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WAVELE TS, P ULSE ANALYSIS, AND THE TH IR D DER IVATIVE O F TIM E

M iguel Irad ier

Summ ar y
Wa vel et anal ysis allo ws ti me mult i-resolution, b es ides b eing an effi cient filt er fo r signal processing and denoi sing. Here we conjectur e the pos sibilit y that th e own mechani cal movement of bodies acts , th rough the th ree successive differ entia l o rders , and b y vi rtu e of th e resonan ces that these gen erat e, as a s electi ve filter of th e sta tisti cal ba ckground noi s e. Fro m this po ssibility, new consid eration s fo r biological infor mation, emergent syst ems and control ari se, a s w ell as for ti me analys is in gen eral . It follo ws a ph ilosophi cal dis cu ssion about the location of this anal ysis in the cont ext of gen eral kno wledge, including topics as f ractional cal culu s, nonholomi c syst ems, et c. Keyword s: Emerg ence, causalit y, evolution , t ransi ent motion, wavel et s, puls e analysi s, Samkhya , third d erivative, f ra ctional cal culu s, i mpul se, ti me.

B ackground
The s angui neous pulse reading has been t he mai n procedur e of diagnosis i n t he ancient medi ci nes . Fo r the mo der n sci entifi c st andards, thes e procedur es have been consider ed, at best , li ke qu alit ative and empiri cal appro aches, i f not pl ai nl y rej ected as grou ndles s. Neverthel ess , it i s cl ear that t he pul se is a per fectl y qu antifi abl e dynami cal si gnal, and, t her efore, we would have to be able to translat e the qu alit ati ve descriptions i n qu antitati ve and verifi abl e ter ms . Pul s e co nti nu es bei ng the mo re f ait hful global i ndicator of t he health and stat e of organis m, and if t he mo dern cli ni cal analysi s cannot gi ve r atio nal accou nt o f the informat io n that it cont ai ns, it woul d also mean t hat i t i s incapable to acco mmo dat e t he most element ar y facts of lif e. In pr eviou s wri tings [1 , 2] , I have t ried to r elate the cat egori es of t he Ayur veda and t he Samkhya phi loso phy to the pri nci pl es of Newto n's mechani cs. Basicall y, t he t hr ee humours , kapha , pitta and vata, and t he corr espo ndi ng and more general mo dalit ies, tamas, raja s and satt wa, can be res pectivel y su per pos ed wit h t hat defi ned t hrou gh t he f irst, s eco nd and t hir d Newto n's laws -inertia, the for ce or accel er atio n, and t he balance between actio n and r eact io n- wit h t he conditio n t hat al ways exi sts a relevant ti me between t he actio n and r eactio n ­ t hat i s to s ay, thes e ar e not st ri ctl y si mult aneous . Of cours e, all known real sys t ems r equir e a ti me o f reactio n; but bei ng t his ti me dif fer ent for any of them, it happens to be consi der ed acci dental or mi scell aneou s. Neverthel ess , thi s meanwhil e bet ween actio n and reactio n is i ndi spens abl e to at l east have a mi ni mum i ntuitio n of cause, beyond t he des cription of a general bal ance, whi ch is what t he o r dinar y equations of dynami cs est abli s h for stationar y s yst ems. The t hi r d pr i nci ple, i n t hi s co nt ext, i s equi val ent to a sensiti vit y t er m bet ween t he actio n and reactio n. Pri nci ples apart , t he for m of t he pul se, as t he do ctor per cei ves it , is an additio nal co mpo nent not des cri bed i n t he u su al o scillogr aphs, alt hou gh now t his is ful ly r ecor dabl e. We had t alked about that s pecifi c for m li ke an elusi ve quint ess ence diffi cult to gr as p; and in t hat r es pect , we s po ke ver y


vaguel y of pseu do - deri vati ves and t he measur ement of t he i mpu lse consi der ed li ke u nit o f for ce per time. In phys ics, t he t er m "i mpuls e" i s equi val ent to the int egr al of t he force wit h r es pect to t he time; nevertheless , in t his cont ext we wanted to introdu ce ot her consider atio ns wit h r es pect to t he s peci fic fo r m of t he pul se profil e, t he variat ions of t hickness in res po nse to t he pr essure, t he co ntr actil e impact of t he heart, et c. Of cour s e, we woul d l i ke to remain wit hi n purel y mechanical par ameters .

Th e third d erivat ive
The t hr ee pri nciples o f t he Ayur veda and Samkhya philoso phy can be mat ched wit h t he charact eristics of t he temporal s eri es and t heir graphs; but even so, we r emai n without havi ng a dir ect and i ntuitive underst andi ng of what t he t hir d element, the sensit i vity o f t he s ys tem, could mean. The s i mpl est possi bl e answer woul d be t he t hir d deri vati ve wit h res pect to ti me, t hat i s to say, t he r at e of change of t he fo rce or acceleration: d3s / dt3 = d2 v/ dt2 = da/ dt The fir st s pecul atio n o n t he po ssible r el evance of t hird deri vati ve i n mechani cs i s as l at e as 1962. W. O. Davi s et al [3] co nj ectured on t heir pos si bl e appli catio ns to sys t ems wit h tr ans ient states, f ar from the ideal, st atio nar y st at e ­i mpacts, t he entr ance of a ro cket i n t he at mos pher e, and other phenomena wit h viol ent r at es of change. But, i n fact , t he disco nti nuou s appli catio n of for ces is the no r m, and not t he exceptio n, for most of t he obs er vabl e phenomena. The physi cists and t he engi neers have pr ef er red to ignor e t he perti nence of the t hir d derivative or t he co ntrol o f t he accel er atio n, co nsi deri ng it as t he o pt io n of t he oper ato r ­t hi s i s , li ke an exter nal co mpo nent of t he s ystem. Davis approach can be applied no t onl y to sudden i mpacts and exceptio nal t ransi ent co nditions, but, more gener all y, to dri ven os cill ato rs wit h a perio d of appli catio n of t he for ce mi nor than t he criti cal t i me of the syst em. The si gnal of t he pulse i nvolves i mpacts i nevit abl y, havi ng pau ses as mu ch aft er sys tole as aft er di astole. Ther efor e st arti ng co nditions of t he si gnal and, pr esu mabl y, a criti cal time or ti mes ; but appeari ng her e co ntro l, ho meo st as is and s tabil it y co nditions i mplicitl y, nobo dy will say i n t his cas e t hat t he t hi rd deri vati ve values ref ers to so met hi ng exter nal to t he s yst em. B esi des, and i n a dif fer ent domi nio n, t he criti cal time of actio n i s al so recogni zed implicitl y i n hydro dynami cs and aerodynamics for Mach o r Reynol ds nu mbers. In cert ain conditio ns, t he appli catio n o f the t hir d derivati ve off ers quite u nexpect ed solutio ns . Since "Davi s mechanics " does not admit t he simultaneou s action and reactio n ­i n the same way t hat Samkhya does n't - , o r, s aid anot her way, the mo ment of a r eal o bj ect cannot change instantaneousl y and i ndependentl y of t he magnitude o f t he appl ied for ce, t he exi stence of a C riti cal Actio n Ti me (CAT) is to be o bs er ved for each s ys tem. Admi tti ng a time del ay f acto r, o ne coul d int er pret t hat t he co ns er vation of t he ener gy du ri ng t hat l aps e o beys to a net cont ributio n of t he enviro nment of t he sys t em ­i n or der to co ns er ve t hat ener gy mo mentari l y, i ndeed. All t hi s sounds too exotic, if we do n't repai r i n the fact that we ar e tryi ng to make co mmensur abl e t wo ver y dif fer ent t ypes of des cr i ptio n. In parallel, for t he lo gic of t he Samkhya or t he Ayur veda it i s r equired that t he t hir d princi pl e, satt wa or vata, -in f act, t he fi rst one of t he t hree i n its o wn o r der of causality, it i s t he most dir ect expr essio n of the i nt er action wit h t he medium or environment . That i s to say, bot h lo gics agree outstandi ngly, and they do it si nce t hey do not loo k fo r t he i deal ization of the event s t hat they tr y to des cri be, and even t hough t heir descri ptio n can be lar gel y i nco mpl ete. In additio n, t he sys tems wi t h t ransi ent st at es and a critical ti me del ay for the action ordinaril y generat e reso nances ­t ransfo r matio ns bet ween ki netic and pot enti al ener gy, which ar e amplif ied i n as mu ch t he deno minator t ends to zero . Even being quit e s mall , this co mpo nent never vanis hes absolutel y, which allo ws to explo re a mu ch more ampl e s pectru m of r el atio ns i n ter ms of series and r eso nances i n an undefi ned medium. That i s to s ay, it allo ws anot her t ype of r elations bet ween pheno mena of ver y di ffer ent o r der. The new s et of reso nances appeari ng i n t he Davi s


equatio ns are det er mi ned by t he r elatio ns between t he fi rst and t hi r d deri vati ve, and t hei r dampi ng, by the coeffi ci ent o f t he s econd, equi val ent to t he mas s. Po ssibl e hyper boli c solutio ns al so may have i mpo rtance, but t hey woul d take to u s too f ar now.

Arthur Young' s Theory of Pro cess
The follo wi ng who spo ke of t he i mport ance of t hir d deri vati ve was t he American engineer and t hi nker Art hu r You ng. You ng pro pos ed a hi ghl y si mplified scheme, but wit h s ense, i n whi ch the po sitio n, t he s peed, the acceler atio n and the co nt rol -the deri vati ves of zero, fir st , second and thi rd or der - co nfo r med a ci rcl e map of fou r mo ment s, "u nco ns cious action", "u ncons cious r eactio n", "co ns ciou s reactio n" and "cons ciou s actio n". This s cheme also i s ver y si mi lar to the one of Samkhya, s ince for thi s philoso phy t he mo vement and t he mi nd woul d happen i n t he t hr ee l ast ones , bei ng t he firs t or t he positio n an i ndi s pens abl e as sumptio n, about whi ch, li ke about co ns cious nes s, not hing wit h sense can be s aid ­ bei ng o n t he co ntr ar y t he co ndition o f t he r est . Young belo nged to that li ne of maveri ck t hi nkers and gener alist li ke Bu ckmi nst er Fuller, who co nsi ders t he pres ent s pecial ized s ciences as co mpl et el y i ncapabl e to gi ve accou nt of t he mo st fundament al and basi c fact s o f l if e. You ng argu ed reaso nabl y enou gh t hat without t he i nclu sion of a thi rd deri vati ve ­t he co ntrol -, we coul d not explai n anyt hi ng of our dail y lif e, li ke dri vi ng a car, for exampl e. Thi s i s quite clear, but, being alr eady i n t he s cope of t he exter nal acti vit y, t hey remai n so mewhat dis soci ated of t he i nt er nal dynamic process es . But do "i nt er nal dynamic process es exist? B y s elf-definition, dynami cs is t he science t hat s tu dies ext er nal vari atio ns, r easo n why t he qu estion can be revers ed. Without doubt, Young would have fi nd bett er argu ment s i n the dynami c analys is of t he pul s e, alt hou gh at his ti me di d not exi st tools to r egist er it s mo re s pecif ic for m fait hfull y. In fact, Samkhya, bei ng t he philosophy of Yo ga, i s not hi ng but the mo st basi c description o f t he co ntrol mechanis ms. W hat You ng descri bes i s a process t hat ­as i n t he sangu i neous pul s e, or any evolutio nar y moti f of Samkhya- is su bject of sedi mentation. That is to s ay, a cons ciou s actio n wit h t he ti me happens to be cons cious r eact io n, and even uncons ciou s reactio n i n many cases. Samkhya descri bes thi s l i ke t he t ransfo rmatio n of t he guna s, t he t hr ee basi c mo dal iti es or pri nci ples we deal wit h. And alt hou gh t hes e transfo r mations seem to have a conti nuous and i nfi nit e s pectrum, they follow one anot her accor di ng to a logi c sequence and pro portio nalit y. Young hi mself was perf ectl y awar e that , even being the thi r d derivative i mport ant, whi ch one o bt ai ns wit h hi gher or der diff er enti al t er ms ar e not but subs equent di vi sions of ti me mo r e geometri co, r emai ning t he r eal time of t he event s u ndefi ned. He appealed for t hat r easo n to t he i dea of dif ferent ti mes nested o ne withi n another, an idea that i n a more t echnical manner aros e about t hat ver y years and became i ncreasi ngly popul ar l at er wit h t he introdu ctio n of fract al patt er ns and cor relatio ns o n di ff er ent s cales in t he anal ys is of ti me seri es . This t ype o f correl atio ns wi th selfsi mil ar ti me structure appears, for exampl e, in t he gr aphs of the EC G; bu t t he mo der n hi sto gr ams usual l y stu dy long i nt er val s, wit h ti me r ecor ds about o ne hour , wher eas a t ypical traditio nal pul s e readi ng takes a mi nut e. Wi t hout doubt , self- si milar it y can be fou nd i n t hes e mor e reduced i nter vals , alt hou gh it is not necessar y to t hi nk about it s i nf init esi mal charact er , as many have come, inevit abl y, to s peculate. The successi ve applicatio n of t hree dif f erential or ders l eads natu rall y to qu est io n if their values gi ve us so me clu es o n t hese dif ferent ti me s cal es or si mil arit y o r ders .


Wavelet s and new te chn iques o f t ime se rie s an alysis
This leads us to mentio n t he new modaliti es of anal ysi s of t empo ral seri es t hat have emer ged si nce t he arri val o f t he co mput ers . It i s kno wn t hat until t he last decades t he har mo nic o r Fourier analys is was t he o nl y refer ence in t his domi nio n. The harmo ni c anal ysi s onl y yi elds t he s pect ru m of f requ enci es by means of su m of motio nl ess si ne waves ; that is to s ay, it is i ndependent of time and glo bal wit h res pect to t he i nter val i n qu estio n. Ther efor e, it has great rel evance fo r waves wi t h si mpl e dependenci es, li ke li ght and sou nd i n ho mo genous medi a, and it s rel evance decreas e i n as mu ch t he per io dic behaviour of t he syst em pres ents co mpl ex dependenci es and bo nds, as well as char acteri sti c si ngul arities. In or der to co ver t his void new mo daliti es of analys i s have emer ged, li ke wavel ets anal ys is wit h ti me mul ti-r esolution; this one in tur ns admit s many dif ferent crit er ia of electio n, dependi ng on ho w t he mot her wavel et is defi ned. Indeed, one of t he most i nt eresti ng aspects of wavel et analys is is that it allo ws to gr asp disco nt i nuiti es i n hi gher order derivati ves , besides to fit well t he parti cul ar featur es of the seri es ( si nce the di ff erent derivati ves admit di ff er ent signs si mult aneousl y, and t he s peed can i ncr eas e whil e t he accel er atio n di mi ni shes , et cet era, t hi s pro vides additio nal crit eri a for resolution) . That i s to s ay, it allows a lo cal anal ysis wit h a gr eat ver s atilit y i n t he resolut ion. To day, wavelet anal ysi s i s routinel y appli ed i n t he mor e var ied fiel ds, from dat a co mpr essio n to seis mology or parti al diff er enti al equations , and bei ng medici ne and physiologi cal si gnals o ne of their main fro nts ; ot herwi se, t he fi el d is i n co ntinuou s and acceler at ed expansio n.


W avel et anal ys is, by means of s el ectio n o f cri teria, take co ntact wit h s elf-si mil ar fractal s and it erat i ve anal ys is, t hrou gh other t echni ques of fu nctional appro xi matio n, as r adi al basis functio ns, et ceter a. Alt hou gh we don't want to ent er i n the ars enal of moder n tool s, an appro priate est imatio n of t he magnitu de and r ank of i nfor matio n t hat can render a si gnal li ke the one of t he pul se i s needed. The anal ysi s o f wavel ets also allo ws a connection wit h t he p-adi c anal ys is and ultrametri c crit er ia in gener al: t hes e are import ant whenever the po ssibility o f hi erarchi c st ructur e wit h layer s or level s o f informatio n aris es, and bei ng t hi s case of t he pul se acco r ding to t he under st anding of t he t r aditional medi ci ne. In t he stu dy o f biolo gi cal si gnal s it i s cru ci al to under st and what i s dependent and what independent of t he t empor al and space s cales. Ot her wise, wavel ets anal ysi s i s its elf an opti mu m i nfor matio n filter , tending to redu ce t he di sti nct and r el evant i nfor matio n to it s mi ni mu m di mensio ns . R eci procally, it is also an o pti mum filter for denoi sing, t hat is to s ay, to f ilt er t he ir rel evant part of t he si gnal . Therefor e, it is alr eady gi ving a clos e esti mat e on t he disti nct and char act eristi c amount of i nfo r mation ­ "hi ghest per so nalized i nfor mat io n", as modern medi ci ne cl ai ms i n its pu bli cit y- t hat t he puls e si gnal pro du ces . Thi s des erves to be noti ced, becaus e mo der n medici ne i s pro ne to co nclu de t hat t he pul se is a too poo r si gnal in t er ms of i nfo r matio n, and ther efo re i nef fecti ve for the di agno sis, wher eas , on the co ntrar y, t he pr actitioners of t he tr aditio nal medici ne co mpl ain and stru ggl e wit h a si gnal co nsi dered in practi ce too rich and subtl e i n it s conti nuous var iabi lit y for t he ju dgment, even pro vi ded t hat a suf ficient sensiti vit y has been develo ped. It i s so obvious t hat t he mo der n medi ci ne has u nder esti mat ed the volu me of pos si bl e i nfo r mation of t his si gnal , as it has no t make t he effort to extract it and to stand at it s pro per complexity l evel. Si mpl e nu mbers can t ell u s co nclu si vel y the amou nt o f po ss ible stat es i nvo l ved and t he corr elati ve capacity of r esolut io n fo r t he diagnosi s ­ whenever we grant to t hat i nfo r mation a st ructu r e of glo bal char act er, and not t he mere r ank of a si gnal about t he car dio- cir cul ator y apparatus o nl y.

Discu ssion
Alt hou gh for t he moder n medi cine it is al most i mpo ssi ble to co ncei ve t hat t he si gnal of t he pul se can cont ain t he mai n r el evant informatio n for t he diagno sis, we do n't have many dou bt s about it. Co mmo n s ense itsel f i s i n f avour of t hi s aff ir mation, if we fo r get for a mo ment all the theoreti cal devi ces t hat we have, either to explai n t he i nfor mation of t he pul se, or to explai n the or ganis m i n chemi cal or r eductionis t t er ms. By commo n sense we u nder stand not hi ng els e t han t he po stul at e, if not a s i mpl e f act, of t he u nit y of t he or gani s m. Therefor e, we will not i nsist o n th e po ssibilit y of a sat isf actor ily deep di agno sis of the state of t he healt h by means of t he puls e, but rat her i n it s statute and it s mor e el ement ar y i nter pr et ation. The t hr ee pri nci ples o f t he Samkhya and t he Ayur veda are to t he descri ptio n of somethi ng ali ve ju st li ke t he t hree pri nci pl es of Newto n ar e to clas sical mechanics ; t hat is to s ay, t hey are t he mo st si mpl e and irr edu cibl e i n its o wn l evel. W hen t he Chi nes e medi ci ne tal k about yin and yang, also as su mes a vacuu m or mean li ke a t hir d el ement that r el ates bo t h. Ho wever , ou r endorsement of these t hr ee pr i nci ples wit h t he t hr ee deri vati ves i s a pu re s pecul atio n, and per haps i t does not have the s mall er just ifi catio n. W hat i s to be kno wn is if we can descri be t he t hr ee pri ncipl es of the Samkhya ­ whi ch literall y means analysi s, aft er al l- i n a d edu cti ve way i n r el ation to a dynami c s ys tem li ke the pul s e, or if we can o nl y r each an indu cti ve, heurist ic and appro xi mat e quantifi catio n o f them. Lacki ng experi ment al studi es i n this dir ectio n, t he qu estion is not t ri vial at all. Never t hel ess , t he s ame philo so phy of t he Samkhya des cri bes t he t hr ee guna s li ke i nter dependent agent s , whi ch never can be separated. But , per haps t he t hr ee pri nci pl es of mechani cs can be s epar at ed? Nevertheles s, we are s peaki ng abou t ver y different t hings. The t hree pri ncipl es of mechanics are axio matic i n natu re and independent of any measu rement, and t he t hree pri nci pl es of Samkhya ar e al ready i nclu ded i n t he empiri cal and measur able dat a. Samkhya, i n additio n, t alk about co ncr et e causality, and mechanics


not ; Samkhya defi nes t he ti me f luctuations wi t hin and from the i nt er ior of a sys tem, and mechani cs onl y defi nes u nivo cal l y metri c of an exter nal s pace. Fi nall y, Physi cs is an activit y about predict io n of events ext er nal wit h res pect to t he o bser ver , and Samkhya, being Yo ga philosophy, takes car e of the i nternal co ntrol of t he pres ent by t he o wn su bj ect. So gr eat differ ence and so gr eat parall eli s m is what makes f asci nati ng t hi s fiel d of stu dy, stil l to begi n wit h. And al thou gh t he cli nical anal ysi s of the pul se i s wi del y independent of t he fundamental physics, is wort h t he trou bl e to make one sho rt ref lection o n t he pri nci pl es or fou ndatio ns of P hys i cs. On t he ot her hand, it i s evi dent t hat t he mai n int er est o f Phys ics for t he human cu rios ity i s ju st what f ail s to expl ai n, namely, life and subj ect. A ver y stri king featur e of XX century phys ics i s its s pecifi c dualis m. In eight een centur y XI X, wit h t he stu dy o f el ectro magnetis m and i nclu ding a Maxwell and Lor entz, a new l evel for t he qu est io n arose about t he r el atio n bet ween i ner tial and accel erat ed s yst ems, char ges and fi el ds , throu gh an underl yi ng medium or et her . Indeed, it was at st ake t he r edefi nition o f t he t hr ee pri nci ples of mechanics, o n whos e general vali dit y nobo dy dou bted. The ado ptio n of r elati vit y indeed su ppos ed t he r efus al to t hat po ss ible redefi nit io n, ado pt i ng co nventio ns of measur ement for statio nar y clo cks t hat made any co nsi deratio n about the mediu m or its variabilit y u nnecessar y. That is to s ay, t he "fourt h pri nci ple" of Newtonian mechani cs, no ne other than t he absolut e ti me or glo bal synchro ni zatio n was co nsoli dated and rei nfor ced. A mo dest gai n in t he pr edi cti ve fr ame was obt ai ned, at t he co st o f igno ri ng ot her multi ple pos si bl e variable co nditio ns . Bot h extremes co nfor ms t he pol es of t he phys i cs acti vi ty; but t he i ncr ease of t he nu mber of variables i ntri nsicall y co mpromi s e t he vi abilit y o f t he pr edi ctions . Nevert hel es s, t he probl ematic of t he mediu m emer ge one ti me and anot her i n t he diff er ent l evels of fu ndamental Phys ics , eit her to s pecif y what t he inerti a is , o r for t he mas s, or to det ermi ne t he ener gy o f t he vacuum, et cet er a. The s ame pro blem ari ses when we as ked ours elves, i n t he most i ngenuous and l egiti mat e manner, what makes a parti cl e to "kno w" t hat cannot go f ast er than li ght ; as well as when we as k fo r t he o ri gi n and reason of t he so call ed fu ndament al co nst ant s. Then and not before ari se, i n a natur al manner, questions rel at ed to control . What s ho ws to us another way, t hat t he dual ist s cheme o f pr esent phys ics is incapable to descri be t rue cau s es, i n any i ntuiti ve sens e t hat we can unders tand. We cannot expect fro m t his s cheme somet hi ng t hat it cannot give; and pres ent phys ics , by its stru ctur e, cannot yi el d not hi ng els e t han dispersed masses mo ving randoml y i n ti me by for ces equ ally o paque ­just l ike in the days o f Lu cret ius . Its outli ne do es not gi ve for more, and we fill up t he r est wit h our f ant asy. Be worth t his to s ee t hat t he i nt roductio n of a t hi rd der i vati ve not neces s aril y is a tr i vial su bject ; i n fact, it tu rns to i ntro duce in other level t he qu estions r elated to t he mean and t he fr ame o f ref erence. Onl y t hat i n most of t he o ccasio ns, and s peci all y comi ng f ro m t he pers pective of phys ics , coul d s eem dou bt ful and little i ntu itive its neces sit y, u nli ke t he "ingenuous " qu estio ns about t he mediu m and t he refer ence. In t he t empo ral anal ysi s we have bett er fortu ne, becaus e always i s allowed t he r ef er ence to t he si ne or har mo ni c waves, i ndependent of the mo vement , alt hough so meti mes decompos e it exemplaril y, as it happens in t he case o f sound. The wave of t he pulse and its sound ar e ver y di ffer ent t hings , as it i s the spectro gram of t he series of t he mechani cal wave and t he s pect ro gr am t hat its sou nd pro du ces . We tend to i magi ne t he thi rd deri vati ve li ke pur e brut e for ce or impact, alt hou gh i n f act what i ndicat es i s onl y with what rapidit y i s t he for ce appli ed, it s degr ee o f avail abilit y i n t empo ral t er ms: agai n, t he most r ealist ic for m to co ncei ve t he co ntrol, i n any of t he poss i ble l evels. Neverthel es s, it happens t hat t his co mpo nent s eems barel y r el evant for t he ti me t he beat has arri ved muffl ed to t he wri st, havi ng lo st the great er part of t he prof ile of the impact of t he heart. Never t heless , a great part of t he sou nd t hat can be per cei ved with a mi cro pho ne co mes fro m t hat co ntr actil e impact , pro pagated i n addition faster t han bloo d i ts elf . Many ques tions ari se o n the rel atio ns bet ween t he acousti c waves and t he pro pagatio n of the sou nd with t he compres sion wave as it i s per cei ved wit h t he f i ngerti ps . Evi dent ly, t he s ensori al capacit y o f a vadya or docto r t hat r eads t he pul se is not out of hu man or di nar y s cope, bu t it i s hi ghly amplifi ed by the trai ning. In addition to t hat s enso rial capacit y, a gr eater t rai ning for t he i nf er ence and t he ju dgment i s still r equir ed. In spite of all t his , it is not eas y to state a defined li mit to t he s enso ri al capaci ty when s ynest hes y pro ces s es t ake pl ace, as


in t he cas e of t he vadya ; i n par ticul ar, a synes t hes y or asso ci atio n of the sens es of heari ng and touch. Then, it seems i ndi s pens abl e an expl anation of t he r el atio ns bet ween t he aspects pro perl y acousti c and t hose mor e mechani cal of t he pres sur e wave; amo ng ot her t hi ngs, becau se it i s ver y impo rtant for t he docto r to t ake a readi ng at di ff er ent l evel s of pr essure. But al so becaus e we ru n the ris k of underestimating the mo dul ator role of t he sound i n t he or gani c, from t he i ndis cer nibl e backgrou nd noi se to t he mo re locat ed r eso nances. Fortu nat el y, wavel et anal ysi s has as t he li mit cas e Fourier analys is and t herefo re i nclu des it; and si mu ltaneou sl y, wavel et anal ysi s i s a fine filt er for denois i ng; t her efo r e, t her e are not great er i mpediments to gras p the mai n t heme of t hes e rel atio ns, still deepl y mysterious . It i s not necess ary to r emember t he fundamental rol e of t he sou nd i n t he cl assi c Indian conceptio n, o r t hat withi n it s pace its elf i s not but the medium in whi ch t he sou nd pro pagat es . In anyo ne of t he appro aches we can tr y to t ransl at e t he t hr ee pr i nci ples o f t he Samkhya and the Ayur veda to qu antit ati ve ter ms , whether deduct i ve or i nducti ve, a mean bet ween action and reactio n must t ake pl ace ­ becau se is i n t hat mean t hat lif e takes sens e, as each s enti ent being can feel it. It is dif ficu lt to t hi nk t hat t hi s mean is r educed to a mer e r atio , l i ke fo r exampl e, t he o ne t hat can exist bet ween t he s ysto le and di astole i nter val s, even t hough t his r atio co nt ri but es proper data; evi dently, and by t he o wn irreduci ble defi ni tio n of guna s, t her e mu st be mu ch mor e t han thi s. Ot her wise, an etiologi cal or cau sal mo nitori ng wou l d not be po ssi bl e, nor woul d exi st any po ssi bilit y for a hierar chi c stru ctur e of t he i nfor mat ion avail able in t he pul se. The i nt er pr etat ion of the gunas i n t er ms of t he t hree deri vati ves coul d be erro neou s, but it allo ws explor e cert ain po ssi biliti es, li ke t he r el atio n of t he reso nances wit h the stat ionar y as pect of t he sou nd s pectrum of these s ame waves , i n an att empt to clo s e t he ci rcle of t he fou r po ssi ble as pects. Of cour se, we can co nt empl at e also t he s peed and the acceler atio n wit h r es pect to t hat stationar y backgrou nd, et cet er a. It happens t hat the def i nitio n o f the gunas cannot be mo re element ar y; i n f act, not even so me precise defi nitio n exist, but a si mple qualit ati ve characteri zatio n, and even this one is u su all y su ppos ed i n t he cl assi c texts. P reci s el y becaus e t hey ar e so element ary, we can hope to fit t hem i n a perfectly natur al way i n a dedu cti ve descri ptio n, or ot herwi se t hey ar e not dedu ctibl e at all and t hen we onl y can i nf er t hem indirectl y. A half way defi nitio n do es not s eem pro babl e. Wit hout a dou bt, and even assu ming we ar e tal ki ng about real t hi ngs and no t about fi ctio ns, t he s eco nd o pt io n would seem mor e lo gical . One woul d be t he fir st sur prised in t he case t hat quali tat i ve princi pl es could admit dedu cti ve char act er ; t hat t hey admit a quant itati ve correl atio n, s eems trivi all y cer tain. And nevert hel es s, we have r epeatedl y aff ir med t hat t he Samkhya philoso phy demands a s pecifi c cau s al frame, in t he s ame way that dynamics prevent s it o r makes it tri vial (Poi ncar È) . Let us emphasi ze that Samkh ya i s a t heo r y of the tempo ral f luctu atio ns, wit hout any appeal to the s pace o r a fr ame of ref erence. Ther efo r e, lacki ng experi mental evi dence, we can o nl y t hi nk t hat a gr eat voi d to cover in our t empor al metri c exi st, contr ar y to t he gr eat pro fusio n of metrics for t he s pace and t he s pace-ti me in mo der n sci ence. It i s not pos sibl e to underes ti mate what can fit i n thi s gr eat void. Finall y, i t i s neces sar y to r etur n to take i n co nsi der atio n ot her f actor s i n t he pul s e di agno sis gi ving additio nal i nfor mation. Thes e ar e mainl y two: t he variabl e pres sur e with t he fi ngerti ps , and the cor relatio n of t he i nfor matio n of t he pul se i n bo t h wrist s. The rol e of thes e t wo f actor s is co mpl etel y di ff er ent. The mo dul atio n o f t he pres sur e in t hree diff erent poi nt s of t he wr ist , at super ficial, mediu m and deep l evel , remai ns as a heuri sti c approach, whi ch o ther wis e can i mitat e si mpl e adju st able pr essu re s ensor s perf ectly. The i nt entio n of t his is to gr asp better t he su btleti es o f t he for m of t he wave, its t hicknes s, which i s not r ecor ded i n t he usual es phygmo gr aphs . Natur all y, t his is ver y useful to o bt ai n mo re i nfor mation, and has no count er part i n the usu al mat hemati cal tool s o f analysi s o f ti me s er ies. So mewhat humo rously, i t coul d be s ai d t hat t he docto r s ets out empi ri cal l y hi s own parti al di ff er ential equ atio n, ali ke as a mat hematici an dedu ce t he evolution o f a variable whil e mai ntai ns t he ot her variables co nstant. In fact, what t he do ctor att empt to gras p wit h t hes e thr ee changing levels is a mor e fo cused ref erence for t he t hr ee humour s, pitta, vata and kapha. So me will be tempted to s ay t hat t hi s i s all t he mys t ery of t hes e t hree pri nci ples , alt hou gh we thi nk


that t his is to confuse cau ses and eff ects . The state of t he t hr ee humours i s an o bjecti ve f act, independentl y of t he form of measurement. But , pr eci s el y because t he i mpor tance o f thi s addit io nal infor matio n cannot be underesti mat ed, it i s necess ar y to follow it i n its consequ ences . The t hr ee gr adu al level s of t he pu ls e are not a separ ation of t he pri nci ples ­bei ng t his i mpossi bl e al so by pri nci ple - , but one mor e i ndex of t heir rel atio n. And it agr ees to say that , doi ng wit hout for a mo ment t he i mmediat e char act eri sti cs of t he dynami c profil e o f the pu ls e, t hes e t hr ee l evels and t he thr ee princi pl es fi nd a logi cal and full corr es po ndence wit h t he t hree foli atio ns o f t he embr yolo gi cal develo pment - endo der m, meso der m and ectoder m, wit h all t he r ami fications her e i mpl ied. As far as t he di ffer ences o f the pu ls e bet ween both wri sts, so me do ctors co nsider t hem, and so me other s not . Agai n, fo r the west er n mo der n medici ne i t will seem nearl y i mpossi ble that su ch dif fer ences, if t hey exis t, can have t he l east si gnifi cance; but for the mo der n medici ne, even t he whol e hu man bil at eral s ymmetr y is a biolo gical coi nci dence. The alt er natio n of t he breat hi ng i n bot h nost rils, wit h a cl ear perio di cit y, is well report ed. In gener al , it i s hard for us to i magine si gnifi cant di ff er ences bet ween the puls es o f bot h wri sts ; but it i s l ess dif fi cult to co ncei ve si gnifi cant di ff er ences i n th e sound of bot h pul s es , as, for example, can det ect accu rate micro pho nes di s pos ed to t hi s ef f ect . And, wit h t he sound, t he di s sonances also . The detail ed r ecor d of thes e dif fer ences, i nclu di ng i ts possi ble perio dici t y, is a subject t hat coul d leave us even to al gebr ai c qu est io ns ; l et u s s ay o nl y t hat t he diff er ence bet ween bot h puls es cor res ponds i n the mo st gener al manner wi t h di ff er ence between t he vegetat ive and t he volu ntar y ­ but here i n t he measu r able f rame of time s eri es. A su bject li ke t hi s never has been pro perl y t ackl ed, i n spite of it s great i mpli catio ns for co gniti ve s ciences and t he study of time its el f. The s pati al symmet ry hides a dynami c asymmetry. This as ymmetr y mu st have su bst anti al corres pondences with t he deco mpositio n of ot her or gani c fu nctions i n t heir extr emes: t he i ns pir atio n and t he expir ation, sys tol e and diastol e, the relatio n bet ween t he ar teri al and venou s cir culation. Both extr emes expr ess also in t he most dir ect and i mmedi at e manner how t he hi gher fu nctio ns co nst r ains t he lower ­ volu ntar y means -, and ho w t he lo wer fu nctio ns co nstr ai ns the hi gher o nes ­ vegetative root s. These ar e the t wo mai n co nstr ains, by wil l and by s tat e, fu ll y i ntert wi ned, i n additio n, wit h t he dissi patio n and t he mai ntenance o f t he u nity of t he o r ganis m. Thes e t wo extr emes find t heir natur al corr es po ndence with t he fi rst t wo pri nciples of Samkhya, i ner tia and activit y, and bei ng t he t hir d the i ndi cator of t heir r elatio n. It is r eall y sur prisi ng t hat so el emental aspect s have not fou nd its pl ace in a measur abl e and experi ment al fr ame. Even we emphasi zed i n a pr evious es s ay how this is full y and glo ball y li nked wi t h the cogniti ve diff er ence bet ween bot h br ain hemi s pheres. In additio n, t he cor relat ion bet ween bot h pu lses , indica ting simultan eously th e t wo ends of the a r row of o rgani c ti me, t he past and t he futu r e, helps us to define a potential o r gradi ent for t he union of t he t hr ee humours or pri nci pl es , and t his i s co mpl et el y necess ar y si nce t he mo ment t hat the indissolu ble u nio n of t he t hree pr i nciples i n any indi vi dual i s it s elf , befo re any ot her thi ng, a gr adi ent or reacti ve slo pe. This al lows us to save i mmense amou nts of wor k in t he l abor ato r y at t he time of i dent if ying the nature o f t he t hr ee princi pl es in t he empi rical vi a time s er ies. Also allo ws us to ext r apolate past or futur e co nditions , alt hou gh it is to see wit h what degr ee of pr ecisio n. All it incli nes to t hi nk t hat, for a complex evolutio n li ke t he o ne of an or gani s m, t he "r etro di cti ve det er mini s m" i s much mor e f easi bl e t han "predi cti ve det er mini s m" pro per of P hys i cs . On t he ot her hand, it is sur prisi ng t hat moder n medi cine tri es to acquire predi cti ve det er mini s m, bei ng t his o ne quite s ens eless in t his area. That i s to s ay, i n medici ne, l ike i n many ot her fi elds , the "pr ediction" is reduced to a di agnosis i n whi ch we must su ppo s e t hat t he futur e co nditio ns wil l be si mil ar to the pr esent and past co nditions. But it i s known ho w to esti mat e these past and pres ent conditio ns? Not , except fo r t he most tri vi al cas es . It i s much mor e "r evolut io nar y" to be able to u nderstand what it happens and r eall y has happened t han to pr edi ct what it is not u nder stoo d. R. M. Ki ehn has dedi cated a great part of hi s lif e to show ho w t he irr ever si bl e and no nequili briu m s ystems, as wel l as their entro py, can be des cri bed wit hout st ati stics , by means of coor di nat e fr ee met ho ds of ext erior dif ferential for ms. Consi deri ng t he ambi guous and pr ecariou s


charact er of all the st ati sti cal t r eat ment s o n t he ent ro py, it i s an extr aor di nar y achievement, whi ch woul d have to l ead to many l at er develo pment s . Ki ehn has stres s ed repeat edl y t he mat hematical vi abilit y of the "r etrodi cti ve deter mini s m", qu estio ning t hat pr edicti ve models are t he o nl y way to under st and nature. Har dly t he mai n one, we would add. Savi ng t he dist ance bet ween the dynami c des cr i ptio n of t he s ys tems and t he profil es of t heir tempor al seri es , we t hink that Ki ehn's des cr i ptio ns of co ntinuous evo lutio n i n topolo gi c di mensio n 4 coul d fit and des cribe in t he most co mpact fo rm t he r ealit y o f the changes of t he pul se in t he lo ng t er m, but t he experi ment al verificatio n of t hi s would take whole gener atio ns. And when we say mor e "compact ", borro wi ng the t er m from topology, we ar e thi nki ng also about t he irreduci bl e form of body agi ng, wit h t he added di mension ­literall y embodi ed- of ti me. Since r ever si bl e s yst ems have a zero tor sion co mpo nent, and ir r eversi bl e o nes a co mpo nent wit h a positi ve valu e, it is co ncei vabl e t hat t his vector, equivalent to t he ar row of t he ti me, woul d be also r el at ed to t he Crit ical Act io n Ti me impli ed i n t hir d der ivat i ve of ti me. Finall y, i t i s i nevit abl e to r emember that t he pulse r eadi ng i s telli ng mu ch mo re t han t he beats of t he heart. In f act, t he most of t he si gnal , i n quantit ative t er ms, i s rel ated to t he sto mach and the associ at ed acti viti es o f assi mil atio n, and not even to the heart, t hat pl ays a s mal ler part i n the amou nt o f bloo d. The heart pro pels the bloo d, but it does not pro du ce it. Indeed, mo der n phys iology, t hat so mu ch has studi ed t he mechani s ms o f medi ation i n t he or ganic ho meostasi s, woul d have to concei ve easier t he pol ys em y of a si gnal like the pul se. Wil liam Har vey knew perfectly t hat t he bad perfo r mance of an or gan o bstruct s the sangui neous cir cul atio n locall y and secondaril y aff ect s to t he gener al cir cul atio n; so met hi ng so evi dent t hat many o f hi s successo rs t end to for get . E ven in t he most el ement ar y anal ysis of t he s angui neous pressure, we obs erved at l east four f actor s: t he volume o f ej ectio n, t he to tal volume o f bloo d i n t he cir cul ator y s ys t em, t he flexi bi lit y of t he arteri es, and t he vascul ar r esi st ance, t hat i s co ntroll ed by t he autono mous nervous s ystem. Therefor e, inexcu s abl y, dif fer ent or gani c level s are i nvolved, but an accept able key to arti cul ate t hem of element ary fo rm i s not found. The o nl y postul at e is t he u nit of the or gani s m ­ and the fir st t hi ng we woul d have to u nder take s eriousl y. Fo r t he tr aditio nal medi ci ne, t he pro bl em o f thi s t ype of diagno sis i s not it s mer e pos si bilit y, but it s diffi cult y wit h pu rel y inducti ve met ho ds. A cru ci al aspect to evaluat e the perti nence of a t hi r d deri vati ve is t he identi fi cat io n of t he Crit ical Ti me of t he s ys t em and its r el atio n with t hir d or der vari ations and their associ ated resonances. In t he cas e of t he pul s e, it can be t hou ght t hat t he cr iti cal ti me is the time i nt erval o f t he beat ­or, at least, i s the fir st r el atio n co mi ng to t he mi nd. The r el atio n between t he t hird compo nent and t he backgrou nd noi se mu st fi nd it s equi val ence in t he t emporal perturbatio n of t he s eries. That is to s ay, t he mor e t he cont rol component is fitt ed, t he mor e fitt ed will be t he r el atio n bet ween beats and even bet ween t he two phas es of each beat ­ what it does not imply al ways mor e r egularit y. The time delay can var y al so, and it s var iat ions can be deco mpos ed i n aver age co mpo nent and a fluctu ating co mpo nent su bject to auto corr elatio n. Obviousl y, t he fu nctio nal char act er o f t his t hir d el ement has to be demo nst rable, o r at least, co ngru ent with t he gener al evolu tio n of t he s eri es . It has to play an acti ve role i n t he mai nt enance of the s tabilit y. Therefo re, also mu st gi ve accou nt of a part of t he random compo nents t hat al ways appear i n t hese s eri es ­of t he mo st essenti al part o f it , indeed. In ot her words, the reso nances o f t he t hr ee deri vati ves i n t he pul se series must s how a causal feedback loo p with t he car di ac acti vit y, t her efore bei ng di rectly r elevant for cardiolo gy also. The t hird order gi ves us t he more clos e measur ement o f that which medi ates and is i nt er pos ed bet ween t he actio n and reactio n alo ng t he cycl e or t he i nter val . Immediat el y ari se t he qu estio n about in which i nter val is eff ecti ve t hi s fit nes s, and to what ext ent has vali dit y in t he direction of t he past or to t he future. About t hi s and many ot her qu estio ns o nly t he experi mental sur vey will deci de. If t he t hir d deri vati ve has not found uni vers al appli catio n sti ll, it is parti all y due to t he inf init y o f po ssibl e criti cal t imes for so many ot her s ys t ems . Nevert hel es s, it is t his s ame thi ng, t he pro per ti me of each s yst em and it s s ensiti vit y to the enviro nment , which is to define. On t he other hand, many cycli cal proces ses have in pri ncipl e a sour ce o f co nti nuous perio dic perturbatio n, as for


exampl e, t he weat her wit h r es pect to t he daily and annu al perio d; it coul d s eem t hen t hat do es not make sens e to appl y a t hir d or der to t hem. Yet, we hear t he medi a and even many meteo rolo gists tal k about an "accel er atio n" o f t he glo bal war mi ng, when at the ot her hand we ar e experi menti ng so me of t he col dest wi nter s. If t hat suppos ed accel er atio n exist , it woul d have to be wit h fluctu atio ns, and f rom t hat we coul d gai n co nclu sio ns o n to what ext ent t he cli mati c bal ance i s aff ect ed with r espect to its capacit y of control, name it t he capacit y of i nterchange ­whet her wit h outer s pace, or wit h it s own t hermally acti ve i nter nal mass . It i s reall y very diffi cult to t hi nk about real changes without di mensio ns o f impact, and thu s we tal k about t he i mpact of the hu man acti vit y on the cli mat e al so. If so, we woul d have to be able to measur e i t. W e believe t hen t hat t he t hird derivative is always t he most gener al i ndex of t he co ntrol i n a s ystem, but o nly t he experi mental dat a of the di ff er ent s ys tems must deci de about i ts pos si bl e rel evance. It wi ll be necess ar y and of gr eat i nter est to apply t he tool s of di mensio nal anal ysis to di sco ver simil ari ties and ir redu ci bl e as pect s of s ys t ems wit h a r elevant t hi r d or der. Definit el y, we s ee t he t hir d der i vat i ves wit h reso nances as t he most generi c for m of tempor al i nterf ace ­of cont act or tr ansition bet ween po ssi ble behaviou rs or stat es. They are inti mat el y r el at ed also to t he t heor y of phas e t ransitions wit h critical po i nts , but her e we onl y co nsi der t emporal i ndi ces , doi ng co mplete abst raction of t he u nderl ying dynami cs. That 's to say, under a r el ati vely si mpl e f eatur e, co mplexit y i s i mplied. Besides, wit h t he t er m "phase t ransitio n", we under st and so met hi ng much more gener al t han t he term usu al i n physics of st ates, and we leave its out line for l at er wor ks . The i dea i s that the emergent surf ace o f a co mpl ex s ys t em fi nds the mai n i ndex i n t he rel atio n of the t hr ee der ivat i ves. It mus t be so, if we under st and as "emer gence" a si gni ficant change in t he r el ations bet ween a s ys tem and it s envi ro nment. Since all real thi ngs s ho w co mpl exit y and si mpli cit y onl y remai ns for ideali zed clos ed s yst ems, what we get t his way i s t he generi c index of the deviation of a s ys t em from its clos ed and i deali zed mo de, u nable to creat e no velt y. So we can trans cend t he s har p di choto my bet ween cau salit y and or gani zation ­ bet ween arti ficial hi erar chi cal crit er ia and a purel y fo r mal and devoi d dynami c causalit y. In t hi s co nt ext of wavelet anal ysis and higher o r ders , it seems qu ite logi cal to as k for the role t hat here coul d pl ay t he fr actio nal cal culu s, wit h no n- i nteger or ar bit rar y i nt egr al s and derivatives. E ven to day mat hemati cians ar e far fro m co nsensus wi t h res pect to t he geometri c and phys ical meani ng t hat fractional cal culus can t ake, alt hough wor ks as t he o ne of Po dlubny [ 4] pro po s es t his o ne li ke an appro ach to t he lo cal t i me of a syst em, in contr ast wit h the absolut e ti me usual i n physi cs. The fr actional calculus arose from the develo pments of Liouvil le and Riemann, alt hou gh al ready Leibni z i n 1695 st at ed that it s ado ptio n "It wil l lead to a parado x, f rom which one day u s eful con sequ en ces w ill b e dra wn ". Natur all y, fractio nal calculus may be co nnect ed wit h wavelet anal ysi s, and even i n its more explicitl y analyti cal for m, as pol yno mial s pli nes and t he derived fr actio nal s pli nes ar e; i n additio n, t he fr actio nal deri vati ves are not det er mi ned by t he local behaviour of t he fu nction, but by t he whol e do minio n of i nterest , co mpl eti ng t he cir cle to r eturn fro m t he lo cal to t he global behaviour . The f ractio nal cal culus is bei ng appli ed now to problems of co ntrol , pro babilit y, dif fusion, vis coelasti cit y and hereditar y mechanics wit h memor y o f st ates, as mu ch for st atio nar y and tr ansi ent s ystems. Transient r esonances must have f ractional r el atio ns and bo nds. Therefo re, ever ythi ng we ar e s aying on a t hi r d di ff er enti al o r der and its i nter pret atio n can and mu st put it self under t he li ght o f t he fr actio nal cal culu s, that natur all y o beys to ques tions on tempor al metri cs and fluctuat i ng, i nho mogeneous t i mes. An ywa y, we must r ecall t hat fr actio nal calcu lus does not support a si mplist ic i nter pret atio n in terms of geo met ri cal f ract al s, alt hou gh, of cour se, many r el ations can be fou nd. On t he o t her hand, bot h fr actio nal deri vati ves and tr ansi ent states allo w i mport ant connexio ns wi t h the Ri emann zet a fu nction, as was s howed s i nce 1975 by Keiper and by Pavlov and F adeev, r es pecti vel y. Besides the int erpr etatio n i n ter ms of r esonances , the s ame lo cal- glo bal r elation we notice bet ween wavel ets anal ysi s and fractional derivatives bri ngs to us clos er to t he cor e of t he zeta function.


The f act t hat fr actio nal cal culu s has not admitted u ntil now a physi cal o r geo metric int er pretat ion o nl y coul d be sur pr isi ng for t hose who co nsi der t he develo pment of moder n phys i cs like t he u ni qu e po ssible and t he natural one. Indeed, t his ver y f act i s indi cati ng i n another f as hio n to us the voi d of mo dern physi cs wit h res pect to ti me and t he t emporal metrics. Befor e we have tal ked about to "duali sm" of modern physi cs ; anot her way to s ee t his duali s m is its reco gnition of t wo t ypes of fu ndament all y di ff er ent magnitudes, scal ar s and vecto rs , i ncompati ble i n it s repr es entation. As Gus tave Le Bo n al ready noti ce a centur y ago , it do es not exi st any good reason to t hi nk t hat cannot exi st ot her kinds of es s enti ally di ff er ent magni tu des, not les s fu ndament al ; however , i t i s indeed through hi gher and arbit rar y cal culus or der s t hat thes e ot her magnitu des, for ms o f energy and behaviour s have to be outl i ned. What is really arbi tr ar y is to thi nk t hat wit h t wo i nt eger dif fer enti al or ders we have exhaust ed t he possi bilit ies o f natur e. In addition, if we were abl e to phys icall y i nt er pret t hi s ext ens ion of calculu s, it is perf ectl y pos sibl e t hat we not onl y accede to mu ch great er degr ees of di versit y i n natur e, but al so to a gr eat er si mpl icity and u nit . What we cal l resonances alr eady ar e a co nnexio n bet ween t hi s t wo so diff er ent ki nds of magnitudes, and will s how conti nuit y as pects where we can see s epar at e t hi ngs o nly, and, on t he cont rar y, separ at e t hi ngs in evolutio ns consi der ed co nt i nuous no w. In a r eall y u ni fied frame, t he s ame fu ndament al for ces woul d be deri ved effect s mor e t han cau ses ­ and al so "di ff er enti al s ectio ns" of a mu ch more vast tempor al evo lutio n. Bu t we thi nk t hat it is not possi ble to co me to su ch a l evel without a specifi c appro ach to t he pro blemati c of time i n mechani cs. P. Fizi ev and H. Kl ei nert, [ 5] for example, give us a new anholo no mic actio n pri nci ple for pur e rotatio ns arou nd a fi xed point of a bo dy ­Euler equ atio ns - without r ef eren ce to stationar y systems . Non- holo nomi c s yst ems ar e t hos e whi ch ar e path- dependent, a car for exampl e, and besides t he usu al cont rol o r di ff er enti al degrees of f reedom, the histo ry o f t he s ys tems must be known. We will us e t his for an exampl e l at er. Tr ansi ent sys t ems, r esonances and anholo nomi c behaviour can des cri be each ot her , when t he naÎ ve appli cation o f hamiltoni an actio n pri nci pl e f ails. This al so must yi el d po wer ful connexio ns bet ween chaoti c behaviou r and nu mber t heor y ­ellipti c int egr als, mo dular for ms and so o n, becau se t he nu mber sys t em seems not to be sensiti ve to anholo no mic conditio ns, but anho lo no mi c s yst ems are s ens itive to numeri cal co nditions. An yway, there is mu ch to fi nd i n the al ways mo mentary conditio n o f natur e.

Vacuum, in for mat ion and other metapho rs
It seems t hat if ther e were somethi ng able to t ransmit all the shades and subtl eti es i mpli ed i n thi s t ype of diagno sis, it had to be t he sound; but t he li mi tat ions of t he sound li ke source of infor matio n s eems evi dent . The fr equenci es ar e ver y lo w i n rel atio n to many levels of activit y, t he ubi quit y of uncorr elat ed whit e nois e, et cet era. Nevert heless , all Indi an liter atur e has insi sted in t his res pect , alt hou gh it s notio n of sou nd i gnor es al mos t all t he f eatur es of moder n acou stics . In it s co nceptio n, t he sou nd i s not o nl y i ndependent o f any s pace s cal e, but t he s ame waves cr eate t he s pace. Thi s co nnects with t he well- kno wn diff er ences t hat we have find bet ween the dynami cs o f obj ects i n t he s pace and t he Samkhya li ke des cri ptio n of ti me flu ctuatio ns. It do es not exi st either, of course, t he s mall er consi der atio n of t he noi s e li ke st atisti cal phenomeno n. The s ci ence of t he pul s e di agno sis is called nadi vig yan , exami natio n o f t he channel s or du cts . What t he du cts or channels t rans mit is ju st t he sound, or what it i s under stoo d like that in t hi s no n- s pati al co nceptio n, but pheno menal per ception. The Upanis hads makes an empirical and tes timo ni al enu mer atio n o n the diff erent l evels of no is e or backgrou nd sou nd ­ no di sti nctio n is


made bet ween bot h- t hat ar e au di bl e i n the own bo dy and beyo nd it ; and t hi s s ame gradatio n is o ne of t he cano ni cal fo r ms to descri be t he u nio n process in whi ch t he Yo ga cons ist s. It turns out natur al to co nt emplat e al l t hi s process like a noise- filt ering pro ces s, and reci pro call y an i dentifi catio n of the fundament al patt er ns . Beyo nd det ails , we thi nk t hat any t hing that is movi ng i s filt eri ng i n real ti me t he backgrou nd noi se: wi t h t he co nditio n, it's cl ear, that the mo vement has an articul at ed co mpo nent , that is to s ay, a thir d derivative of ti me wit h resonances. Thi s woul d be appli ed i n t he fir st place to the pul se, but also to i nf init y o f real sys t ems . The u biquitou s 1/ f noi s e coul d fit i n t hi s co nt ext, i f it reall y allows so me gener al explanatio n. An y ki nd of t empor al anal ysis cont ains in i ts nucl eu s i ts own u ncert aint y r elatio ns. It is not po ssi bl e to kno w exactl y t he f requ enci es i n an exact i nst ant of ti me. Heis enber g' s u ncert aint y rel atio ns, f ar from bei ng a fundamental pri nci pl e of natu re, are o nl y a co ns equence of t he limitat ions of t he Fouri er anal ysis as a mat hemati cal tool. Today are wor ki ng routi nely many devi ces, li ke o ptical mi cro sco pes, t hat get arou nd t hi s last u ncer tai nt y su bsu mi ng it u nder a much more general s et of uncertai nt y rel atio ns ­ just i n t he s ame way t hat t he har monic analysi s i s onl y a limit case for wavel et anal ysis [6]. Obs ervat ions much belo w t he wavel engt hs ar e made diar y and the o nl y li mi t i s not t heor eti cal, but depends o n t he t echnical capacit y to fi lter t he noise sour ces. Si nce we s ee to what extent mo der n t heori es ar e co ndit ioned by the mat hematical tools available, i t is eas y to s ee t hat we are i n a s ilent revolution t hat wi ll have ver y f ar -r eachi ng co ns equ ences. B e enou gh to t hi nk t hat u ntil now t he so-called "cl assi cal t i me anal ysi s " was fully i ndependent of ti me its elf. In ot her wo r ds, o nl y no w we are begi nni ng to penetr at e i n the tempor al do mi nion. An ywa y, what we tou ch her e is the su perpositio n o f two t ypes of s ys tems appar entl y dif fer ent: an articul ated mechanical mo vement generati ng reso nances, and a st ati sti cal backgrou nd noi se. Thi s las t one includes all ki nd o f random motion. The qu estio n i s to what degr ee of accuracy bot h, movement and nois e, can int erfer e to each ot her, and yiel d an additio nal preci sion. Natur all y, all this has to do with t he criti cal ti me of t he s ystem. All t he cells ­ not o nl y t ho se of t he heart- pulse and have art icul ated motions , r eason why we can even appl y an analo gou s tr eat ment to t hem. Thi s is equi val ent to evaluat e t he glo bal reactio ns of a cell i n r el atio n to the underl yi ng medium, includi ng t he bifur catio ns of the cellul ar di visio n. The study of t he cellul ar puls atio ns, for example i n cell cu lturi ng, i s walki ng its fi rst s teps right now. Resonances ar e not an exot ic pheno menon; amo ng o ther t hi ngs, we hear thanks to t hem. In fact, t hey exi st al ways and ever ywher e, and the onl y qu estio n i s to kno w to what ext ent and i n what frame can be r elevant ; when t hey co nverge towards the stabili t y and when t hey gener ate di vergence or di ssonance. On t he other hand, t he arti cul at ed mo tio n, motio n wi t h i mpact s, is t he nor m and not it exceptio n. In fact , t hey are t he o nl y event to which t he di s cr eet pro ces s es can be attri buted, and not to any ar bitrar y measur ement of qu anti zatio n, t hat si nce we have s een, aris es fro m t he har mo ni c analysi s and its ti me-i ndependent cr iteri a. If we ar e t echni cally beyo nd t hes e li mitations , it beco mes an absurdit y to grant t hem an absolut e char act er . The r eal wor l d is made of art iculat ed co nt acts, not of "emissio ns " and "absor ptio ns" o f ghost massl ess parti cl es , suited onl y fo r the co nveni ence of t he phys ical pr edi ctio ns. Alr eady Descar tes, in t he fi rst days of kinemati cs, tried to develop t he i dea t hat all mo vement is rotation, and t her efor e, accel er atio n. Wit h t hes e att empts was also r el at ed hi s progr am of vorti ces mechani cs. To day o ne t ends to s ee t hes e ideas l i ke clums y pr ehi stori c, pr evious attempt s to t he arr i val of t he "tru e" Newton' s mechani cs ; but the qu estio n i s t hat bot h mechanics i mplied co mpl etel y di ver gent poi nt s of vi ew, and di dn' t go i n t he s ame directio n at all. In or der to begi n, the vortices can be so complex dynami c s ystems t hat not even today t he mat hemati ci ans full y agree about how to def i ne t hem. They al so admi t to be co nsi dered li ke obj ect s wit h i nt er medi at e pro per ties bet ween waves and parti cles, a quit e i mport ant featu re. Decis i vel y, t hey also i mpl y accel er atio ns o f accel er atio ns and torsio n co mponents, which also co mplicate enor mou sl y t he calcu latio ns. It coul d be s ai d t hat t he vo rt ex is t he si mplest and archetypical for m of co mpl exit y


its elf, and t her efor e, t he fi rst to be avoi ded i n a pr edi cti ve fr ame fo r "fu ndament al" phys i cs . Until Descartes, and even alt hou gh t his o ne i nau gur at es t he su bj ect-o bject du alis m, t here i s s eriou s int er est to t hi nk about t he real cau s es of the natural events ; since Newto n, t he decisio n i s made i n favour of t he gener al balance equations in o rder to predi ctio n. Natur all y, if all movement i s accel er atio n, it mu st have rates of change i n t he acceler atio n to give account of t he pheno mena ­ local t ransitio ns. Still to day there ar e phys i cis ts like Gennady Shipo v tr yi ng to develop t he Cart esi an pri ncipl es, who even has been abl e to unfold a whole ars enal of gener al equations wi t h phys ical s ense. Without a dou bt, a t hi r d di ffer enti al or der makes mo re compli cated t he cal culatio ns , mai nly if o ne t hi nks about hi gh energi es and hi ghl y no n-li near events . But , on t he ot her hand, gi ves us more general i ndi ces i n a diff er ent dir ectio n. An ywa y, i n co mpariso n, t he mo delling of t hes e ideas in a s ys tem so lowl y no n- li near as t he pul s e would have to be a chil d's pl ay. Let us pro po se an analo gy to outli ne what can des cri be t he pulse diagnosi s. In a "Cartesian" car , even when we tr avel at co nst ant s peed, ther e ar e accel er atio n variations. That is to s ay, even t hou gh t he s peedometer s eems to be fixed, t her e are o pposit e for ces bei ng compensat ed: t he for ce of dr aft of t he motor and t he friction of t he ro ad and t he ai r r esist ance. But i f we make suf ficientl y exact measu res of t he actio n of t hos e for ces , we wou ld see t hat t hey never reall y co mpens at e each ot her , and t herefor e accelerations and deceleratio ns take pl ace co nst antl y (So far , I have t aken the pur ely kinemati c exampl e from Shi pov). In t his f eatur e, we see that t here i s no real inertial sys t em of refer ence. In addition to t his, we ar e fr ee to accel er at e t he automo bil e, i mpo si ng other additio nal condi tio ns to the flu ctuations of t he accel erat ion at co nst ant s peed. It coul d be s ai d t hat t he flu ctuations pro duced at co nstant speed ar e char acteri sti c of a cert ai n car t r avel i ng o n a cert ai n grou nd or pavement ; and t hat t hos e flu ctu atio ns will change at dif ferent s peeds, gi ving us a mor e co mpl et e profile or s pectru m of po ssi biliti es. The accel erat ion, t he s peed changes, will stil l give us a mor e exhau sti ve pro fil e of t hes e flu ctu ations, and t hey will allo w us to know mor e of t hat black bo x t hat t he car i s. As f ar as t he t hi r d el ement, t he o ptio nal us e o f t he br ake or t he accel er ator, it s eems to be i ndependent of the car, al t hou gh not of the grou nd. If we are measu ring all it fro m t he outsi de and withou t knowi ng t he circu mstances, we have a bl ack bo x wit hi n ano t her bl ack bo x withi n another bl ack box: t he grou nd, t he car, t he dri ver. It is already dif ficult to say so met hi ng about each o ne s epar ated, no t to s ay about the rel atio ns among them. The dri ver sees thi ngs t hat we do not s ee, and i n additio n, no bo dy is i n his head. Then, l et us su ppo s e t hat t her e i s no head, no dri ver . Or t hat the dri ver must mo ve without seeing, in complete bli ndness , bei ng abl e to li st en u ntil t he mi ni mu m detail t he noi s es, reso nances and res po nses of t he car at ever y moment. Let us su ppo se, i n additio n, t hat it have no t to deal wit h other cars and traf fi c, havi ng enou gh with not to l eave t he road. Wit hou t a doubt , t he car would go wit h an extraor di nary care and slo wnes s. And i f the car wer e i n addi tio n ver y fr agil e, t he "dri ver " woul d make an effort to o ptimi ze hi s r espo nse to each new signal: t he s mall est cur ve woul d be noticed i n a l apse of ti me, woul d accel erat e when l eavi ng it , et cet er a. Road, car and dri ver woul d be reveal ed i n a same s i gnal. The purpo se and t he ai m, t he i ntentio nali t y, become i nclu ded i n t he adjus t ment to t he gi ven co ndit ions ­here, as mu ch i nt er nal as ext er nal. Wit hout t he l east par ado x, the o bj ecti ves have so me sens e in as mu ch as t hey are not ar bit r ary ­ we are not ent ir el y free to choos e them. Thi nk wel l i n this . This is a met aphor of t he lif e; mai nl y from her i ni tial, mor e stutt eri ng phas e, than i t i s so dif fi cult to imagi ne for us . Onl y t hat t he ground is much more varied t han what t he li near fi gur e of the road coul d suggest to u s . Lif e i s bl i nd, but it is i nco ncei vabl e wit hout s ensi ti vit y. Li f e, al so, ari ses i n a cavit y, but not a st ati c o ne, but a cavity i n motio n, ali ve it sel f. It s own motio n is a fil ter of the enviro nment. E ver ythi ng we see now or that we beli eve to see, previou sl y has been felt and att empt ed i n t he dark. It has happened i n t he cells, and even in t he ti ni est molecu le; and t hey had not r eached here without t hat f eeli ng, attempti ng activit y. If Pr i gogi ne s aid t hat matt er i s bli nd i n equili briu m, but out of equ ili brium sees, we woul d say t hat mat ter i n r esonant co nditions is still bli nd, but hears and li st en.


The pr esent evo lutionar y t heo r y, t hat so mu ch has fought to pr evail , can take refuge peaceful l y in it s statisti cal backgrou nd to avoi d any descri ption of real ti me evolutio n. In the analo gy of the car call s the att entio n t he slo wness whereupo n ever yt hi ng woul d have to t ake pl ace. But, do es somebo dy as k which can be t he per ceptio n of the local r eal ti me for a cell or a mol ecul e? The t hird deri vati ve gi ves u s t he i ndex of t hat t i me. There is too much discours e o n biologi cal pro gr ammi ng and i nfor matio n no w. However, the informatio n pro ces sing ­i n r eal time, agai n- i ndeed demands t hat t he reactio n of a s yst em i s unequal wit h r espect to the act ion t hat r ecei ves ; thi s is , it do es not t ake place ­i t cannot be co ncr ete and lo cal- wit hi n t he f ramewor k of Newto n laws wit h an absolut e ti me li ke glo bal s ynchroni zer [7]. In ot her wo rds , the informatio n, t hat we us e to consi der so concret e, not even can o ccur wit hi n t he framewor k of mo dern physi cs ; it i s su ppos ed and su per pos ed li ke a s imple met aphor . Only a Cart esi an mechani cs of the ki nd pro po sed by Shipo v, descri bi ng lo call y t he trans itio n bet ween inerti al and accel er at ed sys tems , coul d generat e and pro ces s informatio n. This s houl d be a war ni ng. Therefor e, taki ng i nto account t he diff er ent angl es, not even has been co ns i dered t he pro bl em of life, no matter how mu ch o ne s peaks abou t "i nfor matio n". Let us loo k at t hi s clo ser. Cl assi cal physics can make t he tr ans missio n o f i nfor matio n po ssi bl e, but cannot make it u ni vo cal ­Poi ncar È's co nclusi ve ar gument [8] o n t hat t he gener al dynami c equations wit h extremal or statio nary pri nciples admi t i nfi nit e caus al i nt er pr et ations. Then, one can appeal to t he t her modynamics and quantu m mechanics, whi ch gover ns t he i nter actio ns of ato ms and mo lecul es. The consensu al t her modynamics not o nl y cannot creat e i nfor mat io n, but, i n additio n, des tro ys it . Quantum mechani cs , o n whi ch all ki nd of myt hifi catio ns proli ferate, i s a lin ear theor y; it is cu rious ho w l ittle t his ess enti al charact eri sti c is stres sed. In addition, the reversi ble as pect s ar e emphasized and t he irr ever si bl e as pect s ar e mai nly i gnor ed. Ther efor e it i s i ncapabl e to gener ate i nfo r matio n. What remai ns t hen to make poss i ble t he cr eation and even the mer e univocal pro ces sing of i nfor mation? Info rmatio n it s elf, devoi d o f any ph ysi cal reali t y. Moreo ver , i nfor matio n is measured i n pur ely quantit ati ve t er ms and wit h total i ndependence of t he time of pro cessi ng invol ved. And when t his o ne i s taken i nto accou nt, like i n t he mi cro processo rs , a clo ck cycl e is used co mpl etel y analo gous to t he absolut e ti me o r "global s ynchroni zer " of cl as si cal phys i cs . It i s eas y to see, t herefo re, t hat no body at all knows about what i s phys i cal l y speaki ng when t he concept of infor matio n i s appl ied to Biolo gy: it s expl anator y valu e is i n t he same metaphys i cal and indemo nstr abl e l evel t hat t he vit ali s m and t he "i nt elligent desi gn". Infor mation is a pur el y exter nal co ncept, requ iri ng for its proces si ng ot her equ ally ext er nal concept s li ke the desi gn, t he s ynchroni zat io n, t he s tatisti cal s el ectio n, et ceter a, t hat i n additio n ar e not mutu ally compati ble to each ot her. Do not loo k for the logi cal combinatio n of all t hese elements , becau s e i t do es not exi st. The i nfor mat io n i s for pres ent s ci ence a co ncept as voi d as t he concept o f caus ality, but still mor e co nfu sed, becaus e it i s ubi quitousl y pat ched i n o ne's o wn i nter est with t he notio n of chance and rando mness. To say t hat t he worl d is caus ed by the cau s alit y is not to say mu ch, mai nl y when we co nsi der t hat causal it y necessarily r emains to defi ne, as i n t he case o f phys i cs. But i n the case of infor matio n i t i s still worse, becaus e to t he i nfor mation concept a s pecif ied and u ni vo cal char act er is su ppos ed, and cert ainl y t he thi ngs don't i mpro ve addi ng to t hem the chance and randomnes s, t he co ncept of the uns peci fic it self . Then, somebo dy co mes to u s s aying that we have our ori gi n i n "C hance and Neces sit y", with capit al letters added: br ave and pr ecis e answer. Neodarwi nis m does not ri s k nor explai ns mor e t han cr eatio nism, having onl y more scient ifi c pret ensions . And all t hi s i s fatal and unavoi dabl e, becau se without a specifi catio n and lo cal defi nitio n of inerti a, the who le phys ics evades t he do mi nion of t he r ealit y. In ot her words, r emai ns unph ysical . B y the same, t he "phys icali st " expl anations of t he mind remai n equ ally unphysi cal and equal ly voi d of real co nt ent ­t hey belo ng to "par all el worlds ". Hume's criti ci sm o n t he co ncept o f causalit y, as well as the much mor e r efi ned fro m Poi ncar È, ar e vali d for t he t ype o f caus alit y of moder n phys i cs, that is t he empties t caus alit y possi bl e; but t hey gradual l y lo s e it s vali di t y in other do mi nions , li ke for exampl e, t he r edou bled anal yti cal versio n of the Samkhya t hat we ar e pro posi ng. That i s to say, not o nl y it i s not co ntr adi ctor y to co ns i der t he causalit y and the emer gent pro perties of an o bj ect


toget her, but it is neces sary to preci se t he domi nio n of caus alit y it s elf. E ven St andar d Model phys ics must appeal to phase tr ansitio ns wit h emer gent pro per ties to defi ne its grou nd and t he rul es of t he game, not to mentio n t he pro per ties of any materi al ; although, sur ely, it do es not do it wi t hout ar bit rarines s. But t his has ver y littl e to do with t he l evel s o f caus alit y and emer gency that we pro po s e here, bas ed o nl y o n r edefi ning t he eff ects of i nerti a at a su perior level by means of a thir d dif fer enti al or der: wit h di mens ions of impu lse, to gi ve it the ri ght name. The electio n of the inertial r ef er ence f r ame i s th e on ly t heor eti cal bet of wester n phys ics , not onl y si nce Galil eo , but alr eady f ro m Co per nicus hi mself. And by t he same, t here is no way ot her to close t he ar ch o f it s pro pos als and to gi ve t hem co nt ent t hat t he local defi nition of i nerti a, t he definit ion of t he i nertial fi el d. This i s t he botto m o f all t his matt er, and t he l atest t hi ng t hat who ever who allows hi ms elf to t hi nk can grant as a matt er of cou rs e. Wit hout it, not even we can know what means the wor d "mechani cal"; wit h it, we woul d ent er dir ectly t he problems of cont rol. And thu s, for exampl e, t heori es li ke Shi po v' s one, whi ch does not need any of the fundament al co nst ants , mu st s et out necess ari l y t he pro bl em o f the co nt rol o f t he local metri c s pace. Of cour se, and as theori es li ke t he o ne o f Shi pov or Hei m sho ws , all t he i nter actio ns and equ ations of t he well - kno wn phys ics can be rewritt en and r ei nt er preted wit h ot her crit erio n of t he fu ndament al di mensio ns , havi ng the same qu antu m of act io n the di mension of angul ar mo ment, and not to ment io n t he rel atio n between "stabl e" parti cles and t heir resonances . Fro m our view, we coul d do wit hout t he underl ying physi cs and just obs er ve a still cau sal evolution i n ot her l evels. But it is neces sar y to say in addi tio n that the lack o f defi nit io n fo r t he inerti a i s entir el y parall el to the lack of defi nitio n for the memo r y for t he pr esent co gniti ve sciences . Bot h, i n eff ect, have a natur al corres pondence. And, as t he nai ve exampl e o f t he Cart esi an car dis co ver s to t he most element ary anal ysis , t he questio n ari se o n t he co nser vatio n and destru ctio n o f st ates and t he accu mulated r ecor d of the car i n its pr esent mechanical st at e, consi dered li ke t he pr esent dynamic r espo nse. Ho wever, i n that t est of res po nse, t he stru ctures, t ho se "fro zen conti ngenci es ", ar e no more t han t he s ame pr esent dynami c res po nse, and any other t hi ng can be i gnored as a co nti ngency, t hat hel p us to sol ve not hi ng. The backgrou nd i s t he r es po ns e, becau s e t he res po nse i s the uni que t hi ng t hat makes per cei ve and su ppos e a backgrou nd to us . W hat can be appl ied to the "st ructures ", also can be applied to t he memor y and it s ghost s. The structure is a stabilized dynami cs t hat i t has to dest abili ze it self to retur n to be noticed. Ther efore, whi ch can be pr edi cat ed of i nerti a and t he memo ry can be pr edi cated of t he notio n of s tru ctur e and co nsequently appli ed. The mere manif est atio n o f i ner tia i s the most i mmediat e fo r m o f ori entation. There is no un- manifested i nertia, other wis e we woul d not ask abou t it . In ot her wor ds, i nerti a i s no t a pri nci ple or so met hi ng r edu cibl e to a poi nt or st at e, but t he more element ary r ela tion ; t hat 's t he notio n of t he so- called Mach's princi pl e. In t his s ense, al ready it i s an emer gent propert y, mor e t han an automati c derivation of t he caus alit y. Therefor e, it will yi eld as much i nfo r mation as we know to extr act to it in a gi ven cir cu mst ances. Any fast enou gh change i n t he acceler atio n has a mo mentary i nert ial yi el d that do es not follo ws from t he seco nd deri vati ve di rectl y, but i ndir ectl y i n co nju nctio n with t he other t wo: t his tran si ent margi n i s fundamental i n o r der to expl ai n many thi ngs . In Shi po v's Cart esi an vehi cle, i nert ia and t he appar ent const ant speed ar e irr edu cibl y i nfor mati ve, becau s e inerti a implies t he cont rol. In ou r extended ver sion o f t he s ame vehi cle, t he "ext ernal " co ntrol of t he co ndu ctor is not ar bitr ary either ; t he co ntrol do es not depend her e o n doi ng what one wants , but o n the measur e i n as much t he ci rcumstances can be appr eciat ed, r espo ndi ng to them with t he s mall er po ssi bl e i nt erf erence. Sensiti vit y i s the capacit y to per ceive i ner tia: t hat s ensi ti vit y is al l t he immediat e informatio n that we have. To i nt erf ere mor e is to lo s e "i mmedi at e i nfor matio n" and co ntrol . Nothi ng of thi s is contr ar y to mechani cs and to t he simples t reason, and we o nl y add an additio nal level of i nfor mation. Fro m t his new l evel, ot her u ncertai nt y r elatio ns are deri ved. Natur ally, all t his s eems equall y valid for our o wn behaviour, and as an element ary corollar y can be added t hat losi ng t he fu ndament al i nfor mat ion and t he control by means of our i nterf er ence, al so we lose auto no my and fr eedo m. The s ame Cart esian vehi cle i s a clo ck of t he lo cal ti me, whi ch can become more expl ici t u si ng li ke clock an appro priate t ype o f gyros cope. The t hi r d deri vati ve of t he


time, t he cont rol o f the impuls e, gi ves u s an index of t he anisotropy and no n- ho mo geneit y o f the enviro nment , as a n eces sarily ori ent ed s ys t em per ceives it ; an i ndex al so of its o wn ti me in t erms of infor matio n ­o f ef fecti ve processi ng o f info rmatio n. It i s quite curious t hat all t ype o f anomali es , lar gel y verified in t he l abor atori es, but wit hout po ssi bl e place for t he const itut ed and co nstruct ed t heor ies, has to do in o ne way or anot her wit h t hi s thi rd diff er enti al o r der, and not wit h "coll at er al " or "hi dden" "pertur bations". E ven dis counti ng t he gr eat percent age o f spuriou s cas es, t he amount o f li teratur e on t he su bject r emai ns i mmense and amazi ng, wait i ng for a t heo retical fr ame to gi ve it so me mo re s ens e. Thi s i s o nl y anot her indication of t he clearly non-trivial char acter of t he t hi rd di ff er enti al o r der. Machi nes seem mechanical to u s becau s e we have s ynchro ni zed it s parts avo idi ng as far as po ssi bl e u ndesirabl e eff ects , li ke fri ctio ns and r eso nances. Their desi gn i s a time- bi ndi ng cutting of functio ns to be opti mized. Even so , the own li f e of a machi ne and its dur atio n depend to a gr eat ext ent on t hes e factors , in addition to t he us e suf fered. Natu re has us ed si nce the ver y beginni ng and wit hout begi nning t hese pertur bati ve elements li ke a co nstru cti ve pr i nci ple, and t his i s t he main reaso n, i n t he long run, of t he eno r mous dif ference, even starti ng fro m i denti cal pri ncipl es. But these "identical pri nci pl es " ar e of ten co mpl etel y o pposit e, because of t he i ncommensurable crit eria of i solatio n or r el ation wit h the envi ro nment: Natu re oft en u nites many t hi ngs t hat we s epar at e, and on the co ntrar y. Unli ke the engi neers, phys i cist s and mathematicians, t he ho nest Natur e lau ghs at the analyti cal diffi culti es, and makes an indiff er ent us e of all s he has wit hi n r each. B y t he way, there exi st s a stro ng r el atio n, so mewhat antago nisti c, bet ween fr ict io n and reso nance, but t he int er esting thi ng i s that we can treat t he reso nances i n a bett er defi ned t emporal frame, doing wit hout a goo d part o f t he always ambi guou s statisti cal element s. One t hinks that not a si ngl e beat of a heart is au tomatic, except for our i gno r ance. Terms li ke "r ando m", "automatic" "i nerti a" ar e too voi d still to day, and i ndeed what we are doi ng is to loo k for a fr ame i n which t hey can mean so met hing. The gr eat historical iro ny is that Descart es, cr eator o f t he mo der n du ali s m o f bo dy and mi nd, pro pos ed a physi cal t heo r y o ppo sed to t hat du ali s m and wit h pot enti ality a vant l ett re to reconcile it and to r edu ce it to a no nsens e; whereas t he physi cal mo nis m deri ved fro m t he succes s o f Newto n' s mechanics, o ppos ite to t he Cart esian mechani cs , has tur n out to be t he co nsu mmat ion of the su ccess of dualism i n f act . Tal ki ng about t he f at her s of mo der n s ci ence, i t i s i nevit abl e to as so ci ate our Cartesi an car wit h t he celesti al mechani cs and t he planet s. The measurement o f t he gr avit y i n t hi s s ame E ar th has an experi ment al u ncer taint y as soci ated of mor e t han a part i n ten t hous and, and bei ng t hi s o nl y t he mo st conservative aver age esti mation. The os cillatio ns s eem r ando m, but appl yi ng t he proposed crit er io n, it s eems pos si bl e to filter a good part o f t his nois e and to dedu ce rel evant f acto rs. If t he tini est part icl e needs a time reactio n, ho w coul d we beli eve t hat the enor mou s pl anet ar y mass es have to r eact i nstantaneou sl y without abso r ptio n. In additio n to voi d, t hi s i s compl et ely irrational and it i s o nly bas ed on our bli nd f ait h i n the "natur al nes s " o f cl as si cal mechanics. But t he absor ptio n of t hes e r eactio ns o r j er ks must have a clo se r el atio n wit h t he flu ctu atio n of t he valu es o f the gravit y and t he mass separatel y, remai ning the pro duct co nstant and bei ng o bs er ved the or bit al r egul arit y of Kepl er's l aws. Cassini 's fourt h degr ee o val s, toric s ectio ns , al so can be r elated to all thi s. W e do n't need to st ress t he relevance of t hi s to fi nd a rea l li nk bet ween quantu m and classi cal mechani cs . Once agai n, i n or der to mai nt ai n t he fi ctio n of a uni vers al co nst ant , we ar e i gnori ng t he precious local i nfor mation. Retur ni ng to t he diagno si s of t he puls e, our su bj ect i s to what ext ent a r el ati vel y slo w mo vement but wit h a component of resonances can dif f erentiate the background nois e, to filt er it . Alt hou gh it i s evi dent t hat a vad ya must r esort to t he i nf er ence i n a ver y ample degree and at dif fer ent l evel s, which we want to kno w i s to what ext ent al l t hi s can have a deducti ve su ppo rt. And alt hou gh t he co nsi der ations on t he u nderl yi ng mechanics are not absolut el y necess ar y for t he pur po s e of di agnos is and u nder standi ng, it hel ps to s ee t hei r pertinence i n t he mo st fundamental


level. Not onl y ti me, but t he s pace and t he i nerti a t hems el ves ar e pri vate of content and redu ced to a pas si ve paper i n mo der n phys ics. All t he co mpl ex and r eal s ys t ems have a relevant t hir d dif ferential order , and onl y in t he i deali zed scheme of t he "fundamental fo rces " t hi s thir d el ement is excluded necess aril y and by defi nit io n. It i s to be not ed t hat t he thi r d deri vative has a s trictl y ph ysi cal meani ng; su rel y t his cannot be sai d of higher diff erent ials orders , which could o nl y be i nter pretabl e like r eso nances wit hi n t he resonances alr eady pres ent i n t he lo wer or ders. Si nce t he t hird deri vati ve i mplies a conditio nal rel atio n between t he exter nal enviro nment and t he i nt er nal st at es , t he t hir d or der must mark also a phys ical li mit i n t he capacit y of filtr atio n and absor ptio n of t he stati sti cal backgrou nd noise. That is to say, whi chever be t he degr ee of non-linearit y obs er ved i n the rel atio n of t he t hree time derivatives, t hey defi ne th e li mit of ph ysica l causal ity of a s yst em, and ever ythi ng beyo nd t hi s li mit mu st be co nsi der ed as phys ical ly rando m. W e woul d go furt her to aff irm t hat wit hout t his ki nd of reso nances t he memory and t he same i nerti a woul d never beco me manif est ed, and t hat t his manifest atio n al ways exi st withi n a critical ti me t hat r eall y i s t he s pecious present of t he s ys tem, its r eal time. And if inerti a alr eady is the fir st mani fest ation, furt her o nl y the unmani fest ed r emai ns, not to be necess arily confused wit h the no n-exist ent. Thus , fo r exampl e, t he three deri vati ves of the pul se si gnal would have to gi ve t he si mpl er po s si bl e "r adio gr aphy" of t he pr es ent st at e o f t he or ganism, in it s o wn f eeli ng and sentience, wit hout excludi ng at all t he exi stence of many ot her "radiographi es" of t he s ame order that can be taken fo r t he s ame mo ment , be t hey an electroencephalo gram or a measu rement of t he el ectri cal conducti vit y of t he s ki n. Thi s is i nevit abl e, if we t ake i nto account that the thr ee derivatives mu st yi el d always a cou pli ng i ndex wit h any o t her possi ble s ection of t he s ys tem. There are goo d reasons to t hi nk that if t hes e notions fi nd t heir just ifi catio n i n t he anal ys is of a si gnal l i ke t he s angui neou s pu ls e, they al so will fi nd some rank o f application for t he processi ng of ot her t ypes o f si gnals; si nce we s po ke of ver y fu ndament al and basi c concept s of t he t emporal analysi s. The question is, to day and al ways , but wit h t he new means at our dispo sal, to fi nd t he natur al arti cul atio n of t he o wn time of a sys t em ­and to gi ve it a sense and i nter pret atio n as r atio nal as pos sibl e. An y s ystem i n motion is filt eri ng t he backgrou nd nois e, whi ch i s si mul taneousl y insi de and out si de: be the syst em t he glo bal cl i mate and t he at mo s pheri c evolut io n, or o f t he flu ctu atio ns of t he sto ck market . Of course, each of t hes e s ys tems has its own par ameter s and co ndi tions , whi ch to a l ar ge ext ent are tot all y unr elat ed. But , preci sel y, of most i nt eres t i s t hi s littl e they can have i n co mmo n ­ t his littl e could wei gh mu ch. But we i nsi st agai n o n t he probabilit y, not very i ntuiti ve for the u su al t hinki ng, that a great er u nder standing of gener al as pect s i n thi s ground do es not i mply automati cally a gr eat er pr edicti ve power . If we do n't u nderst and thi s cir cumstance, we won' t under st and the meani ng of all we have s po ken. Let us s ee a bit clearer. All we kno w and we assu me t hat i n the lo ng t er m t he sto ck- exchange behaviour cannot be pr edi ct ed ­thou ght no body who pl ays r esi gn hi ms elf to it, si nce we kno w also t hat, i n s pite o f t he hu ge number of r ando m o r un cont rollable aspects, t her e ar e pr es ent tendenci es too t hat fi nis h i n logical co nclu sio n ­"lo gi cal" mai nl y when t he f act s al ready have happen, but not as mu ch befor e. Thi nk about a sto ck-exchange coll aps e. But the qu estio n is t hat i n t he tendency t he control co mpo nent is cont ained, i n the same way t hat i n t he vari abl es o f the pul s e i s co nt ai ned t he r eactio n of t he subj ect and i ts r el atio n with t he environment . It i s exactl y this whi ch we t hink that can be co nsi dered in an expli cit manner i n the anal ys is of t he t emporal s eri es. However , it i s exactl y this which t he compani es i n t heir stock- exchange poli cy or t he eco no mi c au t horities ar e imp licitly maki ng. That is , t hey tr y to exert t he co ntro l as mu ch as they can and t hey t r y to avo i d being co ntrolled as much as pos si bl e. Natur all y, t his has ver y del icat e mar gi ns , and i n t hi s co nsist t he politi cal s ens i bilit y in order to t ake measur es. The eco no mi c news conti nuou sl y speak to us about the s peed of t he gro wt h, and it s accel er atio n or deceler atio n. In additio n, all we s peak about t he eff ect of t he econo mic measur es ( mor e or l ess arbitr ar y or neces sar y) i n ter ms of impact: "t he impact go ver nment 's measures", et c. Al so i n t he bo ar ds and cou ncil s i s dis cuss ed endl essl y o n


"how to articul at e" the measu r es and "how to manage t heir i mpact o n"...t he ot hers. Go ver nment its elf is not another thi ng t han t hi s kind of cont rol ; neit her polit ics i n gener al no r the eco nomi c policy in parti cul ar . The el ementar y di al ecti cs of all thi s is r edu ced to t he convi ction , no body kno ws to what ext ent justifiabl e, t hat when t he mo re co ntrol, t he least poss i biliti es are o f bei ng cont roll ed and have to accou nt . On t he ot her hand, accou nt s with t he futu r e ar e the mos t dif fi cult to render , alt hou gh t his is al most t he u ni que t hing pro pos ed and sold. In s hor t, and to be bri ef , I believe that it is possi ble the obj ecti ve co ntro l and mo nitoring of t he measur es of control and monitori ng o f tho se that exert t hem optionally and arbitr ar y. W e can co ntro l the co nt rol. To o bt ai n t hi s woul d be mu ch more "revolutionar y" t han to t r y to pr edict futur e its elf , a futur e whose predict io n alr eady co mes inclu ded i n t he sale package. Control is measur abl e and then co ntro llable also. But t his does not lead to an i nf i nite r egr essio n, because ti me its elf i mpos es restr ictio ns o ver t his as a li mit of t he int er actio n wit h t he enviro nment. Then, co ntrol must be explicitl y expr essi bl e i n any ki nd of co mpl ete bal ance. Beyond t he usu al pr edi cti ve hori zon, techni cal parado xes li ke the effi cient market parado x have a part ial , but concret e solutio n. I t hink that to pas s wit h all t he cons equences f ro m t he s eco nd to a t hi rd diff er enti al o rder is literall y equi valent to goi ng fro m t he worl d of predi ction wi th i nexplicable but effi ci ent cau ses at a parti al level, to a worl d of control wit h explicable causes and an eff ici ency o r u s e of glo bal t ype. Reall y, t his co ntrol gr avit ates to war ds s elf - control . The gr eat par ado x at pr esent, cl earl y vi si ble for everybody, i s t hat predictio n i s pu rsued in order to get mor e co ntrol , but even so we ar e losi ng t he co ntrol in an i ncr easi ng incontroll able way. The su bject is so general , t hat I do not beli eve so mebody can co nsider it a chance. Beyond the predict i ve "cau salit y," a whole worl d to explore exists , but surel y not a whole worl d to explo it. This is a gener al and philosophi cal ess ay, and we cannot expect mu ch more pr ecisio n; i n any cas e what i s writ ten i s enou gh for t hos e who want to r es ear ch it. It can be s ai d t hat, if our pro po s al makes sense, t he o nl y thi ng we do is to i ntrodu ce a thir d gr ammar element i n t he habitual gr ammar of dynamics , whi ch o nl y have two cases pres entl y, t hi s i s, ver bs and predicat es wit h ri gid co nnectio ns. The i ntro duction of t his t hird element i s equi valent then, and withi n t he si mplifi cation of t he cas e, to t he i nt ro duct ion of t he su bj ect i n dynamics. I am alr eady heari ng t he angr y protests ; in parti cul ar, t he protest s o f the so- mis call ed "r edu ctio ni sts ", t hat, nevert hel ess, hol d much mor e immo dest pret ensio ns , as t he cr eat ion of "i ntelli gent machi nes " or t he "stro ng artifi ci al int elli gence". Had t hey called it Automati c Int elli gence i nst ead of Arti fi cial, no body had taken it seriously. But her e we ar e s peaki ng of mu ch more el ement ar y and si mple t hi ngs. The di s cour se of mo der n s ci ence o nl y s eems to be able to enunci at e phras es of t he t ype "to eat pot ato es", "co me back tomo rrow", or "natur al sel ectio n"; at l east, i n ter ms of s ense, and i n spit e o f t he f ant asti c techni cal so phistication r eached. And t hat i s i n t he most generou s cas es, becau se oft en ver b and pr edicat e are co nfu sed by t he expedi tious pro cedur e of turni ng t hem equi val ent . Thus , i n s pi te of t he supers peci ali zation, ever yt hi ng leads to war ds a f atal confusio n o f pl anes, and t he s peci ali st s ar e t he fi rsts who exploit t hi s ambi guit y and co nfusion. An y movement expres sed i n t hr ee diff er enti al o rders maint ai ns t he possi bilit y o f a li nguistic equi val ence, and, i n addit io n, of many other analo gi cal t ranslatio ns o r r epro ductions . This, t hat seems co mpl et el y dis pensabl e i n moder n sci ence, is of deci sive i mport ance to o pen to t he su bject other pos si bilit ies i n t he knowl edge and its us e. And, i n additio n, mo der n s ci ences cannot eit her do wit hout t hat analo gical co mpo nent, as it s ho ws Poi ncar È's ar gu ment on t he abs ence of u nivo cal causes in mechani cs. Natur all y, to i nt ro duce a t hir d gr ammar cas e do es not i mpl y automati cally to take t he gr ammar to a high level of ref i nement , but at l east a co mpl et el y new for m of arti cul atio n is reached. In additio n, ever ybody kno ws t hat the t hir d el ement always has been pl ayi ng hi de- andseek i n all t ype of discours es, and i n all the scientifi c dis cour ses al so . But t he cas e i s that pr ecisel y the t r ansi ent motio n is t he o nl y motion t hat can demand uni vocal caus es, or , anywa y, it i s t he o ne gi ving the clo sest approach to it .


The Indian theo ry of l angu age makes a deci si ve distinction bet ween the arti cul at ed and unarti cul at ed l angu ages ; we will co nti nue fi ndi ng t his di sti nctio n and r el atio n i n any approach to the motio n li ke nature's l anguage. We have alr eady written in ot her places t hat sur el y is not a metaphor to speak about the l anguage of nature, and t hat, on t he contr ary, t he most pro babl e i s that hu man langu ages are a poor met aphor of t he edeni c langu age of cr eatio n. One can as k fi nall y wh y so si mpl e i deas, if t hey have so me subst ance, have not fou nd alr eady a r ank of appli catio n. It is necessar y to res pond, on t he contr ar y, that they mu st be su bst anti at ed befo r e any appli catio n, and t his is not t he cas e yet . We still mo ve i n a grou nd of co nj ectur es . Nevert hel ess, a decisi ve f act i s that the tempor al anal ys i s has not begu n to be r eall y tempor al u ntil t hes e ver y l ast years . I t hi nk t hat no body still is awar e of what t his r eally i mpli es , existi ng such diff er ences between t he s pati al anal ys is and t he anal ys is of t he cru de, u ncut t empor al evolution. It happens t hat t hese new tool s ju st forged still ar e exerci sing t hei r wi s do m t eeth wit h inherit ed probl ems, wit hout repai ri ng i n t heir i ndependent pot ential and still tryi ng to for mul ate their o wn questio ns . That i s to s ay, t he mo der n t emporal analysi s al ready is t he answer to a question still not fo r mul at ed. And it t akes wo rk to fi nd a pl ace i n it to that qu estio n, amo ng ot her t hi ngs, becau s e it r ai ses a matt er o f a compl et el y different order , ver y agai nst t he gr ain of t he u nt hi nki ng for mul as and t he routi ne t hou ght. The mo der n t heor y of t he cont rol and t he st abil it y i ncor porates t he mechani cs o n t he one hand and o n t he o t her makes a dis cr etio nar y u s e of statistical tools ; but its mechani cs i s o f cour s e a mechanics of st atio nar y, closed sys t ems . The exter nal relat ions of t he closed sys t em ar e mai nly statisti cal , and t his oft en appli es fo r a gr eat part of t he i nter nal components. Ther efor e, it is easy to see t hat an approach li ke t hi s co nti nues havi ng eno r mous li mit ations and loo phol es , and still mor e if we apply it to biolo gi cal o r ganisms. B y defi nitio n, a li ve o r gani s m cannot be a st atio nar y s ys t em. Then, our o nl y hypot hesi s consist s i n to affi rm t hat t he t ransient co mpo nent of any dynami cs makes its own st atisti cal s electio n, a s election who se r each has to be measurabl e and valuable. Thi s is t he onl y source of natu ral s el ectio n ­and of any po ssi bl e evolu tion, as t he Samkhya alr eady stat ed thousands year s ago. One i s t he fir st har bouri ng dou bts o n t he u ni vers ali t y of thi s pheno meno n, wishi ng critici s ms and att empt s to demo ns tr ate t he u nvi abil it y o f it s oper atio n. In additio n, I will not conceal that t his hypot hesi s is only bas ed o n my personal co nvictio n that it i s i mpos sibl e to give account of a si ngl e beat o f a hear t wit h t he whole ars enal of mechanics and st ati sti cs available yet, and t hat t he phys iologi cal stru ctur es o nl y a- post eriori "expl ain" t he r eal behaviour , but elimi nati ng t he es senti al. It woul d s eem t hat it cannot be an argu ment mor e fr agil e t han t his; it is f ragi lit y its elf . But it can happens al so t hat mechanics i ts elf i s extraor di naril y fr agil e at t he ti me of facing t he gros s, u ncu t tempor al evolutio n, eli mi nati ng what gi ves it t he specifi c ro bu st nes s, t hat i s t he o wn ro bu st ness o f real bei ngs and the world we o bser ve. The cou pling of pendulu m clo cks in a wall by means of resonance no ticed by Huygens i s r eall y the first exampl e i n mo der n sci ence of natu ral and real, spontaneou s s ynchroni zation, i n o pposit io n to t he abst r act and ar bi tr ar y glo bal s ynchro nization or absolu te ti me o f Newto n' s mechani c; but t he pheno menon was kno wn si nce ti me i mmemori al throu gh mu sical i nstru ment s, as for exampl e, tu bes of flut es and or gans . The develo pment of a t heor y based on t hes e new pri nci ples necess ari ly mu st have i mport ant limitat ions in t he pr edi cti ve do mi nion. Thi s is goo d its el f, i n the sense t hat i t indi cat es to us t hat we deal with somethi ng r eal. Not t he pr edi ctio n, tru th i s i mport ant to us . In additio n, mo der n t heori es like t he s ynthet ic t heor y o f the evo lutio n do es not have t he s mall er predict i ve value, no r eit her ret rodicti ve value, and har dly coul d tou ch real ti me and pr es ent evolutio n, and even so it seems t hat many peo ple take it s eriou sly. As we have alr eady sai d i n ot her occasio ns, t he o nly r easo n why these peo ple t ake it seriou sl y is the voi d of mechani cs wit h r es pect to t he u ni vo cal s ense of t he causes . In l ess extent , t his is equall y valid for moder n co smolo gy.


Let us fini s h wi th a co nsi deratio n i n t he symboli c do mi nio n. Mo tio n wit h t hr ee diff er enti al order s and inherent resonances that ar e rel at ed to t he backgrou nd noi se finds a natu r al analo gy with the s ense, bot h indi cati ve and phys i cal , that the Vedas grant to t he s yll able AUM . As it is known, the s acred syll able, bei ng an i nart icul at e sou nd, is al so t he s eed of all t he arti cul ated sou nds and their coupli ng, as wel l as t he backgrou nd i n whi ch t hey finally fuse wit h. A way is i ntended to allude, through the physi cal sou nd, to t hat which dri ves it acros s and tr anscends .

C onclusion : What can we e xpe ct o f pul se d iagnosis
I hope t hat the t hi r d derivati ve and t heir impli catio ns will tur n ou t to be a key to go beyo nd the l abyr i nt h o f s peci ali zed sci ences which have ki dnapped t he commo n real it y. Becaus e wi t hi n tho se s peci ali zed sciences t her e's no lo nger ho pe for so mebody, except for t he experts t hems el ves. W e believe to have gi ven suffi cient ar guments to make pos si bl e to conceive the i nfo r mative richness of the si gnal of t he pul se and it s r el evant s ynt hetic charact er . W e believe al so t hat with t he techni cal tool s no w routinel y avail abl e t he degr ee of r esolu tion o f t he relevant i nfo r matio n can be achieved i n o nl y a f ew mo nths of l abor ator y work and wit h di mi nuti ve expens es . Moreo ver , so me fundament al co rr el atio ns coul d be verifi ed, specifi ed or refuted i n a matt er of days . In any case and si nce t he begi nni ng it i s to be o bs er ved t hat the measu rement and correl atio n of t he t hree pri nci pl es inclu des necess ari l y dif fer ent l evel s of i nt er pret atio n, whi ch nevert heless mu st be co ngruent . Thi s i s not a defi ci ency, bu t an intrinsic vir tue of t his appro ach ­i n f act it is the onl y t hi ng t hat coul d make sense i n t he l evel o f co mpl exit y of an or ganis m. As far as t he qu es tion of what can we hope of t his t ype of di agnosis , we retu r n to t he image of t he car o n t he ro ad. The renewed pul se di agnosis would allo w us to reco gnize wit h ver y reaso nabl e cl arity: a) t he road tr avel , or in o ther wor ds, t he vital vi cissitu des of t he jour ney; b) t he mechanical st at e o f the car ; c) t he behaviour of t he dri ver i n relatio n to bot h previous el ement s. But thi s i s onl y what i s to be expect ed of any r ational and r easo nabl e medici ne. Let us s ay t hat, at t he most , the mo der n bio medi cal mo del i s abl e to di agnos e poi nt b , t hat i s to say, "t he mechanical st at e of the car", and bei ng limi ted by i ts o wn natur e to make su pposi tio ns devoi d of any functio nalit y on t he other two ext remes. The subj ect o nl y exis ts outsi de, to co nvi nce hi m, and his cir cu mst ances can be o nl y co nsider ed acci dents . Present medi ci ne cannot defi ne wit h any crit erio n an o ptimal degr ee of heal t h i n a cert ai n co nt ext and ter m; t he advanced pul s e anal ys is , yes , wou l d have to be abl e to co nsider wit h great accuracy t he r elatio n of our present st at e wit h t he o pti mal, but r eali stic, pos si bl e one; to defi ne co mpr ehensi vely t he l andscape of t he healt h i n t he mo st di rect , i ntu itive and irr edu ci bl e t er ms. An yo ne woul d have to be abl e to check it s elf i n hou se, knowi ng and co mprehendi ng the matt er . Each perso nal opti mal, li ke the bo dy, moo d and mi nd o f each o ne, has absolut el y co ncr et e l i mits and restri ctio ns . The "u nli mit ed healt h", li ke t he "u nli mited fr eedo m", o nl y finds its natural place i n the adverti sing. Si nce now t her e ar e so mu ch wor k and effo rt i n the evaluation and des cri ptio n of t he agi ng pro ces s, l et u s s ay t hat t he pul s e analysi s must be able to gi ve a funct ional and obj ect ive glo bal measu rement of t he degree of disor der of t he or ganism, that is to s ay, o f the ent ropy, but under stood quite i ndependentl y of t he stati sti cal criteri a. Is t her e so met hing si milar now? In additio n, must be abl e to sho w t he di ffer ence between r eversi bl e and irr eversi ble i mbalance, wit hi n a defi ned cont ext and perio d of ti me. Thi s is fundament al al so. B esi des, t he cr iterion o f t hese esti mat io ns does no t emanate from a ho rizo n of pr edi ctio ns, but fro m t he or gani c pot enti al of the co mpl exio n of each per so n and his accu mul at ed hi stor y. W ho s aid "per sonalized medi ci ne"? No need to say t hat the socalled geneti c i nfo r mation of t he i ndi vi dual, an aggr egat e of co nst ructio n materi als, can not r eport indivi dual his tory nor it s i nter actio n wit h t he enviro nment either.


Let us s ay i n addition t hat t he study of t he pul s e in a really anal yti cal fr ame woul d allow fast t ests of co llateral effect s of medici nes , mu ch mor e resol vent dynami c t ests o f ef fort and a robust bri dge wit h co gniti ve s ciences and ps ycholo gy, to mentio n o nly a few. It woul d have to transform our mo st inti mat e u nderst andi ng of ti me process es and, fi rst of all, of we ours elves. Samkhya always was t he anal ysis o f t he t empor al fluctuatio ns , i ndependentl y o f the ar bitrar y di visi bilit y of t he s pace. In as much we develo p an aut henti c t heor y and pr actice of cont rol passi ng throu gh t he filt er of t he per son, and not mer el y t he i ndi vidu al, we will es cape t he co ntrol of anonymous po wers , al ways hi dden behi nd t he o pacity and t he u ni nt elli gi ble char act er of the wor l d, and t he so oft en false pr etensio n t hat t hey hol d a "t echni cal " kno wl edge of superior o rder. The exercis e of the co ntrol is, mai nl y, whi ch t hey hold. W e ar e in t he Age of Control. 25 Janu ar y, 2006 © 2006 , Mi gu el àngel MartÌnez Ir adier

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