Luoi Tuong Giao - Hong Duong

8/3/2019 Luoi Tuong Giao - Hong Duong

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LI TNG GIAOHng Dng

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http://thuvienhoasen.orgChuyn sang ebook 9-8-2009

Ngi thc hin : Nam Thin [email protected] Audio Ti W ebsite http://www.phatphaponline.org

Mc Lc(I) - Mng li ngu duyn.(II) - S xut hin mng li sng(III) - Mng Ton Cu(IV) - Php gii tnh: chng chp, giao thoa, v vng mc

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(I) - Mng li ngu duyn.

Chc ai cng c ln chng kin mt em b ngi khc v l tho chira tng b phn ri sau khng th lp li nguyn vn nh c. Hin gi,cc nh khoa hc cng trong tnh trng ging ht. Vi tr sai bit, sut ba

th k qua, tn hao v k tin ti v cng sc, h tip tay nhau phn x vtr thnh mnh, cui cng n nay lm vo ng ct, khng thy manh milm th no tin pht, ngoi tr tip tc m ln, phn tn nh thm ccmnh.

Lc dn khi mi cng trnh nghin cu khoa hc trong th k 20 lnguyn l quy gim (Principle of reductionism). Theo nguyn l ny, munthng hiu thin nhin thi phi khai ph cc thnh phn ca thin nhin.Mt khi thu t thnh phn, thi nm bt ton th s khng gp kh khn.Bi th nhiu thp nin qua quan im chung l mun hiu v tr thi phihiu nguyn t v cc siu si (superstring); mun hiu s sng thi phihiu cc phn t; mun hiu tp tnh con ngi thi phi hiu cc gen cnhn. Cc h thng phng trnh vi phn tuyn tnh ca vt l hc c inrt thch hp vi php phn tch v tng hp nh vy. C th phn chng ratng phn, mi phn em gii ring bit, cui cng hp cc li gii ring
http://phatphaponline.org/kinh/Audio/Thuyet%20Phap/Phat%20Giao%20Va%20Khoa%20Hoc/http://phatphaponline.org/kinh/Audio/Thuyet%20Phap/Phat%20Giao%20Va%20Khoa%20Hoc/


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bit thi c li gii chung. Do , mt h tuyn tnh hon ton bng tng ccphn ca n.a

Kinh nghim cho thy cng m ln, cng sai bit, thi mc phc hp(complexity) cng gia tng. Theo ngha ton hc, phc hp chng nhng cngha l phi tuyn tnh m cn c ngha bao gm v lng phn t binchuyn vi nhiu s t do (number of degrees of freedom). Ngha l,khng th s dng h tuyn tnh m phi dng h thng phng trnh vi

phn phi tuyn tnh (cn gi l h ng lc; dynamical systems) m t stng tc gia v lng phn t ca mt h phc hp. Ton hc tnh phchp l ton hnh hc v cc mu hnh c phn tch trong khung tp doPoincar khi xng, nh qu o hp dn k d (strange attractors), hnhth bin lp (fractals), chn dung pha (phase portraits), ... Ngoi ra, phi pdng c hc thng k (statistical mechanics) tnh phn b xc sut trong

chuyn ng ca v lng phn t v khng th m t y chi tit s vnchuyn ca tng c th phn t. C hc thng k cho php thnh lp nhngl thuyt thm su v trt t th gii v m, khm ph s hin hu nhngtnh cht thit yu ca cc h thng phc hp m khng cn tm hiu chi titchnh xc ca nhng chuyn ng ngu nhin phc tp v bt quy tc mcvi m.

Cng ngy cng ng khoa hc gia cng nhn khng c hin tng haybin c no hin khi c lp ring bit. H khm ph ngun gc pht sinhtnh phc hp chnh l mng li gm cc giao lin ni kt v quan h nhnqu gia tt c mi s mi vt trong v tr. Do h tin rng mng li

phc hp c mt cu trc rt chnh xc v t chnh cn c nghin cutng tn v lin quan mt thit v nh hng su xa i sng con ngi.Con ngi cng vi mi s mi vt l nhng mt li va l thnh qu tcdng ca ht thy cc mt li khc, va l nhn hu lc d phn cu to,

bi dng, pht trin, v vn chuyn ton th mng li.

Trong nhng nm gn y, nh s dng ton hc biu tng nhng mngli tru xut t php gii trng trng duyn khi, nhiu nh lut ton hc

v nhiu mu hnh c ngha c khm ph trong th gii hin tng vtrong cc sinh hot x hi. Do ton hc, cc nh x hi hc, vt l hc, sinhhc, v nhiu khoa hc gia khc tm thy nhiu quan h bt ng gia nhngsinh hot x hi v tc dng ca nhiu hin tng tng nh khng lin cannhau: t t bo sng v h sinh thi ton cu (global ecosystems) nInternet v no b ngi. S nhn bit nhng quan h ny thun ty pht


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xut t ton hc mng li, soi sng mt s vn by lu cha c giiquyt trong nhiu ngnh khoa hc k c tm l hc v x hi hc.

Ton gia Leonhard Euler c xem nh l ngi khi xng ton hcmng li vo nm 1736, khi ng chng minh khng th c mt con ngchy qua by chic cu, mi cu ch mt ln, trn sng Pregel, thnh phKonigsberg. Mt biu ng phc ha km theo phn lun chng lm

pht khi c mt ngnh ton hc rng ln v rt quan trng. l thuytbiu (graph theory), ct li ca thuyt mng li hin nay.

Lun chng ca Euler tuy n gin v u m, rt d hiu ngay i vingi khng chuyn ton, nhng chnh ci li nhn ca ng mi thc s lmnn lch s. i vi ng, vng by chic cu Konigsberg hin ra nh mt

biu (graph), ngha l mt tp hp gm nt (nodes) ni li vi nhau bi

nhng ng dy ni nt (links).

Cc nt biu din bn vng t b sng chia cch, t tn l A, B, C, v D.Cc ng dy ni nt l nhng chic cu ni kt cc vng y vi nhau. Ldo khng c ng no i qua tt c by chic cu mi cu ch mt ln l vnt no c mt s l ng dy ni thi nt phi l im khi u hayim cui cng ca hnh trnh. Mt con ng lin tc i qua ht thy bychic cu ch c th c mt im khi u v mt im cui cng. Nh th,con ng ny khng th hin hu trong mt biu c nhiu hn hai ntvi mt s l ng dy ni. V biu Konigsberg c bn nt vi mt s lng dy ni cho nn khng th tm ra con ng ni trn.

Nn lu s hin hu ca con ng ni trn khng ty thuc tr thngminh suy l ca con ngi m tht ra l mt tnh cht ca biu . Vi cch

b tr cc chic cu nh Konigsberg hi , du ti gii n u ta cngkhng tm ra c con ng ni trn. Dn chng thnh ph Konigsbergng vi Euler khng cn thc mc v s hin hu ca mt con ngnh vy na v n nm 1875 xy thm mt cu mi ni lin B v C, giatng s ng dy ni B v C ln thnh bn. Do ch cn li hai nt, A

v D, vi mt s l ng dy ni, tr thnh im khi u v im kt thcmt hnh trnh qua tm chic cu, mi cu ch i qua mt ln m thi.

Tm li, cu chuyn trn ch cho thy trong cu trc ca cc biu haymng li n khut nhng tnh cht m tc dng c th hn ch hay tng giakh nng giao lin tc ng ca chng ta vi chng. Cu trc lun lun nhhng trn tc dng, chng hn a hnh cc mng li x hi nh hng s


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loan truyn tin tc hay lan trn cc bnh truyn nhim. Mt trng hp ahnh mng li cc trm pht in nh hng n tnh bn vng ca struyn dn in: Ngy 10 thng tm, 1996, mt li lm trn hai ng dnin Oregon, Hoa k, lm pht khi mt dy hng my in qua cc trm

pht nh dng thc , tt in trong 11 tiu bang Hoa k v 2 tnh Gian i, hn 7 triu nh khng in sut 16 ting ng h. Mt th d khc vnh hng ca cu trc mng li trn tc dng: Ngy 4 thng nm, 2000,con su Love Bug, mt chng trnh ph hoi my tnh ti t nht chatng thy, b lan khp th gii qua Internet gy thit hi hng t M kim.

Bi th nghin cu s hnh thnh cu trc ca mng li l then cht thng hiu th gii phc hp quanh ta. Ch cn mt vi thay i nh trn ccnt hay ng dy ni nt cng pht khi nhiu kh nng mi t saunhng cnh ca n kn. Hin nay ht thy mi ngnh khoa hc nghin cu

h thng phc hp bt u quan tm kho st s hnh thnh v binchuyn cu trc v ng lc ca cc mng li tng giao.

Ban u, cc nh ton hc ch ch tm khm ph v sp hng cc loimng li. Th d: cc mng do nguyn t to thnh trong mt tinh th haycc mng lc gic do ong thit lp lm t l nhng mng li c sp t(ordered graphs). Nhng v sau, vn t ra l cc mng hin khi nh thno? Nhng nh lut no qui nh a hnh, tng dng, v cu trc cachng? Phi i n thp nin gia th k 20, cc vn y mi c giiquyt ln u tin do bi cng trnh xy dng thuyt mng li ngu duyn(random networks) ca hai nh ton hc Hungary, Paul Erdos v AlfrdRnyi.

Hy tng tng t chc mt bui tic gm khong mt trm thc khch.H c chn v mi l v h khng quen bit bt k ai trong danh schnhng ngi c mi d tic. Khi ru tht dn ra thi bu khng kh xa lgia h i hn. H bt u tr chuyn, lm quen vi nhau. Khng bao lu,c chng t ba mi n bn mi nhm hp thnh, mi nhm gm haihay ba ngi. By gi n k tai mt thc khch ni cho ngi ny hay rng

ru cht ng trong nhng chai mu lc m khng dn nhn hiu lth ru rt qu v trm ln ngon hn ru ng trong nhng chai c dnnhn hiu mu . V yu cu v thc khch truyn tin ny n ch nhngngi m v y mi lm quen m thi. Ch vi ngh rng lm nh th thich c thm hai hay ba ngi na bit tin ru qu ct u. Thc ra, khchthng chn ni chuyn vi mt ngi v hay di chuyn nhp vo nhmkhc. C nhng ni kt x hi gia hai thc khch va gp nhau trc


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ng gia cc phn t. Chc chn c s sai bit gia cc qui lut cai quncch phi tr cc ng dy ni nt trong nhng mng li khc nhau. Vmc ch ca mi kho st khoa hc l pht hin cch gii thch n ginnht ct ngha nhng hin tng v cng phc tp, cho nn cc khoa hcgia n lc pht minh mt m hnh chung miu t tt c nhng mng li

phc hp khc nhau.

Mt li gii ton hc u m miu t tt c mi biu phc hp cngtrong mt khung nim c Erdos v Rnyi ngh. Nhn thy cc hthng khc nhau ty thun nhng lut tc d bit qui nh s hnh thnh cutrc ca chng, Erdos v Rnyi quyt nh gt b mi bt ng v chn mtgi thit ht sc n gin l cc nt ni kt nhau mt cch ngu nhin. Nhvy di mt ca hai nh ton hc Hungary, biu v th gii biu tngu c bn tnh ngu nhin, hon ton ngc li vi quan im ca Albert

Einstein (bn thn ca Erdos) cho rng Thng khng chi sc sc viv tr (God does not play dice with the universe). Ni cch khc, mi mngli tru xut t php gii duyn khi khng hnh thnh do ngu duyn, mthng do mt s nh lut c bn xc nh v iu khin.

Hy tr li cu chuyn bui tic v tm hiu c tnh ca mng li nguduyn. Ban u, biu gm mt s ln nt c lp. Sau cc nt c nikt bi nhng ng dy ngu duyn phng theo s gp g tnh c gia ccthc khch. Khi mt s ng dy ni kt c k thm, cc nt s ktthnh nhiu cp. Tip tc thm na thi khng lm sao trnh khi ni ktcc cp nt y li vi nhau to thnh nhng qun t (cluster) tp trung nhiunt. Nu k thm n chng mi nt c trung bnh mt ng dy ni, thit nhin hin khi mt qun t khng l duy nht. Ngha l, hu ht mint tr nn thnh phn ca mt qun t n nht, t bt k nt no lm khiim ta c th di chuyn n mt nt khc thng qua nhng ng dy nint. l lc tin n v ru qu c th lt n tai ca bt c thc khchno trong bui tic. Hin tng l s xut khi (emergence) mt b phnkhng l gm a s nt i vi cc ton gia, l mt s ngm lc(percolation) dn khi mt chuyn tip pha (phase transition) i vi cc

nh vt l hc, l s hnh thnh mt cng ng i vi cc nh x hi hc.Mc du ngnh khc nhau t tn khc nhau, nhng tt c ng rng khichn ngu nhin nt trong mt mng li ni kt thnh cp thi mt binchuyn ln t khi khi s ng dy ni kt t tr ti hn. Trc , ccnt ni kt hp thnh qun t nh c lp, thc khch gp g quen bit trongvng nhm nh ri rc. Sau , xut hin mt qun t khng l vi s thamd ca hu ht thc khch.


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Mi ngi trn qu t l thnh phn ca mt mng li rng ln, mngli x hi th gii hay mng li nhn loi. Khng mt ai b gt b rangoi. Gia hai ngi bt c u trn qu t du khng quen bit nhauvn c mt ng dy ni kt h li vi nhau. Cng vy, c mt ng dyni kt bt c hai neuron (t bo thn kinh) no trong no b, bt c haicng ty no trn th gii, bt c hai ha cht no trong thn th con ngi.Paul Erdos v Alfrd Rnyi gii thch iu kin ni kt vi bt c nt nokhc trong mng l mi v mi nt ch cn c mt ng dy ni. C nhnlm quen t nht mt ngi, neuron c t nht mt ng dy ni vi mtneuron khc, ha cht c kh nng tham gia t nht mt phn ng trong thnth con ngi, cng ty giao dch vi t nht mt cng ty khc. Mt lngng (threshold) ni kt. Ton mng s phn tn thnh nhiu qun t nhri nhau nu cc nt c trung bnh t thua mt ng dy ni; nu c trung

bnh nhiu hn mt ng dy ni thi c nguy mng li phn tn c thtrnh c.

Trong thc t, cc nt thng c nhiu hn mt ng dy ni. Cc nhx hi hc c lng mi chng ta quen bit tn h chng t 200 n 5000 ngi. Trung bnh mt neuron ni kt vi hng t, c khi vi c ngnneuron khc. Mi cng ty ni kt vi hng trm hng cung cp v khchhng, nhiu cng ty ln ni kt vi hng triu. Trong thn th con ngi,hu ht cc phn t tham gia mt s rt nhiu phn ng, nh nc chnghn, tham gia n hng trm phn ng. Theo thuyt mng li ngu duynkhi s trung bnh ng dy ni ca mi nt tng qu tr ti hn, s nt bgt b ra ngoi qun t khng l s gim bt theo hm s m. Ngha l,thm cng nhiu ng dy ni thi cng kh tm ra nhng nt c lp. Nhth cc mng li quanh ta rt dy c, khng nt no thot khi, trong mi nt ni kt vi mi nt.

Trc Erdos v Rnyi, tiu im ca thuyt biu khng phi l ccbui tic, cc mng x hi, hay cc mng li ngu duyn, m hon ton lcc biu tun quy (regular graphs; ordered graphs; biu c sp t) c

cu trc xc nh. c tnh ca biu tun quy l nt no cng c mt sng dy ni kt ging nhau. Th d trong mt mng li phng vungdo cc ng trc giao to thnh, nt no cng c bn ng dy ni. Hoctrong mng li lc gic t ong, nt no cng c ba ng dy ni. Tnhtun quy khng tm thy trong nhng mng phc hp hin hu nhInternet hay t bo.


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Erdos v Rnyi l nhng ngi u tin khm ph, t nhng mng li xhi n nhng mng dy in thoi, hu ht nhng biu trong thc t ukhng c tnh tun quy v v cng phc tp. ng trc bc tng phchp kh vt qua, hai ng thy ch c cch duy nht l gi thit mng lihnh thnh ngu nhin. Hai ng m rng ca ton hc cho thy mt th giimi, mt th gii bnh ng. V cc ng dy c thit lp hon tonngu nhin, nn mi nt c c hi ng u tip nhn mt ng ni. Tuynhin, ch tng lm do ngu duyn m c nt tip nhn rt nhiu ngdy ni v c nt qu ri ro khng tip nhn c ng ni no c. Ci thgii ngu duyn hai ng xng tung nh c tnh cch va bt cng va lng. Tht ra khng phi vy. Nu l mt mng li rng ln thi mcdu cc ng dy ni thit lp ngu nhin, nt no cng tip nhn mt sxp x nh nhau.

thy c iu , hy phng vn cc thc khch sau bui tic, himi thc khch lm quen c bao nhiu ngi tt c. Ri v mt tuyn (histogram) biu din bao nhiu thc khch lm quen k (k=1, 2, ... ) ngitrong sut bui tic.

M dng ca tuyn c chng minh l mt phn b Poisson [do BlaBollobhs, mt mn sinh ca Erdos, gio s ti i hc Trinity College,Anh quc, 1982]. Ngha l c mt chp nh ni bt ch cho thy a s ntu tip nhn mt s ng ni gn bng s ng ni ca nt trung bnh.Hai bn chp nh, s phn b gim xung rt nhanh, cho thy khng cnhiu nt lch xa nt trung bnh.

Nu p dng phn b Poisson vo mt x hi 6 t ngi thi kt qu l sbn b quen thuc ca mi ngi trong a s chng ta xp x bng nhau.Nh vy, nu ghp ngu nhin nhng ng dy ni kt x hi, thuyt mngli ngu duyn d on tin ti mt x hi dn ch trong tt c chngta ai cng l trung bnh v rt t k lch xa chun (norm) tr thnh qu xgiao hay v cng c lnh. Mng li ngu duyn, mt mng li tngng vi trung bnh l chun, qu l mt mng tng giao l tng.

Mi n gn y m t v tr cc tng giao, hu ht ton gia khngtm thy cch g khc hn l ng vi Erdos v Rnyi gi thit cc mng

phc hp hnh thnh trn c s ngu duyn: cc mng phc hp l nhngmng li ngu duyn. Thuyt mng li ngu duyn c xem nh phtminh vo nm 1959 khi Paul Erdos ngh li gii bi ton rt ni ting ca


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thuyt biu , bi ton tm s ng dy ni b nht ni kt cc nt camt biu bt k hai nt no cng c ni nhau.

Tng cn nhc li y mt s nh ngha v kt qu quan trng ca tonmng li. Ton mng li s dng t s m/N tiu biu mt mng ligm N nt v m ng dy ni, mi ng ni hai nt. S ng dy nidnh vo mt nt gi l ca nt y. tnh mi nt trung bnh c baonhiu ng dy ni, hy cng ca tt c nt, ri em chia cho tng snt k c nhng nt khng c ng dy ni. Gi k l s trung bnh ngdy ni ti mi nt, ta c k = 2m/N; k gi l trung bnh. Erdos v Rnyichng minh mt nh l ni ting nay c gi l nh l Erdos-Rnyi: Xcsut xut hin ca mt b phn khng l n nht gm hu ht mi nt camng nhy vt t 0 n 1 khi tng t s tiu biu m/N qu tr ti hn 0.5.Ti im ny, k = 1. Theo Erdos v Rnyi, k = 1 l ngng ni kt, ngha l

mi v mi nt ch cn c 1 ng dy ni thi s ni vi bt k nt nokhc trong mng. Mt dng khc ca nh l Erdos-Rnyi: Khi s ngdy ni ngu nhin m ln hn hay bng (N/2)ln(N) vi ln(N) l logarit tnhin ca N, hay k ln(N), thi hu ht mi mng li ngu duyn u hon ton ni kt.

Gi thit biu c 50 nt, mi nt l mt thnh ph chng hn. Nukhng tnh ton, nhm mt ni mi thnh ph vi 49 thnh ph kia thi phixy 1 225 ng. Nhng theo Erdos, nu ni mt cch ngu nhin thi chcn xy chng 98 ng, ngha l 8 phn trm s 1 225 ng, l ni kt hu ht cc thnh ph vi nhau. Erdos khm ph s nt du ln baonhiu, ch cn mt t l phn trm nh cc ng dy ni ngu nhin cng tht ni kt hp mng li thnh mt ton th. T l phn trm y gimthiu rt nhanh khi mng li bnh trng rng ln thm. [Cng thc tonca t l y l ln(N)/N]. Th d: vi 300 nt, trong s gn 50 000 ng cth ni chng, ch cn 2 phn trm l . Vi 1 000 nt, t l y b thua 1

phn trm. Vi 10 triu nt, t l l 0.0000016.

Tr li vi mng li x hi 6 t ngi trn mt t, th hi s bn b

quen thuc ca mi ngi trung bnh l bao nhiu hai ngi, bt k l ai,bt c u, mt lm ngh nh c Bc cc, mt lm th tng cchng hn, ni kt nhau? Theo Erdos v Rnyi, t l l 4 phn t. Ngha l,trung bnh mi ngi ch cn quen bit 24 ngi l bt k hai ngino trn mt t ni kt nhau.


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Sau y l mt th nghim m phng bi ton mng li ngu duyn caErdos v Rnyi. Tng tng vung vi mt s nt o trn nn nh. Chnmt cch ngu nhin hai nt v ni chng bng mt si dy. Li chn ngunhin hai nt na v ni chng bng mt si dy khc. Lc u nhng ntc chn khng thuc cp no ni trc . Nhng v sau th no cngchn nhm mt nt kt cp ni vo mt nt khc, to thnh mt qunt ba nt. Nu tip tc ni cc cp nt ngu nhin nh th, thi mt lc sau,cc nt ni vi nhau bt u tr thnh mt qun t rng ln. Trong thi gianth nghim, lu lu th nhc ln mt nt bt k v m xem c bao nhiu ntkhc cng nhc theo. Tt c nt cng nhc theo to thnh ci gi l mt

b phn ca mng li ngu duyn. Cui cng, c nhng nt khng ni vint no, trong khi s ln ni thnh cp, thnh b ba, hay qun t ln.

Khi t s tiu biu vt qu 0.5 thi mt chuyn tip pha pht khi, mt

qun t khng l t nhin xut hin. Chng hn, nu s nt n=10 000, bphn khng l s t khi khi s ng dy ni t mc vo khong m=5000. Lc b phn khng l pht hin, hu ht mi nt hoc trc tip hocgin tip ni li vi nhau. Nu nhc ln mt nt, s c c may nhc theo mtlot chng 8 000 trong s 10 000 nt. S ng dy ni cng tng thi snt l loi cn li v s qun t ring bit cng gim thiu v ni nhau spnhp v bnh trng b phn khng l.

Trn y l ng biu din chuyn tip pha ca mt mng li nguduyn c 400 nt. ng c dng ch S. S nt trong qun t ln nht lcu tng chm, ri tng rt nhanh, ri tng chm li, tng ng vi s tngca t s tiu biu m/n. S tng rt nhanh l du ch ca hin tng chuyntip pha. ng biu din vt cao ln vi gic gn thng ng khi t stiu biu vt qua tr 0.5. gic ng ti tr ti hn 0.5 ty thuc tng snt ca mng li. Khi s nt b thi phn gic ng ca ng biu dincn, nhng khi s nt tng, chng hn t 400 n 100 triu, thi phn gicng dng ng thng hn. V nh s nt tng n v cc, thi khi t s tiu

biu vt qua tr ti hn 0.5, ln ca b phn ln nht ca mng linhy vt mt cch gin on t b t n khng l. Hin tng t khi

c xem nh l mt chuyn tip pha, ging trng hp v lng phn tnc t nhin ng bng thnh nc khi nhit va gim thp di 0 bch phn.

nh l Erdos-Rnyi ht sc li ch trong s tm hiu v ch ng cc hintng phc hp nh tnh bn vng ca h sinh thi, ng lc tnh ca thtrng, v t chc phn ng ca h min dch. Kt qu quan trng ca nh


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l l khi t s tiu biu m/n vt qu 0.5, rt nhiu nt bng nhin c nivi nhau to thnh mt mng rng ln trong h thng. S t khi mt b

phn khng l nh vy khng c g l huyn b m ch l mt tnh cht tnhin v tt yu ca mng li ngu duyn. Theo Stuart Kauffman, nhnghin cu ni ting v ngun gc ca s sng, mu hnh t chc ca htthy mi h thng sng (living systems) thng gi l mng li sng cngt khi nh vy. Mng li sng l mt hin tng chuyn ha t xc tc(autocatalytic metabolism), mt mng phn ng t duy tr, mt xut hintnh (emergent property), ng thi cu khi nh mt chuyn tip pha khitnh phc hp ca mng cc ha cht trc thi sinh vt v tng giao phnng gia chng t mc ti hn. Mng li sng xut hin phc hp vhon chnh, tip tc y nhin phc hp v hon chnh.

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(II) - S xut hin mng li sng

t lu cc khoa hc gia chuyn v s sng nhn thy mu hnh t chcca cc h thng sng lun lun l mt mu hnh mng li. Tuy nhinkhng phi mng li no cng l h thng sng. Mng li l mt h thng

phc hp, c cu thnh bi mt s ln thnh phn (nt) giao h tc dngmt cch khng n gin. Cc h phc hp khng nhng ch phc tp mthi. Hoa tuyt phc tp, nhng chng sinh xut t nhng lut tc n gin.

Hn na, cu trc hoa tuyt khng thay i, v kt tinh, t khi hin n lctan khng ging cc h phc hp thng xuyn bin i theo thi gian.Nhng s bin i ca h phc hp khc hn s bin i hn n ca mtdng nc chy cun cun trong mt lng sng cht hp y thc ghnh.Trt t ca h phc hp xut hin trong khong t hon ton trt t ca hoatuyt kt tinh n v trt t ca dng nc lu chuyn hn n. l binduyn ca hn n, xa v tr cn bng, thng gi l trn b hn n (atthe edge of chaos).

Trong h thng phc hp, ton th nhiu hn tng cc thnh phn. y

khng ni theo ngha siu hnh hc m ni theo ngha thc dng, ngha l dbit nhng tnh cht ca cc thnh phn v nhng lut tc chi phi s giaoh tc dng gia chng thi cng chng d g suy din tm ra nhng tnhcht ca ton th. Nhng khi bo ton th nhiu hn tng cc thnh phn,th hi ci g c thm nhiu ni ton th m khng c ni cc thnh phn?Xut hin tnh (emergence) l cu tr li. Thuyt h thng phc hp tmcch gii thch s xut hin mt s hin tng v m qua nhng giao h tc


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dng phi tuyn tnh gia cc phn t vi m trong h phc hp m khng cnbit n ht thy mi chi tit ca cc tng giao tng tc. C hc thng kc s dng gii thch xut hin tnh tc s xut hin nhng hin thnhthng k tun qui tng ng vi s xut hin cc hin tng v m. Cc lutthng k pht biu rng trong nhng phm vi rng ln cc hin thnh thngk tun qui c th xut hin mc v m, hu nh hon ton khng lin hvi nhng chi tit chnh xc ca nhng chuyn ng ngu nhin phc tp v

bt qui tc ang vn hnh mc vi m.

Thuyt xut hin tnh (emergence theory) gii thch ngun gc pht sinhnhng tnh cht sinh hc thit yu ca cc h thng sng khng ty thuccc chi tit giao h tc dng gia cc thnh phn ca h. n nay mi chtrng v ngun gc ca s sng khng nng vo thuyt xut hin tnhu gp nhiu kh khn khng gii quyt c. Th d, trong mt bi vit

ng tp san Scientific American trong nm 1954, George Wald, gii NobelSinh l hc 1967, a ra thc mc khng hiu lm th no c th xy ra hintng mt tp hp phn t t hi ng cch to thnh mt t bo sng. TheoWald, sau v s ln th t hi theo cch ny hay cch khc, cui cng vithi gian, cc phn t thnh tu hnh thnh mt t bo sng. Thi gian lyu t quyt nh s ci bin bt kh thnh kh nng, kh nng thnh hochu, hoc hu thnh thc t.

phn bc kin yu t thi gian, Robert Shapiro trong tp sch Origins(Ngun gc) tm cch trc ht tnh trong lch s ca tri t c baonhiu ln th to s sng mt cch ngu nhin v thy rng con s y vcng ln: 25 nhn 10 ly tha 50 ( 25 o theo 50 zero). Sau cn phitnh mi ln th c bao nhiu c duyn thnh tu. ng cho bit hai nh thinvn hc, Fred Hoyle v N. C. Wickramasinghe, tnh xc sut thnh tuca mi ln th l 1 phn ca 10 ly tha 40 000. thy 10 ly tha 40000 ln nh th no, hy so snh vi s nguyn t Hydro hin c trong vtr l 10 ly tha 40 m thi. Nh th vi xc sut 1 phn ca 10 ly tha 40000, s sng gn nh khng bao gi c c duyn sinh khi.

Mt s khoa hc gia khc bo l mt s pht sinh t nhin (spontaneousgeneration). Nhng nu tnh xc sut mt bin c t pht nh vy xy rathi c th so snh xc sut tnh c vi c duyn mt cn lc xon cthi qut mt bi ph thi gp nht cc th vt liu to thnh mtchic Boeing 747!


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Theo Stuart Kauffman, s sng l mt xut hin tnh, xut hin theo cchthc mt chuyn tip pha t nhng h thng ha cht xa v tr cn bng baogm nhng chu k xc tc (catalytic cycles). Cht xc tc thng thng lenzim, l bt k phn t no thi xc tc ca mt phn ng ha hc mkhng bin i hay b tiu th trong qu trnh. Mt sinh vt l mt h thngha cht c kh nng xc tc s t ti sn xut.

Kauffmann m phng s xut hin mt h thng t xc tc bng cch thitlp mt biu phn ng gm nt l cc polymer [hp cht ha hc gmnhiu cht n phn (monomer); th d: protein, phn t RNA] v ngdy ni l nhng phn ng ha hc. Mi polymer c hai ngha: va l qu vl c cht hay sn phm ca mt phn ng ha hc, va l nhn v l chtxc tc trong mt phn ng khc. Trong thc t ht thy mi phn t hu cu c hai ngha nh vy. Trypsin chng hn, l mt enzim c chc nng

phn ct cc protein ta n vo thnh mnh nh (nhn ca s phn ct) ngthi t phn ct n ra mnh nh (qu ca s phn ct). Cng th, cc proteinv phn t RNA l polymer c cht (substrate; cht trn enzim tc dng)hay sn phm ca cc phn ng, nhng ng thi tc dng xc tc cc phnng khc.

Biu phn ng c gi thit gm ch hai loi phn ng, phn ng buctht (ligation; kt lin nhau) v phn ng phn ct (cleavage; chia phn ra).Th d mt polymer gm bn cht n phn abbb. Nu xt trn phng din

phn ng buc tht thi n c th l kt qu buc tht a vi bbb, hay ab vibb, hay abb vi b, nh vy n hnh thnh ba cch khc nhau, do ba phn ngkhc nhau. Nu tng di ca polymer thm mt cht n phn, abbba, s

phn ng ca polymer s tng: abbba c th l kt qu buc tht a vi bbba,hay ab vi bba, hay abb vi ba, hay abbb vi a. V mt polymer c di Lthng c L-1 lin kt cho nn n c th hnh thnh t nhng polymer bhn theo L-1 cch khc nhau. Nu xt trn phng din phn ng phn ct,thi abbb c th xem nh kt qu phn ct a ra khi pha bn phi ca

polymer abbba. Ni tng qut, s phn ng c kh nng sn xut ccpolymer nhiu hn s polymer.

By gi gi thit thm rng cc phn ng trong biu u l phn ng cxc tc, ngha l khng xy ra t nhin m c s thi xc ca cc polymertrong h thng. Ta trn phng php ni ngu nhin cc nt ca Erdos vRnyi, Stuart Kauffman ghp ngu nhin vi mi polymer mt s phn ngm polymer y c th xc tc. T s m/N (ng dy ni/nt) tc t s(phn ng c xc tc/polymer) tng theo vi s gia tng mc phc hp ca


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cc polymer trong h thng. Khi t s y vt qu tr ti hn thi mt bphn khng l gm ton phn ng c xc tc t khi theo cch thc mtchuyn tip pha, to thnh ci gi l tp hp phn t t xc tc (autocatalyticset of molecules). Ngha l, mi phn t ca tp hp l sn phm ca t nhtmt phn ng c xc tc bi t nht mt phn t khc ca tp hp. Do

polymer ny c th xc tc phn ng pht sinh polymer kia, cc tp hp txc tc sinh khi, tin ha vi thi gian, c kh nng xc tc tp th mngli phn ng ha hc v to nhiu loi phn t phc hp, ht thy u nikt qua mt chui phn ng. Bng cch tiu tn vt cht v nng lng, hayni vn tt l n v bi tit, chng t t chc v duy tr cu trc phc hpca chng mc du c mt s b phn hin n v bin i vi thi gian.

Ngoi ra, chng cn t ti sn xut na. Cc c tnh t xc tc, t t chc,t duy tr, v t ti sn xut l c tnh ca s sng.

Kt qu m phng ni trn cho thy s xut hin ca mng li sng l mttnh cht ca biu phn ng, mt mng li ngu nhin. Khi mc phchp ca h thng cc ha cht c trc thi sinh vt tng gia vt qungng phc hp thi ton hc chng minh s t khi ca s sng. Trnquan im xut hin tnh, s sng xut hin ton th, vin dung, hon chnh.S sng khng trong cc phn t cu thnh m trong nhng tnh chtxut hin tp th ca ci ton th m chng to sinh. Khng c g huyn bv xut hin tnh (emergence) v ton th tnh (holism) mc du s xuthin ca s sng c tnh cch huyn diu. Khng mt sinh lc hay cht liuno c mt trong ci ton th ng thi cu khi v t ti sn xut. Tp thh sng c mt tnh cht k diu m cc thnh phn ca n khng c. lkh nng t ti sn xut v tin ha. Tp th h sng linh hot, cc thnh

phn ch l ha cht.

Nhiu nh sinh hc cho rng v DNA v RNA ct gi bn vng cc thngtin di truyn nn rt cn thit c tin ha. Nhng nu tin ha cn khunDNA ti bn v m di truyn sn xut protein thi y ng l bi tonvng vo g - trng ci no n trc. Bi v khng th c tin ha nukhng c nhng c ch ti bn hay sn xut v nhng c ch ny ch xut

hin khi c tin ha. Nh vy cn t cu hi: Nu khi u s sng l mttp th t xc tc, th hi lm th no s sng c th tin ha m khng cnn nhng bin ha phc tp ca mt b gen?

Mng li nh phn.


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gii p thc mc trn, Kauffman khai trin thuyt mng li nh phn(binary networks) kho st s pht trin v tin ha ca hin tngchuyn ha tc ca ton th cc tin trnh vt l v ha hc trong mt c th(metabolism). Ta c th hnh dung mng li nh phn nh mt mng dyin ni kt nhiu bng in. Nt (bng in) c th l cc phn t enzim,c cht, hay sn phm ca cc phn ng ha hc. Gi thit giao h tc dnggia cc phn t ch c hai cch: km hm hay xc tc phn ng sn xut.Do mi bng in v nh ci cng tc ng-m, khng in hay c in.

Nh vy, nt no trong mng li nh phn cng c hai kh nng, HU(ON) v KHNG (OFF). Cc nt c ni kt mt cch rt phc tp khngnh trong mt mng c sp t. Cc mng nh phn cn gi l mng liBoole, theo tn ca nh ton hc ngi Anh George Boole s dng cc

php ton nh phn (yes-no, c-khng) vo gia th k 19 khai trin mtlogic k hiu thng gi l i s Boole.

Kt qu k l ca s tng giao ng m cc nt khng phi l mt trngthi hon ton hn n m ngc li, l kh nng mng li t t chcthnh nhng mu hnh hot ng bn vng. Lm th no nhng thao tcng-m tung nh ngu nhin ca mi nt c bit iu ng c ton thmng li t phi tr thnh mt cu trc bn vng hu hiu? Nu y lmng li gen ca t bo, thi thuyt Darwin khng th gii p tha mn vthuyt ny ch trng nhng kiu c th mi ch c th sinh khi do nhngt bin ngu nhin v s chn lc t nhin m thi. Theo Kauffman,nguyn do l cc h thng phc hp c c tnh t ng t chc thnhnhng mu hnh bn vng hu hiu. ng bo: Darwin khng bit g vtnh t t chc.

Sau y l th d mt mng li nh phn n gin gm 6 nt, hai en (ON;HU) v bn trng (OFF; KHNG).

Mi nt ni kt vi ba nt k cn. Mu hnh HU-KHNG ca mng nhphn bin i gin on tng bc. Cc nt c mc ni theo th cch khnng sp n ca mt nt do kh nng hin ti ca cc nt k cn xc nh

theo mt qui lut ng-m (a switching rule). Th d, vi mng nh phnn gin trn, ta c th tng tng mt qui lut ng-m nh sau: Trong

bc sp n mt nt s HU nu hin ti c t nht hai nt k cn HU, vs KHNG trong nhng trng hp khc. Nhn hnh sau y ta s c mt nim v trnh t bin thi ca mng li n gin theo s iu khin ca quilut ng m.


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Ba trnh t bin thi A, B, v C ty thuc trng thi u v tun theo qui lutng-m. Trnh t A dn n mt trng thi bn vng vi tt c nt uHU sau hai bc bin i t trng thi A1 qua trng thi A2, ri qua trngthi bn vng A3. Trnh t B bc t trng thi B1 qua B2, ri dao nggia hai trng thi b sung B2 v B3. Trnh t C, vi mt trng thi bnvng ngay t lc u, lp i lp li mt trng thi hay mu hnh khng thayi: n t ti sn xut trong mi bc.

Vi h thng chuyn ha t xc tc, tng s loi phn t ca mng linh phn c th ln n 1 000. Mi phn t c hai kh nng, HU (xc tc)v KHNG (km hm), do tng s trng thi kh hu ln n 2 ly tha1 000. Mi mu hnh (pattern) hay trng thi (state) c xc nh bi 1 000

bin s nh phn (HU-KHNG). Tp hp ht thy trng thi kh hu tothnh ci gi l khng gian trng thi (state space), trong mi im biu

tng mt trng thi. Khi mng li bin i tng bc k tip t trng thitrc sang trng thi sau, im trng thi v mt qu o trong khng giantrng thi. Qu o ca cc trnh t bin thi c phn hng theo loi vnghp dn (attractors). C th tng tng mt loi vng hp dn l mt ci hv lu vc vng hp dn l vng nc chy vo h. Ging nh mt vng nic nhiu h, mt mng li nh phn c nhiu chu k bin thi, mi chu klu chuyn trong lu vc vng hp dn ca n.Trong th d mng nh phn 6 nt ni trn, trnh t C ch c c nht mttrng thi bn vng khng c lu vc vng hp dn. Trng thi ny ch tc khi no mng li khi u t . V gm c nht mt trng thi, nnchu k bin thi c di 1. di ca mt chu k bin thi l tng s trngthi bao gm trong chu trnh. Trnh t B dao ng nn lit vo loi vnghp dn tun hon (periodic attractor). di chu k bin thi y l 2 v

bao gm ch hai trng thi b sung B2 v B3. Trnh t A v tin n mttrng thi bn vng nn lit vo loi im hp dn (point attractor).

Kauffman v nhm cng s Vin Santa Fe, New Mexico, dng mngli nh phn m phng nhng h thng ha cht v c th v cng phchp m phng trnh vi phn khng th miu t c. Trnh t bin thi

ca nhng h thng phc hp y c biu din bi nhng qu o trongkhng gian trng thi. V tng s trng thi kh hu ca bt k mng linh phn no cng hu hn mc du c th v cng ln, cho nn mng li

bt buc phi quay tr li mt trng thi tri qua trc kia. Vo lc , hthng ti din trnh t bin thi trc kia v tp tnh ca h thng hon tonquyt nh. Do , h thng s lp li mi mi vn mt chu k bin thi,mng li nh phn v ra mt qu o trong lu vc vng hp dn tun


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hon. Bt k mng li nh phn no cng c t nht mt lu vc vng hpdn tun hon. Nu t nhin thi cui cng h thng s vn hnh mi mitrong mt lu vc vng hp dn tun hon no . Theo kt qu ca nhiucng trnh nghin cu, s ln h thng sng nh mng gen, mng min dch,mng t bo no, h thng cc c quan, v h sinh thi, u c th biutng bi nhng mng li nh phn vi nhiu loi vng hp dn.

Trong mt mng nh phn, di ca cc chu k bin thi c th khc nhaunhiu. C nhng chu k vi c nht mt trng thi bn vng, nhng cngc nhng chu k vi s trng thi v cng ln khng tng tng c.Trong nhiu mng, di chu k tng theo hm s m khi s nt tng.Kauffman t tn nhng vng hp dn c chu k v tn vi t t trng thikhc nhau l vng hp dn hn n (chaotic attractor). Nu chu k bin thi

b, thi h thng vn hnh c trt t. Nhng nu chu k qu ln thi h

thng vn hnh hn n, khng lng trc c. Hn n y c nghal trt t bc v hn, i li vi hon ton trt t l trt t bc thp nht.[Xem bi Hu th v Thi gian]

tm hiu quan h gia hon ton trt t v hn n trong cc mng nhphn, Kauffman kho st v s mng nh phn phc hp vi nhiu qui lutng-m khc nhau, k c nhng mng trong ti cc nt khc nhau, s(ng dy) tn hiu vo khc nhau. Hai thng s, N, s nt, v k, s trung

bnh (ng dy) tn hiu vo ti mi nt, c s dng tm lc s vnhnh ca cc mng y. Sau 30 nm gia cng tm kim iu kin thun li ng lc trt t xut hin t mng li nh phn, ng trnh by nhng ktqu gt hi c trong tp sch At home in the universe do ng vit vo nm1995.

Hy tng tng mt mng li nh phn gm N=80 000 bng in, mibng (nt) trung bnh nhn vo k tn hiu (k ng dy ni) v c kt hpngu nhin vi mt qui lut ng-m (mt hm s Boole kh hu).

Khi k=1, mi bng in nhn mt tn hiu vo t mt bng khc. Trnh t

bin thi ca mng bin i rt nhanh chuyn thnh nhiu qu o vi chuk rt ngn, c chu k gm duy nht mt trng thi. Trong mng xut hinmt b phn khng l ng bng gm nhng bng c nh trong kh nngHU hay KHNG v nhiu o nh gm nhng bng nhp nhy gia HUv KHNG. y l mt mng hon ton trt t, lp i lp li mt mu hnhng c khng thay i, khng vng hp dn.


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u kia thang, k=N, mi bng in nhn tn hiu vo t khp tt c bngin, k c chnh n. Trong trng hp ny, di cc chu k bin thi tnhra l 2 ly tha 40 000, bng cn s bc hai ca s trng thi kh hu 2 lytha 80 000. Nh th qu di, khng th qun st hay on nh bt k chuk bin thi no. Tuy nhin nu tnh s vng hp dn (=N/e, e=2,71828... lc s ca logarit t nhin) thi mng s c 30 000 vng hp dn. So vitng s 2 ly tha 80 000 trng thi kh hu thi s 30 000 qu b. Bi vyc th bo l du hiu ca trt t. ng tic l khi mng li b nhiulon i cht, chng hn i kh nng mt bng in HU thnh KHNGhay ngc li, thi s tin ha ca mng s thay i i quy m khng thlng trc c. Nhng trng thi u tng t tr thnh mi lc mi d

bit hn, do lu chuyn theo nhng qu o cng lc cng tch ra xa.Nhy cm i vi iu kin u mng k=N l mt mng li hn n. Huht cc mng nh phn u hn n. Ngay nhng mng trong k nh hn

N nhiu, k=4 hay k=5, s vn hnh cng hn n, khng th d on c.

Khi k=2, trt t tc thi kt tinh. Khng gian trng thi gm tt c 2 ly tha80 000 trng thi kh hu, tc vo khong 1 o theo 24 000 zero, dn nnli trong mt s vng hp dn, trung bnh l N=283. Chu trnh trong cc lu vc vng hp dn thng gm mt s nh trng thi, nhng cng c khithu gn thnh mt im bn vng. Chng khc no mng li rng ln b pvo trong mt phn nh xu ca khng gian trng thi. Nh vy trong mngli nh phn k=2, ng lc trt t t pht thi ng dn p h thng vomt gc v cng b ca khng gian trng thi, v gi mi .

Trong nhng mng nh phn k=2 trt t biu hin theo nhiu cch khcnhau. Nhng trng thi u tng t tr thnh cng tng t hn, do luchuyn theo nhng qu o hi t gn nhau hn, v tp trung h thng vcng mt vng hp dn. Nhng h thng nh vy khng nhy cm i viiu kin u nn khng hn n. H qu l mng li mt khi chuyn vomt lu vc vng hp dn thi hu nh lun lun quay tr li lu vc ydu b nhiu lon. gi l tnh ni cn bng (homeostasis), iu kin cn h thng l mt mng li c trt t. Mng li c trt t c th tri qua

mt t bin (mutation) nh sa i cch t ng dy ni hay qui lutng-m m khng tr thnh hn n. Vng hp dn v lu vc vng hpdn thay i rt t v h thng tin ha u n. Cui cng, tuy c trt tnhng khng hon ton trt t ng bng nh cc mng k=1, mng li k=2 kh nng hnh hot nh mt h phc hp.


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Bernard Derrida v Gerard Weisbuch, gio s vt l trng thi rn ti coleNormale Suprieure, Paris, cho bit trong trng hp trung bnh k lnhn 2, c th dng mt thng s gi l P chuyn mt mng hn n thnhmng c trt t. Thng s thin p P (bias parameter) m t khuynh hngnhiu kh nng HU hay nhiu kh nng KHNG trong hm s Boole kthp vi mi bng in (qui lut ng-m).

Tm li, ch cn hai thng s, k v P, l iu khin mng li nh phnvn hnh trt t hay hn n. Nu b phn khng l ng bng xut hin,thi mng li trong ch trt t. Nu n khng xut hin thi mngli trong ch hn n. Ngay gia hai ch trt t v hn n, ngaygn lc chuyn tip pha, ngay trn b hn n, c th xut hin nhng mng

phc hp nht, c trt t bo m tnh bn vng, nhu nhuyn, v lunlun i mi. Kauffman tin rng chnh lut tin ha l nguyn nhn h thng

phc hp hin hu trn, hay trong ch trt t gn, b hn n. S chnlc t nhin thin v v chi tr cc h thng sng trn b hn n, bi vchng c u im l iu hp bn vng vi nhu nhuyn, c kh nng thchnghi v tin ha.

M hnh mng li nh phn c Kauffman p dng kho cu cc h genca sinh vt. Mi gen l mt nt nh phn, c th HU hay KHNG. Khnng HU hay KHNG ca mi gen ty thuc hot ng iu tit ca mts gen khc. Phn ng ca mi gen khi nhn tn hiu vo c xc nh bihm s Boole, qui lut ng-m kt hp ngu nhin vi n. Nh vy, h genl mt mng li nh phn trn b hn n.

C hai cch nhiu lon mng gen. Cch th nht, nhiu lon ti thiu l domt nt nh phn tnh c chuyn t HU qua KHNG hay ngc li. Dotnh ni cn bng, c tnh ca mi h sng, cc chu k bin thi ca mngkhng b lay chuyn bi nhiu lon ti thiu. Cch th hai, nhiu lon thayi vnh vin cu trc ca h thng. Chng hn, bin i mu hnh ni ktcc nt hay thay i qui lut ng-m. Nhiu lon nh vy xem nh mt t

bin trong h gen. Thng t bin khng my nh hng tp tnh ca mng

gen trn b hn n. Tuy nhin mt s t t bin c th x y qu oca mng vo trong mt lu vc vng hp dn khc, to mt chu k binthi mi v mt mu hnh tp tnh mi. Do , Kauffman ngh rng mnggen, mt mng li nh phn trn b hn n, c th dng lm m hnh cas thch nghi tin ha.


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M hnh mng li nh phn trn b hn n gii thch hin tng t bobit ha (cell differentiation) trong qu trnh pht trin c th. Mc du hnhdng v chc nng sai khc, tt c kiu t bo (cell type) trong mt c thcha nhng lnh di truyn ging nhau. V vy cc nh sinh hc cho rngkiu t bo khc nhau khng phi v cha gen khc nhau, m tht ra v ccgen trong t bo c hot tnh khc nhau. Ni cch khc, trong tt c t bocu trc mng li gen ging nhau, nhng trng thi (mu hnh) hot ngca gen khc nhau. Cc trng thi hot ng ca gen tng ng vi cc chuk bin thi khc nhau trong mng nh phn cho nn theo Kauffman cc kiut bo tng ng vi cc chu k bin thi khc nhau, v do , vi cc vnghp dn khc nhau. Kiu t bo trong c th v nh vng hp dn trongmng gen.

Quan im xem t bo bit ha nh nhng vng hp dn cho php d on

nhiu kt qu kh chnh xc. Mi t bo trong thn th con ngi cha mtmng gen chng 80 ngn gen. S trng thi hot ng kh hu ca genv cng ln: 2 ly tha 80 000. Tuy nhin, s vng hp dn trong mt mngnh vy bng 80 000=283. Do , theo Kauffman, mt mng 80 000 gen

biu hin 283 kiu t bo khc nhau. S 283 y rt gn s 256 t bo bitha tm thy trong thn th con ngi.

Mt trong nhng vn kh gii quyt nht trong sinh hc l gii thch chcnng ca gen trong qu trnh pht trin c th (ontogeny). Trong con ngi,qu trnh y bt u l mt gen n nht, trng th tinh hay zygote. Zygotetri qua chng 50 ln phn bo to ra vo khong 10 ly tha 15 (1 otheo 15 zero) t bo cu thnh a tr s sinh. Cng mt lc, zygote bit hahnh thnh chng 260 kiu t bo trong thn th, nh t bo m mm cagan, t bo thn kinh, t bo hng huyt cu, t bo bp tht, ... Nhng kiut bo khc nhau ca phi v nhng qu o trong qu trnh pht trin c th

biu th tp tnh ca mng gen phc hp. Mng gen trong mi t bo ca btk c th no tuy l thnh qu ca t nht mt t nm tin ha, nhng trt txut hin (emergent order) trong qu trnh pht trin c th khng do luttin ha pht khi.

Thuyt mng li nh phn thuyt minh trt t xut hin l trt t t pht,biu hin tnh t t chc v t iu chnh v cng phc hp ca mng li.Cc mu hnh bn vng t pht ging nh nhng vng hp dn ca mt hng lc. V chnh do s giao h tc dng gia cc vng hp dn bn vngv khng bn vng, gia cc hot ng hp tc v cnh tranh, m cc muhnh ca s bin i v cc thi k ca trng thi ngng nhin c th dn


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hnh nh ton b ca vt th ging nh khi nhn n trn ton c tm knhnh.

Gin Feynman (Richard P. Feynman, gii Nobel Vt l 1965 chung vihai vt l gia khc v cng trnh khai trin lng t in ng lc hc) cth gip ta c mt nim v trt t thu nhip nm trong chuyn ng phctp ca cc in t trng di dng sng nh sng. Sng nh sng chuynng truyn dn khp ni v trn nguyn tc, s chuyn ng truyn dn thu nhip ton th khng thi gian ca v tr vo trong mi mi vng. Khi nim nhn bit khi ln thi vi mt cp mt tt hay mt knh vin vng lc th thy mi s vt thu nhip phng khai tr li, tng dng hin ra nhnhng tng tru xut t ton th hon chnh ca v tr.

Gin Feynman l mt cu trc gm nhng ng thng biu hin chuyn

ng ca cc sng. Trc ht mt sng nh pht ra t mt im c nh Pc v ra nh sau.

Cc ng thng tun ra t P cho thy cch thc sng truyn t im y.Sau mt im bt k Q, ni gp sng nh t P lan n, tr thnh ngun

pht khi mt sng nh khc, v c nh vy m c sng lan n im R,im ny tr thnh ngun pht khi mt sng nh khc, v..v...iu ng lu y l mi mi im thu nhip mi sng truyn n tkhp ht thy cc im khc v ng thi l ngun pht khi mt sng vicng ln hay b ty theo cng ca ln sng lan n.

Nu nhn qu trnh truyn dn sng nh mt ton th, thi tt c sng xutpht t mt im A truyn dn n mt im B tri qua rt nhiu bcchuyn tip trung gian, to thnh mt sng tng hp ti B bao gm ht thycc sng truyn dn theo ht thy mi qu o kh hu ni A vi B. Mtkhc, khi nhn hnh cc ng thng tun ra t P din t trt t phng khait mi mt im lan ra khp ton th, ng thi ta nhn thy cc sng tton th dn vo trong mi mt im theo trt t thu nhip, nh hnh sauy.

Nh vy chuyn ng sng l tng hp hai bin chuyn ng thi v nghchchiu, thu nhip v phng khai, cun li v m ra, co rt v gin n theo lng nht duyn khi, khng nh nguyn tnh ca Hoa nghim.

Php Tng gii thch chuyn ng y nh sau. Ht bi khng c t tnh.Khi bn cht ln trc v hon ton thm thu khp mi phng, thi lgin n. Mi phng khng c bn cht v hon ton hin thnh trong ht


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bi do duyn khi, thi l co rt. ... ... ... Khi co rt, mi vt u hinthnh trong mt ht bi. Khi gin n, mt ht bi thm thu ph cp khpmi vt. Gin n l lun lun co rt, v mt ht bi lin can mi vt. Co rtl lun lun gin n, v mi vt lin can mt ht bi. l ct ngha th nol gin n v co rt mt cch t ti. (Hoa nghim ngha hi bch mn).

---o0o---

(III) - Mng Ton Cu

Gi th ht thy thng tin cha ng trong my tnh khp ni c nikt ... Tt c nhng thng tin gi tr nht trong mi my tnh ca CERN(Trung tm u chu Nghin cu Ht nhn) v trn th gii sn sng tiv mi ngi s dng. Th l xut hin mt khng gian thng tin ton cu

n nht. l mng c ca Tim Berners-Lee khi ng lm vic thochng ti CERN, Geneva, Thy S. Chng trnh in ton ng lp vonm 1980 ni kt my tnh hu chia s thng tin khng ng mi nmsau bin thnh Mng Ton Cu www (World Wide Web), mng li nhnto rng ln nht t trc n nay. Mng Ton Cu l din b ca Internet,Internet l hnh th ha thn ca Mng Ton Cu, l mt mng my tnh nikt qua nhng ng truyn dn in.

Hu gip tm kim d dng ti liu ct gi vi mt b my su cu (search

engine) n gin, ni dung cc trang Mng (Webpage) c sp xp theothng liu (information; ti liu thng tin) ch khng theo v tr (location).Ted Nelson, gio s i hc Brown, Hoa k, l ngi u tin c kindng my tnh thit k mt h thng t chc thng liu mi m ng gi lsiu bn (hypertext). ng c nhu cu vit mt quyn sch v trit l trnmy tinh trong ng mun trnh by ton b t tng ca ng mt cch ch thng. Theo ng siu bn vi nhng ng dy ni (links) i khp mihng mi c th truy dng tc thi trn my gim th (monitor) nhng ling ch thch, k c bt k bn vn no khc m ng dn chng.

Trong bn sch ch in, cu, on, chng, v trang ni nhau theo mt trt tc quyt nh khng nhng bi tc gi m cn bi cu trc vt l v tht theo chui ca chnh cun sch. Tuy c th ngu nhin lt n bt ctrang no v tnh c t mt nhn vo bt k on no, cun sch ch in mimi b gi cht trong khun kh c nh ba th nguyn. Khng gian thngtin khng b hn ch nh vy. Cu vn ph din mt nim hay mt chuit tng thng nh theo mt mng du hiu a th nguyn ch ni ct gi


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mt nt ca Mng Ton Cu di mt hnh thc no . Cng nng caMng l do cc thit b URL cho php click trn con chut l c th dichuyn t trang ny sang trang khc. Nh cc ng dy ni URL m ta cth lt (surf), nh v v xu ni thng tin li vi nhau. Do cc ng dyni ny m thu tp nhng ti liu c nhn bin chuyn v do nhng clicktrn con chut m mt mng li thng tin khng l c bn thnh. Nuct b cc ng dy ni thi Mng Ton Cu b hy dit, v s c s dliu ha thnh v dng.

Do siu bn hy b gii hn ca trang ch in, cuc sng trn mng tr nnc lp i vi mt v tr nht nh vo mt lc xc nh. Ngoi ra, v tr cnc th truyn chuyn na. Ngi ti mt ni m vn c th chng kin trnMng cnh hot ng n o no nhit mt ni khc nh tung ang ngti . C nhng vic ca s c th lm ngay ti nh ngi trc mt my

tnh c nhn, khng khc g ngi trong vn phng ti s. Ngay nh nghath no l a ch cng thay i v hin nay mang mt ngha mi c tnhcch nh mt s an sinh x hi (Social security number) ch khng cn lta trn mt con ng. a ch ha thnh o.

Hy v siu bn vi mt tp hp thng ip co dn, thun li hay trng raty theo tc ng ca ngi c. tng c th khai pht v phn tch nhiu mc chi tit khc nhau. Ta c cm gic ht thy biu tng khpmi phng v ni chn th u ha hp trong cng siu bn, th tthng xuyn thay i, v truyn t bt k lc no, bt c u, ty thunquyn li ca ngi gi v tnh kh ca ngi nhn. Ni cch khc, MngTon Cu to ra mt m phng thc ti trn my tnh, mt thc ti o(virtual reality). Thc ti o l thc ti ca chng ta v chnh ci khung nim v cc h thng biu tng phi khng gian, phi thi gian y l ni ta yc to lp cc phm tr v hon khi cc nh tng, chnh ci khung nim y hnh thnh tp tnh, nui dng vng tng, v gy phin no.

Nu sng tr li thi i thng tin hin nay, n hong V Tc Thin chcchn s khng cn n th d S t vng hay cn phng y mt knh vi

chnh gia mt ngn n t sng t bn cnh mt tng Pht ca ngiPhp Tng. V l c nhin n hong tha thng minh bit cch tn dngMng Ton Cu, nhn thy Mng c nhiu tnh cht ca li bu Thch, v do thng t ngha vin dung ca Hoa nghim tng. Nhngth no l li bu ca Thch? Hu gii thch ngha vin dung, Thun, khai t ca Hoa nghim tng, miu t li bu ca Thchtrong Hoa nghim ng gio ch qun nh sau, Tu S dch:


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[T45n1867_p0513b09] Mng li bng cc ht chu ca tri Thchc gi l li ca Nhn--la. Mng li ca Thch ny c lmthnh bng chu bu. Do nh sng ca cc ht chu ri sut, ln lt hinnh ln nhau, ln vo trong nhau, trng trng v tn. Trong mt ht chu mt nhin ng thi xut hin. C mi ht chu u nh vy, hon tonkhng c n hay i. Nay hy nhm v pha ty nam, ly mt ht chu mnghim. Ngay ni mt ht chu m ng lot hin nh ca tt c ht chu.Ht chu ny nh vy, mi mt ht chu khc cng nh vy. Mi mt htchu cng mt lc ng lot hin ht thy ht chu vy, mi mt ht chukhc cng vy. Nh vy trng trng v tn, khng c bin t. C bin tchnh l bng cc ht chu trng trng khng bin t, thy u hin trongmt ht chu, r rng xut hin trn cao. Nhng ci khc khng phng hin ci ny. Khi ngi trong mt ht chu tc l ngi trong ht thy ht chu,

trng trng v tn. V sao vy? Trong mt ht chu c tt c ton b htchu. Khi trong tt c ton b ht chu c mt ht chu, chnh ci ton b ycng mang tt c ht chu. Chun theo y m t duy v ton b (nht thit).

Tt c ton b ht chu ln vo trong mt ht chu m hon ton khng rakhi mt ht chu ny. Mt ht chu ln vo trong tt c ht chu m honton khng dy ln mt ht chu ny.

Hi: ni tt c ton b ht chu ln vo trong mt ht chu m hon tonkhng ra khi ht chu ny, lm sao li c th ln vo trong tt c ht chu?

p: Ch do khng ra khi ht chu ny nn mi c th ln vo tt c htchu. Nu ra khi mt ht chu m ln vo tt c ht chu, tc l khng thln vo trong tt c ht chu vy. V tch ra ngoi ht chu ny bn trongkhng c ht chu no khc na.

Hi: Nu tch ra ngoi ht chu ny m bn trong khng c tt c ton bht chu, vy th mng li ny c lm thnh ch do bi mt ht chu; vy

s kin do nhiu ht chu m lm thnh l th no?

p: Ch do c nht mt ht chu mi bt u tng ht mt kt nhiuht thnh mng li. V sao vy? V do mt ht chu ny c nht lm thnhmng li. Nu b i ht chu ny, ton th khng c li.

Hi: Nu duy c nht mt ht chu, lm sao c th bt u lm thnh li?


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p: S kin kt nhiu ht chu lm thnh li, chnh l duy c nhtmt ht chu. V sao vy? Mt chnh l tng tng, c sn ci nhiu lm thnh. Nu khng c ci mt, tt c ton b cng khng. Cho nn, bngmt ht chu m lm thnh mng li vy. Tt c (nht thit) ln vo mt,chun theo y m bit.

Trong on vn trn, c cu: Do nh sng ca cc ht chu ri sut, lnlt hin nh ln nhau, ln vo trong nhau, trng trng v tn. Trong mt htchu m t nhin ng thi xut hin. C mi ht chu u nh vy, honton khng c n hay i. Trn Mng Ton Cu cng vy. Khi lt Mng,tt c nhng trang hin trn my gim th (monitor) xut khi t cc trm ctgi ti liu (servers) khp ni trn th gii, c khi no mt ta ri khi trangnh trn mn nh ca my gim th, tc ht chu m ta chm ch quan st

nh mt nh chim bc nhn vo qu cu thy tinh? Mi ln bt buc philt Mng, c phi ta tht s chng bao gi n hay i?

c bit l Mng Ton cu phn chiu chng nhng tt c ht chu m cncu trc cc ng dy ni gia cc ht chu, mt cu trc nht a tngdung hay tng tc. Cc gi thng liu tuy khc nhau nhng khng rinhau, v chng h tng nhip nhp trong mt khng gian phi khng gian,trng rng v mi nt hay trang nh phn chiu ton Mng, ng nh li ca Thun: Tt c ton b ht chu ln vo trong mt ht chu m honton khng ra khi mt ht chu ny. Mt ht chu ln vo trong tt c htchu m hon ton khng dy ln mt ht chu ny.

Thun cn ni: S kin kt nhiu ht chu lm thnh li, chnh lduy c nht mt ht chu. V sao vy? Mt chnh l tng tng, c snci nhiu lm thnh. Nu khng c ci mt, tt c ton b cng khng.Cho nn, bng mt ht chu m lm thnh mng li vy. Mi ht chu lnhn ca ton th m ng thi cng l qu do ton th ht chu khc lmnhn. Trong ton th, nhn qu ng thi. Nh vy, khi lt Mng, bt cmn no mc ra trn my gim th khng phi ch trn Mng m tht ra

l ton Mng. Mn l hin thn ca tm thm Mng. Trong mt mngli khng c trung tm, bt c nt no cng l trung tm.

Mng hnh thnh l do s t do ng gp xy dng ca nhiu ti nng khpth gii v do tng giao tc dng rt t do vi hng triu ngi s dng n.V phn mm c phn pht rng ri v bt c ai cng c th ty tin ghpthm nt vo Mng rt d dng chng tn km bao nhiu cho nn nhng


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ngi s dng ng thi gp phn sn xut k thut, un nn Mng thchnghi vi nhng nhu cu ring bit. Hn na, thi gian cch bit gia tintrnh hc hi bng cch s dng v tin trnh sn xut bng cch s dng,c bit thu ngn rt nhiu. Ngha l c mt s hi tip ci tin gia struyn b v s hon chnh k ngh, nguyn nhn Mng Ton Cu pht trinvi mt tc khc thng. S ngi s dng tng vt t 20 triu trongnm 1996 ln 300 triu vo nm 2 000. T mt s t trang nm 1993 nhyvt ln hng triu trang nm 1998, v c su thng ln ca Mng gia tnggp i.

S tng trng ca Mng vi mt tc khng ngng gia tng l do tn kngh in t, my tnh, v vin thng pht trin nhanh chng, dn khinhng vng hi tip khin Mng phc hp cng phc hp thm. Khithng liu thay i, cc ng dy ni v tn s thm ving mt s dch

trm (site) cng thay i theo. Mng bin thnh mt h sinh thi vi sthng liu nhiu n i khng my su cu ti tn u hng no c th sphng s trang khng ngt tng gia trn Mng.

Ngoi tc dng thng tin, Mng cn l ngun sanh li v cnh tranh i viht thy mi ngnh thng mi. Mng cho php thit lp nhng c s giaodch bun bn trc tuyn (online) thng gi chung l e-B, e tc electronic(in t) v B tc business (giao dch thng mi). Cc c s ny thc hinnhng dch v khng thc th, nh gii tr, du lch, thng tin, v ngn hng,ng thi bun bn nhng hng ha nng n ca kinh t tp truyn nh xehi v my tnh. Mng bin i l li giao dch thng mi trong quan hvi ngi cung cp v ngi tiu th, trong phng php qun tr v iuhnh, trong tin trnh sn xut, trong s hp tc vi nhng hng khc, trongcch xut vn v lng nh gi c phn trong th trng chng khon.

Mng xut hin nh l mt h thng thng tin phc hp c tc dng giaolin truyn chuyn nhng kinh nghim nhn thc v hnh ng ca conngi, iu chnh v phi hp ht thy mi th kin thc b chia ch v phntn trong khng gian v thi gian. Hin Mng cha c chng hng trm

triu trang nh y p thng liu ni kt nhau mt cch rt hn tp v tytin cng thm rt nhiu c cu truy nhp. Cc trang thng liu chuyn vnxoay vng, trang thng liu cung cp trang thng liu to thnh nhng vngt phn thn (self reflexive loops). Ngha l, Mng cung cp nhng trangthng liu, ri n phin cc trang thng liu tr li ti thit Mng, Mng trli cung cp nhng trang thng liu, c xoay vn nh vy tng t mt hthng sng lin tc t to t sinh (autopoietic system). Cc vng t phn


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thn khng khp kn m tri li m ng cho nhng trang thng liu giaolin vng mc vi h thng khc, mng li khc. Do tng tc v bini, cc trang nh khng ngng ti xy dng Mng, ni pht sinh chng.

Tm li, Mng Ton Cu l ton th h tng giao thip a th nguyn giacc trang nh vi trang nh v gia cc trang nh vi Mng. Mng v cctrang nh h tng y tn, h tng nhip nhp. Mng Ton Cu ng cxem l mt th d c th biu dng ngha tng giao v nht th ca Hoanghim.

Bit: Khng hay Bt khng.S pht trin Mng Ton Cu bt ngun t cuc cch mng phng phpkho st th gii hin tng, ngun gc pht sinh vn ha mng li(network culture). Th gii khng do nhng mi quan h tuyn tnh cu

thnh m l mt h thng gm v s mng li phc hp tng tc tngnhp. Th gii khng phi l mt h thng my mc m l mt mng lirng ln bao gm v s h sinh thi (ecosystem) h tng nhip nhp.S xut hin vn ha mng li xy ra ng thi vi cuc cch mng thngtin (information revolution) pht xut t quan nim thng tin l bn cht cathc ti. M u bn tuyn ngn (Manifesto) ca cuc hi tho v Tnh

phc hp, Entropy, v Vt l Thng tin (Complexity, Entropy, and thePhysics of Information) do Vin Santa Fe, New Mexico, Hoa k. bo tr voXun 1989, khoa hc gia Wojciech Zurek phng theo cu m u Bn tuynngn ca ng Cng sn (1848; A spectre is haunting Europe the spectreof communism) vit v cuc cch mng thng tin nh sau: Qu thng tinang quy nhiu cc ngnh khoa hc. (The specter of information ishaunting the sciences) Sau , ng nhn mnh s gia tng tm quan trngca thng tin trong nhiu ngnh khoa hc: Nhit ng hc, phn ln cn

bn ca c hc thng k, thuyt lng t v o lng, vt l hc v k ton,v rt nhiu vn v thuyt h ng lc, phn t sinh hc, di truyn hc,v khoa hc my tnh, tt c cng chia x mt chung l thng tin. Nhngth hi i vi cc nh vt l hc th no l thng tin? Mun hiu th no lthng tin, thi phi nh ngha, nhng mun nh ngha thi phi hiu th

no l thng tin. Vy bt u t u?

Cc nh vt l hc thng thi thit nhng khi nim mi mt cch rt thctin. V ton l ngn ng ca vt l hc, v ton lin h s, cho nn mtthnh t ch yu ca mi l thuyt vt l l o lng, s ghp lng vo

phm. Bi th cc khi nim mi u c nh ngha bng cch m t cchthc o lng chng. nh ngha nh vy gi l nh ngha kh dng


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(operational definition), khng bt buc phi bit r vt em o lng l cig. Th d: Vo khong nm 1600 khi nim nhit c nh ngha l ilng o bng mt nhit k. Sau mt phn t thin k tc l vo gia thk 19, nh s hiu bit thm v nhit bng th nghim, nhit c nhngha l o tc trung bnh ca cc phn t.

n v o lng thng tin trong th gii hin tng l bit (binary digit; chs nh phn). Bit khng mu sc, kch thc, hay trng lng, v c thtruyn dn vi tc nh sng. Bit l phn t b nht ca thng liu. Bit lmt trng thi ca hu: m hay tt, ng hay ct, ln hay xung, vo hay ra,en hay trng. V l do thc dng, ta xem bit biu tng s la chn giahai ch s l 1 hay 0. ngha ca 1 hay 0 l mt vn khc. Mc du bit lmt khi nim tru tng, nhng v khng trnh khi dng vt liu nh giymc, chip vi tnh, hay t bo no m ha, cho nn mt chui bit l mt ti

nguyn vt l. C th hnh dung th gii cc bit nh mt th gii v tngchu bin hm dung trong th gii hin tng gm nguyn t (ht) v bcx (sng).

Mt tp hp k hiu 0 v 1 c gi tr thng liu ch khi no t chc thnhnhng mu hnh c th ring bit. K hiu xy dng h tng c s, thngliu chuyn ch ngha. Trong bui ban s ca my tnh, mt chui bitthng biu tng mt thng liu s. Nhng trong vng ba chc nm nay,nhiu th thng liu khc nh thnh m (audio) v in th (video) cng c m ha nh phn, biu tng bng bit.

c mt nim v cch thng liu trong thin nhin truyn qua mt dnn no b, hy ngh n mt my chp hnh s t (digital camera) c chto m ha hnh nh thnh bit. Thin nhin bin i mi th thng liu tach thnh xung in sai bit trong khng gian v thi gian. Nhng xungin ny c chuyn ti n mt bi cc ht photon (quang t), thc racng l c cu m ha nh phn. Khi cc xung in truyn t n mt, tcthi b mt m ha nh do bi ci my chp hnh s t. Thng liu cng

c m ha qua tai, mi, li, v thn ging nh qua mt ri truyn chuynn no c x l v ghi thu. B no cng vy, bao gm ht thy ccgiao lin trao i tn hiu gia cc t bo no, l mt tin trnh x l thngliu m ha rt cng hiu. Thng liu c x l khng duy nht trong bno m trong tt c mi cht sng. Tht vy, mn phn t sinh hc m t cct bo nh ni cha ng thng liu di truyn, s sinh trng v tp tnh ccsinh vt nh do m di truyn kim nh.


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Ging nh trng hp nng lng, thng tin c th m t bng ngn ngton hc v xem nh mt sn vt c th o lng, mua bn, ch nh, vnh thu. Tuy nhin, khc vi nng lng, thng tin c tnh ch quan(subjectivity). Khng hon ton trong mt h thng vt l, nh nng lngchuyn ha trong ko bnh, in nng trong bnh cquy, ha nng trongthng xng, ng nng trong ln gi, thng tin cn c mt phn trong tmthc. Hy ly s 14159265 lm th d. i vi ai cha tng lm quen vi s

pi thi s khng c ngha g c. Nhng i vi cc nh khoa hc thi l phn l ca mt thng liu khoa hc quan trng.

Thng tin nh ch sch chng hn, khng nhng biu dng mt thngip vit m cn ch th nhng k hiu t mu s, a, , c, h, dng vit ch y.V vy, thng tin xem nh c hai ngha. Mt, trong ngn ng hng ngy,

thng tin mang ngha ca mt thng ip no , v hai, n l k hiu ccng dng truyn chuyn thng ip, k hiu c th l ch ci, s, hay chui0 v 1. Theo ngha th hai, cng ngh thng tin (information technology)l ngnh k thut chuyn ct gi, truyn chuyn, ph by, v x l k hiu,khng cn bit n ngha ca chng.

Cc thnh phn chnh yu ca khoa hc thng tin, theo vt l gia BenjaminW. Schumacher, c th lc gin thnh mt phng php ba giai on:

1.- Xc nh mt ti nguyn vt l. Th d mt chui la chn nh phn, mtchui cu hi ch c hai cch tr li: c hay khng? ng hay sai? sp haynga? zero hay mt? Claude E. Shannon, nh khoa hc sng thit thuytthng tin, tng hp mi la chn vi mt bit.

2.- Xc nh mt cng vic x l thng tin c th thc hin vi s s dngti nguyn vt l xc nh trong giai on 1. Th d cng vic phn u l pnn (compression) xut liu (output) t mt ngun thng tin, nh bn vntrong mt quyn sch chng hn, vo trong mt chui bit, v phn sau l khp (decompression) chui bit y, tc phc hi thng tin nguyn th p nn

trong chui bit.

3.- Xc nh mt tiu chun v s thnh tu cng vic xc nh trong giaion 2. Th du: tiu chun bo rng xut liu sau khi kh p phi hon tontrng hp vi nhp liu trc khi p nn.


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Nh vy cu hi cn bn ca thng tin hc l Ti thiu cn bao nhiu slng ti nguyn vt l (giai on 1) thc hin cng vic x l thng tin(giai on 2) theo ng tiu chun thnh tu (giai on 3)? Cu hi ny tuykhng chuyn t ht tt c nhng g thuc khoa hc thng tin nhng c thgip ta nhn xt v phn tch nhng cng trnh nghin cu thuc lnh vcthng tin.

V nh trong trng hp p nn d liu (data compression), cu hi l: Tithiu cn bao nhiu bit cha ng thng tin do mt ngun no snxut? gii quyt vn ny hu gip cc k s in thit lp nhng hthng vin thng cng hiu, Shannon pht minh mt cch o lng thng tindo mt ngun thng tin sn xut v ph bin kin ca ng trong bi boni ting Thuyt ton hc v truyn thng (The Mathematical Theory ofCommunication; 1948).

p dng cch o lng Shannon o s lng thng tin trong mt thngip thi khng cn nh ngha th no l thng tin, v ngay c ngha cathng ip cng khng cn bit. Phng php o lng ca Shannon pdng d nht l vo cc thng ip gm nhng chui la chn gia haitng phn: ng hay sai, sp hay nga, 0 hay 1. Mun o s lng thngtin ca mt thng ip do mt ngun sn xut, hy m ha nh phn thngip thnh mt chui gm ton ch s 0 v 1, ri m c bao nhiu ch strong chui y. S ch s m c ng nh ngha l s bit ti thiu cn cha ng xut liu t ngun. Biu thc ton hc v s lng thng tin nayc gi l Shannon entropy v k thut o thng tin bng cch m gi l

php m bit (bit-counting).

Theo Shannon, s d dng m nh phn trong php m bit v y l phngcch t tn km nht o s lng thng tin. Mc du rt cng hiu trongvic truyn dn, cha ng, v x l d liu nh phn, bit v php m bithon ton khng gii p nhng cu hi lin quan n tnh ch quan cathng tin, c bit l vn ngha, Cc k hiu chuyn t ngha cathng ip ng n mc no?, v vn hiu nghim, Thng ip nhn

c tc dng trn hnh vi hiu qu nh th no so vi mun? Shannonch trng nhng g lin can ng ngha u khng thch hp vi vn kthut. Ch trng ny rt thch hp vi vt l hc lun lun gt ra ngoinhng vn lin can tnh ch quan.

Trong Ta Nhn thc v Tnh Khng, c on Thy Tu S t cu hi:Phc Hy pht hin khi nim nh phn bng hai ho. ng chng ba bit-ho


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thnh mt qu; thu hoch c tm qu. Ri chng na, ng c b nh 6bit-ho, nhn c 64 k t-qu, ni ghi tt c mi hin tng, tthin nhin, x hi, con ngi. Ghi bt c ci g m con ngi c th suyngh v tng tng. Nhng pht hin ca Phc Hy c thy l hu chcho vic bi ton hn l h tr b c ca con ngi, nh vi tnh ngy nay,ti sao?V tr li: Ngi hc Pht ch c th ni: cn, cnh, thc; ba s ha hipxc. Duyn xc pht sinh th. Xc d bit nn cm th d bit. Khng cngmi trng thc n th khng th nhn ging nhau c. Hai b sng

Ngn c hai chm sao. T ng hay Ty, nhn ln u thy. bn ny Thibnh dng nhn ln, l Ngu lang, ngi chn b, v Chc n, c gi dtla. V mt thin tnh s no lng. Cn bn kia i ty dng nhn ln, l con thin ng v cy n by giy. Khng c du hiu g chng t conchim ang c vt sng Ngn sang b bn kia nghe n, m c thy l

ang i tm tri tim ca v thn n cp la. Cch nhn khc nhau vch ra nhhng lch s khc nhau, v to dng nhng nn vn minh khc nhau.

ng vy. Nh khoa hc, trit hc, v ton hc Gottfried W. Leibniz (1646-1716), ngi pht minh ton vi tch phn (Calculus) ng thi v c lp vi

Newton cng l ngi u tin t nm 1666 tm cch sng ch mt h thngk t ph qut (characteristica universalis) trong mt logic hnh thc(symbolic logic; calculus ratiocinator; lut t duy) chuyn dch mi pht

biu bng li ni thng c tnh cch m h thnh nhng mnh ton hcchnh xc, qui gim ht thy mnh chn tht ca lun l v ngn ng caton vi tch phn. p dng php m nh phn, ng ch s dng hai ch snh phn 0 v 1 lm k t thnh lp cc biu thc s hc.

Leibniz tin tng trn nguyn tc mi vn u c th gii quyt. Trcht, to mt mi trng ph qut trong cc tng tng phn c thng thi cu khi v tng h. H thng k t ph qut ta trn mt logicnh phn l ng php c kh nng chuyn dch tt c khi nim v kin btng vo cng mt tp hp k hiu. im khc bit vi ngn ng thngthng l h thng k t ph qut khng pht m v khng b cht liu ni

dung hn ch. Khng ni dung v im lng, ng php nh phn c th chuyni mi mnh c ngha thnh nhng thut ng ca logic vi tch phn,mt h thng chng minh nhng mu hnh lun chng ng hay sai, hoclin kt chng thnh mt ma trn (matrix). Do , cc tin trnh t duy tringhch c th ng thi din bin cng trong mt mi trng. Mi s btng v thi hay nim tin, mt khi chuyn dch qua k t tng ng, cth dn khi nhng php din ton khng vp phi mu thun phi l. Kt


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qu l logic vi tch phn ch ch ng sai ca bin lun, ra ngoi nhng phtbiu m h, nhng li nhn thnh kin.

Do y, Leibniz hay vit v nhng vn thn hc lin h n ngi TrungHoa v thng trao i th t vi cc linh mc Dng Tn truyn o Trung Hoa ang nghin cu Kinh Dch tm im tng ng gia tnngng ca ngi Trung Hoa v Thin cha gio. Leibniz c tin choJoachim Bouvet, linh mc Dng Tn ngi Php Bc kinh bit cch ngm bng hai s 0 v 1. Chng bao lu sau khi nhn c th tr li kmtheo hnh 64 qu kp trong Kinh Dch ca Bouvet cho bit c s tng quangia cc qu y v php m nh phn ca ng, ng trnh Vin Hn lmHong gia Khoa hc (1703) bi Gii thch s hc nh phn ch dng k t 0v 1, km theo on bnh v s li ch ca n v v s n gii thch nghanhng hnh tng Trung Hoa thi c i i vua Phc Hy (Explication de

larithmtique binaire, qui se sert des seuls caractres 0 et 1, avec desremarques sur son utilit, et sur ce quelle donne le sens des anciennesfigures Chinoises de Fohy). C on ng vit: im bt ng trong phptnh ny l s hc ch dng 0 v 1 cha ng iu b n v cc vch ca vuav trit gia thi c tn Phc Hy ... ... ... Nhiu qu c cho l do ng vua yvch ra, tt c u c th suy ra t s hc ny.

Nhng ch cn a ra y hnh ca tm qu n gi l Bt qui l nhnghnh c bn, v thm vo li gii thch, tht ra hin nhin, hiungay mt vch lin c ngha l n v hay 1 v mt vch t

c ngha l

zero hay 0.

Ngi Trung Hoa nh mt i s hiu bit ngha ca Bt qui hay nhngvch ca Phc Hy, c th hn ngn nm nay, v h vit nhng li chgii cc qu, tm kim ti khng bit ngha xa xa no, cho nn by gi trnn cn thit i vi h l c li gii thch chn tht t pha ngi u chu.

Ngoi ra, Leibniz gia cng ch to my tnh thch hp vi ngn ng nhphn c kh nng din ton trn cc chui s nh phn theo qui tc logic

hnh thc nhng khng thnh cng. Mi hn hai th k sau nh nhng cngtrnh tip tc nghin cu nhng kin ca Leibniz do nhng tn tui nhBoole, Venn, Russell, Whitehead, Shannon, v nhiu nhn vt khc na,logic hnh thc mi c th vn dng chng minh bng php din dchtrong cc mch in t. Sau , John von Neumann p dng s hc nh phnca Leibniz khai thit my in ton s t (digital computer).


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---o0o---

(IV) - Php gii tnh: chng chp, giao thoa, v vngmc

Tng cn nhc li y mt s tnh cht c bit ca c hc lng t(quantum mechanics) trc khi bn v khoa thng tin lng t (quantuminformation). Lng t hay ht c hai loi phm tnh, tnh v ng. Cc

phm tnh tnh c kch thc khng thay i khi o lng v dng phnbit cc loi ht. Ba phm tnh tnh quan trng nht l khi, in tch, v ilng ca spin. Trong s cc phm tnh ng biu trng tnh ng ca htc th k v tr, xung lng, v nh hng ca spin.

Nn tng ca c hc lng t l nguyn l bt nh Heisenberg c s

dng xc nh mc chnh xc trong s o lng nhng phm tnhng ca ht chuyn ng. Cc phm tnh ng lun lun pht hin thnhtng cp b sung, chng hn v tr v xung lng, nng lng v thi giantrong mt tin trnh vt l. Theo nguyn l bt nh, du dng c, phng

php, v ngi o lng hon ho n mc no i na, ta khng bao gic th ng thi bit c chnh xc c hai phm tnh b sung ca mt htang chuyn ng. Theo Bohr, nhng phm tnh biu trng tnh ng calng t khng thuc bn tnh t nhin ca lng t m pht hin t tonth trng hung trong cng vic o lng c thc hin. Ht t nkhng c phm tnh v tr v xung lng. Nhng phm tnh y tht ra lquan h gia ht v dng c o lng. Dp b dng c o lng thi nhng

phm tnh y cng bin mt. Phm tnh ng ca ht kh d nh ngha vquan st c ch khi no t ht trong quan h h tng tc dng vi nhngh thng khc. Nh vy, thay v c v tr v tc c quan st v nhngha ring bit, cc ht c mt trng thi lng t (a quantum sate) tc mtt hp v tr v tc .

C hc lng t thng khng d on mt kt qu duy nht ca mt thnghim. N trng dn nhiu kt qu khc nhau, nu r mi kt qu c bao

nhiu c duyn thnh tu. Ngha l, nu p dng cng mt php o lng vkhi s trong iu kin ban u ging nhau o mt s ln h thng tngt nhau [y mun ni l o mt h thng rt nhiu ln, h thng tt nhinkhng bao gi yn trong cng mt trng thi] thi kt qu o c s l Atrong mt s trng hp, B trong mt s trng hp khc, v..v... Ta c thd on gn ng bao nhiu ln kt qu l A hay B nhng khng th don kt qu chnh xc sau mi ln o lng c. Nh vy c hc lng t


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thm vo khoa hc yu t ngu duyn bt kh d tri. V th mt s khoa hcgia nh Einstein chng i c hc lng t, bo rng: Thng khngchi sc sc. Nhng a s chp nhn bi c hc lng t hon ton phhp vi thc nghim. C hc lng t chi phi s vn hnh ca cctransistor v mch t hp l nhng thnh phn chnh yu ca cc thit bin t nh tivi v my tnh, ng thi l nn tng ca ha hc v sinh hchin i.

Lng t nh sng (photon) cng nh lng t vt cht (th d: electron) chai hnh tng, ht v sng. Tri vi quan im ca Niels Bohr cho rngkhng bao gi c th thy photon tc dng nh ht v sng cng mt lc,nm 1992, cc vt l gia Nht bn hon thnh mt th nghim do mt nhmvt l gia n thit k v quan st c hin tng photon tc dng ngthi nh ht v sng. Nh vy, hnh tng pht hin l ty theo trng hung

trong th nghim c thc hin. Ni theo ngn ng Pht gio, lng tl mt php hu vi siu vit v hm dung hai hnh tng sng v ht tngi i nghch. y l c tnh mu thun m nht thng ca tnh Khngca lng t.

Sng chuyn ng tun hon v c xc nh bi hai phm tnh: bin din t cao ca sng v pha din t sng vo thi k no ca chu kchuyn ng. Pha ca sng iu tit hin tng hai sng gp nhau. Nu haisng ng tn s tip xc nhau vi pha ng nht thi ta bo chng trng

pha (in phase), vi pha khc nhau na chu k thi ta bo chng phn pha

(out of phase).

Khi hai sng gp nhau thi tng hp thnh mt sng c bin bng bin ca hai sng cng li. S kin bin cc sng gp nhau bt k ucng thnh bin ca sng tng hp c gi l nguyn l chng chp(superposition principle). Nguyn l ny ch p dng trong trng hp bin khng ln v khi khng p dng c thi gi l trng hp phi tuyntnh (non linearity). Khng c g thm hay mt i mi khi sng gp nhau.c bit l khi mt sng truyn dn ra khi sng tng hp, bin ca n

vn nh trc khi gp cc sng khc. Sng tng hp ch l mt s chngchp sng tm thi.Nguyn l chng chp quyt nh rng khi cc sng dao ng cng li thibin ca sng tng hp ty thuc s tng quan lin h gia cc pha. Khihai sng trng pha, nh sng ging hng vi nh sng, y sng ginghng vi y sng to thnh mt sng mnh hn vi bin ln. Nu bin ca chng bng nhau (chn lm 1 n v) thi sng tng hp c bin


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bng 2 n v. y l trng hp giao thoa xy dng. Khi chng phn pha,nh ca sng ny ging hng vi y ca sng kia v nu bin cachng bng nhau thi hai sng h giao tng trit, tng hp thnh mt sngc bin trit tiu. Trng hp ny gi l giao thoa ph hy. Nu pha u trong khong gia trng v phn pha thi bin tng hp nmtrong khong 0 v 2.

Ngu duyn v giao thoa, hai nt c th ca c hc lng t c din tton hc bng mt hm sng do Schrodinger sng thit vi mc ch minhgii s giao thoa ca cc ht vt cht. Hm sng khng m t ht m thngtin v c duyn c th tm thy ht u ti nhiu v tr khc nhau. Bnh

phng bin ca sng ti bt k ch no cho bit xc sut tm thy phmtnh v tr ca ht ch v dng sng thng tin cho bit v tt c phmtnh khc. Hm sng chnh l trng thi lng t biu tng va hin tng

giao thoa ca cc ht va tp tnh ngu duyn ca chng. Quan h gia tnhkh d tri ca hm sng v tnh bt kh d tri ca ht tng t quan h giahai mnh c v mu thun nhau: Xc sut ng tin ri nga l 50%,mt i lng hon ton kh d tri v ng tin ri xung sau mi lngieo khng bit l sp hay nga, chnh l mt iu bt kh d tri. Hmsng c th biu trng hai mnh tng phn nh th, qu l mt s kinkhc thng!

Tm li, hm sng khng vn ti nng lng nh sng nc hay sng m,m vn ti nhng kh nng, hay tim nng chng chp tuyn tnh ln nhau.

Ni theo Duy thc, hm sng l nhng ln sng chng t to nn thc a lida, thc ny hng chuyn, tng tc bt on.

Von Neumann l ngi u tin t thnh vn nhng khng gii quyt so lng phm tnh lng t. ng cng l ngi u tin ch cho thythuyt lng t dn khi vai tr tm thc ca ngi quan st th nghim.ng cho rng vt th t n khng c phm tnh nu quan st vin khng chtm quan st n. Khi nim then cht trong s o lng lng t l s sp ca hm sng pht hin trong th nghim vi mn chn c hai khe: Mt

ht n nht nh mt photon hay mt nguyn t natri khi truyn dn thi cdng sng, nhng khi n ni thi c dng ht. Theo nhm Copenhagen doBohr lnh o, chnh tc dng quan st, hay o lng, sng lm n sp thnh ht.

Ht n nht khi i qua mt khe tung nh ng thi bit c khe kia bche kn hay h, do cui cng chn la kiu hnh v ra trn mn ln


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quang, mt vng im trng hay kiu hnh sng giao thoa. Ngha l, n thc c iu kin chng nhng ti mt khe m khp ni trong ton th thnghim [Nn nh so vi kch thc ca ht khong cch hai khe v cngln]. Tnh ni kt phi cc b (non-local connection) ny l nt c th trngyu ca c hc lng t. Bo rng A ni kt phi cc b vi B c ngha l (1)ni kt khng qua trung gian mi cht no gia A v B; (2) nh hng cas ni kt khng b khong cch gim thiu; nh hng vn ging nhau ducch xa hng vn dm hay ch mt phn rt nh ca mt ly; v (3) c tnhtc thi, khng b tc nh sng hn nh.

Trong c hc lng t, tnh ni kt phi cc b c tn gi l pha vng mc(phase entanglement). Mi khi h lng t A gp h lng t B, pha cachng hn hp: sng ca A sao mt phn pha ca n vo trong sng ca Bv ngc li. S trao i pha nh th ni kt vnh vin hai h thng A v B.

Tnh pha vng mc ni kt ht thy mi h thng tng gp nhau mt lntrong qu kh thnh mt sc sng duy nht, s ni kt khng qua trung gianmi cht no, khng b khong cch gim thiu nh hng, v c tnh tcthi.

Nhm tm hiu ngha ton th (holism) ca trng thi chng chp v vngmc, hy ly spin lm th d. Spin l mt tnh cht vt l ch c cptrong c hc lng t. C nhng h thng nh electron c spin 1/2 vi haitrng thi m thi, hoc trng thi spin ch ln spin up) hoc trng thispin ch xung (spin down). Gi thit hai h thng c spin 1/2 cng pht ra

t mt ngun, ri sau la nhau theo hai ng ng ngc hng. Du lycch bao nhiu i na, trng thi spin ca ton th, ngha l trng thi spinni ca hai h thng y hp nhau, l trng thi chng chp ca h thng uc spin ch ln v h thng th hai c spin ch xung vi h thng u cspin ch xung v h thng th hai c spin ch ln.

Trong trng thi chng chp, ring mi h thng, khng c h thng no trong trng thi c spin ch ln hay spin ch xung. Nh vy c ngha l, tuyspin cc b (local spin) tc spin ca ring mi h thng l mt phm tnh

kh quan trc (local observable), nhng trong cch th chng chp n khngc mt o chnh xc m ch vi mt xc sut bao nhiu phn trm ng.Spin ton th (total spin) ca trng thi chng chp mi c mt o xcnh. Khi o spin ca mt trong hai h thng v bit kt qu thi xc sut ospin ca h thng kia bin i thnh 1, ngha l ta c th bit chc spin can l ch ln hay ch xung.


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Tnh chng chp v pha vng mc l mt th d khoa hc v php gii tnhl tnh bn nhin ca tt c s vt, ngha l ca tt c cc chuyn ng vcc hin tng trong v tr. Tnh bn nhin y l tnh trng trng duynkhi, ngha l tnh nh hng dy chuyn ca mt s vt i vi tt c svt, ca tt c s vt i vi mt s vt. V nh mt con c nh vy ui,tuy rung ng rt t, nhng nu c kh nng o lng chnh xc, th cng cth thy nh hng cng khp bn b. (Kinh Th Lng Nghim. Li niu. Tm Minh L nh Thm)

Vt l gia John Stewart Bell chng minh mt nh l ton hc xc nhn rngthc ti lng t phi phi cc b. Kt qu ca nh l Bell khng ty thucthuyt lng t, nh vy c ngha l mt ngy kia nu thuyt lng t cnhn thy khng cn gi tr, khng li ch na, v b dp b, thi nh lBell vn ng vng v lun lun ng. Nn nh rng nh l Bell buc thc

ti ch khng phi hin tng phi phi cc b. o lng lng t l phngtin vt l gia s dng tip xc vi thc ti. Tt c mi o lng lng tu cu thnh bi nhng nhy lng t, chng hn nh nhng chp sng letrn mn ln tinh. Cc nhy lng t ln xung t thc ti lng t tothnh nhng mu hnh tn ti v ti din c tnh cc b, ngha l tng giaotc dng qua trung gian nhng mi cht trong khng gian v thi gian. Dotnh pha vng mc m hin thnh mt ton th hon chnh trong cclng t ni kt phi cc b vn hnh theo quy lut ca hm sng.

Qubit: Khng v Bt khng.

tm hiu thng tin lng t, hy t cu hi theo phng php ba giaion ca Schumacher. Trong c hc lng t, ti nguyn vt l mi nothay th chui cc bit? Cng vic x l thng tin no c th thc hin?

Nhng tiu chun thch hp no v s thnh tu cng vic x l thng tin?

V ti nguyn vt l thi phi k n cc trng thi chng chp, ging nhtrng hp con mo ca Schrodinger l s chng chp hai kh nng sng vcht. Cng vic x l thng tin c th lin can n s vn dng tnh ni kt

phi cc b tc pha vng mc. So vi trng hp thng tin c in, tiuchun v s thnh tu tinh t hn nhiu bi v mun gom thu kt qu camt cng vic x l thng tin thi phi quan st, hay o lng, h thng.

Nhng trong c hc lng t, hnh ng nh vy s bin i h thng, hydit nhng trng thi chng chp c bit ch hin hu trong vt l lng tm thi.


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Ti nguyn cn bn ca thng tin lng t gi l bit lng t, quantum bit,hay qubit (c l kiubit), danh t do Schumacher ngh v c cng ngvt l gia chp nhn vo thu 1992. Ging nh bit l tng tru xut tnhng nguyn l ca vt l hc c in, qubit l tng tru xut t nhngnguyn l ca c hc lng t. Bit, n v ca thng tin c in, c miut bi trng thi ca n, 0 hay 1. Cng vy, qubit, n v ca thng tin lngt, c miu t bi trng thi lng t ca mt h thng lng t hai thnguyn. C hai trng thi lng t ca qubit gi l trng thi c bn tngng vi hai trng thi 0 v 1 ca mt bit c in. Hai trng thi c bn nythng c k hiu l |0> (c l ket 0) v |1> (c l ket 1). Tuy nhin,trong c hc lng t, ht no c hai trng thi lng t khc nhau tt cmt tp hp gm v s trng thi chng chp ca hai trng thi . V thqubit c th c miu t bi v s trng thi chng chp ca hai trng thic bn |0> v |1>. Biu thc ca qubit c dng:

a|0> + b|1>

a v b l phc s, mt trong hai phc s ny phi khc khng. (Xem Biton A li da duyn khi. Sch Tnh khi v Duyn khi. Hng Dng). Cth ni vn tt, qubit l chng chp 0 v 1, cng nh ni bit l tr s 0 hay 1.

Bt c h thng lng t no c hai trng thi nh spin ca electron hayphn cc ca photon u l ha thn ca mt qubit. Trong mt qubit cnhiu hn mt bit thng tin. Tuy nhin khi o qubit thu lm thng tin

thi ch t c ch mt bit m thi.

Xin m du ngoc gii thch s lc phn cc ca photon lin h nh thno vi qubit. nh sng l nhng sng ngang, thng gc (90 ) vi chiusng truyn dn (chiu dc), kt hp dao ng di chuyn ca in trng vt trng. Mt b lc sng phn cc nh kin mt Polaroid chng hn, ccng dng phn cc nh sng, ngha l nh sng truyn xuyn qua kintheo mt chiu ring bit, chiu ca trc truyn dn ca b lc. Nu chiuca trc b lc thng ng thi ch c nh sng phn cc thng ng truynqua nguyn vn, cn nh sng phn cc nm ngang thi hon ton b chnli. nh sng ca mt tri hay ca n in v l hn hp nh sng phn cckhp mi hng khc nhau cho nn gi l nh sng thng, khng c chiu

phn cc no c bit. Mi photon ca nh sng phn cc c th hnh dungnh c gn mt mi tn ch hng phn cc ca n, thng gc vi chiutruyn dn nh sng. C hc lng t thng ni n nhng photon phncc theo hai chiu thng gc vi nhau v vi chiu truyn dn ca nh sng.


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Nh vy, photon l trng thi chng chp ca hai sng phn cc, sng phncc chiu ng v sng phn cc chiu ngang, cho nn c xem nh hathn ca mt qubit.

Th nghim no c th to ra mt qubit? Cch n gin nht to qubit ldng mt b tch chm tia (beam splitter). B tch chm tia khng g khcl nhng a thy tinh dy hn na phn, ng knh ln trong khong tmt n hai phn, mt mt c ph mt lp mng kim loi, kim loi muvng, mu bc, mi mu, hu phn chiu nh sng mu sc khc nhau.B tch chm tia c mt hu nh khp ni, trong nh, trn xe, n gip kimsot cc tia chp laser vi t trong cc my chi CD. Chc nng ca n ltch ra hai chiu mt chm tia sng chiu xin trn mt n: mt tia truynthng xuyn qua thy tinh v tia th hai phn chiu trn n nh trn mt mtgng. c im l n bo ton nng lng ca chm tia, khng bin

chuyn phn no ra nhit. N c tnh i xng, ngha l tch chm tia thnhhai phn bng nhau: tia truyn thng v tia phn chiu, sng ca mi tiabng na sng ca chm tia chiu ti n.

By gi t mt b tch chm tia nm ngang song song vi nn nh. Chiuxin mt photon ti mt bn trn ca n, mi photon gi thit chuyn ti mt

bit thng tin. Kt qu l s c hai tn hiu, mt pha trn, mt pha dib tch. Tuy nhin khng mt photon th hai hay mt bit thng tin th haino c to. Theo quy lut lng t, thng tin hin ang nm trong trngthi chng chp ca 1 v 0. Nu t hai my d, ci trn, ci di b

tch, thi mt trong hai my d s pht hin thng tin nhng khng bittrc my no. Theo quy c, nu photon hin ni my d pha trn thi cngha l 1, hin ni my pha di thi c ngha l 0. l u mi quantrng nhn ra mt qubit 1 v 0 c tc thnh. N c chuyn ti

bi hai chm tia vi t, c hai cng li va nng lng ca mt photon nnht.

hp hai chm vi t y li thnh mt photon hy dng hai tm gng G1v G2 phn chiu hai tia ca b tch th nht, tia truyn thng v tia phn

chiu, n gp nhau trn mt b tch th hai. Ta c mt giao thoa k vi haimy d A v B nh hnh sau y.

Cng dng ca giao thoa k l trin chuyn 1 thnh 0 hay ngc li, ngnh cng dng ca mt cng NOT (BT). [Cc phn t ca mch logic gil cng (gate) v chng kim sot dng thng tin ging nh cng p nckim sot dng nc]. V bit ch c hai kh nng, nn BT kh nng ny


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tc l chn kh nng kia. Nh vy, b tch chm tia th nht c th xemnh cn s bc hai ca BT, bi v p dng hai ln lin tip qua hai btch, cn bc hai ca BT nhn cn bc hai ca BT, ha thnh BTli. Cn bc hai ca BT, mt khi nim ch c hc lng t mi c, li phn logic ca khi nim ton hc cn bc hai ca 1, cn gi l s oi. iu ny chng t trong tng mc su thm c mt s lin h gia vtl (b tch chm tia) v ton hc (o s). Theo quan im Duy thc, s linh y chnh l thc, a li da thc.

S o i tng ng vi gc quay 90 , do s so snh vi s o cho tahiu ti sao mt hnh cu c th dng biu tng mt qubit trong khnggian ba th nguyn.

Hnh A: Mt bit ch c th c mt trong hai trng thi l 0 hay 1. C th biu

din bit bi mt mi tn ch xung hay ch ln.Hnh B: Mt qubit c rt nhiu trng thi kh nng. Mi trng thi c th

biu din bi mt mi tn ch vo mt v tr trn mt hnh cu. Bc cctng ng vi 1, Nam cc vi 0. Tt c nhng v tr khc l s chng chphai trng thi 0 v 1.

Hnh C: Mt qubit khc vi bit ch l c th ct cha nhng tr s khong gia 0 v 1, v th c th ct cha v hn s lng thng tin. Nhng

phi o lng mi trch dn c thng tin ct cha trong qubit. Tuy nhin,

theo quy lut lng t, o lng xa b ht thy mi thng tin trong qubitngoi tr c nht mt trong hai trng thi, 0 hay 1, c pht hin. Kt quo qubit lun lun l mt bit, 0 hay 1. Xc sut ca mi kt qu ty thucv ca qubit. Kinh ca qubit biu tng pha, sai bit tng igia chu k ca hai sng. Ti kinh tuyn Greenwich vi kinh zero, haisng trng pha, bn kia na vng quanh hnh cu, kinh l 180 , haisng phn pha. Tm li, qubit c xc nh bi hai s: v chia thnh

phn tng i v kinh miu t s sai bit pha tng i gia hai trngthi 0 v 1.

S khc bit c ch u tin gia bit v qubit l kh nng ct chathng tin. Mt b ghi vi hai bit (2-bit register) c th ct cha mi ln chmt trong 2 ly tha 2 tc 4 s: 00, 01, 10, 11 tc theo php biu din nh

phn, mt trong bn s thp phn: 0, 1, 2, v 3. Hai qubit cng ct chanhng s t 0 n 3 nh bit. Tuy nhin, v hai qubit l trng thi chng chpnhng trng thi k trn cho nn mt b ghi vi hai qubit c th ct cha cc


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s 0, 1, 2, v 3 cng mt lc. Nu gm tm qubit b ghi c th ct cha 2ly tha 8 tc 256 s cng mt lc. Khi s qubit trong b ghi tng ln 100,thi s ct cha tng ln 2 ly tha 100 tc chng 10 ly tha 30 (s 1o 30 zero) s cng mt lc. Hin ti hay trong tng lai gn y khng thc siu my tnh no c th x l s lng thng tin ln nh vy.

Trn y trnh by cc th d v thng tin lng t theo ng phng phpba giai on ca Schumacher: Cn bao nhiu qubit (ti nguyn vt l) ctcha mt s lng thng tin c in (cng vic x l thng tin) hu c thtrch dn thng tin ct cha mt cch xc thc (tiu chun thnh tu).

Kh nng ct cha v lng thng tin pht xut t trng thi chng chp lnguyn nhn thc gic cc khoa hc gia tm cch sng ch my tnh lngt (quantum computer), mt loi my tnh c kh nng ct cha cng mt

lc mt s lng thng tin v hn trong mt s qubit tng i b. Ngoi ra,hin tng chng chp lin h tnh pha vng mc. Vng mc l kh nngcc h thng lng t hin by nhng tng giao gia nhng trng thitrong mt chng chp. Vng mc cho php hai ht chuyn vn nh mt,du chng cch xa bao nhiu i na. Nu c hai qubit vng mc, o trngthi ca qubit ny lp tc xc nh c trng thi ca qubit kia.

Cc vt l gia p dng kh nng tnh ny tm cch chuyn thng tin i xav tc thi (teleportation) m khng b c ln. Trc ht, h dng mtdng c nh b tch chm tia to s vng mc gia hai ht, hai photon A

v B chng hn, nhm mi khi bin i trng thi ht A thi trng thi ht Bbt k u cng tc thi bin i theo. Sau to trng thi lng t cntruyn chuyn i xa v tc thi ni mt photon th ba, C, ri to s vngmc gia ht A v ht C. Tc thi trng thi ca B b i thnh trng thi toni C, v trng thi nguyn th ni C b hy dit. Mt trng thi bin mt timt ch tc thi hin ra ti mt ch khc!

Nhm vt l gia i hc Innsbruck, Austria, l nhng khoa hc gia u tinthnh cng dng nguyn t chuyn thng tin tc thi xuyn qua si quanghc (optical fiber) di 800 mt t trong mt cng nc di y sngDanube ni lin hai phng th nghim hai bn sng. Tin ny c tngthut y trong tp ch Nature, ngy 16 thng 6 nm 2004, lm phn khicc khoa hc gia ang tm cch sng ch nhng siu my tnh vn chuyn tnhiu tc thi trong tnh vng mc c s dng nh nhng mch dylng t.


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John Archibald Wheeler, gio s i hc Princeton, quan tm n vai trquan trng ca tm thc trong vt l hc, nu ln nhng thc mc m nggi l Nhng cu hi thc s rng ln (Really Big Questions). Nm cutrong s l ngun cm hng ca nhiu cng trnh nghin cu vt l hcv trit hc hin i: Ti sao lng t? (Why the quantum?), S hu nnh th no? (How come existence?), Hin tng pht xut t bit? (It from

bit?), Mt v tr tham gia? (A participatory universe?), v Ci g lmthnh ngha? (What makes meaning?)

V cu hi Hin tng pht xut t bit? vt l gia David Deutsch, Vin Kton lng t, i hc Oxford, khng chp nhn quan im thng tin to rath gii hin tng. Tri li, ng cho rng ci th gii trong c ci gi lthng tin (information) v nhng tin trnh gi l k ton (computation) hincha hay t nht sn sng cha nhng my tnh ph qut (universal

computers). Trong bi It from Qubit ng gii thch: Th gii l do qubitcu thnh. Mi li gii p cu hi trong thin nhin mt vt g cquan st l c hay khng, tht ra l mt vt kh quan trc nh phn (Booleanobservable). Mi vt kh quan trc nh phn l thnh phn ca mt qubit, hthng c bn i vi thc ti vt l nhng xa l i vi kinh nghim hngngy ca chng ta. ... ... Ci m ta tng chng nh mt th gii gm cc

bin s ch c duy nht mt tr s tht ra l thnh phn ca mt thc ti rngln hn trong cu tr li y cu hi c-khng khng th no ch l chay khng, khng th no l c hai, c v khng, i song i, m l mtlng t kh quan trc, mt vt th c th biu tng ton hc bng mt matrn Hermite ln.

David Deutsch lu chng ta rng mc du theo thuyt thng tin c indung lng ca qubit ch chuyn ti c nht mt bit, nhng trong thinnhin khng c h thng c bn no tng ng vi mt bit. Ch c qubit mihin thnh trong thin nhin. Theo ng, bit, bin s nh phn, v k ton cin ht thy u l nhng phm tnh xut hin (emergent) hay gn ng(approximate) ca qubit.

Nhn qu ng thi.V electron v photon u xem nh ha thn ca qubit cho nn thay v nitheo ngn ng ca thuyt thng tin lng t, th gii l do qubit cu thnhta c th ni theo ngn ng ca thuyt lng t in ng lc (quantumelectrodynamics; thuyt v nh sng v vt cht, sau ny s gi tt l QED),mi s vt u xc nh bi s tng tc gia cc electron (vt cht) vi


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nhau v vi cc photon (nng lng). Th gii v c chng ta tt c u donguyn t cu thnh, v nguyn t gm mt ht nhn c st gia baoquanh bi mt m my electron. Electron l tng mo ca nguyn t, vtng tc gia nguyn t v phn t tht ra l tng tc gia cc m myelectron. Theo QED, electron tng tc bng cch trao i photon. Mtelectron pht ra mt photon v chuyn ng git li, hay mt electron hpthu mt photon v tip nhn mt ci . Mi bin c do tng tc gia ccelectron u c th din t nh vy.

i vi cc thuyt lng t vn nan gii l phi gii thch hin tngvng mc, ci m Einstein gi l tc ng ma qu qua khong cch(spooky action at a distance). Kh khn y l phi ct ngha lm th noc s ni kt tc thi v hai chiu gia hai lng t vng mc pha. QEDgii thch nh th no?

Trc ht tng cn nhc n thuyt in t ng lc hc ca James ClerkMaxwell (1864) c tm tt trong bn phng trnh, c th dng gii

bt c bi ton in v t no khng lin can n hiu qu lng t. cbit l cc phng trnh ny cha mt hng s k hiu l c tuy xut pht tkt qu o lng in tnh v t tnh ca cc in tch di chuyn hay ngyn l nhng s kin khng lin quan sng v tc ln, th m tr s oc ng l tc ca nh sng. Do , nh sng c quan nim l sngin t truyn dn vi tc c bng ba trm ngn cy s mi giy.

Phng trnh Maxwell c hai li gii, li gii sng tr (retarded wave) m tsng truyn dn i ti trong thi gian t qu kh ti v lai, v li gii sngsm (advanced wave) m t sng truyn dn i li trong thi gian t v laili vo qu kh. Hai sng ny truyn dn ngc chiu thi gian nhng cngmt tc , tc nh sng trong khng. Gi l sng tr v n n ni saukhi c pht ra, cn sng sm thi n ni trc khi c pht ra. Sng tr

phn no c th v vi cc ln sng lan rng u khp mi hng trongkhng trung t mt anten rai hay cc sng nc lan rng t im mt vinsi ri xung mt h; sng sm phn no c th v vi cc ln sng truyn

ti anten rai t khp mi phng hay cc sng nc bt u t b htruyn dn cng v mt im l trung tm mt h.

T trc n nay khng c th nghim no pht hin sng sm v tt csng nh sng bit c u l sng tr cho nn li gii sng sm b gt bmt bn xem nh khng li ch mc du sng sm l mt phn ca cu hi


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rng ln hn: ti sao mi tn thi gian trong khi ht thy mi nh lut cbn ca vt l hc khng pht hin mt chiu thi gian no c bit?

Vo u nm 1941, trc mt c ta gm sinh vin v gio s i hcPrinceton, trong c Einstein v Pauli, sinh vin cao hc Richard Feynman(c gio s hng dn l John Wheeler v sau ny l mt trong ba khoa hcgia c Gii Nobel Vt l 1965 v c cng khai ph QED) trnh by vc tn ng kt qu nghin cu u tay l s dng sng sm gii thchv sao khi sng pht ra va la khi electron thi electron git li theo chiungc li. Li nhn khng phn bit sng tr v sng sm ca Feynman lnhn quan cn bn ca thuyt thit b hp thu bc x Wheeler-Feynman(The Wheeler-Feynman absorber theory of radiation).

Theo Wheeler v Feynman, s pht sng khng lm electron git li nh

cch gii thch tc ng v phn ng ca vt l hc c in. Electronkhng tng tc vi sng do n pht ra. N git li l do tc ng ca mtsng sm pht ra t mt electron khc khi electron ny hp thu sng tr don pht. Thuyt Wheeler-Feynman m t hin tng trao i photon giahai electron nh sau. Electron A pht ra nhng khng git li mt na sng(sng tr) truyn ti trong thi gian vi tc nh sng. Sng ny khi chp thu, ng lng ca n lm git li thit b hp thu n, mt electronkhc gi l B. Kch ng bi chuyn ng git li, electron B pht ra mtna sng (sng sm) truyn li trong thi gian n electron A vi tc nhsng. ng lng ca sng ny lm electron A git li khi hp thu n.

Theo thuyt tng i hp, thi gian khng hin hu i vi mt photon.Thi gian trao i photon l zero. Photon khng phn bit s truyn dnsng ti hay li trong thi gian.

Thuyt Wheeler-Feynman ch cp cc sng in t. Vt l gia John G.Cramer, i hc Washington, p dng thuyt y vo cc sng lng t m t s tng tc gia cc h thng lng t. Phng trnh sngSchrodinger sau khi c bin ci chp nhn nhng hiu qu ca thuyttng i cng c hai li gii ging nh trng hp phng trnh Maxwell.Cramer dng n m t s tng tc m ng gi l s giao dch(transaction) gia hai h thng lng t. ng v giao dch nh ci bttay (handshaking) gia hai h thng u trong khng gian v thigian. l cch ng dng ngn ng thng thng (khng ton hc) nin s tng tc tc thi, ngha l xy ra theo hai chiu ngc nhau mng thi. Tic rng ng khng hc Duy thc v s tng tc tc thi vi


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electron nguyn th. Nhng g quan st c gm ton sng tr lan truyntheo mi tn thi gian, cn sng sm bt kh quan trc thi xc nh v trtng i ca electron trong ton th mng li v biu hin qua phn nggit li.

im c sc y l electron git li ng thi vi khi bc x. Hiu qu rrng nht ca cc sng sm l nhip nhp mi mi electron vo trong tonth mng li in t ph kn V tr. Nu mt electron trong mt phng thnghim trn qu t tri qua mt s bin, phn ng git li ca n l bngchng cc sng lin h ngc (feedback waves) c hp thu, bo tinmi ht tch in trong V tr cch xa qu t bao nhiu i na cng bittc khc s bin y, mc du khng tn hiu no truyn chuyn qua li giacc ht tch in trong V tr nhanh hn tc nh sng.

Git li l ni theo ngn ng thng thng din t mt i lng gi ltnh cn tr bc x ca electron (radiation resistance). Electron bc x mikhi tng tc v b y, tuy nhin nng lng bc x khng nhiu nhnng lng dng y n. Cn nng lng y n v phi ch phc tnhcn tr bc x ca n. Gi l tnh cn tr bc x bi v tnh ny lin hp vigia tc pht sinh bc x. Theo cch gii thch lng t tng tc trn y,thi tnh cn tr bc x ca electron l mt xut hin tnh (duyn khi), ktqu tc dng ca tt c sng sm pht ra t ht thy mi ht tch in trongV tru hp thu sng tr n pht. Nh vy mi electron u l va nhnva qu ca ton mng li sng in t, hay ni theo Php Tng, va

Khng va Hu, va hu lc va v lc.

Th gii ca electron v photon trong thuyt thit b hp thu bc x c thxem nh mt m hnh ton hc ca Php gii Hoa nghim. Sng truyn tiv lai hay li vo qu kh din t khi nim thi gian qu kh v v lai nhcun trn trong giy pht tc thi hin ti, mt ci hin ti vn hnh bttuyt. Trong th gii phi thi gian , tng tc gia cc bin tng c bitxy ra tc thi, ngha l theo hai chiu ngc nhau v ng thi. Trong Hoanghim ngha hi bch mn ca Php Tng c nhng on ng ngha vi

khi nim vn hnh ca sng v ht nh trnh by trn: Ht bi gn v thgii mi phng xa. Nhng ht bi khng c th cht nn nhip nhpkhp mi phng. Ni cch khc, mi phng l tt c phng ca ht

bi. Do xa lun lun l gn ... Mi phng nhip thu trong mt htbi cho nn lun lun gn mc du xa, v ht bi ph cp khp miphng cho nn lun lun xa mc du gn.

8/3/2019

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