Natural Encoding of Information through Interacting Impulses

Transcription

1 Naural Encding f Infrmain hrugh Ineracing Impule Vladimir S Lerner ReiredN Affiliaed Marina Del Rey USA lernerv@gmailcm Abrac Sandard uni f infrmain Bi generae any naural prce hrugh dicree (ye-n) ineracin including ineracive macr impule in claical phyic and elemenary micr impule f quanum ineracin he elemenary ineracin f randm impule meaure (ye-n) prbabiliy even accrding Klmgrv -0 law fr randm prce Oberving randm prce under hee impule prbing prbabiliie lin Bayeian [(0-) r (-0)] prbabiliie which increae each perir crrelain and reduce cndiinal enrpy meaure up cuing hi enrpy by infrmain impule In a naural ineracive prce each impule ep-dwn acin cu he crrelain f he prce prir ineracive even hi cu he prce enrpy defined by i prbabiliy and memrize he cuing enrpy a infrmain hidden in he crrelain Memry freeze he infrmain impule in he cuing ff crrelain he ineracive impule reveal infrmain a phenmenn f ineracin he inerval f each ineracin hld quaniy f energy Each Bi i naurally exraced r eraed a he c f cuing hi energy and encding infrmain in he ineracing phyical ae (by he impule ep-up acin) he ineracing acin curve impule whe curvaure creae aymmery and allw encding qubi in memrized bi he impule equenial naural encding merge memry wih he ime f memrizing infrmain and cmpenae he cuing c by running ime inerval f encding he infrmain prce preerving he invarian impule cuing infrmain bind he inner impule reverible micrprce and he muliple impule irreverible macrprce in infrmain dynamic he encding prce unie he infrmain pah funcinal inegraing berver gemerical cellular infrmain rucure which cmpe raing helix f he equencing cell Bi hi naural encding aified Landauer principle and cmpenae fr he c f Maxwell Demn he energy f pecific ineracin limi he univeral cde lengh and deniy he cndiin and reul validae he cmpuer imulain muliple experimen in cding geneic infrmain experimenal encding by piing neurn quanum infrmain her Keywrd impule ineracin; cuing crrelain; curvaure eraure; merging memry wih naural encding; impule reverible micr and irreverible macr prcee; inegraing infrmain pah funcinal; newr; cellular helix rucure cmping Bi; univeral naural cde lengh; validain I HE PRINCIPLE OF NAURAL ENCODING INERACIVE INFORMAION IMPULSES IN AN OBSERVER S INFORMAION SRUCURE Regular cmpuain eiher run u f ime r run u f memry [] and cann cncurrenly encde infrmain during naural ineracin wih envirnmen lie DNA r elemenary qubi (Naural prce prduce Naure raher han he human being) In randm ineracin f a Marv diffuin prce ime crrelain bind he ineracive impule hi mdel he naural ineracive prce f bervain in which impule replicae he frequencie f an berver prceing he ineracin he enrpy inegral f he prce n rajecrie (EF) [2] cnvey he crrelain and he ime inerval f he crrelain which allw meauring enrpy by bh crrelain and he relaed ime inerval imulaneuly he diribued acin f a muli-dimeninal delafuncin n he EF mdel ineracive prce f elemenary infrmain impule where cuing he enrpy crrelain and he ime inerval cincide he dela-impule ep-dwn acin maximize he cuing enrpy hidden in he crrelain while he ep-up acin minimize he enrpy hu imping a max-min infrmain principle n he ineracin ha lead cuing enrpy f he invarian impule and he variain max-min exremal prblem (EP) fr he EF [3] Ineracin curve dela-impule bu EP independenly f ize cale preerve he invarian cuff enrpy he grwing deniy curve an emerging ½ ime uni f he impule ime inerval and iniiae a diplacemen wihin he impule n w pace uni-a cunerpar he curved ime A beginning f hi impule ar a raing cu f ep-dwn acin ha injec an exernal energy which i a finie rani wih he cnjugae enangled enrpie and end wih eraure f he cuing enrpy Wihin he ineracive impule evlve a micrprce f cnjugaed enrpie [4] where wih he raing raniin emerge a pace inerval hlding raniive acin

2 which aring n angle f rain π/4 iniiaed enanglemen f he cnjugaed enrpie he rain mvemen f finie acin ele a raniinal impule which finalize he enanglemen a angle π/2 frming an enrpy uni wih a vlume he raniinal impule hld ranien acin ppie he primary impule which inend generae he micrprce cnjugaed enanglemen invlved fr example in lef and righ rain ( ) he raniinal impule ineracing wih he ppie crrelaed enanglemen revere i n ± he ineracing mvemen alng he impule brder end wih cuing he prce crrelain accmpanied by penial eraure f he delivered energy Since he enrpy impule i virual raniin acin wihin hi impule i al virual and i ineracin wih he frming crrelaing enanglemen i reverible Such ineracin lgically erae each previuly direcinal raing enangle enrpy uni f enrpy vlume hi eraure emi minimal energy e l f quana ε = ω el = ε[exp( ε / Bθ) ] which lwer he energy qualiy cmpared wih he injeced energy ( i Plan cnan ω i frequency i Blzmann cnan and θ i ablue emperaure) he raniinal impule abrb hi emiin inide f he virual impule which lgically memrize he enangle uni maing heir mirrr cpy he curvaure f ineracing impule creae aymmery and allw encding qubi in memrized bi Such perain perfrm funcin f lgical Maxwell Demn [4] he enangle lgic i memrized emprary unil he raing ep-up acin ending he main impule mve ranfer he enangle enrpy vlume he ending epup acin ha ill and finally memrize he jin enangle qubi in he impule ending ae a he infrmain Bi he illing i irreverible eraure encding he Bi which require energy frm an exernal diipaive irreverible prce aifying he Landauer principle [7] and cmpenaing fr he c f Maxwell Demn Lgical energy e l in a claical-macrprce limi a 0 i ranfrmed real energy f he elemenary Bi: e r = θ B Cncluively he impule ep-dwn cu exracing each Bi hidden piin erae i a a c f he cuing B real ime inerval which encle he enrpy and energy f he naural ineracive prce he impule ep-up pping ae a he end f he impule ime inerval memrize (encde) he infrmain Bi f he impule fllwing nex ineracin Each impule encding merge i memry wih he ime f encding which minimize ha ime he invarian dicree infrmain uni which being cu ff frm he EF inegrae an infrmain pah funcinal (IPF) [3-4] he IPF inegrae he encded Bi in infrmain macrprce and EF predic he nex cuing crrelain he muli-impule perien Bi equenially and aumaically cnver enrpy infrmain hlding he cuff infrmain f he randm prce he Bi equence jin in riple a pimal macruni f he exremal minimax (EP) infrmain prce which naurally cperae Bi and riple during bervain while he IPF exremal analyically decribe hee perain generaing infrmain macrdynamic prce he inegral pace-ime infrmain dynamic generae and cperae he berving infrmain gemerical rucure he prce f bervain iniiae a pah frm prir uncerainy-enrpy perir infrmain-cerainy I reluin cnverin each perir infrmain and aumaic encding in a cperaive lgical rucure build Infrmain Oberver [5] hi prce ar wih grwing memry f he cuing prce crrelain Each crrelaed cu bind he impule cde equence and memrize bh he cde ime fllwed by i lengh becming a urce f lgical cmplexiy [6] Since every ineracin wih i elemenary dicree iner-acin define he andard uni f infrmain he Bi he impule cde i univeral I riginae in any naural prce generaed hrugh i ineracin Each prce dimeninal cu meaure he IPF finie Feller ernel infrmain which a infinie dimenin apprache he EF meaure rericing maximal infrmain f he Marv muli-dimeninal diffuin prce he variey f impule phyical ineracin unie hee impule infrmain cde which EF-IPF inegrae in he encding infrmain prce generally decribing he divere naural ineracive prcee via univeral cde lgic Each impule cmmn Bi infrmain encde hi univeral lgic in bh micr and macrprce he ineracive impule infrmain prce naurally cnnec i enrpy cu wih encding and memry I prgreively develp he encding infrmain rucure by memrizing he curren real ime wihin he prce a he c f he cuing ime-energy 2

3 he energy quaniy (pwer) f pecific ineracin limi he univeral cde lengh by final Bi infrmain deniy he energy qualiy evaluaed by he energy enrpy limi he prbabiliy and i enrpy when f he cde lengh ar he univeral cde lgic encde differen energy f ineracive impule ha limi he cde algrihm hi principle ubaniae he hereical bai fr differen naural encding in univeral cde f pecific lengh deniy II VERIFICAION AND DISCUSSION Accrding Landauer principle [7] any lgically irreverible manipulain wih infrmain uch a encding lead eraure he infrmain in a diipaive irreverible prce Eraure f infrmain Bi require pending enrpy S = B ln 2 Maxwell Demn [8] aciae he enrpy f Landauer principle wih he acquiiin f infrmain Bi equal he enrpy ineviable c fr he eraure Eraure f Bi require a lea wr W = θ ln 2 B a ablue emperaureθ which hereically limi he finie energy reurce r he ime f perfrming uch perain Benne [9] fund ha any cmpuain (encding) can be perfrmed uing nly reverible ep which in principle require n diipain and n pwer pending Hwever pecific reverible cmpuer need reprduce he map f inpu upu eraing everyhing ele ha require he energy c Infrmain cann be cpied wih perfec accuracy accrding n-clning principle [0]; berving he cpy diurb he riginal ae f he yem creaing he errr requiring eraure Bell [ 2] hw ha infrmain can be encded in nnlcal crrelain beween he differen par f a phyical yem which have ineraced and hen eparaed In Shr algrihm [] he prperie f he crrelain beween he inpu regier and upu regier f cmpuer funcin require huge memry re n hi nnlcal infrmain i hard decde he ime f perain grw faer han any pwer f ln( n ) Pracically uch cmpuain eiher run u f ime r run u f memry herefre infrmain define he memrized enrpy (uncerainy) cuing frm he crrelain hidden in bervain which prce he ineracin ha definiin cnnec he impule enrpy a he lcaliie f he phyical rigin f infrmain wih i encding memry and energy c he impule ineracive prce prgreively develp he encding infrmain perain memrizing in he prce curren real ime a c f he cuing ime energy Applying he Jarzyni equaliy (JE) f irreverible hermdynamic raniin [3] cnverin energy in infrmain and uing reul f i experimenal verificain [4] lead he JE frm F/ Bθ W/ Bθ e < e >= γ0 γ 2 where F i incremen f free energy needed prduce energy Wγ i parameer f he verificain which ue he experimenal cnrl; aγ = he JE aifie exacly hermdynamic prce aifying he JE fr all i ae equence hld he able irreverible hermdynamic Quaniy f infrmain I equivalen energy W i I w = Bθ I aing lgarihm frm bh ide f e F/ Bθ lead = γ F /b θi = ln γ /I Applying hi frmula cuing ime inervalδ wih influx f penial energy F = F δ cnnec i JE: Fδ( b Iδ) = ln γ / Iδ he equivalence f JE in bh frmula fr he infrmain raniin require I δ = [] where [] i a uni f infrmain per impule cmpenae fr he Maxwell Demn (DM) energy by he ime f ranmiin hu aify he DM infrmain prducing by each impule ime inerval huld be invarian hlding cnan uni (Bi Na) in I δ I cnfirm ha he impule minimax exremal principle (EP) aifie he JE fr impule infrmain raniin r vice vera each impule ime inerval enable encding invarian uni f infrmain (4) Or he EP fllw frm he JF in he phyical prce whe ineracive ime inerval i an equivalen f he impule infrmain cuing frm he crrelain carrying he energy he cuing crrelain ime inerval hld he infrmain equivalen f hi energy and any real ime inerval f ineracin bring he enrpy equivalen f energy F δ which cmpenae fr he DM while prducing infrmain during he ineracin In ineracive randm prce whe equence f cu aify he EP each impule encde he cuing 3

4 crrelain and all infrmain f he prce cuff crrelain encde he infrmain prce fulfilling he minimax law which i independen n ize f any impule he infrmain prce la perir cuing impule encde he prce al infrmain inegraed in i IPF Such an impule naural encding merge memry wih he ime f memrizing infrmain and cmpenae he cuing c by running ime inerval f encding he infrmain prce preerving he invarian cuing infrmain hld he invarian irreverible hermdynamic in i infrmain dynamic Each impule (Figb) ep-dwn acin ha negaive curvaure ( K e ) crrepnding aracin ep-up reacin ha piive curvaure ( + K e 3 ) crrepnding repulin he middle par f he impule having negaive curvaure Ke ranfer he aracing enrpy beween hee par In he prbing virual bervain he riing Baye perir prbabiliie increae realiy f ineracin ha bring energy When an exernal prce inerac wih he naural impule i injec energy capuring he enrpy f impule ending ep-up acin hi iner-acin generae nex impule epdwn reacin mdeling 0- bi (Figab) he ppie curved ineracin prvide a ime pace difference (a barrier) beween 0 and acin neceary fr creaing he Bi he ineracive impule ep-dwn ending ae memrize he Bi when he ineracive (exernal) prce prvide Landauer energy wih maximal prbabiliy cled he ep-up acin f naural prce curvaure + K e 3 encle penial enrpy e = Na which carrie enrpy ln 2 f he impule al enrpy Na and may rani i ineracing (exernal prce) he ineracing ep-dwn par f he exernal prce impule invarian enrpy Na ha penial enrpy ln 2 = e Acually hi ep-dwn ppie ineracing acin bring enrpy 025Na wih ani-ymmeric impac 0025Na which carrie he impule wide 005Na [27] wih he al 03Na e ha i equivalen hu during he impule ineracin he iniial energyenrpyw = Bθe change W = B θ e ince he ineracing par f he impule have ppie: piive and negaive curvaure accrdingly; he fir ne repule he ecnd arac he impule energie he exernal prce need minimal enrpy e 0 = ln 2 fr eraing he Bi which crrepnd Landauer energy W θ ln 2 = B If he ineracive exernal prce accep hi Bi by memrizing (hrugh eraure) i huld deliver he Landauer energy cmpenaing he difference f hee energie-enrpy: W W = W in balance frm Bθe+ Bθe= Bθln 2 Auming he ineracive prce upplie he energy W a mmen f appearance f he ineracing Bi i lead Bθ( ) = Bθ( ) ha bring he balance frm Bθ Bθ( ln 2) = Bθln 2 θ / θ = (2 ln 2 ) / = he ppie curved ani-ymmeric ineracin decreae he rai f abve emperaure n he amun f ln 2 / 0087 (2 ln 2 ) / = wih rai (2ln 2 ) / ln Naural impule wih maximal enrpy deniy e d = / = ineracing wih exernal curved impule ranfer minimal enrpy deniy e d = ln 2 / = Rai f hee deniie d = ed / e d = equal d = / ln 2 Here he impule ineracing curvaure encling hi enrpy deniy lwer he iniial energy and he relaed balanced emperaure in he abve rai Frm ha fllw Cndiin creaing a bi in ineracing curved impule he ppie curving impule in he ineracive raniin require eeping enrpy rai /ln2 2 he ineracing prce huld pe he Landauer energy by he mmen ending he ineracin 3 he ineracing impule huld hld invarian meaure [] f enrpy Na whe plgical meric preerve he impule curvaure ha fllw frm he impule max-min mini-max law under i epdwn-epup acin which generae invarian [] Na ime-pace meaure plgical meric π (/2circle) preerving he ppie curvaure Reul [5] prve ha phyical prce hlding invarian enrpy meaure fr each phae pace vlume ( ve 242 per prce dimenin in [4]) characerized by abve plgical invarian aifie Secnd hermdynamic Law Energy W ha deliver he exernal prce will erae he enrpy f bh aracing and repulive mvemen cvering energy f he bh mvemen which are ending a he impule pping ae he eraed impule al cuff enrpy i memrize a equivalen infrmain encding he impule Bi in he impule ending ae he ending lgic f naural ep-up acin capure i enrpy mving alng he acin piive curvaure rani ineracing ep-dwn acin negaive curvaure and by 4

5 vercming enrpy-infrmain gap [46] acquire he equal infrmain ha cmpenae fr he mvemen lgical c hu he aracive lgic f an invarian impule cnvering i enrpy infrmain wihin he impule perfrm funcin f lgical Demn Maxwell (DM) in he micrprce plgical raniiviy a he curving ineracin he impule f he exernal prce hld i Na raniive enrpy unil i ending curved par inerac creaing infrmain bi during he ineracin hereically when a cuing maximum f enrpy reache a minimum a he end f he naural impule he ineracin can ccur cnvering he enrpy infrmain by geing energy frm he exernal ineracive prce he invarian plgical raniiviy ha a duplicain pin (raniive bae) where ne dene frm change i cnjugaed frm during rhgnal raniin f hiing ime During he raniin he invarian hld i meaure (Figb) preerving i al energy while he deniie f hee energie are changing he raniive bae in plgical raniin eparae bh primary dene frm and i cnjugae dene frm while hi raniin urn he cnjugaed frm rhgnal A he raniin urning mmen a jump f he ime curvaure wiche a pace curvaure (Figa) wih raiing a pace wave [6] in a micrprce A a diincin frm radiinal DM which ue an energy difference in emperaure frm [8] hi apprach iniiae ha hrugh difference f curvaure f naurally creaed impule Frming raniinal impule wih enangled qubi lead pibiliy memrizing hem a a quanum bi ha require fir prvide he aymmery f he enangled qubi which ar he ani-ymmeric impac by he main impule ep-dwn acin ineracing wih ppie acin f aring raniinal impule hi primary aniymmeric impac = 005Na ar curving bh main and raniinal impule wih curvaure Ke encling 0025Na while he aring epup acin f he raniinal impule generae curvaure e = Na K e encling Difference ( )Na eimae enrpy meauring al aymmery f main impule Na = Sa he enangled qubi in he raniinal impule evaluae enrpy vlume Na which define he pending enrpy n ranfer minimal enangle phae vlume ve 242 he enrpy-infrmain gap [6] while primary impule impac bring minimal enrpy 005Na aring he enangled curved crrelain hu he crrelaed curved enanglemen can memrize ( )Na in he equivalen infrmain f w qubi ha i he infrmain demn c fr he enangled curved crrelain he middle par f he main impule e curvaure K e which encle enrpy Na Difference = Na add aymmery he aring raniinal enrpy while = 0005Na eimae he difference beween he final aymmery f he main impule and he ended aymmery f raniinal impule Wih aring aymmery enrpy f he curved raniinal impule Na and he ending enrpy f he raniinal impule 0005Na he difference =000655Na eimae aymmery f raniinal impule Memrizing hi aymmery need cmpenain wih a urce f equivalen energy I culd be upplied by ppie acin f he raniinal ep-dwn and main ep-up ineracing acin ending raniinal impule ha acin will creae he needed aymmery f raniinal impule Na and/r relaed aymmery f main impule Na hu Na = a i enrpy f aymmery f enrpy vlume ev = 00636Na f raniinal impule; wherea Na = S i enrpy f aymmery f main a impule which generae he ame enangled enrpy vlume ha ep-acin f he main impule ranfer fr ineracin wih he exernal impule Uing he aymmerical curvaure f raniinal impule ha hld he enangle vlume encling he enangle crrelain inead f direc evaluain hi crrelain allw memrizing infrmain w qubi in impule meaure Na ha evaluain i cled [26] bained differenly and cnfirmed experimenally During curved ineracin hi primary virual aymmery cmpenae he aymmerical curvaure f a real exernal impule and ha real aymmery i memrized hrugh he eraure by he upplied exernal Landauer energy 5

6 he ending acin f exernal impule creae claical bi wih prbabiliy 2 P = exp (00636 ) = Since he enanglemen in he raniinal impule creae enrpy vlume he penial memrizing pair f qubi ha he ame prbabiliy herefre bh memrizing claical bi and pair f qui ccur in prbabiliic prce wih high prbabiliy bu le han i happen and cmplee n alway he quein i hw memrize enrpy encled in he crrelaed enanglemen which naurally hld hi enrpy and herefre ha he ame prbabiliy? If raniinal impule creaed during ineracin ha uch high prbabiliy hen i curvaure hld he needed aymmery and i huld be preerved fr muliple encding wih he indenified difference f he lcain f bh enangled qubi Infrmain a he memrized qubi can be prduced hrugh ineracin which generae he qubi wihin a maerial-device (a cnducr-ranmier) ha preerve curvaure f he raniinal impule in a Blac Bx by analgy wih [46] A uch invarian ineracin he muliple cnneced cnducr memrize he qubi cde he needed memry f he raniinal curved impule encle averaged enrpy Na he ime inerval f he curved ineracin If he naural pace acin curve he exernal ineracive par he jin ineracive ime-pace curved acin meaure i ineracive impac Bu if he naural impule inernal curvaure Ke encling 0025Na preen nly by mmen befre an ineracin hen ineracing imepace inerval meaure he difference f hee inerval = Na Fr ha cae he exernal curved iner-acin arac he energy f naural ineracive acin unil exernal prce deliver energy W by mmen If N par i preen a and Ye par arie by hen he exernal impule pend ln 2 + ln 2 = Na n creaing and memrizing a bi If he naural prce hi he exernal prce having energy W he iner-acin f hi prce bring ha energy by mmen a he reacin which carrie W hld he bi he ame energy will erae he bi and memrize i accrding he balance relain he exernal impule pend Na n creaing and memrizing a bi while i ge ln 2 Na hlding ( ln 2) 03Na a i free infrmain he curved plgy f ineracing impule decreae he needed energy rai accrding he balance relain hu ime inerval creae he bi and perfrm he DM funcin Muliple ineracin generae a cde f he ineracing prce a he fllwing cndiin: Each impule hld an invarian prbabiliy enrpy meaure aifying he naural Bi cndiin 2 he impule ineracive prce which deliver uch cde mu i a par f a real phyical prce ha eep hi invarian enrpy-energy meaure equivalen meric π ha prce memrize bi and creae infrmain prce f muliple encded bi building prce infrmain dynamic rucure Fr example a waer cling a naural drp f h il in he fund rai f emperaure enable pending an exernal h energy n i chemical cmpnen encde her chemical rucure r he waer ineic energy will carry he acceping muliple drp bi a an ariing infrmain dynamic flw 3 Building he muliple Bi cde require increaing he impule infrmain deniy in hree ime wih each fllwing impule acing n he ineracing prce [6] Such phyical prce generaing he cde huld upply he needed energy fr hree bi free infrmain which equenially arac each her Each ineracive impule prduced a Bi huld fllw hree impulemeaure π ie frequency f ineracive impule huld be f=/3 π=~006 he inerval 3π give ppruniy jin hree bi impule in a riple a elemenary macr uni and cmba he nie and redundancie frm bh naural and exernal prcee m Muliplicain ma M n average curvaure Ke2 equal m he impule deniy Na/Bi=44 r M = 44 / K e 2; m K e2 = lead relaive ma M = he ppie curved ineracin lwer penial energy cmpared her ineracin fr generaing a bi he muliple curving ineracin creae plgical bi cde which equenially frm mving piral rucure Fig 2-3 herefre he curving ineracin dynamically encde bi in naural prce develping infrmain rucure Fig 2-4 f he ineracing infrmain prce 6

7 Hw find an invarian energy meaure which each bi encle aring he DM? Since i minimal energy i W = θ ln 2 i i pible find uch emperaure θ ha i equal invere value f B If he ineracing prce carrie hi emperaure hen i minimal energy hldw = ln 2 aθ = / B which i equal he bi ime-pace Na meaure f enrpy invarian 5 Le u evaluae θ a = ev / K and Kelvin B / emperaure K = 20 / 293 = C K equivalen 20 C 5 hen θ = /ev If we aume ha hi primary naural energy bring ev amun equivalen quana f ligh -9 e = 240eVnm nm=0 m hen we ge q C / m = / eq 0 m / eq θ Or each quan huld bring emperaure deniy C / m θ = which i reanably real Wih hiθ he ineracing impule will bring energy W = ln 2 creae i bi Fllwing he balance relain he exernal prce a hi B θ huld have emperaure C / m θ = θ = brugh by a quan hi energy hld an invarian impule meaure M = Na wih meric π r each uch impule ha enrpy deniy Na / π he ineracing impule bi ha minimal deniy energy a emperaureθ equivalen ln 2 / π = 022 he impule cuing acin f he grwing deniy curve an emerging ½ ime uni f he impule ime inerval meaure M while a fllwing raing curved ime-jump iniiae a diplacemen wihin he impule ppie raing Ye-N acin [4] ha riginae a pace hif quanified by he curved ime; he impule hld invarian prbabiliy ( r 0) fr w pace uni (a a cunerpar he curved ime Fig) he Figa hw frming a pace uni during he curved ime-jump accrding relain 2 πhl [ ]/4= /2 p[ τ] fr a pace crdinae/ime rai h/ p which lead he rai f he meaure fr he ime and pace uni: [ τ]/[ l] = π /2 wih elemenary pace curvaure equal invere radiu K = hl [] hu he jump queezed ime inerval riginae bh curvaure and pace crdinae When he w pace uni replace he curved ½ ime uni wihin he ame impule uch raniinal imepace impule preerve he impule prbabiliy meaure 2 / 2 = f he iniial ime impule M M ha allw encding he micrprce qubi in he raing raniinal impule n a middle p f he curved impule he curving impule ge frm (Figb) whe curvaure hld raniinal infrmain and cmplexiy he EF-IPF inegrae he prgreively curving impule gemery in he raing duble pace piral rajecrie lcaed n a cnic urface Each piral egmen repreen a hree-dimeninal exremal f he equain f he impule infrmain micrprce and he infrmain riple macruni f he muliple impule cperaing in macrprce [6] he implemenain f he minimax principle lead equenial aembling a manifld f he prce exremal in elemenary binary uni (duble) and hen in riple prducing a pecrum f cheren frequencie Manifld f he exremal egmen cperaing in he riple pimal rucure frm an infrmain newr (IN) wih a hierarchy f i nde (Fig 2) where he IN accumulaed infrmain i cnerved in invarian frm he lcal enrpy minima are encled hrugh equenial cperain f he IN nde creaing infrmain rucure which cndene he al minimal infrmain being prduced a he end f each egmen (including free infrmain) he infrmain ranfrmed frm each IN previu riple he fllwing ne (in he hierarchy) ha an increaing value becaue each fllwing riple encapulae and encle he al infrmain frm all previu riple he nde unique ime-pace lcain wihin he IN hierarchy deermine he value f infrmain encapulaed in hi nde A equence f he ucceively encled riple-nde repreened by dicree cnrl lgic creae he IN cde wih a hree digi frm each riple egmen and a frh frm he cnrl ha bind he egmen he cde erve a a virual cmmunicain language and an algrihm f minimal prgram deign he IN he pimal IN cde ha a duble piral (helix) riple gemerical rucure (DSS) imulaed n Fig3 which i equenially encled in he IN final nde allwing he recnrucin f bh he IN dynamic and plgy he IN aumaically reque fr i higher infrmain value prediced by he meaure f IN upper nde hierarchy he deniy f berving prce cuing crrelain generae an adapive feedbac infrmain frce a he IN free infrmain ha infrmain pace 7

8 curvaure define which aache each requeed infrmain he IN he IN infrmain gemery hld he nde binding funcin and an aymmery f riple rucure In he DSS infrmain gemery hee binding funcin are encded adaping he requeed exernal infrmain he Oberver elf-build he IN infrmain pace ime newr which hierarchically enfld muliple berving infrmain riple encding he Oberver lgical rucure in riple cde (Fig4) Hence he infrmain f berving prce mve and elf rganize he infrmain gemerical rucure creaing he Infrmain Oberver he naural encding infrmain during differen ineracive prcee f an berver wih envirnmen (a limiain [4]) explain elf-ariing infrmain Oberver he DSS pecific depend n he rucure f he EF funcin drif and diffuin in () and (2) Since variu ineracin carry energy differen quaniy and qualiy he impule univeral lgical cde enfld he paricular pwer f hee quaniie and qualiie When each impule cuff capure he pecific needed energy i qualiy deermine he curren cuing enrpy and he energy quaniy define he infrmain deniy f encding Bi herefre each ineracive prce encde he pecific infrmain cde equence ending wih maximal Bi infrmain deniy which limi he cde lengh he encding energy qualiy deermine he berving prce enrpy (9) hrugh he cndiinal prbabiliy when encding he impule infrmain ar P hi prbabiliy m i limied by minimal uncerainy meaure h α = /37 - he phyical rucural parameer f energy [7] which include he Plan cnan equivalen f energy and cun a ub- Plan p uncerain during he bervain f an ineracive Baye prbabiliy f he prbing impule (20)(Specifically wih prbabiliy N ha ub-p pibly i cvering a micrprce [6]) Afer enrpy vlume f he grwing prbe increae vercme he uncerain meaure he enrpy reache he edge f cerainy-realiy wih an abiliy f increaing abve prbabiliy up and revealing he prce infrmain Marv prce mdeling naural prce ineracin whe cuing equence aifie he EP may naurally encde hee ineracin in he relaed infrmain prce which he IPF encle in i Feller ernel he n -dimeninal prce cuff generae a finie infrmain meaure inegraed in he IPF whe infrmain apprache he EF meaure a n ha reric maximal infrmain f he Marv diffuin prce and he abiliy f encding which limi maximal infrmain deniy f he cde uni Cmmen Number M f he equal prbable pibiliie deermine Harley quaniy f infrmain H = ln M which fr he impule M = 2 hld H = ln 2 Na he impule infrmain meaured in Bi hld I = / ln 2ln M = bi he crrelain cuing by he impule bring infrmain 075Na frm which δ Su 00568Na deliver he impule cu Minimal phyical ime inerval limi ligh ime inerval ec δ τ defined by he ligh wavelengh 7 δlm 4 0 m hi eimae maximal impule infrmain deniy: I Na ln 2 / / he IPF inegral infrmain evaluae maximal deniy encling infrmain in he finie impule ime inerval which i he impule cuing ime inan delivering he crrelain hidden infrmain ln 2 All inegraed infrmain enfld he Feller ernel whe ime and energy evaluae reul [8] Enrpy inegral () n rajecrie f Marv diffuin prce cnvey bh crrelain (7) and ime inerval () (2) cvered by he prce crrelain in (8) Each cuff equenially cnver enrpy infrmain while cuing he EF freeze he prbabiliy f even f he prce he EF preen a penial infrmainal pah funcinal f he Marv prce unil he applied impule carrying he cuff cnribuin ranfrm i he IPF he muli-dimeninal dela-acin n he EF mulidimeninal inegran-addiive funcinal (2) f () allw analyical luin fr he impule encding and i repreenain by Furie erie Each IPF dimeninal cu meaure he finie Feller ernel infrmain which a infinie prce dimenin apprache he EF meaure rericing maximal infrmain f he Marv diffuin prce he final finie impule ha he IPF inegrae i Krnicer impule-dicree analg f Dirac delafuncin wih value 0 and (20) which cncenrae all berving infrmain in hi rucured Bi wih he eimaed maximal deniy Rai f he impule pace and ime uni h / = c define he impule linear peed c 8

9 Uing he invarian impule meaure hi peed deermine rai c 2 = M /( ) Mre Bi cncenraing in impule lead 0 and c which i limied by he peed f ligh he periing increae f infrmain deniy grw he linear peed f he naural encding which aciae wih a rie f he impule curvaure he curvaure encle he infrmain deniy and enfld he relaed infrmain ma [4] M m which ha cun abve he infrmain Oberver prgreively increae bh i linear peed and he peed f naural encding cmbined wih grwing curvaure f i infrmain gemery he IPF inegrae hi deniy in berver gemerical rucure (Fig4) whe raing peed grw wih increaing he linear peed Cnidering any curren infrmain berver wih peed c relaive a maximal a c > c lead a wider impule ime inerval f berver c fr geing he invarian infrmain cmpared ha fr berver c he IPF inegrae le al infrmain fr berver c if bh f hem ar he mvemen inananeuly Auming each berver al ime mvemen memrizing he naurally encding infrmain deermine i life pan implieha fr berver c i i le han fr he berver c which naurally encde mre infrmain and i deniy A c / c bh berver apprach he maximal encding he dicued apprach f a mving berver inrduce an infrmain verin f Einein hery f relaiviy he iniial Klmgrv prbabiliy diribuin f prbabiliy field and he fllwing EF () repreen all n - dimeninal Marvian mdel f he berving prce Prbabiliie f each prce dimenin are lcal fr each i randm enemble being a par f whle prce enemble All prce dimenin ar inanly bu wih differen lcal prbabiliie aciaed wih lcal randm frequencie Lcal prbabiliie f each randm enemble are ymmerical and Marv prce decribe Klmgrv equain fr direc and invere raniinal prbabiliie Each abrac aximaic Klmgrv prbabiliy predic prbabiliy meauremen in he experimen whe prbabiliy diribuin eed by even ccurrence relaive frequencie aify ymmery cndiin f he equal prbable even [9] In he prbabiliy field equence f randm even ω η clleced n independen erie frm Marv chain [9] wih muli-dimeninal prbabiliy diribuin he crrelaed value f n -dimeninal impule enrpie emerge a he prce prbabiliic nnlcal lgic creaed hrugh he berver prbe-bervain [6] which prceing and encding muliple nnlcal qubi and bi he micrprce emerge inide randm prce decribed by ub-marv diffuin prce [27] when he impule acin bring negaive enrpy meaure S * a = 2 wih relaive prbabiliy p a ± = exp( 2) = 0353 he ineracive jump iniiae he micrprce a reaching minimal relaive ime difference a he diplacemen edge [6] where he micrprce aifie nly muliplicaive prbabiliie a a quanum prce he micrprce ime in Quanum Mechanic i reverible unil ineracin meauremen affec quanum wave funcin Real (phyical) arrw f ime arie in naural macrprcee which average he muliple micrprcee wih heir reverible lcal ime inerval maing a empral hle in he arrw f a macrcpic ime Naural arrw f ime acend alng he muliple ineracin and peri by he prce grwing crrelain Bh virual and infrmain berver hld wn ime arrw: he virual - ymmeric empral he infrmain - aymmeric phyical which memrize he naural encding berver infrmain Wherea he al ime direcin hld each a nn-lcaliy f he quanum micrprce prvide reverible ime-pace hle while prceing he irreverible ime-pace impule admi lcaliie which acquire he energy f he randm field Since paricular bervain accee nly a par f he enire randm field bh bervain ime inerval and ime arrw diinguih hu he ime hld a dicree equence f impule carrying enrpy frm which emerge a pace in he equence: ineracin-crrelain ime-pace he real ime prcee memry encding he prce infrmain wih a perien lgical caualiy fr berver ime A ILLUSRAIONS (a) 9

10 (b) Fig (a) Illurain f rigin he impule pace crdinae meaure hl [] a curving ime crdinae meaure /2 p[ τ ] in raniinal mvemen Fig(b) Curving impule wih curvaure K f he impule ep-dwn par e curvaure K e f he cuing par curvaure K e2 f impule ranferred par and curvaure K f he final par cuing all impule enrpy e3 A virual impule (Figb lef) ar ep-dwn acin wih prbabiliy 0 f i penial cuing par; he impule middle par ha a raniinal impule wih raniive lgical 0-; he ep-up acin change i -0 hlding by he end ineracing par 0 which afer he iner-acive ep-dwn cu ranfrm he impule enrpy infrmain bi On Fig b righ he impule in Fig a lef aring frm inance wih prbabiliy 0 rani a inance 2 during ineracin he ineracing impule wih negaive curvaure which i ppie curvaure analgu ha a beginning he impule Figa) B COMPUER SIMULAIONS K e f hi impule ep-dwn acin + K e3 f ending he ep-up acin K e i Fig2 he IN infrmain gemerical rucure f hierarchy f he piral pace-ime dynamic f riple nde (r r2 r3 );{ α i} i a ranged ring f iniial eigenvalue cperaing in ( 2 3) lcain f -L ime pace { γ i} i parameer meauring rai f he IN nde paceime lcain Fig3 ime-pace ppie direcinal-cmplimenary cnjugaed rajecrie + SP and SP frming he piral lcaed n cnic urface rajecry n he piral bridge ± SPi bind he cnribuin f prce infrmain macr uni ± UPi hrugh he impule jin N-Ye acin which mdel a line f wiching ineracin (he middle line beween he piral) w ppie pace helixe and middle curve are n he righ Fig 4 Srucure f he cellular gemery frmed by he cell f he DSS riple cde wih a prin f he urface cell (-2-3) mdeling he pace frmain f Infrmain Oberver hi rucure gemery inegrae infrmain cnribuin imulaing in Fig 3 III BASIC MAHEMAICAL FORMALISM he inegral meaure f he berving prce rajecrie are frmalized by an Enrpy Funcinal (EF) which i expreed hrugh he regular and chaic cmpnen f Marv diffuin prce x [2]: u u [ ] /2 x { ( ) (2 ( )) ( ) } Sx = E a x bx a x d = x () B u ln[ p( ω)] P ( dω) = E [ln p( ω)] x x where a( x ) = ax ( u) i a drif funcin depending n cnrl u and b ( x ) i a diffuin funcin deermined by cvariain funcin in I Equain [20] he EF inegran i he prce addiive funcinal [2]: /2 ax ( ) (2 bx ( )) ax ( ) d ( x) axd ( ) () ϕ = + σ ξ (2) which decribe ranfrmain f he Marv prcee randm ime ravering he variu ecin f a rajecry; () 0

11 E i a cndiinal he iniial ae x ( x ) mahemaical expecain aen alng he x = x () rajecrie Righ ide f () i he EF equivalen frmula expreed via prbabiliy deniy p( ω ) f randm even ω inegraed wih he prbabiliy meaure Px ( dω ) alng he prce rajecrie x () B which are defined a e B Generally a randm prce (a a cninuu r dicree funcin x( ω ) f randm variable ω and ime ) decribe elemenary change f i prbabiliie frm ne a diribuin (a priri) Px ( dω ) anher diribuin (a p periry) ( ) p P dω in frm f heir ranfrmain [22]: x P ( dω) = (3) a x ( ω) p Px ( dω) Sequence f hi prbabiliie rai generalize divere frm f pecific funcinal relain repreened by a erie f differen ranfrmain he prbabiliy rai in he frm f naural lgarihm: a p ln p( ω) = ln Px ( dω) ( ln Px ( dω)) = a p = ap (4) decribe he difference f a priry a > 0 and a periri p > 0 randm enrpie which meaure uncerainy reuling frm he ranfrmain f prbabiliie fr he prce even aifying he enrpy' addiiviy A change bring a cerainy r infrmain if i uncerainy i remved by me equivalen eniy ap call infrmain iap : ap iap = 0 hu infrmain i delivered if ap = iap > 0 which require p < a and a piive lgarihmic meaure wih 0 < p( ω) < Cndiin f zer infrmain: i ap = 0 decribe a redundan change ranfrming a priri prbabiliy equal a periry prbabiliy r hi ranfrmain i idenical infrmainal undiinguihed he remval uncerainy a byi a : a ia 0 equivalen cerainy r infrmaini a abu enrpy a = bring an he lgarihmic meaure (4) f Marv diffuin prce prbabiliie apprximae he prbabiliy rai fr her randm prcee [23] Mahemaical expecain f randm prbabiliie and enrpie in (4): E x{ ln[ p( ω)]} = E x[ ap ] = Sap Iap 0 (5) deermine mean enrpy S a equivalen f ap nnrandm infrmain I ap f a randm urce Being averaged by he urce even hrugh a prbabiliy f muliple randm variable-ae r by he urce prcee (hrugh prbabiliie in ()-depending n wha i cnidered a prce r an even) bh (5) and () include Shannn frmula fr relaive enrpy-infrmain f he ae (even) Fr a cninuu randm variable (5) bring al an equivalen f Kullbac Leibler (KL) divergence meaure [24] expreed hrugh a nnymmerical lgarihmic diance beween he relaed enrpie in (5) (4) he KL meaure i cnneced bh Shannn cndiinal infrmain and Bayeian inference f eing a priri hyphei by he bervain f a priri-a periry prbabiliy diribuin A Marv diffuin prce wih i aiical inercnnecin f ae repreen he m adequae frmal mdel f he infrmain prce where funcinal () include Baye prbabiliy lin direcly aen alng he prce rajecrie wih given drif and diffuin he lin cncurrenly updae and inegrae each a priri fllwing a periry prbabiliy alng he prce he EF inegran in () (2) are parially bervable hrugh meauring nly cvariain funcin n he prce rajecrie Fr a ingle-dimeninal EF () wih drif funcin a = cx ( ) a given nnrandm funcin c= c () and diffuin σ = σ() he EF acquire frm cndiinal berving prce ς which ha he ame diffuin a he iniial prce bu he zer drif: ς = σ( v ξν) dξν Such cndiinal EF hld frmula [ / ς] = /2 [ () () σ ()] = σ x = S x E c x d (6) /2 [ c () () E [ x ()] d /2 c [2 b()] r d where fr he Marv diffuin prce he fllwing relain rue: b() = σ () = dr / d = r Ex [ x ()] = r (7) hee relain idenify EF () n berved Marv prce x = x () by meauring he cvariain (crrelain) funcin a applying piive funcin

12 c 2 () = u () and repreen he EF funcinal hrugh a regular inegral wih he inegran (6) equal he funcin: ( ) [2 ( )] A = r b = rr (8) he EF inegral (6) decribe raigh u () and relain (8): [ / ς ] = /2 u( ) rr d S x (9) he n -dimeninal funcinal inegran in (8) fllw direcly frm relaed n -dimeninal cvariain in (7) and diperin marix applying n -dimeninal funcin u () Crrelain funcin (7) n mall inerval () in frm: lead + ( ) r () = 2() bd= 2()() b A = b b = () [2()] 2()() () and funcin (0) A ( ) = b ( ) ( ) / b ( ) = ( ) () which bring inegral (9) frm S[ x / ς ] = / 2 u( ) ( ) d (2) If funcin u () cu ff he diffuin prce n ime inerval δ = ( ) i cu crrelain funcin (0) f funcin () which bring enrpy f cuing crrelain (2) Inegran (8) and () i a frm f funcinal (2) fr (6) he impule δ -cuff f acin u () evaluae he quaniy f infrmain which he funcinal EF cnceal when he crrelain beween he nn-cu prce ae had bund he cuff lead dilving he crrelain beween he prce cu-ff pin ling he funcinal cnnecin a hee dicree pin Applying dela-funcin c 2 ( τ) = δu( τ) inegral (2) deermine he cuing enrpy funcin: 0 < τ + / 4 ( τ ) τ = τ = Sx [ / ς ] (3) = τ = + + / 4 ( τ ) = τ + / 2 ( τ) = τ τ < τ < τ + aτ < τ < τ he cuff bring direc meaure f (): i maximum S[ x / ς] = τ = /2 ( τ ) /2 = Na a S[ x / ς ] /4 ( τ ) Na = = τ -n lef brder f inerval ( τ ) and i minimum + S[ x / ς] + = /4 ( τ ) Na = τ -ranferring n he inerval righ brder he umming cuing inerval: + = τ + Sx [ / ς] = /4 ( τ ) + /2 ( τ) + /4 ( τ ) = (4) = τ evaluae he invarian Na fracin f he cuff EF n inerval which he inerval encle In uch impule repreened hrugh ppie N-Ye (0-) acin each N acin carrie he cuing impule par wih a maximum f cuing enrpy while Ye acin fllwing he impule cuing par gain he maximal enrpy reducin he δ = ( ) impule cu f crrelain () r a mmen maximize hi enrpy par he crrelain maximal jump a fllwing curren mmen dilve muual crrelain r ( ) 0 ha maximize i derivain minimizing par r f he enrpy inegran (8) ha lead max-min principle f relainal enrpy beween impule par () ranferring prbabiliie (3) he max-min variain principle implie he invariance f funcinal (9) (2) under u () Sequenial cu ranfrm he enrpy cnribuin frm each maximum hrugh minimum he nex maximal infrmain cnribuin where each nex maximum decreae a he fllwing cuff mmen Each δ -cuff a hee pin le he amun f 05 Na minimizing curren inegral (2) he equain f max-min variain principle fr he EF decribe exremal rajecrie f infrmain prce which he pimal EF inegrae he cmplee equain f he micrprce and he EF exremal f macrprce are in [6] Infrmain pah funcinal (IPF) unie dicree infrmain cuff cnribuin Ix [ / ] ς aing alng δ n dimeninal Marv prce: = n ς = ς δ ς = n = Ix [ / ] lim Ix [ / ] Sx [ / ](5) where he IPF alng he cuing ime crrelain n pimal rajecry x in a limi deermine inegral 2

13 [ / ς ] x = / 8 [( ] = / 8 [ln () / ( )] I x r r r d r r r (6) Wherea relain (5) in he limi: = lim S[ x / ς ] ( ) (7) = equalize he EF wih i ime inerval which fllw frm he EF definiin hrugh addiive funcinal (2) he IPF i infrmain frm f Feynman pah funcinal (FPF) in quanum mechanic while EF inegrae enrpy (uncerainy) and limi infrmain (acual) cnribuin including he ime evluin in berving prce he FPF i quanum analg f acin principle in phyic and EF expree a prbabiliic caualiy f he acin principle while he cuff memrize a cerain infrmain caualiy inegraed in he IPF he encded Bi wihin ime inerval ha maximal hereical admiible deniy (3) cncenraing he IPF in Feller ernel during he abve minimal ime inerval and pace inerval he EF-IPF caualiy cnnec he infrmain deniy curvaure and cmplexiy Cndiinal Klmgrv prbabiliy PA ( i / B) = [ PA ( i) PB ( / Ai)]/ PB ( ) afer ubiuing an average prbabiliy n PB ( ) = PB ( / Ai) PA ( i) i= define Baye prbabiliy by averaging hi finie um r inegraing [9] Fr each i randm even Ai B alng he berving prce each cndiinal a priri prbabiliy PA ( i / B ) fllw cndiinal a periry prbabiliy PB ( / A i + ) Cndiinal enrpy n S[ A / B )] = E[ ln P( A / B ))] = [ ln P( A / B )] P( B ) (8) i i i i = average he cndiinal Klmgrv-Baye prbabiliie fr muliple even alng he berving prce Randm curren cndiinal enrpy i S i = lnp( Ai / B ) P( B ) (9) he experimenal prbabiliy meaure predic aximaic Klmgrv prbabiliy if he experimen aifie cndiin f ymmery f he equal prbable even in i aximaic prbabiliy [9] Cndiinal prbabiliy aifie Klmgrv -0 law [9] fr funcin f( x) ξ f ξ x infinie equence f independen randm variable: f( x) ξ ) 0 Pδ ( f( x) ξ ) = (20) 0 f( x) ξ ) < 0 hi prbabiliy meaure ha applied fr he impule prbing in an bervable randm prce which hld ppie Ye-N prbabiliie a he uni f prbabiliy impule ep-funcin [4] Lgical perain wih infrmain bi achieve a gal inegraing he dicree infrmain hidden in he cuing crrelain in infrmain rucure f Oberver encling he need infrmain newr wih he hierarchy f qualiy infrmain encded in riple cde he Oberver cgniive mechanim elf-aemble he berver IN hierarchy hrugh he aracing infrmain rain gverning cperain f each IN level and muliple IN Cgniin a each IN level cnrl he angle f he piral rain (Fig 3) in hee lcain [6] while each lcal feedbac can change i and renvae all hierarchy he enire rain cnrl uch angle a a highe level f he IN wih maximal cperaive qualiy he Oberver inelligence meaure maximal cperaive cmplexiy [28] which enfld maximal number f he need IN rucure IV EXPERIMENAL VERIFICAIONS AND APPLICAIONS Naural increae f crrelain demnrae experimenal reul [29] [30] Cding geneic infrmain reveal muliple experimen in [3] [32] Experimenal cding by piing neurn demnrae [33] Evluin f he geneic cde frm a randmne review [34] Mre uch evidence are cied in [4 6] ha uppr naural encding hrugh he cuing crrelain and phyically verifie reliabiliy f naural encding infrmain prce he impule cu-ff mehd wa pracically applied in differen lidificain prcee wih impule cnrl aumaic yem [35] hi mehd reveal me unidenified phenmena-uch a a cmpulive appearance cener f cryallizainindicar f generain f infrmain cde inegraed in he IPF during he impule meal exracin (wihdrawing) (In uch meallic ally he up-hill diffuin creaing deniy gradien i fen berved [5]) he frequency f he impule wihdrawing cmpue and regulae he deigned aumaic yem reach a maximum f he IPF infrmain indicar (he deailed experimenal daa f he indurial implemened yem are in [35] and [36]) 3

14 he aumaic cnrl regular in he impule frequency cuing mvemen wa implemened fr differen uperimping elecr-echnlgical prcee [37] ineracing naurally Example f he mehd applicain in cmmunicain bilgical and cgniive yem her are in [38] [39] and [40] he develped cmpuer prgram i in arxiv: Reinal Ganglin Cell are he Eye dicree impule recepr ineracing wih bervain and generaing infrmain which ranmiin inegrae [4] Encding hugh naural chemical reacin cnnecing chemical mlecule are in [42] Experimen [43] cnfirm encding cheren qubi in pinning elecrn lced in aracive hle pin Oher example are quanum lar d f emicnducing paricle uing fr he infrmain cding rerieving image and encding quanum infrmain [44-46] V CONCLUSION A SIGNIFICANCE OF FINDING ) he andard uni f infrmain Bi generae any naural prce hrugh dicree (ye-n) curved ineracin which include ineracive macr-impule in claical phyic and elemenary micr-impule f quanum ineracin 2) he impule naural iner-acin cu infrmain hidden in crrelain exracing each Bi hidden piin erae i a c f cuing real ime inerval and memrize encding infrmain in he ineracing phyical ae 3) he difference curvaure f naural ineracing impule allw equenially encding and merging memry wih ime f encding which minimize ha ime 4) he ineracive impule reveal infrmain be a phenmenn f ineracin 5) he naural encding include raniinal lgical memry which aifie Landauer principle and cmpenae fr he c f Maxwell Demn 6) he energy f a pecific ineracin limi he univeral cde lengh and deniy 7) he reluin cnverin f he impule cuing enrpy infrmain prce and aumaic encding in a cperaive rucure build rucure f Infrmain Oberver which aifie he infrmain frm f relaiviy B SEPS OF EMERGING HE INFORMAION OBSERVER ) Reducin he prce enrpy under prbing impule berving by Bayeian prbabiliie increae each perir crrelain; he grwing crrelain cnnec he berving prce Baye prbabiliie in prbabiliic caualiy 2) he impule cuff crrelain equenially cnver he cuing enrpy infrmain ha memrize he prbe lgic in Bi which naurally encde and paricipae in nex prbe-cnverin a a primary Infrmain Oberver which i buil wihu any a priry phyical law 3) he repeaed bervain acing by prbing impule n an bervable randm prce generae he infrmain micr-and macrlevel which gvern he impule naural minimax infrmain law 4) Elemenary impule ineracive prce creae ime pace inerval and emerging reverible ime pace micrprce wih cnjugaed enangled enrpy curvaure and lgical cmplexiy Sequenial ineracive cu inegrae he cuing infrmain in he infrmain macrprce wih irreverible ime cure 5)he memrized infrmain bind reverible micrprce wihin impule wih irreverible infrmain macrprce f he muliple impule he raniive gap eparae he micr-and macrprce n an edge f realiy 6) he lgical perain wih infrmain uni achieve a gal inegraing he dicree infrmain hidden in he cuing crrelain in infrmain rucure f he Oberver he relainal enrpy cnvey prbabiliic caualiy wih empral memry f crrelain while he cuff memrize cerain infrmain caualiy in he bjecive prbabiliy bervain he berver Bi- Paricipar hld gemery and lgic f i prehiry 7) he elf-rganizing infrmain riple i a macruni f elf-frming infrmain ime-pace cperaive diribued newr enable elf-caling elf-renvain and adapive elf-rganizain 8) Obervain ineracing via virual-imaginable r real impule creae a pah frm he prce uncerainy cerainy f real infrmain 9) he emerging elf-rganizain f berver infrmain elf-creae law f evluin dynamic ward inelligence where cgniin elf-rae he inegraing qualiy f infrmain 0) he apprach aring wih Klmgrv prbabiliie creae he phyical infrmain micr and macr prcee and he Oberver wihu Phyical paricle hery Infrmain begin in a pah frm uncerainy and wr ward cerainy REFERENCES [] PMShr Plynmial-ime algrihm fr prime facrizain and dicree lgarihm n a quanum cmpuer SIAM Cmpuingvl26 pp [2] VS Lerner he bundary value prblem and he Jenen inequaliy fr an enrpy funcinal f a Marv diffuin prce Jurnal f Mah Anal Appl vl353 () pp [3] VS Lerner Sluin he variain prblem fr infrmain pah funcinal f a cnrlled randm prce funcinal Jurnal f Mah Analyi and Applicain vl334 pp [4] VS Lerner he impule bervain f randm prce generae infrmain binding reverible micr and irreverible macr prcee in Oberver: regulariie limiain and cndiin f elf-creain arxiv: v2 206 [5] VS Lerner An berver infrmain dynamic: Acquiiin f infrmain and he rigin f he cgniive dynamic Jurnal Infrmain Science vl84 pp

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