現代易學﹕“四”的“回授系統”現象 - “四”象


中原文明大燬滅的悲哀﹕文明遲滯3000年不進﹐
要等到3000年後唐明來破解開來﹐

這3000年來﹐羌人Chinese作什麼去了﹖


花非花､霧非霧､道非道(非“常道”)､名非名(非“常名”)﹕

兩儀﹕兩非二(Two)﹐四象﹕四非肆(Four)﹐八卦﹕八非捌(Eight)


“兩”､“四”､“八” 都是直接了當(straight forward)的“象形”文字﹐
要直接從他們的“字”顯出的“圖(Figure,picture)”去解:


“四”的“圖”就是“迴授系統(Feedback System)的圖示﹕

............______________.............________________
............|.............|----------->|..............|
............|.............|............|..............|
............|.............|............|..............|
............|.............|............|..............|
............|.............|............|..............|
............|.............|............|..............|
............|.............|............|..............|
............|.............|............|..............|
............|.............|............|..............|
............|_____________|<-----------|______________|



四象已經用到“致知在格物”的格(Block Diagram)。

所以先由系統理論的Block Diagram 開始解說起﹕



在系統(System)理論:

“格” 的 轉換函數(Transformation Function)﹕

..............______________............
..............|.............|...........
..............|.............|...........
.....左..I....|.............|...右..O...
......------->|......格.....|------>....
....Input.....|.............|...Output..
..............|.....日.H....|...........
..............|_____________|...........



H = O/I﹔

日 = 右/左﹔



O = H.I﹔

右 = 日.左



左﹐I ﹕ Input

右﹐O ﹕ Output

日﹐H : Transformation Function 轉換函數


以上又稱 Open Loop 開放式 的 Transformation function




當兩個格互為 Input, output

即成 “與”合的“耦合”(Coupling)

如下圖所示﹐成為 Closed Loop 閉合式﹔

即為“四”象的“四”﹔

“四”是 Closed Loop 閉合式的 Feedback System 回授系統。

............______________.................________________
............|.............|--------------->|..............|
............|.............|..Feed.Forward..|..............|
............|.............|................|..............|
............|.............|................|..............|
............|.............|................|..............|
............|.............|................|..............|
............|.............|................|..............|
............|.............|................|..............|
............|.............|..Feed.Backward.|..............|
............|_____________|<---------------|______________|
..........................(Positive Feedback)..............
..........................(Negative Feedback)..............



但在數學解析上﹐經常把“四”圖轉了 90度來看﹕成為

.............Feed.Forward..
............______________.................
............|.............|
............|.............|..
............|.....天......|................
.....左..I..|.............|........右..O...
....---♁-->|.............|--------------->
.......A....|.............|........|........
.......|....|......A......|........|........
.......|....|.............|........|........
.......|....|.............|........|............
.......|....|_____________|........|............
.......|...........................|.............
.......|...........................|.............
.......|...........................|.............
.......|.....Feed.Backward.........|............
.......|....________________.......|.............
.......|....|..............|.......|.............
.......|....|..............|.......|.............
.......|....|......地......|.......|.............
.......|....|..............|.......|.............
.......<----|..............|<------♁-----.......
............|..............|....................
............|......F.......|....................
............|..............|....................
............|..............|....................
............|______________|....................
...........(Positive Feedback)..............
...........(Negative Feedback)..............


“兩儀生四象”將“兩儀”的“天”“地”二個 “STATE”
代入格中﹕Feed Forward 的“天”格在上﹐Feed Backward“地”格在下﹐

這個STATE Equation 是一個

與合的二維(2D)微分方程式(Differential Equations)﹕


d/dt[x,y]『 = 《M》 [x,y]『


d/dt[天﹐地]『 = 《人》 [天﹐地]『



『 ﹕ Transpose Vector

《M》﹔《人》: 2x2 matrices

t : time



經過 Laplace Transformation 轉換後﹐

再經過向量空間旋轉﹐可找出 複變數的

本徵向量 eigen vector 及

本徵值 eigen value ﹔

更可解出﹕


O/I = 1/(1 + A(S)F(S) )


右/左 = 1/(1 + 天(S)地(S))


再作 Inverse-Laplace-Transform, 得出

複變數(Complex Variable)

右(t) = C. exp [(a+jb) t]

exp : exponential 指數


這結果答案可用“象圖(Phase Diagram)”表示﹕



[發散型﹕Run-Away or diverging from equibrium point or initial point]

...............A......................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|......................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|......$...............~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|......$...............~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|.....$...............~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|....$.................~~~~~~~~~~~~~~~~~~~~~#~~~~~~~~~~
...............|..$...................~~~~~~~~~~~~~~~~~~~~~/\~$~~~~~~~~~
...............|.$....................~~~~~~~~~~~~~~~~~~~/~~~\~~$~~~~~~~
---------------#---------------->.......~~~~~~~~~~~~~~~/~~~~~~~\~~$~~~~~~~
...............|......................~~~~~~~~~~~~~~~/~~~~~~~~~~~\~~$~~~
...............|......................~~~~~~~~~~~~~/~~~~~~~~~~~~~~\~$~~~
...............|......................~~~~~~~~~~/~~~~~~~~~~~~~~~~~~\~~~
...............|......................~~~~~~~/~~~~~~~~~~~~~~~~~~~~~~~~
...............|......................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|......................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|......................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



[收斂型﹕Arriving or converging equibrium point or final point]

...............A......................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|......................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|......$...............~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|......$...............~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|.....$...............~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|....$.................~~~~~~~\~~~~~~~~~~~~~~~~~~~~~~~~
...............|..$...................~~~~~~~~~~\~~~~~~~~~~~~~~~~~~~~$/~~~
...............|.$....................~~~~~~~~~~~~\~~~~~~~~~~~~~~~~$/~~~~~~
---------------#---------------->.......~~~~~~~~~~~~\~~~~~~~~~~~~$/~~~~~~~~
...............|......................~~~~~~~~~~~~~~~\~~~~~~~~~$/~~~~~~~
...............|......................~~~~~~~~~~~~~~~~~\~~~~~~$~/~~~~~~
...............|......................~~~~~~~~~~~~~~~~~~~~\~$/~~~~~~~~~
...............|......................~~~~~~~~~~~~~~~~~~~~~#~~~~~~~~~~
...............|......................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|......................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|......................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



[摩盪型﹕Arriving or converging equibrium cycle or limit cycle]

...............A......................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|......................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|......$...............~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|......$...............~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............|.#...$...............~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............#....#$................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
.............#.|..$$..#................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$/~~~
...........#...|.$...$#..............~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$/~~~~~~
---------#-----|-------#------->.......~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$/~~~~~~~~
.........#.....|........#..............~~~~~~~~~\~~~~~~~~~~/\~~~~~~~~~$/~~~~~~~
.........#.....|.......#...............~~~~~~~~~~~\~~~~~$~/~~\~~~~~~$~/~~~~~~
.........#.....|......#................~~~~~~~~~~~~~\~$~~/~~~~\~$/~~~~~~~~~
..........#....|....#..................~~~~~~~~~~~~~~~#~~~~~~~~#~~~~~~~~~~
...........#...|...#...................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
............#..|.#.....................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
...............#......................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


還有[旋轉發散型][旋轉收斂型][Chaos渦泫型]....
就不一一列舉了。


再配上 time-domain 的 waveform, frequency domain 的spectrum 解析方法...


..A....
..|............xx
..|..y.......x....x
..|...y...x........x...y
..|....yx...........y.x
..|....xy.........y.....x
..|..x...yyyyyyyyy
..|____________________________>time



................A..................
..........y.....|.....y.............
..........y.....|.....y.............
..........x.....|.....x.............
.....y....x.....|.....x....y.........
.....y....x.....|.....x....y.........
..___y____x_____|_____x____y______>frequency



這才能顯出“四”的“迴授系統”的“象”﹕“四象”﹗

不知“四”是“迴授系統”,怎能知“象”﹖

不知象﹐怎能“卜止抉卦”作國家之決策﹖

可憐羌人Chinese 不知“四象”﹕“瞎子摸象”3000年﹐

文明遲滯不進3000年.....


[明教易經明明德﹕橫看成明縱成易]


“明”的四象﹐明﹕左日右月 之四象也(NETWORK)

............______________.................________________
............|.............|--------------->|..............|
............|.............|..Feed.Forward..|..............|
............|.............|................|..............|
............|.............|................|..............|
............|.....日......|................|......月......|
............|.............|................|..............|
............|.............|................|..............|
............|.............|................|..............|
............|.............|..Feed.Backward.|..............|
............|_____________|<---------------|______________|
..........................(Positive Feedback)..............
..........................(Negative Feedback)..............


“易”的四象﹕ 易﹐上日下月 之四象也(NETWORK)

.............Feed.Forward..
............______________.................
............|.............|
............|.............|..
............|.....日......|................
.....左..I..|.............|........右..O...
....---♁-->|.............|--------------->
.......A....|.............|........|........
.......|....|.............|........|........
.......|....|.............|........|........
.......|....|.............|........|............
.......|....|_____________|........|............
.......|...........................|.............
.......|...........................|.............
.......|...........................|.............
.......|.....Feed.Backward.........|............
.......|....________________.......|.............
.......|....|..............|.......|.............
.......|....|..............|.......|.............
.......|....|......月......|.......|.............
.......|....|..............|.......|.............
.......<----|..............|<------♁-----.......
............|..............|....................
............|..............|....................
............|..............|....................
............|..............|....................
............|______________|....................
...........(Positive Feedback)..............
...........(Negative Feedback)..............


欲“明明德”﹐必先知“四象”的萬千變化
易經是“字字珠璣”聖人所研幾...
我只能導讀到此了﹐....

真要看懂我寫的﹐
你的 Applied Mathematics 要很好﹐
這大概是台大電機系學生要
在柏克萊電機計算機系博士班研究所
熬上5年以上的功力才可﹐整天聽大教授
如 De Soer 罵你在Bull-Shit....



九五含章 聖雄唐明 嘆息說﹕

有人埋怨看不懂唐明寫的什麼﹖真是一些不知長進的東西...
如果你們看得懂﹐唐明稍加指點﹐你們就可以作巡弋導彈了...

這一代的新新人類是沒有一個好樣子可以作模仿的﹔
我回來了﹐我帶著好樣子回來的﹐
鞭著時間的罡風､擎一把火,我挾著天風海雨､血淚史實﹐
如果當年經國總統不被李登輝毒殺﹐唐明回台灣﹐
今天是台灣拿著核子巡弋飛彈嚇北京
而不是北京拿著核子巡弋飛彈嚇台灣...因果報應､絲毫不爽﹗
看著台海風雲殘局､以卓絕千古治學功力整理解說易經﹐
內心倒是別有一番風味在心頭﹐
這盤棋給李登輝走成這樣﹐還說是民主先生改革先生﹐
不知死活的東西...﹐有的哭的...還在後頭呢﹗