
which are somewhat reminiscent of
the Iching patterns themselves.
After marking the original pattern or
hexagram, sometimes a second follow-up hexagram
is developed by swapping throws of 6 for a 7
and throws of 9 for a 6. These swaps effectively
trade a broken line(6) for a whole line(7)
and a whole line(9) for a broken line(6).
The throws for the changing lines (6&9) may not always
be come out in the first hexagram or
its component lines, so the followup hexagram
may not exist {under consistent rules}.
If the first hexagram is interpreted on a line
by line basis, any changing lines(6&9) or second
hexagram offers some modification or discount on
the interpretation of the first hexagram. In developing a computer program or application,
it is helpful to develop analogs
for the individual tasks of the application.
An Iching application would have to compose,
beg, or borrow TCL procedures for random casts,
tallies of scores, accounting files,
display hexagram lines on a screen,
swapping changing lines, hexagram pattern
recognition and ranking interpretations.
In fact, some TCL one liner procedures
and text swapping routines might be useful
as utilities in a starter
application program, since unruly
text strings are expected in the Iching.
Casting the sticks or bones
for each Iching line is analog for random lpick
subroutine below.
Adding the top sides of three sticks and throwing
six times is analog for the "for 6 times" statement
in the bonereadxx procedure below. In the West,
Leibniz etc recognised that
the whole and broken lines
in the hexagram patterns could
be counted as ones and zeros, respectively in
a binary number system. For example, a cast or TCL list
of { 6,7,8,9,6,7 } could be expressed as a binary
number, 010101. The binary numbers are the analogs
for the binaryexchange subroutine below.
For computer procedures, the patterns are effectively a
horizontal bar code of 6 lines. In the process of designing the basic
subroutine tasks, we could throw in some
switches, logic chains, or daisy chains
that break the outset rules given above.
For example, TCL is so good at swapping lines (6&9)
for the second hexagram, that it would
be easy to put a switch that generates or
swaps all hexagram lines (6,7,8,&9) for their opposites.
Also from some scripts of the Chinese Chou dynasty,
different Iching fortune methods of
yarrow sticks or coins would generate
different probabilities of obtaining
each hexagram line. Might be interesting to
have a back door in the program
to check (or adapt} the different probabilities
of stick or coin throws. Several authors
have pointed out that a few of the hexagrams
look similar to Chinese characters or even
Mayan calendar notation. Without wading too
deep into alternate realities, the Iching
hexagrams could be used as numerals,
script alphabet, game tokens, symbol recognition code,
or maybe a programing language (like Greek
letters for APL operators).
Such rule breaking helps keep the finished
program more flexible. #!/usr/bin/env wish
#start of deck
#Iching_Fortunes
# or Itching For Tunes [%>}
# 6Feb2007, [gold]
# working on XP starter code
package require Tk
global bookvalue bookvalue2
set colorground bisque
set wow "bone number"
proc xlistlistbox {} {
.labellabel delete 0 end
foreach filefile [glob .* *] {
if [file isdirectory $filefile] {
set filefile "$filefile/"
}
.labellabel insert end $filefile;
}
}
proc xskipskipdirectory {dir} {
cd $dir
.realcommand configure -text [pwd]
xlistlistbox
}
proc clickclicklistbox {} {
set index [lindex [.labellabel curselection] 0]
set filename [.labellabel get $index]
if [file isdirectory $filename] {
xskipskipdirectory $filename
}
}
wm title . "File Starter"
frame .labelframe
pack .labelframe -expand no -fill x
label .labellabel1 -text "Directory:"
label .realcommand -text "" \
-relief groove
pack .labellabel1 -in .labelframe \
-side left -expand no -fill x
pack .realcommand -in .labelframe \
-side left -expand yes -fill x -anchor w
frame .listlistbox
pack .listlistbox -expand yes -fill both
listbox .labellabel \
-width 25 -height 3 \
-xscrollcommand ".xxxxaxis set" \
-yscrollcommand ".yyyyaxis set" \
-bg $colorground
scrollbar .yyyyaxis \
-command ".labellabel yview" \
-orient v
scrollbar .xxxxaxis \
-command ".labellabel xview" \
-orient h
pack .xxxxaxis -in .listlistbox -side bottom -fill x -expand no
pack .yyyyaxis -in .listlistbox -side right -fill y -expand no
pack .labellabel -in .listlistbox -side top -fill both -expand yes
frame .buttonbuttonx
pack .buttonbuttonx -fill x
button .caster -text Cast_Bones -command {bonereadxx;castfortune;}
button .done -text Exit -command exit
pack .caster .done -in .buttonbuttonx \
-side top -fill x
bind .labellabel <Double-1> clickclicklistbox
pack [ label .ww -text "Iching holding tank " -bg $colorground]
pack [ text .wxxccc -width 80 -height 3 -bg beige ]
focus .wxxccc ;# allow keyboard input
.wxxccc insert end "xxx starter xxx ";
scrollbar .scr -orient vertical -command ".can yview"
canvas .can -yscrollcommand ".scr set" -width 240 -bg $colorground
pack .can -fill both -expand 1 -side left
pack .scr -fill y -expand 0 -side left
set width 50
set height 50
set w ".can"
set x 100
set y 100
set dx 50
set dy 30
set colors {white black }
set color 0
#suchenwirth_subroutine;}
proc lpick L {lindex $L [expr {int(rand()*[llength $L])} ];}
# utilities
proc plainsub {text item replacewith} {
set text [string map [list $item $replacewith] $text]
}
proc %+ {a } {return [string toupper $a]; #%+ tree >TREE }
proc %- {a } {return [string tolower $a]; #%+ Tree >tree }
proc %++ {a b} {return $a$b;#%+* tree root >treeroot }
proc %-- {a b} {regsub $b $a "" a; return $a;#%-- 5 7>5 }
proc %% {a b} {regsub -all $b $a "";#%% tree root >tree }
proc %1 {a b} {regsub $b $a "" a; return $a;#%1 tree root>tree }
proc %2 {a b} {regsub $b $a "" a;regsub $b $a "" a; return $a;#%2 tree root>tree }
proc %3 {a b} {regsub $b $a "" a;regsub $b $a "" a;regsub $b $a "" a; return $a;#%3 tree root>tree}
proc %2x {a} {return $a$a;#%2x tree>treetree}
proc %3x {a} {return $a$a$a;#%3x tree>treetreetree}
proc %4x {a} {return "$a,$a,$a";#%5x tree>tree,tree,tree }
proc %5x {a} {return "$a $a $a";#%5x tree>tree tree tree }
proc repeat {n body} {while {$n} {incr n -1; uplevel $body}}
proc random n {expr {round($n*rand())}}
proc whitelist {a} {return [lreplace $a 0 -1];#take string,return list without blanks}
set k [split {abcdefghijklmnopqrstuvwxyz} {}]
proc average L {expr ([join $L +])/[llength $L].}
proc srevert s {
set l [string length $s]
set res ""
while {$l} {append res [string index $s [incr l -1]]}
set res
};# RS,
proc lreverse L {
set res {}
set i [llength $L]
#while {[incr i -1]>=0} {lappend res [lindex $L $i]}
while {$i} {lappend res [lindex $L [incr i -1]]} ;# rmax
set res
} ;# RS, tuned 10% faster by [rmax]
proc sumoflist L {expr [join [split $L ""] +]+0} ;# RS
proc convertbase2to10 {jip} {
set l [split $jip ""]
set t 0; set e 0;
foreach n $l {
set exp [ expr int(pow(2,$e))];
incr t [ expr $n * $exp ] ;
incr e;
}
return $t}
proc kvsearch {kvlist item} {
set pos [lsearch $kvlist $item]
if {$pos != -1} {
lindex $kvlist [expr {$pos+1-2*($pos%2)}]
}
} ;# RS
# end utilities
#start iching data
set bookvalue [ list 1 63 43 62 14 61 34 60 9 59 5 58 26 57 11 56 10 55 58 54 38 53 54 52 61 51 60 50 41 49 19 48 13 47 49 46 30 45 55 44 37 43 63 42 22 41 36 40 25 39 17 38 21 37 51 36 42 35 3 34 27 33 24 32 44 31 28 30 50 29 32 28 57 27 48 26 18 25 46 24 6 23 47 22 64 21 40 20 59 19 29 18 4 17 7 16 33 15 31 14 56 13 62 12 53 11 39 10 52 9 15 31 14 56 13 62 12 53 11 39 10 52 9 15 8 12 7 45 6 35 5 16 4 20 3 23 1 2 0 8 2 ]
set bookvalue2 [ list 9999 1 63 43 62 14 61 34 60 9 59 5 58 26 57 11 56 10 55 58 54 38 53 54 52 61 51 60 50 41 49 19 48 13 47 49 46 30 45 55 44 37 43 63 42 22 41 36 40 25 39 17 38 21 37 51 36 42 35 3 34 27 33 24 32 44 31 28 30 50 29 32 28 57 27 48 26 18 25 46 24 6 23 47 22 64 21 40 20 59 19 29 18 4 17 7 16 33 15 31 14 56 13 62 12 53 11 39 10 52 9 15 31 14 56 13 62 12 53 11 39 10 52 9 15 8 12 7 45 6 35 5 16 4 20 3 23 1 2 0 8 2 ]
if 0 { iching hexagrams and trigrams }
if 0 { Little API style database }
if 0 {
+ hexagram_1 : pinyin Qian wade Ch'ien english {The Creative }
+ hexagram_2 : pinyin Kun wade K'un english {The Receptive}
+ hexagram_3 : pinyin Zhun wade Chun english { Difficulty at the Beginning }
+ hexagram_4 : pinyin Meng wade Mêng english {Youthful Folly }
+ hexagram_5 : pinyin Xu wade Hsü english {Waiting }
+ hexagram_6 : pinyin Song wade Sung english {Conflict }
+ hexagram_7 : pinyin Shi wade Shih english {The Army }
+ hexagram_8 : pinyin Bi wade Pi english {Holding Together}
+ hexagram_9 : pinyin Xiaoxu wade Hsiao Ch'u english {The Taming Power of the Small}
+ hexagram_10 : pinyin Lü wade Lü english {Treading}
+ hexagram_11 : pinyin Tai wade T'ai english {Peace }
+ hexagram_12 : pinyin Pi wade P'i english {Standstill }
+ hexagram_13 : pinyin Tongren wade {T'ung Jên} english {Fellowship with Men }
+ hexagram_14 : pinyin Dayou wade { Ta Yu } english {Possession in Great Measure }
+ hexagram_15 : pinyin Qian wade Ch'ien english {Modesty }
+ hexagram_16 : pinyin Yu wade Yü english {Enthusiasm }
+ hexagram_17 : pinyin Sui wade Sui english {Following }
+ hexagram_18 : pinyin Gu wade Ku english {Work on What Has Been Spoiled }
+ hexagram_19 : pinyin Lin wade Lin english {Approach }
+ hexagram_20 : pinyin Guan wade Kuan english {Contemplation }
+ hexagram_21 : pinyin Shike wade {Shih Ho } english {Biting Through }
+ hexagram_22 : pinyin Bi wade Pi english {Grace }
+ hexagram_23 : pinyin Bo wade Po english {Splitting Apart }
+ hexagram_24 : pinyin Fu wade Fu english {Return }
+ hexagram_25 : pinyin Wuwang wade { Wu Wang }english {Innocence }
+ hexagram_26 : pinyin Daxu wade { Ta Ch'u } english {The Taming Power of the Great }
+ hexagram_27 : pinyin Yi wade I english {The Corners of the Mouth }
+ hexagram_28 : pinyin Daguo wade { Ta Kuo } english {Preponderance of the Great }
+ hexagram_29 : pinyin Kan wade K'an english {The Abysmal }
+ hexagram_30 : pinyin Li wade Li english {The Clinging }
+ hexagram_31 : pinyin Xian wade Hsien english {Influence }
+ hexagram_32 : pinyin Heng wade Hêng english {Duration}
+ hexagram_33 : pinyin Dun wade Tun english {Retreat }
+ hexagram_34 : pinyin Dazhuang wade { Ta Chuang } english {The Power of the Great }
+ hexagram_35 : pinyin Jin wade Chin english {Progress}
+ hexagram_36 : pinyin Mingyi wade { Ming I } english {Darkening of the Light }
+ hexagram_37 : pinyin Jiaren wade Chia Jên english { The Family}
+ hexagram_38 : pinyin Kui wade K'uei english {Opposition }
+ hexagram_39 : pinyin Jian wade Chien english {Obstruction}
+ hexagram_40 : pinyin Xie wade Hsieh english {Deliverance}
+ hexagram_41 : pinyin Sun wade Sun english {Decrease }
+ hexagram_42 : pinyin Yi wade I english {Increase }
+ hexagram_43 : pinyin Guai wade Kuai english {Break-through}
+ hexagram_44 : pinyin Gou wade Kou english {Coming to Meet}
+ hexagram_45 : pinyin Cui wade Ts'ui english {Gathering Together }
+ hexagram_46 : pinyin Sheng wade Shêng english {Pushing Upward }
+ hexagram_47 : pinyin Kun wade K'un english {Oppression }
+ hexagram_48 : pinyin Jing wade Ching english {The Well }
+ hexagram_49 : pinyin Ge wade Ko english {Revolution}
+ hexagram_50 : pinyin Ding wade Ting english {The Caldron }
+ hexagram_51 : pinyin Zhen wade Chên english {The Arousing }
+ hexagram_52 : pinyin Gen wade Kên english {Keeping Still }
+ hexagram_53 : pinyin Jian wade Chien english {Development }
+ hexagram_54 : pinyin Guimei wade {Kuei Mei} english {The Marrying Maiden }
+ hexagram_55 : pinyin Feng wade Fêng english {Abundance }
+ hexagram_56 : pinyin Lü wade Lü english {The Wanderer }
+ hexagram_57 : pinyin Xun wade Sun english {The Gentle }
+ hexagram_58 : pinyin Dui wade Tui english {The Joyous }
+ hexagram_59 : pinyin Huan wade Huan english { Dispersion }
+ hexagram_60 : pinyin Jie wade Chieh english {Limitation }
+ hexagram_61 : pinyin Zhongfu wade {Chung Fu} english {InnerTruth }
+ hexagram_62 : pinyin Xiaoguo wade { Hsiao Kuo} english {Preponderance of the Small }
+ hexagram_63 : pinyin Jiji wade { Chi Chi } english {After Completion}
+ hexagram_64 : pinyin Weiji wade { Wei Chi } english {Before Completion }
}
#end iching data
proc binaryexchange {gualisting} {
# converts gualisting as a list
# to binary & decimal numbers.
global dx dy colors color
global guabinary guadecimal guatransform
set guabinary [ whitelist $gualisting ];
set guabinary [ join [ split $guabinary " "]];
set guabinary [ plainsub $guabinary 6 0 ];
set guabinary [ plainsub $guabinary 7 1 ];
set guabinary [ plainsub $guabinary 8 0 ];
set guabinary [ plainsub $guabinary 9 1 ];
set guabinary [ plainsub $guabinary " " "" ];
return $guabinary;
}
proc second_hexagram_compute {gualisting } {
# subroutine under test
global bookvalue second_hexagram
#set gualisting [ lreverse $gualisting];
set second_hexagram [ list ];
set second_hexagram [ join $gualisting ] ;
set second_hexagram [ plainsub $second_hexagram 6 7 ];
set second_hexagram [ plainsub $second_hexagram 9 6 ];
set guabinary [ binaryexchange $second_hexagram ];
set decimalout [ convertbase2to10 $guabinary ];
set bookgua [ kvsearch $bookvalue $decimalout ];
return $bookgua;
}
proc bonereadxx {} {
global dx dy colors color gualisting
global bookvalue bookvalue2 second_hexagram
set dj 1;
set gualisting [list ];
for {set j 0} {$j<6} {incr j $dj} {
set bone1 [lpick {3 3 3 2}]
set bone2 [lpick {3 3 2 2}]
set bone3 [lpick {3 3 2 2}]
set bonereading [expr $bone1 + $bone2 + $bone3 ]
set wow [expr $bone1 + $bone2 + $bone3 ]
lappend gualisting $wow;
}
#set guabinary [ list 1 0 1 1 1 si tiene problema ]
set gualisting [ lreverse $gualisting];
# reading hexagram lines top down,
# opposed to reverse(down top)
# give different binary values
#
set guabinary [ binaryexchange $gualisting ];
set decimalout [ convertbase2to10 $guabinary ];
set bookgua [ kvsearch $bookvalue2 $decimalout ];
set second_hexa [ second_hexagram_compute $gualisting ];
.wxxccc delete 1.0 end;
set outoutfoulspirit " last bone is $wow .gua listing is $gualisting && binary $guabinary && decimal $decimalout &&Iching_gua_# $bookgua && test 2nd hex. $second_hexagram && 2nd h. test $second_hexa && $second_hexagram "
.wxxccc insert end $outoutfoulspirit }
proc castfortune {} {
global dx dy colors color gualisting second_hexagram
set colorx black;
for {set i 0; set y 0} {$i<6} {incr i; incr y $dy} {
set colorx brown;
for {set j 0; set x 0} {$j<3} {incr j; incr x $dx} {
set colorx brown;
if { $j == 1} {
if { [lindex $gualisting $i ] == 6} {set colorx white}
if { [lindex $gualisting $i ] == 7} {set colorx brown}
if { [lindex $gualisting $i ] == 8} {set colorx white}
if { [lindex $gualisting $i ] == 9} {set colorx brown}
}
.can create rectangle $x $y [expr {$x+$dx}] [expr {$y+$dy}] \
-fill $colorx
}}
set dx 50
set dy 30
set colorx blue;
for {set i 0; set y 0} {$i<6} {incr i; incr y $dy} {
set colorx blue;
for {set j 0; set x 0} {$j<3} {incr j; incr x $dx} {
set colorx blue;
if { $j == 1} {
if { [lindex $second_hexagram $i ] == 6} {set colorx white}
if { [lindex $second_hexagram $i ] == 7} {set colorx blue}
if { [lindex $second_hexagram $i ] == 8} {set colorx white}
if { [lindex $second_hexagram $i ] == 9} {set colorx blue}
}
.can create rectangle [expr $x + 180] $y [expr {[expr $x +180 ]+$dx}] [expr {$y+$dy}] \
-fill $colorx
}}
}
xskipskipdirectory $env(HOME)
#endofdeck
#endofdeck [gold] Change:Redundant procedure ? deleted.
[LV] slightly reformatted code to some level of consistency, added a few braces around expr arguments, and removed a redundant proc definition.
[gold] Change 13Mar2007:omitted **(exp) in expr for base2, TCL8.5&>.References:
Appendix Tables
if 0 { iching hexagrams and trigrams }
if 0 {
1. Qian Ch'ien, The Creative
2. Kun K'un, The Receptive
3. Zhun Chun, Difficulty at the Beginning
4. Meng Mêng, Youthful Folly
5. Xu Hsü, Waiting
6. Song Sung, Conflict
7. Shi Shih, The Army
8. Bi Pi, Holding Together
9. Xiaoxu Hsiao Ch'u, The Taming Power of the Small
10. Lü Lü, Treading
11. Tai T'ai, Peace
12. Pi P'i, Standstill
13. Tongren T'ung Jên, Fellowship with Men
14. Dayou Ta Yu, Possession in Great Measure
15. Qian Ch'ien, Modesty
16. Yu Yü, Enthusiasm
17. Sui Sui, Following
18. Gu Ku, Work on What Has Been Spoiled
19. Lin Lin, Approach
20. Guan Kuan, Contemplation
21. Shike Shih Ho, Biting Through
22. Bi Pi, Grace
23. Bo Po, Splitting Apart
24. Fu Fu, Return
25. Wuwang Wu Wang, Innocence
26. Daxu Ta Ch'u, The Taming Power of the Great
27. Yi I, The Corners of the Mouth
28. Daguo Ta Kuo, Preponderance of the Great
29. Kan K'an, The Abysmal
30. Li Li, The Clinging
31. Xian Hsien, Influence
32. Heng Hêng, Duration
33. Dun Tun, Retreat
34. Dazhuang Ta Chuang, The Power of the Great
35. Jin Chin, Progress
36. Mingyi Ming I, Darkening of the Light
37. Jiaren Chia Jên, The Family
38. Kui K'uei, Opposition
39. Jian Chien, Obstruction
40. Xie Hsieh, Deliverance
41. Sun Sun, Decrease
42. Yi I, Increase
43. Guai Kuai, Break-through
44. Gou Kou, Coming to Meet
45. Cui Ts'ui, Gathering Together
46. Sheng Shêng, Pushing Upward
47. Kun K'un, Oppression
48. Jing Ching, The Well
49. Ge Ko, Revolution
50. Ding Ting, The Caldron
51. Zhen Chên, The Arousing
52. Gen Kên, Keeping Still
53. Jian Chien, Development
54. Guimei Kuei Mei, The Marrying Maiden
55. Feng Fêng, Abundance
56. Lü Lü, The Wanderer
57. Xun Sun, The Gentle
58. Dui Tui, The Joyous
59. Huan Huan, Dispersion
60. Jie Chieh, Limitation
61. Zhongfu Chung Fu, Inner Truth
62. Xiaoguo Hsiao Kuo, Preponderance of the Small
63. Jiji Chi Chi, After Completion
64. Weiji Wei Chi, Before Completion
The names of the trigrams
I Ching Trigram Name Translations
Pinyin Wade-Giles (Wilhelm/Baynes) associations
1. Qian Ch'ien the creative, heaven, Father,northwest,head,lungs
2. Kun K'un the receptive, earth,Mother,southwest,abdomen,reproductive_organs
3. Zhen Chên the arousing, thunder,Eldest_Son,east,throat
4. Kan K'an the abysmal, water,Middle_Son,north,liver,kidneys,inner_ear
5. Gen Kên keeping still, mountain, Youngest_Son,northeast,hands,spine,bones
6. Xun Sun the gentle, wind, Eldest Daughter,southeast,hips,buttocks
7. Li Li the clinging, flame,Middle_Daughter,south,eyes,heart
8. Dui Tui the joyous, lake,Youngest_Daughter,west,mouth }