Synergetics and Analytics Re: Micro-Macro

[Aiviet Nguyen <aiviet@cat.syr.edu>]

Hi Anh La^m, Chi. Quy`nh,
  Chi. Quy`nh no'i ve^` ddi.nh nghi~a cu~ng ddu'ng tho^i, nhu+ng kho^ng 
tru'ng ca^u ho?i cu?a anh La^m. Khi no'i macro-micro va` so sa'nh hai 
phu+o+ng pha'p nghie^n cu+'u la` dda~ muo^'n bao ha`m ca'i nghi~a tu+o+ng 
ddo^'i ro^`i. Chuye^.n na`y la` chuye^.n to^i quan ta^m nha^'t trong hai 
ma^'y na(m la`m research. Tuy cha(?ng co' nga~ ngu~ gi` song cu~ng co' 
va`i ideas va` chu't kinh nghie^.m. 

  Pha't bie^?u la.i thi` nhu+ the^' na`y:
 1.Ca'i lo^'i nghie^n cu+'u cu?a Ta^y la` PHA^N TI'CH": ca('t nho? su+. 
va^.t ra tha`nh ca'c pha^`n tu+? gia?n ddo+n ho+n, va` de^~ nghie^n cu+'u 
ho+n ro^`i ra'p la.i. Phu+o+ng pha'p na`y dda(.c bie^.t tha`nh tu+.u tu+` 
sau Descartes. Dda(.c bie^.t thuye^'t nguye^n tu+?, Gia?i ti'ch Toa'n, 
Mo^? xe? ...dde^`u la` tha`nh co^ng cu?a phu+o+ng pha'p na`y. Thu+.c te^' 
khoa ho.c va` Ky~ nghe^. hie^.n ta.i dde^`u du+.a tre^n phu+o+ng pha'p na`y.
Ca'ch na`y ne^'u tha`nh co^ng se~ cho phe'p 2 operation quan tro.ng:
          a) Reproduction
          b) Quantification
Ca'i ddo' cho phe'p u+'ng du.ng va`o co^ng nghe^. va` kinh te^'.
To^i nghi~ phu+o+ng pha'p na`y cu~ng tu+. nhie^n tho^i. Mo^.t tha(`ng 
nho? 2,3 tuo^?i dda~ be? ddo^` cho+i dde^? ti`m hie^?u ca^'u tha`nh.
Tuy nhie^n co' the^? tha^'y nhie^`u vi' du. phu+o+ng pha'p ddo' kho^ng 
xa`i ddu+o+.c dda(.c bie^.t la` trong Biology va` Sociology. Cha(.t dda^`u
ra nghie^n cu+'u ky~ ca'i dda^`u va` pha^`n tha^n va^~n kho^ng ta`i na`o 
ra'p la.i ddu+o+.c. Vi` va^.y du+o+`ng nhu+ ca'i dda^`u khi co`n no^'i 
vo+'i tha^n the^? kha'c vo+'i ca'i dda^`u dda~ ca('t ro+`i. Nghie^n cu+'u 
ca'i dda^`u dda~ ca('t ro+`i mang la.i ra^'t i't y' nie^`m ve^`n ca'i 
dda^`u cu?a mo^.t co+ the^? so^'ng. Ve^` xa~ ho^.i la.i ca`ng nhie^`u vi' 
du. ho+n. To^i se~ pha^n ti'ch ky~ ta.i sao la.i nhu+ va^.y sau khi review
ve^` phu+o+ng pha'p macro ( actually phu+o+ng pha'p collective).
Vi' du. sinh ddo^ng nha^'t ve^` su+. ba^'t lu+.c cu?a su+. mo^? xe? na`y la`
lua^.n thuye^'t " Ca'i lo^~ trong cu.c Cheese". Ca'i lo^~ trong cu.c 
Cheese la` mo^.t thu+.c the^? to^`n ta.i ddo dde^'m ddu+o+.c va` co' impact
vo+'i va^.t xung quanh. Tuy nhie^n ca('t ca'i lo^~ ra kho?i cu.c Cheese 
dde^? nghie^n cu+'u rie^ng re~ tha^.t la ddie^`u kho^ng tu+o+?ng. Nghe 
thi` co' ve? buo^`n cu+o+`i, song theo to^i thi` co' chu+`ng 90% nghie^n 
cu+'u tre^n ddo+`i chi? la` co^' ga('ng ca('t ca'i lo^~ ra kho?i cu.c Cheese
ma` tho^i.

   2) Vi` va^.y co' phu+o+ng pha'p Collective. Ngu+o+`i co^? vu~ ra^`m 
ro^. nha^'t la` Haken, vo^'n la` mo^.t physicist. O^ng kho+?i xu+o+'ng 
cho ra ddo+`i mo^.t mo^n khoa ho.c mo+'i mang te^n la` Synergetics. Trong 
ddo' co' mang nhie^`u ideas quan tro.ng cu?A nhie^`u nga`nh kha'ch nhau 
ma` a?nh hu+o+?ng na(.ng nha^'t la` tu+` Prigogine va` Rene Thom. No'i 
thi` da`i gio`ng. Tu+u trung la` xe't nhu+~ng situation ma` vie^.c ca('t 
vu.n ra kho^ng mang la.i tho^ng tin gi` nhie^`u cho to^?ng the^? ca?.
Nhu+~ng nga`nh trong ca'c khoa ho.c exact kha'c nhau co' lie^n quan la`:
Solitons ( trong physics), global analysis, Chaos,...Ngu+o+`i ta co' 
the^? vo+ ca? nhu+~ng ca'i go.i la` DDo^ng phu+o+ng ho.c nhu+ DDo^ng y,...
va`o ddo'. Nhie^`u ngu+o+`i qua' khi'ch tuye^n bo^' ra(`ng tho+`i dda.i
pha^n ti'ch dda~ qua ddi, chi? co' Synergetics mo+'i la` con ddu+o+`ng 
duy nha^'t....Mo^.t so^' crackpot scientists ( mu+o+.c chu+~ cu?A anh Dam 
Son) suy nghi~ ra(`ng cu+' nghie^n cu+'u kinh di.ch hay Kinh Kim Cu+o+ng 
thi` se~ cho ra ddo+`i khoa ho.c mo+'i gia?i quye^'t blackhole va` Quark 
trie^.t dde^?.

   3) Theo y' kie^'n cu?a to^i thi` Khoa ho.c kha'c dda'nh xo^? so^' ( 
mo^.t chu't). Cho dde^'n khi chu+a co' ly' do gi` ( da^`u chi? la` tru+.c 
gia'c) dde^? chu+'ng to? nie^`m tin ddo' thi` chu+a ne^n tin ha(?n.
Nhie^`u chuye^.n chu+a chu+'ng minh ddu+o+.c ma` va^~n co' the^? tin 
dde^? theo ddo' ma` nghie^n cu+'u khi co' qua' nhie^`u tru`ng ho+.p. 
DDo^ng phu+o+ng ho.c hoa`n toa`n ke'm hie^.u lu+.c trong hai tie^u chua^?n
a) va` b) vi` va^.y chu+a pha?i la` convincing. To^i du+. nhie^`u seminar
co' nhu+~ng y' kie^'n " La('p A va`o B" bie^'t dda^u la.i cha(?ng co' gi` 
hay, ma` cha(?ng co' mo^.t ly' do gi`. Cu~ng gio^'ng nhu+ chuye^.n mo^.t 
ba'c Ta^'n Si~ VN ddo^? nha'o nha`o ca'c loa.i hoa' cha^'t va` ra lua^.n 
a'n va^.y. Synergetics sau 2 tha^.p ky? cu~ng cha(?ng co' gi` co^'ng 
hie^'n lo+'n lao ( tru+` ra^'t nhie^`u Ph.D. kho^ng co' job)

   4. Va^'n dde^` la` o+? cho^~ phu+o+ng pha'p ca('t xe?. Ne^'u mo^.t 
phu+o+ng pha'p ca('t xe? na`o to^'t thi` tu+o+ng ta'c giu+~a ca'c component
pha?i ye^'u dde^? tho^ng tin thu lu+o+.m ddu+o+.c tu+` ca'c tha`nh pha^`n
pha?i lo+'n ho+n nhie^`u so vo+'i tu+o+ng ta'c. Lu'c ddo' mo+'i co' the^? 
no'i la` nghie^n cu+'u xong ca'c tha`nh pha^`n anh dda~ co' pha^`n lo+'n 
tho^ng tin ve^` su+. va^.t. Vie^.c la('p la.i chi? la` obvious hoa(.c 
nho? nhi't. Ne^'u sau khi ca('t ma` tho^ng tin o+? ca'c tha`nh pha^`n 
qua' i't ma` tu+o+ng ta'c la` qua' lo+'n thi` vie^.c la('p ghe'p tro+? 
ne^n la` ma^'u cho^'t dde^? hie^?u su+. va^.t. Lu'c ddo' phe'p pha^n 
ti'ch la` vo^ nghi~a. Va^'n dde^` dda(.t ra la` co' pha?i ba`i toa'n na`o
cu~ng co' mo^.t phe'p pha^n ti'ch co' nghi~a kho^ng. Cha(?ng co' gi` 
chu+'ng minh ddu+o+.c ddie^`u na`y ma` chi? hy vo.ng tho^i. Co' mo^.t 
so^' ba`i Toa'n ma` nhu+~ng ca'i dda^`u tho^ng minh nha^'t cu?A nha^n 
loa.i cu~ng tin ra(`ng kho^ng bao gio+` gia?i ddu+o+.c ba(`ng pha^n 
ti'ch, nhu+ ba`i toa'n Turbulence cha(?ng ha.n.

    5. Tuy nhie^n co' mo^.t so^' hu+o+'ng ddi co' the^? no'i la` kha? 
quan ho+n la` khuynh hu+o+'ng thua^`n tu'y synergetics. Sau dda^y to^i 
chi? ddie^?m qua mo^.t so^' co^' ga('ng trong va^.t ly' ma` tho^i:

     i) Va^'n dde^` tu+o+ng ta'c ma.nh giu+~a ca'c hadrons la`m cho ba`i 
toa'n ti`m hie^?u gia'ng ddie^.u cu?a ca'c he^. hadrons ( nhu+ nucleon. 
meson) kho^ng the^? suy ddoa'n ddu+o+.c khi chu'ng ta bie^'t ra^'t ro~ 
dda(.c tru+ng cu?a ca'c tha`nh pha^`n. Chi? ca^`n he^. hai ha.t nucleons
la` ha.t nha^n deuteron dda~ chi.u cu+'ng. Co' mo^.t model ra ddo+`i va`o 
na(m 1957-1961 cu?a Skyrme kho^ng ddu+o+.c ai chu' y'. Y' tu+o+?ng chi'nh 
na`y xem nhu+ nucleon nhu+ mo^.t ca'i lo^~ trong cu.c Cheese kho^ng the^? 
ca('t ra kho?i ca'c ha.t mang tu+o+ng ta'c la` meson ddu+o+.c. No'i cho 
ddu'ng ra thi` nucleons la` ca'c xoa'y trong mo^.t be^? nu+o+'c meson. 
Chi? co' the^? la^'y nu+o+'c ra dde^? nghie^n cu+'u chu+' la`m sao ca('t 
xoa'y ra ddu+o+.c. No'i theo go'c nhi`n cu?a to^i ddo' la` mo^.t ca'c 
ca('t ( pha^n ti'ch) kha'c. Ly' thuye^'t Skyrme to? ra ra^'t predictive,
nha^'t la` ti'nh ra ca'c dda(.c tru+ng cu?A nucleon va` deuteron....

    ii) No'i mo^.t ca'ch nghie^m chi?nh thi` dda^y la` mo^.t approach xem
nucleon nhu+ la` soliton cu?a meson.  Ca'ch dda^y hai ba na(m, hai o^ng 
Seiberg va` Witten push mo^.t program ra^'t ma.nh thu hu't ha^`u he^'t 
nhu+~ng ca'i dda^`u tho^ng minh nha^'t: go.i la` duality. Hai o^ng cho 
ra(`ng tre^n ddo+`i co' mo^.t ca'i duality: mo^.t ly' thuye^'t tu+o+ng 
ta'c ma.nh co' soliton va` basic component dde^`u co' the^? bie^'n ddo^?i
qua mo^.t phe'p bie^'n ddo^?i go.i la` duality transformation tha`nh mo^.t
ly' thuye^'t kha'c ma` soliton bie^'n thanh basic field co`n basic field 
thi` tha`nh soliton, va` tu+o+ng ta'c tro+? tha`nh ye^'u. Ne^'u qua? 
tha^.t la` nhu+ va^.y thi` bao gio+` cu~ng co' mo^.t ca'ch pha^n ti'ch 
co' y' nghi~a. Su+. ba^'t lu+.c chi? o+? ca'ch pha^n ti'ch tho^ng 
thu+o+`nh nha^'t la` ba^'t lu+.c tho^i. Chi? ca^`n chi? ra duality 
transformation bie^'n mo^.t nha't ba`i toa'n la.i tro+? ne^n de^~ da`ng.

  6. Ne^'u suy nghi~ ro^.ng ho+n ra ca'c nga`nh kha'c se~ tha^'y vo^ so^' 
ddie^`u hay ma` to^i se~ ba`n sau.

Da^`u sao ddi nu+~a Pha^n ti'ch dda~ co tuo^?i tre^n hai tra(m na(m va` 
mo^.t ne^`n co^ng nghe^. hie^.n dda.i dde^? minh chu+'ng. 

Cheers 
Aiviet