Mihai_nebunu Teoria Haosului in Educatie

Analele Universitii Constantin Brncui din Trgu Jiu, Seria tiine ale Educaiei, Nr. 2/2010

Annals of the Constantin Brncui University of Trgu Jiu, Education Sciences Series, Issue 2/2010

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TEORIA HAOSULUI N EDUCAIE,

COMPLEXITATEA I EDUCAIA-

HAOS

Dr. Mihai NEBUNU Universitatea Constantin Brncui din

Trgu-Jiu

Rezumat: Abordm, succint, n excursul de fa o

problematic aflat abia n faz de dezbatere, dar cu profunde implicaii n nelegerea i soluionarea unora dintre chestiunile de fond ale crizei n educaie, trebuind s distingem ntre educaia-haos , ca vid educaional, pe de o parte, centrat pe autoritate i uniformitatea programelor ntr-o lume absolut instabil, i teoria haosului, care leag nvarea de dinamica proceselor naturale, ajutndu- ne s trim cu invizibilul. n alt sens, ncercm s opunem inteligena complexitii, fondat pe teoria haosului determinist n educaie, gndirii unice, de tip maniheist, care impune ordinea, pentru a produce hazardul ilogic, acolo unde, mai mult dect oriunde, guverneaz non-linearitatea i imprevizibilul. Argumentul principal l constituie faptul c teoriile i modelele instruirii, cu originea n paradigmele clasice ale gndirii, sunt mai mult dect apro-ximative i, implicit, cu totul ineficiente, cnd este vorba de a surprinde structura i funcionarea haosului neuronal, definit, n prezent, ca cel mai reputat i mai complex fenomen din univers. Este i motivul pentru care dezbaterile indic adesori o turnur criziologic, structurndu-se aproape invariabil n jurul unei dialectici de fond ntre tradiie i modernitate. ncercarea de depire a acestui dualism paralizant se afl n centrul prezentului demers, nvedernd c viitorul educaiei, al organizrii cunoaterii i al sistemelor educative este, rnd pe rnd, evocat n termenii opui ai schimbrii i ai permanenei, ai nchiderii i ai deschiderii, ai disciplinaritii i ai transversalitii, n ideea de a gsi o modalitate de conciliere etern pasager ntre o ordine profund, implicit, invariant (hidden order), i o ordine explicit (explicate order), exterioar i concret, ntlnind omul i universul (su), ca diafanizri (proiecii) ale unei Raiuni ascunse.

Cuvinte cheie: system, coal, complexitae, haos, educaie(fractal)

THE CHAOS THEORY IN EDUCATION,

COMPLEXITY AND CHAOS-

EDUCATION

PhD Mihai NEBUNU Constantin Brncui University of

Trgu-Jiu

Abstract: We approach, briefly, in the present paper an issue

that is only in the discussion phase, but with profound implications in understanding and solving some of the substantive issues of the crisis in education, must distinguish between "chaos-education" as education vacuum on the one hand, centred on the authority and uniformity of programs in a world completely unstable, and the "chaos theory" that links learning by the dynamics of natural processes, helping us "to live with the invisible." In another sense, we try to oppose "the complexity of intelligence", based on deterministic chaos theory in education, unique thinking, on maniheist type, which requires the order to produce the illogical hazard, where more than anywhere else, governing and non-linearity and the unpredictable.

The main argument is the fact that the theories and the models of training, with the origins in the classical paradigms of thinking, are more than approximate and, implicitly, quite inefficient when it comes to capture the structure and functioning of neuronal chaos, defined in the present as the most reputed and more complex phenomenon in the universe. It is also why the debates often indicate a turn criziological, being structured almost invariably around a substantive dialectic between tradition and modernity. The trying to overcoming this paralyzing dualism is the heart of this approach, demonstrating that the future of the education, of the organization and of the knowledge of educational systems is evoked in apposed terms of change and of the permanent, of closure and of the opening, of disciplinarily and of the transversally, in the idea of finding an eternal way of passenger conciliation between a deep order, default, invariant ("hidden order"), and an explicit order ("explained order"), exterior and concrete, meeting the man and the universe ( His) as diaphanous (projections) of a hidden Reasons.

Key words: system, school, complexity, chaos,

education (fractal)



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1. Consideraii prealabile

Procesul unificrii cunoaterii pare s devin, n era (post)modern, realitate, dac e s pornim de la faptul c pentru tot mai muli oameni de tiin, provenind din orizonturi diferite, teoria haosului (ca studiu al comportamentului aperiodic instabil n sistemele dinamice non-lineare deterministe), avndu-i la origine pe H. Poincar, E. Lorenz, Ilya Prigogine .a., tinde a se institui n factor coagulant al tuturor tiinelor moderne. Se nate astfel o atitudine polemic fa de super-specializare, care condamn la izolare numeroase domenii din cercetarea contemporan. Adepii cei mai convini prezint teoria haosului ca o a treia revoluie a fizicii i nu numai, dup relativitate i teoria cuantic, intenionnd a elimina utopia determinist impus de paradigmele clasice ale tiinei (Alain Boutot,1991). Toate fenomenele din natur i societate, n care nu se poate decela aprioric o logic anume, sunt, n genere, regrupate progresiv sub termenul de haos, denotnd, n esen, o func-ionare haotic. Se nelege, prin urmare, c descoperirea sistemelor haotice ncearc o reconciliere ntre contrarii (haos i determinism n acelai timp). Conform logicii terului inclus: se presupune un al treilea termen care este i A, i non-A, atestnd niveluri de realitate distincte. (B. Nicolescu, 1991). Exist, ntr-adevr, numeroase sisteme (unele extrem de simple), care, n ciuda caracterului lor determinist, prezint un comportament cu totul imprevizibil. Determinarea suitei evenimentelor e dat de efectele obiective, susceptibile a fi precis reperate i msurate, n timp ce comportamentul haotic impune o limit fundamental capacitii noastre de a prevedea ceea ce urmeaz s se ntmple, fie i n situaia n care, ideal vorbind, am dispune de toate datelor cu rol determinant n desfurarea evenimentelor. Nici o form de calcul cunoscut nu poate, de pild, descrie cu exactitudine arabes-curile cderii unei

1. Preliminary Considerations

The process of unifying the knowledge seems to become in the (post)modern age, a reality, if we start from the fact that, for more and more scientists who come from different horizons, the chaos theory (as a study of the unstable non-regular behaviour in the dynamic non-linear determinist systems), based on H. Poincar, E. Lorenz, Ilya Prigogine etc., it trends to be instituted in a coagulant factor of all the modern sciences. Thus it is born a polemic attitude for the super-specialization that consigns to isolation several fields in the contemporary research. The most convinced adepts present the chaos theory as a third revolution of physics, and not only that, after relativity and the quantum theory, wanting to remove the determinist utopia imposed by the classic paradigms of science (Alain Boutot, 1991). All the phenomena in nature and in society, where we cannot reveal a priori a certain logic, are generally regrouped progressively as chaos, denoting essentially a chaotic functioning. As a consequence, it is understood that the discovery of the chaotic systems tries a reconciliation between the contraries (chaos and determinism at the same time). According to the logic of the included third: it is supposed a third term that is both A and non-A, attesting different reality levels. (B. Nicolescu, 1991). There are indeed several systems (some of them extremely simple) that, despite their determinist feature, present a totally unpredictable behaviour. Determining the suite of the events is given by the objective effects that are susceptible to be specifically found and measured, while the chaotic behaviour imposes a basic limit for our ability to foresee what is going to happen, even if, ideally speaking, we own all the data having a determinant role in the development of the events. No type of known calculation may describe exactly, for example, the arabesques of a falling leaf, the scrolls of a smoke rope or the broken route of river. Such an unpredictability is not related to the hazard (as



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frunze, volutele unei funii de fum, sau parcursul fracturat al unui ru. O atare imprevizibilitate nu are nimic a face cu hazardul (ca efect al legii numerelor mari), ci cu o sensibilitate sui-generis la condiiile iniiale. Aleatoriul haotic nu este totuna cu absena ordinii, respectiv - hazardul, dei l implic, n sens constructiv, fiind deopotriv hazard i necesitate. Sistemele pe care teoria le descrie sunt numai aparent dezordonate, teoria haosului cutnd de fapt ordinea interioar ntr-un univers probabilistic. Este, cum vedem, vorba de o tiin holistic ce i propune, contrar reducionismului, s ia n con-siderare totalitatea. Lumea nu mai poate fi explicat exclusiv prin elementele ei constituente (cuarci, cromozoni sau neuroni), trebuind neleas n globalitatea sa. Potrivit teoriei matematice curente, un sistem haotic este definit ca nvedernd o imprecizie sau o sensibilitate la condiiile iniiale de natur a genera traiectorii extrem de divergente n timp. Altfel spus, pentru a deduce cu certitudine viitoarea condiie a sistemului, vor trebui cunoscute, cu o extrem acuitate, condiiile iniiale (t0) n spaiul fazelor, pentru c erorile se amplific rapid fie i n cazul celei mai neglijabile exactitudini (potrivit cunoscutului efect al fluturelui). Cantitativ, creterea erorii este local exponenial n special pentru sistemele foarte haotice (de tip K sau B-sisteme). O atare amplificare face absolut inoperant puterea predictiv care decurge din unicitatea soluiei asigurat de Cauchy-Lipschitz, avnd ca rezultat non-cunoaterea strii finale. Specific unui sistem haotic este faptul c erorile cresc local dup o

lege de tipul : te , unde este un timp

caracteristic sistemului haotic. Caracterul predictibil al evo-luiei sistemului funcioneaz doar pentru momentele t , pentru care exponeniala este aproximativ 1 i deci pentru care eroarea pstreaz mrimea sa iniial. n schimb, pentru t , orice predicie devine practic imposibil, chiar dac teorema Cauchy-Lipschitz rmne adevrat.

an effect of the great numbers law), but to a sui-generis sensitiveness to the initial conditions. The chaotic aleatory feature is not the same thing as the absence of order, respectively hazard, even if it involves it, constructively speaking, being both hazard and need. The systems described by the theory are only apparently messy and the chaos theory is actually looking for the inside order in a probabilistic universe. As we can see, it is about a holistic science that wants to consider its totality, unlike the reductionism. The world cannot be exclusively explained by its constitutive elements (quarks, chromosomes or neurons), and we have to understand it in its globality. According to the current mathematical theory, a chaotic system is defined as proving an imprecision or sensitiveness to the initial conditions that can generate orbits that are extremely divergent in time. In other words, in order to deduct certainly the future condition of the system, we have to know with an extreme accuracy the initial conditions (t0) in the phases space because the errors are emphasized quickly even in case of the most negligible accuracy (according to the known butterfly effect). Quantitatively, the increase of the error is locally exponential especially for the very chaotic systems (K or B systems). Such a magnification makes absolutely inoperative the predictive power that comes from the uniqueness of the solution provided by Cauchy-Lipschitz, having as a result the non-knowledge of the final situation. It is specific to a chaotic system the fact that the errors increase locally after a law such as:

te , where is a time specific to the chaotic

system. The predictable feature of the system evolution works only for t moments, for which the exponential is about 1 so for which the error keeps its initial size. In exchange, for t , any prediction becomes practically impossible, even if Cauchy-Lipschitz theorem remains true. It comes out the fact that the thing generally called chaos by the scientists is



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Rezult c ceea ce, n genere, omul de tiin numete haos se explic mai degrab prin noiunea de imprevizibilitate, de unde i ideea c nici o incertitudine iniial, orict de mic, nu poate fi neglijat ntr-un sistem dotat cu sensibilitate la condiiile iniiale, tocmai n considerentul consecinelor imprevizibile ce le poate avea pe termen infinit de lung. Predictibilitatea pe termen orict de lung este, n acest caz, lipsit de sens, dat fiind numrul foarte mare de perturbaii minime dar in-controlabile la scar extins, pentru care ar fi necesar o cunoatere infinit de precis a strii la un moment dat. n virtutea acestui fapt, evenimente aparent nesemnificative pot avea o influen imens ntr-un univers non-linear. Aplicaiile teoriei haosului, deja extrem de variate n tiin i tehnologie (de la previziunile meteo, modelarea sistemelor economice, teoria deciziei, dinamica populaiei, la astrofizic, biologie i neurotiine) explic, cu att mai mult, i funcionarea indeterminist a sistemului neuronal, deo-potriv cu procesele nvrii, imposibil de previzualizat i proiectat dup o logic i o mentalitate pedagogic retrograd, de tip clasic, fiind, evident, diferite de orice evenimente de tip stocastic. Teoria hoasului aplicat la fenomenele vieii, cu att mai mult cele ale universului psihic i ale formrii/ educaiei, tinde s probeze c ascensiunea organizrii materiei spre complexitate nu este posibil dect ntr-un mediu haotic, genernd structuri ele nsele haotice. Nu ntmpltor creierul privit, n mod paradoxal, ca o structur haotic, este considerat obiectul fizic cel mai complex, mai organizat i ordonat din universul cunoscut. Determinismele persoanei, fie ele predispoziii genetice, dar i itinerarul vieii (de la dezvoltarea intrauterin la percepiile senzoriale, educaie, religie, sex, tot ceea ce e rezident n memorie) nu epuizeaz niciodat devenirea absolut imprevizibil a fiinei noastre. Existena unui eu (subiect) nu este (i nici nu are cum fi) reductibil la suma operaiile neuronale care se desfoar n

rather explained by the unpredictability notion, from where it results the idea that no initial incertitude, as small as it is, can be neglected in a system that has sensitiveness to the initial conditions because of the unpredictable consequences that can occur on an infinite term. The predictability on an infinite term makes no sense in this case because of the very big number of minimum, but incontrollable at the extended scale perturbations for which it would be needed an infinitely accurate knowledge of the situation at a certain time. Under this fact, apparently insignificant events may have an immense influence in a non-linear universe. The applications of the chaos theory that are already extremely different in science and technology (from meteorological prognostics, modelling the economic systems, decision theory, population dynamics, to astrophysics, biology and neurosciences) explain also the indeterminist functioning of the neuronal system and the processes of learning that are impossible to preview and project according to a retrograde pedagogic classic mentality and logic, being obviously different from any stochastic events. Chaos theory applied to the life phenomena, and also to the ones of the mental universe and of training/education, trends to prove that the increase of organization the matter towards complexity is possible only in a chaotic environment, generating structures that are chaotic themselves. Not accidentally, the brain seen paradoxically as a chaotic structure is considered as the most complex, organized and ordered physical object in the known universe. The persons determinisms, either genetic predispositions or the life itinerary (from the intrauterine development to sensorial perceptions, education, religion, sex, everything that resides in the memory ) never exhaust the absolute unpredictable becoming of our being. The existence of an ego (subject) is not (and it cannot be) reducible to the sum of the neuronal operations that develop in our brain. If it happened this way, the exhaustive knowledge



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creierul nostru. Dac ar fi astfel, cunoaterea exhaustiv a derulrii acestor procese ne-ar permite s descifrm meandrele cele mai intime ale psihismului persoanei i chiar s prevedem/ proiectm evoluia ei. Este ns categoric exclus o asemenea identitate ntre procesele neuronale care au loc n creier i experiena personal (mental) trit.

Numeroase argumente pledeaz n acest sens. Unul dintre ele este, de pild, distorsiunea duratei: timpul trit nu este echivalent cu timpul neuronal. Este ca i cum, n anumite situaii, contiina s-ar extrage din timp.Viaa i spiritul s-au nscut, prin urmare, din haosul generator de informaie i complexitate. Dincolo de ele sunt de bnuit o mulime de alte variabile indeterminabile, n virtutea crora omul este liber i unic, imposibil de format ( i de evaluat) cu mijloacele clasice tiute. Or, teoriile nvrii/formrii i modelele instruirii cunoscute ignor, n ciuda attor declaraii de intenii, tocmai funcionarea invizibilului din fiina noastr, fantasmaticul imposibil de msurat, nici mcar aproximat, cu echerul i aa cu plumb, pentru c haosul nu este exclusiv guvernat de logici deterministe. Proiectanii de constructe umane, planificatorii i reformatorii de orice fel de sisteme ideologice, implicit, educaionale, nu se vor mai putea, prin urmare, regsi, ntr o lume care este, deopotriv haotic i determinist. Care sunt, pn la urm, sensul i utilitatea miraculoaselor demersuri de proiectare tiinific a instruirii/formrii, ale aa-zisei inginerii educative, ambiionnd, dincolo de anumite limite, construcia tipului uman dorit, pentru a rspunde exigenelor de eficacitate le ntreprinderii moderne? Rspunsul este aproape inevitabil : moartea omului ca om, ntr-o modernitate prin excelen mortifer (moartea (dumne)zeilor, moartea naturii, sfritul istoriei .a.m.d.). n teoria sa asupra structurilor disipative, Ilya Prigogine a artat c sistemele deschise (orga-nismele vii ndeosebi) sunt perturbate de variaii de energie provocate de multiplele

of the development of these processes could allow us to decode the most intimate meanders of the persons psychism and even to foresee /project its evolution. But we categorically exclude such an identity between the neuronal processes that occur in the brain and the personal (mental) experience that has been lived.

Several arguments plead in this sense. For example, one of them is the time distortion: the time that has been lived is not the equivalent of the neuronal time. It is the same as, in certain situations, the consciousness would be extracted from the time. Life and spirit were born thus from the chaos generating information and complexity. Beyond them, we suppose a lot of other indeterminable variables under which the human is free and unique, impossible to train (and to evaluate) by means of the classic known means. But the theories of teaching/training and the known models of instruction ignore, despite so many declarations of intentions, the functioning of the invisible feature in our being, the phantasmagorical feature that is impossible to measure, not even with the setsquare and the slug thread because chaos is not exclusively governed by determinist logics. The projectors of human constructions, the planners and the reformers of any kind of ideological systems, including the educational ones, will not be able to find their place in a world that is both chaotic and determinist. Finally, what are the sense and the utility of the miraculous approaches of scientific projection of instructing/training the so-called educational engineering, motivating, beyond certain limits, the construction of the desired human type in order to answer the efficiency exigencies of the modern industry? The answer is almost unavoidable: human death as a human, in a modernity that is mortal above all (death of gods, death of nature, end of history etc.). In his theory about the dissipative structures, Ilya Prigogine showed that the opened systems (especially alive organisms)



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interaciuni cu mediul, ceea ce presupune de-structurarea lor. Logica/dialectica haosului este cea care face posibil stabilirea de noi interaciuni i restructurri, n ali termeni - auto-organizarea, respectiv com-portamentul lor dinamic, de natur s conduc la o nou ordine de nivel superior. Cu ct evo-luia i organizarea unor astfel de structuri disipative sunt mai profunde, cu att mai mult sporesc schimburile de energie i comportamentul imprevizibil pentru a suine o complexitate deruntant, inimaginabil i tot mai obsedant ntr-un univers al realitilor multiple. Este tocmai ceea ce genereaz dinamismul sistemelor deschise de genul universului psihic, prin excelen definite de o inextricabil estur de interaciuni. De unde i fragila lor (in)stabilitate, surs posibil de noi forme de (auto)organizare, ca alte posibile, infinite sisteme non-lineare. Dac ns non-linearitatea este uor de observat n tiinele fizice (exacte), ea este cu mult mai dificil de explicat cnd vine vorba de fenomenele cogniiei. Analiza linear, specific paradigmei clasice, pleac de la ideea c orice fenomen poate fi neles ca efect al uneia sau al mai multor cauze, c legiti anume permit stabilirea unor interrelaii care fac posibil previzualizarea i planificarea schimbrilor, ntr-o lume main perfect reglat, din care demiurgul nsui este eliminat ca o fals ipotez. n sens invers, analiza non-linear este construit pe ipoteza c n sistemele deschise schimbrile se produc n situaii tranzitorii, indeterminabile, n absena unor caracteristici com-parabile comune, regizate de logici diferite. Este tocmai ceea ce definete zona de perturbare sau spaiul tranziiilor de faz (haosul), staz ce se sustrage oricrui model descriptibil, deci oricrei teorii fundamentat pe o paradigm de ordin formal.

Drept urmare, nvarea/formarea, inseparabil de omul accident al complexitii nu are cum fi privit altfel dect ca un act impenetrabil, ireductibil la suma modelelor, tehnicilor i pro-cedeelor psiho-pedagogice puse n joc. Dac, potrivit

are disturbed by variations of energy provoked by the multiple interactions with the environment, fact that supposes their de-structure. The logic/dialectic of chaos is the one that allows the establishment of new interactions and restructures, in other terms the auto-organization, respectively their dynamic behaviour able to lead to a new order at a superior level. The more the evolution and the organization of certain dissipative structures are deeper, the more the energy exchanges and the unpredictable behaviour increase in order to support a confusing, unimaginable and more and more obsessive complexity in a universe of the multiple realities. It is the fact that generates the dynamism of the open systems such as the mental universe, defined above all by an inextricable tissue of interactions. This is the reason of their fragile (in)stability, a possible source of new types of (auto)organization, as other possible, infinite non-linear systems. But, if the non-linearity is easy to notice in the physical (exact) sciences, it is much more difficult to explain when it is about the cognition phenomena. The linear analysis, specific to the classic paradigm, starts from the idea that any phenomenon can be understood as an effect of one or several causes, that certain regularities allow the establishment of certain interrelationships that allow to preview and to plan the changes in a perfectly set world-machine where the demiurge himself is removed as a false hypothesis. Inversely, the non-linear analysis is built on the hypothesis that in the open systems the changes are produced in transitory, undeterminable situations, in the absence of certain commune comparable features that are directed by different logics. It is the fact that defines the disturbing area or the space of the phase transitions (chaos), a stage that backs out from any describable model, so from any theory based on a formal paradigm.

As a consequence, the teaching/training, inseparable from the accident of complexity human, regarded differently from an impenetrable act that is irreducible to the sum



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neorealismului postmodern, lumea este ceea ce este nseamn c ne aflm n prezena unei inconsistene proteice n raport cu care orice ordine, ierarhie, gndire sau cunoatere nu au dect relevana unei naraiuni supuse celei mai radicale i mai deconstructive polisemii, evident, alta dect demonul lui Laplace (pentru care totul putea fi cunoscut), dect soluia final a lui Hilbert, ca logic total, sau dect omul neuronal imaginat de Changeux, golit de orice experien psihic personal: Omul nu mai are nimic de-a face cu spiritul, i este de ajuns s fie un om neuronal.

2. Complexitate i haos

Complexitatea, ca i teoria haosului reprezint achiziii relativ recente. Sunt cuvintele magice ce par a se afla (dac nu cumva i sunt), n contextul ideologiei postmoderne, printre conceptele-cheie ale unor noi paradigme de cunoatere contestnd supremaia raiunii formale n preteniile ei de a nelege, prezice i ordona. Figura modern a haosului, aflat n vecintatea noiunii de complexitate, pare s retraseze o alt cale, n care forma se deschide seriilor divergente, aleatoriului, im-previzibilului. Chiar dac, la origine, complexitatea avea s intereseze predominant matematicile i fizica, sistemica i teoria informaiei - care i sunt asociate -, fantasma ei preocup deopotriv filozofia, artele i educaia. Cu toate ncearc s afirme i s neleag complexitatea, generat de noile evoluii ale cunoaterii, o complexitate sfidnd metodele tradiionale de analiz i aciune. Kant pune n eviden aporiile (limitele) raiunii, Nietzsche este primul care vorbete despre o criz a fun-damentelor certitudinii, Ardono di Horkheimer formuleaz, la rndul lor, nu doar o critic a raiunii clasice, ci construiesc i o filozofie/ gndire a complexitii, la confluena unor orientri iconoclaste (teoria informaiei, teoria sistemelor, teoria haosului .a.m.d. Filozofii i oamenii de tiin moderni confer noi dimensiuni complexitii. Printre

of the psycho-pedagogical models, techniques and proceedings that are being used. If, according to the postmodern neorealism, the world is what it is it means that we are in the presence of a protean inconsistency reported to which any order, hierarchy, way of thinking or knowledge have only the importance of a narration liable to the most radical and deconstructive polysemy that is, obviously, different from Laplaces demon (for whom everything could be known), from Hilberts final solution, as a total logic, or from the neuronal human imagined by Changeux, emptied from any personal mental experience: Human has nothing to do with spirit, it is enough for him to be a neuronal human.

2. Complexity and Chaos

Complexity, like chaos theory, represents a relatively recent achievement. They are the magic words that seem to be (maybe they really are) in the context of the postmodern ideology, between the key-concepts of certain new knowledge paradigms, contesting the supremacy of the formal reasoning in its claims to understand, foresee and command. The modern figure of chaos, placed next to the complexity notion, seems to trace again another way where the shape is opened to the divergent series, to the aleatory and unpredictable feature. Even if, at its origins, complexity was going to be a real interest for mathematics and physics, the systems and the theory of information that are associated to it -, its ghost concerns in the same way the philosophy, the arts and the education. Although he tries to affirm and understand the complexity generated by the new evolutions of knowledge, a complexity that bids defiance to the traditional methods of analysis and action, Kant highlights the aporias (limits) of reasoning, Nietzsche is the first who talks about a crisis of the certitude fundaments, Ardono di Horkheimer formulates, at his turn, not only a critique of the classic reasoning, but also constructs a philosophy/way of thinking of complexity, at



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ei, E. Morin este cel care propune, n introduction la complexit o frumoas abordare a acestei necunoscute care este complexitatea, definit ca o e-stur () de constitueni eterogeni inseparabil asociai (E. Morin, 1990), acolo unde inadec-varea profund i grav dintre cunotinele compartimentate pe discipline i realitatea inter- i transdiciplinar, global i polidimensional prea s anune moartea naturii i a omului A nelege, aadar, complexitatea (i omul ca accident al complexitii) este un imperativ categoric i poate fi unul din scopurile majore ale acestui secol. Mizele sunt enorme, ntruct vizez viitorul, innd seama de fragilitatea, de limitele resurselor noastre, de echilbrele vitale. Paradigma complexitii se declar, n primul rnd, mpotriva reducionismului scientist i mecanicist, afirmnd c exist limite n tiin, c incertitudinea i imprevizibilul in de natura nsi a Fiinei. Este ceea ce deosebete complexitatea de faptul complicat. Dac lucrurile complicate pot fi, n final, tangibile i comprehensibile, complexitatea nu se las niciodat integral surprins. Putem avea percepia global a unui sistem complex, dar nu-i putem nelege ansamblul n toate detaliile i nici nu-i putem anticipa, ntru totul, dinamica, dat fiind c realitatea este constant incomplet. A admite complexitatea nseamn a admite incidena unor reele ascunse, subiacente aparenelor fenomenale, provenind, pe de o parte, din interaciunea unor multiple procese, iar pe de alt parte, din relaiile circulare, non-lineare i din combinaiile lor, supuse unor reguli i legiti, care scap puterii noastre de nelegere (reprezentri, limite ale informaiei i ale cunoaterii). Complexitatea const deci n incapacitatea funciar a facultilor noastre raionale de a calcula (sau, cel puin, aproxima) aprioric comportamentul unui sistem, determinat n special de recursivitatea funcionrii componentelor sale, susceptibil a genera fenomene inteligibile, dar

the junction of certain iconoclast orientations (information theory, systems theory, chaos, etc. Modern philosophers and scientists confer new dimensions of the complexity. Between them, E. Morin is the one who suggests, in introduction la complexit a beautiful approach of this unknown complexity defined as a tissue (...) of inseparable heterogeneous associated constituents (E. Morin, 1990), where the deep and serious inadequacy between the knowledge grouped on disciplines and the inter- and trans-disciplinary, global and poly-dimensional reality seemed to announce the death of nature and of human. Therefore, understanding the complexity (and human as an accident of complexity) is a categorical imperative and may be one of the major purposes of this century. The stakes are enormous whereas they refer to the future, considering the fragility, the limits of our resources, the vital balances. The complexity paradigm declares to be, at first, against the scientist and mechanical reductionism, affirming that there are limits in sciences, that incertitude and unpredictability are related to the nature of Being. It is the fact that makes differences between the complexity and the complicated fact. If the complicated things may be finally tangible and comprehensible, complexity never remains totally surprised. We may have the global perception of a complex system, but we cannot understand its ensemble with all its details and we cannot totally anticipate its dynamics either, given the fact that reality is constantly incomplete. Accepting the complexity means accepting the incidence of certain hidden networks subjacent to the phenomenal appearances, coming, on one hand, from the interaction of multiple processes, and on the other hand, from the circular, non-linear relationships and from their combinations that are liable to certain rules and regularities that get away from our understanding power (representations, limits of information and knowledge). So complexity consists in the landed inability of our rational faculties to calculate (or, at least, to approximate) a priori the



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imprevizibile. Ea este cea care face dup o expresie a lui G. Bachelard miraculosul inteligibil. Teoria haosului este probabil ultimul avatar al complexitii, n msur a ne face s nelegem faptul c fenomene aparent dezordonate se comport ca i cum ar fi guvernate de o ordine ascuns, metaforic definit ca atractor straniu. Vorbim, prin urmare, de o inteligen a complexitii, o nou ideologie, careia i repugn tot ceea ce este categoric previzibil ori calculabil, pentru a se replia asupra individului izolat i fr repere ntr-o lume ostil i greu de controlat. Aceast inedit viziune asupra lumii, rezultat al filozofiei complexitii, permite apropierea demersurilor fundamentale ale gndirii analiza/ sinteza, ne ajut s nelegem c natura este un organism viu, iar universul - un spaiu al poten-ialitilor, o sum de energii, de fluxuri, procese i entiti subtile, c supravieuirea omului, a popoarelor, a culturilor este direct legat de calitatea relaiilor i depinde de felul n care aceste interdependene vor putea fi nelese i trite. Strvechiul principiu taoist: totul particip la tot afl, prin urmare, aici expresia sa plenar. Cele dou concepte (haosul i complexitatea), avnd n centru problema predictibilitii, sunt, cum se vede, n curs de a fi pretutindeni manifeste. Ar fi interesant de tiut care sunt consecinele practice pe care le-ar putea trage educaia dintr-o atare emergen a complexitii, atunci cnd se pune problema proceselor nvrii. Un fapt este cert: accedem ntr-un univers pe care l percepem ca fiind inextricabil, nelegerea lui necesitnd mai mult o formare general dect una specializat, ceea ce nu nseamn neglijarea specializrii, ci mai degrab implicarea ambelor pentru a face fa funcionrii complexe n societatea cunoaterii. Acest demers necesit o repoziionare radical, de ordin epistemo-logic, o reform a gndirii, n msur s (im)pun n centrul culturii i al educaiei o inteligen a complexitii sui-generis. Cu att mai mult cu ct hibridarea tehnologic a devenit un factor de accelerare i co-evoluie.

behaviour of system, determined especially by the recursive feature of their components functioning, liable to generate intelligible, but unpredictable phenomena. It is the one that is made according to G. Bachelard the miraculous intelligible feature. Chaos theory is probably the last avatar of complexity that is able to make us understand the fact that apparently messy phenomena behave as if they were governed by a hidden order defined as an strange attractive thing. As a consequence, we are talking about an intelligence of complexity, a new ideology that rejects everything predictable or calculable, in order to double back the isolated individual having no reference points in a hostile, hard to control world. This unprecedented vision on the world, a result of the complexity philosophy, allows to get closer the basic approaches of the analysis/synthesis way of thinking, helps us understand that nature is an alive organism and the universe a space of potentialities, a sum of energies, flows, processes and subtle entities, that the survival of the human, of the peoples, of the cultures is directly connected to the quality of the relationships and depends on the way these interdependences will be understood and lived. The old Taoist principle: everything participates to everything, finds here its plenary expression. The two concepts (chaos and complexity), having in centre the predictability problem, are, as it is seen, about to be manifested everywhere. It would be interesting to know which are the practical consequences the education could get out from such an emergency of complexity when it is about the processes of learning. A fact is certain: we accede in a universe that we perceive as inextricable and its understanding needs more than a general training than a specialized, fact that does not mean to neglect the specialization, but rather to include both of them in order to face the complex functioning in the knowledge society. This approach needs a radical epistemic-logic repositioning, a reform of thinking able to impose in the



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Noile magistrale ale informaiei i comunicrii, de pild, sunt, prin excelent, emergente, spontane, eminamente descentralizate, nvedernd c haosul este generator de informaie i complexitate.

Se resimte, n prezent, o imperioas nevoie de a lega, de a interfera, de a identifica analogii i dife-rene, de a reintegra i sintetiza, de a pune n conjuncie ceea ce, dup secole de gndire disjunct, fusese fracturat. ntr-un anume sens, nevoia unei abordri plurale este imanent creierului nostru, este o stare de spirit, rezultat al interaciunii dinamice dintre nivelurile energetice ale diferitelor activiti cerebrale, necesitnd un alt tip de educaie, care s ia n considerare toate dimensiunile fiinei umane. Cercetarea conjunct (natur/imaginar, univers/om .a.m.d.), din perspectiva unei epistemologii a complexitii/complementaritii, convergena coninuturilor, le-ar putea facilita celor ce nva o implicare mai direct n real i le-ar permite o confruntare mai suportabil cu diversele provocri ale problematicii lumii n care trim, eliminnd, pe aceast cale, decalajul enorm dintre noua viziune a lumii, privit ca numr nedefinit de realiti, i prejudecile rezidente nc n filozofie, n art i tiinele omului, ca urmare a unui determinism mecanicist generat de pozitivismul secolelor trecute. n timp ce nvarea/cunoaterea fragmentat izoleaz, atrofiaz fiina interioar i condamn la in-comunicare, idolatriznd omul-obiect, tiina complexitii pentru care logica existentului nu mai este, pur i simplu, reflexul determinrii, ci un background al gramaticii de semne, o reconstrucie a ei din perspectiva neuro-spiritului uman leag cunoaterea de aciune, nscriindu-se n istoria trit, pentru a-i conferi o nou dimensiune existenial.

3. Teoria haosului /vs/ haosul n educaie

n uzul comun, sintagma denot un sens

pervertit: educaia-haos, ntr-o coal a

culture and education centre a sui-generis complexity intelligence.

We currently smack an imperious need to connect, to interfere, to identify analogies and differences, to reintegrate and synthesize, to put in conjunction what have been broken after centuries of disjunctive thinking. In a certain sense, the need of a plural approach is immanent to our brain, is a mood, a result of the dynamic interaction between the energetic levels of different brain activities, needing another type of education that should consider all the dimensions of the human being. The conjunct research (nature/imaginary, universe/human etc.), from the perspective of an epistemology of complexity/complementarity, convergence of contents, could make it easier for the ones who learn a more direct involvement in reality and would allow them a more supportable facing with the different challenges of the problems in our world, removing by these means the enormous disparity between the new vision of the world, regarded as an undefined number of realities and the prejudices still resident in philosophy, art and human sciences, as a consequence of a mechanic determinism generated by the positivism in the past centuries. While learning/knowing partially isolates, emaciates the inside being and sentences to communication, worshiping the human-object, the complexity science for which the logic of the existent feature is not the determination reflex anymore, but a background of the signs grammar, its reconstruction from the perspective of the human neuro-spirit connects knowledge to action, registering in the lived history in order to confer it a new existential dimension.

3. Chaos Theory /vs./ Chaos in Education

In common use, the syntagm denotes an

abnormal meaning: the education-chaos, in a school of chaos. As much as the official propaganda and its preachers try to make the current educational system look like a postal



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haosului. Orict se strduiete propaganda oficial i predicatorii ei s pun n culori de carte postal nvmntul actual, un lucru este cert: aproape toat lumea este de acord (mai puin, un numr de iresponsabili gestionari ai educaiei ) n a considera c sistemul social este n pan, c, n fapt, vorbim de o coal a eecului fabricnd neosclavii de care puterile oculte par s aib nevoie. Se afirm, m-potriva frapantei evidene, c nivelul urc(dei, exceptnd elita, nu vedem dect contrariul), c se tie mai mult (poate, dar capacitatea de reflecie este grav ameninat !). Nu mai este de mult o noutate faptul c elevii/studenii i, n genere, omul modern, sunt invadai de cantiti enorme de informaie disparate, al cror sens i logic le scap, n timp ce muli dintre ei (i, poate, dintre noi) au uitat deja s-i foloseasc propria limb. n raport cu informaia destructurant i agresiv, invaziv i divers, ei se simt nu de puine ori sceptici, pierdui i ameninai. Este tocmai ce pare c definete constructul uman (post)modern, produs al colii de serie, n genul unui automat biologic, logico-matematic, cu un comportament apropiat de simulatorii activitii intelectuale.

Putem fi, n acest sens, de acord cu opinia lui Lopold Flam (1964), dup care modernul, un fel de supercalculator uman, tie totul, dar gndete puin i nu crede n nimic, . Termenul "a ti este luat aici cu sensul exclusiv de a poseda multe informaii. A tri n miezul informaiei (cum se ntmpl n contextul noilor comunicaii intersatelitare) nu nseamn, implicit, a dobndi cunoatere. Informaia n exces, neconvertit n cunotine, este moartea cunoaterii autentice, moartea omului ca subiect, transformat n burete informaional. Info-poluarea a devenit deja un nou factor de risc, care transmut individul incapabil de a fi Sine n obiect al experimentelor ideologice, pseudo-tiinifice, de-subiectivat, formalizat i manipulat. ntr-un asemenea context, Jerome S. Bruner (1996), de pild, sugereaz necesitatea unui logo-catharsis (sau a unei

card, one fact is certain: almost everybody agrees (less, a number of irresponsible financial administrators of education) with considering that the social system is broken, that we are actually talking about a school of failure fabricating the neo-slaves the hidden powers seem to need. It is affirmed, against the shocking evidence, that the level increases (even if, except the elite, we can see only the contrary), that it is known for a long time (maybe, but the reflection ability is seriously threatened!). It is not new the fact that pupils/students and generally the modern human are invaded by enormous quantities of disparate information whose meaning and logic gets away from them, while a lot of them (and maybe, of us) have already forgotten how to use their own language. Comparing to the destructive, aggressive, invasive and diverse information, they often feel sceptical, lost and threatened. It is the fact that seems to define the human (post)modern construction produced by the series school, such as a biological, logical-mathematical automat having a behaviour close to the simulators of the intellectual activity.

In this sense, we may agree to Lopold Flams (1964) opinion according to which the modern one, some kind of human supercomputer, knows everything, but thinks less and does not believe in anything. . The term to know is understood here exclusively as owning lots of information. Living in the centre of the information (as it happens in the context of the new inter-satellite communications) does not mean, implicitly, gaining knowledge. The information in excess, non-converted in knowledge is the death of the authentic knowledge, the death of the human as a subject transformed in an informational sponge. The info-pollution has already become a new risk factor that transmutes the individual unable to be Himself in an de-subjectivised, formalized and manipulated object of the ideological, pseudo-scientific experiments. In such a context, Jerome S. Bruner (1996), for example, suggests the necessity of



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logo-terapeutici) care s vindece disfunciile cunoaterii, generat de izolarea i standardizarea disciplinelor, menite a ne oferi cel mai adesea reprezentri pariale ori fragmentate care nu se potrivesc contextelor dinamice de via. Acest logo-catharsis ar trebui s permit construcia indi-vidului ca fiin angajat, plurivalent, participnd activ la experiena cognitiv-afectiv a speciei, situaie n care vorbim de o tiin personal (personal knowledge), implicnd, bineneles, i multidimensionalitatea. Modernul redus cel mai adesea la staza de obiect (al educaiei/cunoaterii) necesit a fi de urgen recuperat ca Subiect al (educaiei/cunoaterii).

Care este, n fond (i succint), realitatea ? Devaloriznd cunoaterea n profitul aa-zisei tiine de a face, dar n detrimentul lui a fi, opunnd simulacrele gadget culturii autentice, coala pare a fi abdicat de la misiunea ei fundamental: de asigurare a unei educaii integrale, n spiritul com-plexitii, formabililor situai, fr voia lor, la intersecia unor sisteme simbolice diferite. Cohortele de chiulangii eludnd programele colare i fraudnd examenele, putanii care hruiesc organele de ordine public, anunnd bombe n coli sau dnd foc mainilor, exhibiiile pornografice juvenile pe net, violenele de orice fel i insecuritatea, toate n numele democraiei fr limite, dau impresia c sunt produsul celor aproape dou decenii de experimente colare aberante, al populismului i electoralismului, care au generat haos i confuzie, ndeprtnd instituia educativ de soluionarea problemelor reale cu care se confrunt efectiv. E ca i cum s-ar voi trimiterea n neant a ceea ce s-a ncetat a se adora. Cum altfel s-ar putea purta aceti tineri, de cele mai multe ori lipsii de ideal, defazai i demotivai dac nu abhornd tocmai sistemul ineficace care i-a produs ? Eecul, n msura n care se nregistreaz, nu pare a fi dect urmarea iniierii i a relei aplicri a reformelor de fond de dup anii `90. Ele, n primul rnd, se afl

a logo-catharsis (or a logo-therapy) that could heal the knowledge dysfunctions generated by the isolation and the standardization of the disciplines most of the times meant to offer us partial or fragmented representations that do not match to the dynamical life contexts. This logo-catharsis should allow the construction of the individual as a hired, polyvalent being actively participating to the cognitive-affective experience of the species, situation where we talk about a personal knowledge, involving of course the multidimensionality, too. The modern one reduced most of the times at the object stage (of education/knowledge) needs to be urgently recovered as a Subject of (education/knowledge).

What is basically (and succinctly) the reality? Devaluing knowledge in the advantage of the so-called knowledge of making, but in the disadvantage of being, opposing the gadget travesties to the authentic culture, school seems to have abdicated from its basic mission: to provide an integral education, in the complexity spirit, to the trainable ones that are unintentionally placed between certain different symbolic systems. The big groups of skippers who elude the school programs and fraud the exams, the kids who harass public order organs by announcing bombs in schools or by starting fires in cars, the pornographic juvenile exhibitions on the internet, the violence of any kind and the insecurity, all of them in the name of the democracy with no limits, give the impression that they are the product of almost two decades of aberrant school experiments, of populism and electoralism that have generated chaos and confusion, removing the educational institution from the solving of the real problems it actually faces. It is like we wanted to send to nothingness what stopped to be worshipped. How could behave these teenagers, most of the times having no ideals, no phases and no motivations, but abrogating the inefficient system that produced them? The failure, as it is registered, seems to be only the consequence of initiating and badly



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printre cauzele majore ale disperrii unei lumi dezorientate, ntruct, dei proclam descentralizarea i flexibilizarea parcursurilor curriculare, deopotriv cu facilitile corespunztoare, continund s rmn, prin autoritatea care reprob dez-ordinea, dar i aparena dezordinii, nu doar un concept excesiv pentru schimbrile iniiate n educaie, ci i un instrument de lucru ineficace sub raportul complexitii fenomenului reformat, care este departe de a se supune ordinii manifeste i rigorilor ei, uitndu-se c diversitatea un trebuie con-fundat cu dezordinea. Meninerea centralizrii autoritii i uniformitatea cosmetizat a programelor sunt exemplul cel mai concludent al impunerii ordinii, acolo unde guverneaz non-linearitatea i impre-vizibilul. coala ar trebui s trag ea nsi o lecie. Dac metodele, pe de alt parte, sunt o component a reuitei, se ntmpl, i nu de puine ori, ca metodologia s le impun ca un dictat. Ca s nu mai vorbim de faptul c este cu totul de neconceput a se proceda la o reform de anvergur, i de acuratee, n acelai timp, n sisteme deschise, cum este nvmntul, prin natura lor permeabile schimbrilor ce se produc n situaii tranzitorii, i deci indeterminabile, n absena unor caracteristici comparabile comune guvernate de logici diferite. Dincolo de toate acestea, problemele grave ale educaiei-haos rmn mereu aceleai : subfinanarea sistemului, multiplicarea claselor cu niveluri multiple i bineneles nediferenierea instrurii, lipsindu-i de un ajutor suplimentar pe elevii n dificultate. Chiar dac nu toi pot accede, prin natura lucrurilor, la poziii sociale nalte, regula este c educaia trebuie s-l duc pe fiecare acolo unde i este locul, n funcie de capacitile proprii, produsul contrar fiind interminabile generaii de frustrai. S-ar curma astfel inflaia de atestate superioare, fr acoperire, care compromit valorile autentice. n numele falselor bune intenii, al egalitii de anse zgomotos clamate i al sloganelor insidios democratice de genul

applying the basic reforms after the 90. In the first place, they are between the major causes of desperation of a disoriented world whereas, even if the proclaim the decentralization and the flexibility of the curricular routes and also the corresponding facilities, continuing to be, by the authority that disapproves mess, but also the appearance of disorder, not only an excessive concept for the changes initiated in education, but also an inefficient working tool for the complexity of the reformed phenomenon that is far from being liable to the manifest order and to its rigours, forgetting that diversity shouldnt be mistaken by mess. Maintaining the centralization of the authority and the disguised uniformity of the programmes are the most conclusive example of imposing the order where the non-linearity and the unpredictability govern. School should learn a lesson. On the other hand, if the methods are a component of success, it often happens that methodology imposes them as a dictator. In addition, we cannot conceive at all to proceed at an important and accurate reform at the same time in open systems such as the educational one, that allow changes produced in transitory, so undeterminable situations, in the absence of certain common comparable features governed by different logics. Beyond all of these, the serious problems of the education-chaos are always the same: sub-financing the system, multiplying the classes on multiple levels and of course not differentiating the instruction, not giving an additional help to the pupils having difficulties. Even if not everyone can accede, by the nature of thins, to high social positions, the rule is that education must lead everyone at their place, depending on his or her own abilities and the contrary product is represented by infinite generations of frustrated people. Thus, we could stop the inflation of superior confirmations having no cover, that compromise the authentic values. In the name of the fake good intentions, of the loudly claimed chances equality and of insidiously democratic slogans such as centring the education on the one who studies,



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centrrii educaiei pe cel ce nva, formatorii s-au transformat n negustori de iluzii, cobornd nepermis exi-genele formrii. Reprimarea flagelului terorist, a spiritului gregar i a creierului formatat n vid, generate de educaia-haos, necesit de urgen resurecia unei strategii de ruptur care s induc sperana i ambiia, sentimentul solidaritii i al responsabilitii acolo unde par s troneze alienarea i vidul. Teoria haosului, neleas, de data aceasta, ca mod de gndire i aciune, extrapolat la nivelul sistemelor educaionale, ar reda colii o libertate pedagogic i curricular nengrdit, avnd drept consecin conlucrarea educatorilor ntr-un proiect real de educaie, care s fie mai aproape de interesul comunitar al celor ce nva. Pentru c viaa are aparena unui turbillon pe care ni-l organizm ca urmare a experienei, structurat n procese de gndire. Ascensiunea organizrii materiei spre complexitate nu este, de altfel, posibil dect ntr-un mediu haotic, producnd, la rndul su, structuri complexe, ele nsele haotice. Gndirea, ca proces de sintez, este cea care ordoneaz universul eclectic n care trim, n forma unitii cunoaterii, construind nc de la natere reele semantice ntre evenimentele disparate cu care se confrunt, ca urmare a filtrrii stimulilor din mediu. Ea tie s fac foarte bine asocierile i regruprile proprii unei situaii, fr a fi necesar s recurg la o taxinomie universal, astfel nct simbolurile abstracte, constitutive ale reprezentrilor pe baza limbajului i manipulate de procese cognitive, sunt proiecia n spiritul uman a acestei lumi aparent haotice. Spiritul nsui s-a nscut din haos, iar sistemul neuronal, ca sediu al gndirii, are nevoie de stimulare prin dezechilibru haotic pentru a genera sensuri complexe, convergente. Pentru c ceea ce se ntmpl n att de mult disputata cutie neagr sunt efectiv evenimente inseparabile care nu ascult de regulile clasice specifice corelaiilor cauz-efect. Mrimile care le definesc, departe de a varia n timp, ntr-un

the trainers transformed in illusions merchants, decreasing too much the exigencies of training. Repressing the terrorist scourge, the group spirit and the brain set in emptiness generated by the education-chaos needs urgently the resurrection of a breaking strategy that should induce hope and ambition, solidarity and responsibility where alienation and emptiness govern. Chaos theory, understood this time as a way of thinking and acting, extrapolated at the level of the educational systems, would give the school a pedagogic and curricular unlimited freedom, having as a consequence the co-working of the educators in a real educational project that should be closer from the community interest of the ones who study. Because life seems to be a twirl organized as a result of the experience structured in processes of thinking, the ascension of organizing the matter towards complexity is possible only in a chaotic environment, producing, at its turn, complex structures that are also chaotic. The thinking, as a synthesis process, is the one who orders the eclectic universe where we live as a knowledge unity, building since the birth semantic networks between the disparate events it faces, as a consequence of filtrating the environmental stimulations. It knows how to make the associations and regroupings appropriate to a certain situation without needing to use a universal taxonomy, so that the abstract, constitutive symbols of the representations based on the language and manipulated by cognitive processes are the projection in the human spirit of this apparently chaotic world. The spirit itself was born from chaos and the neuronal system, as a headquarters of thinking, needs stimulation by chaotic lack of poise in order to generate complex, convergent senses. Because what happens in the disputed black box are inseparable events that do not listen to the classic rules specific to the cause-effect correlations. The sizes that define them, far from varying in time in an absolutely aleatory way, appear to us as confined, governed by an order element named strange attractive



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mod absolut aleatoriu, ne apar ca fiind confinite, guvernate de un element de ordine numit atractor straniu1. Pe de alt parte, nimic din ceea ce se ntmpl n interiorul sistemului neuronal nu este iraional, devenind comprehensibil ca urmare a conjunciei imprevizibile a diferitelor serii autonome de evenimente/procese definite ca atractor straniu. Drept urmare, nvarea este mai eficace dac este ajutat s urmeze procese naturale mult mai apropiate de sensul aparent haotic al lucrurilor. n consecin, sistemele de educaie s-ar dovedi mult mai suple i mai eficace dac, n locul unei proiectri generale uniforme (chiar i cu derogrile descentralizatoare de rigoare recomandate, ele nsele (prestabilite), al clasificrilor aberante i al spiritului excesiv analitic ar adopta modele de instruire bazate pe ceea ce noile paradigme ale cunoaterii/aciunii consider a fi teoria haosului. Ni se pare, prin urmare, cu totul forat, i, pn la urm, cu totul improductiv, a ne opune logicii haosului natural, pentru a controla funcionarea celui mai dinamic i mai complex sistem educaional care este nvmntul, tocmai datorit faptului c el nu funcioneaz ntr-un context stabil cu schimbri lente, susceptibile de a fi previzualizate, i deci de a identifica, la nivel instituional, corelaii liniare ntre cauze i rezultate. Timpul educaiei clasice este linear, dat fiind c modelele instructiv-educative nu in seama de fluctuaiile temporale, de efectele imprevizibile i complexitatea proceselor instruirii. S rezulte, oare, de aici imposibilitatea conceperii i realizrii unor sisteme de instruire/educaie predictibile ? n parte, poate fi un adevr. Dar este incontestabil faptul c adoptarea unei dinamici ne-controlate, implicit, nalt permeabil la nou, guvernat de un alt tip de strategii, care s fie construite n spiritul teoriei haosului, ar putea constitui fora creativ necesar pentru a rspunde uriaei nevoii de flexibilitate i inovare a sistemelor de instruire i educaie moderne. Organizarea

feature3. On the other hand, none of the things that happen inside the neuronal system are irrational, becoming comprehensible as a consequence of the unpredictable conjunction of the different autonomous series of events/processes defined as strange attractive features. As a result, the learning is more efficient if it is helped to follow natural processes much closer to the apparent chaotic meaning of the things. As a consequence, the educational systems would prove to be much suppler and efficient if, instead of a uniform general projection (even with the recommended decentralizing derogations, they (pre-established) of the aberrant classifications and of the excessive analytic spirit would adopt models of instruction based on what the new knowledge/action paradigms consider to be the chaos theory. Therefore, we think it is totally forced and, after all, totally not productive to oppose the natural chaos logic in order to control the functioning of the most dynamic and complex educational system just because of the fact that it does not work in a stable context with slow chances liable to be preview, so to identify at the institutional level linear correlations between causes and results. The time of the classic education is linear, given the fact that the instructive-educational models do not consider the temporal fluctuations, the unpredictable effects and the complexity of the instruction processes. Is this where the impossibility to conceive and accomplish certain predictable training/education systems come from? It can be partially true. But we cannot contest the fact that adopting a uncontrolled dynamics that is implicitly high permeable to new features, governed by another type of strategies that should be built in the spirit of chaos theory, could build the creative force needed in order to respond to the huge need of flexibility and innovation of the modern systems of training and education. The organization of the training processes based on the chaos theory changes the perspective of the needs of the modern educational



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proceselor instruirii pe fondul teoriei haosului modific perspectiva sub care sunt nelese nevoile instituiilor educaionale moderne i aduce schimbri de esen la nivelul gndirii manageriale. Se pune problema de a proiecta sisteme de instruire cu un numr redus de grade de libertate, mult mai uor de definit, al cror comportament, dei n aparen dezordonat, este reglat de acest atractor straniu, care explic, n fond, funcionarea haosul determinist n educaie. Un atare gen de management educaional ar poziiona educaia n centrul tuturor strategiilor de construcie a viitorului.

4. Pentru o educaie ce leag fractal viaa, materia i contiina

tiina de a organiza ideile, elementele cunoaterii, ncercarea de a fi fidel complexitii pot fi marile provocri ale acestui din urm secol. Pentru c tot astfel cum imaginea fractal se autoge-nereaz progresiv prin iteraii succesive, avnd la origine o ecuaie simpl, educaia bazat pe logica haosului i inteligena complexitii va trebui s-i ajute pe cei ce nva n a construi relaii ntre diferitele niveluri epistemice aducnd mai multe discipline n acelai spaiu, pentru a elibera astfel cunoaterea din graniele ei tiute. Educaia gndit fractal 2 stimuleaz funciile operatorii, elementele complexificrii, oferind concepte-cheie, scheme algoritmice, pattern-uri de aciune .a.m.d. Predarea/nvarea se va interesa nu att de coninuturi (cunotine declarative), ct mai ales de metode i proceduri de nvare (cunotine metacognitive). O dat cu avalana de date, disponibil pe marile rute ale infomaiei este n curs de a se impune o nou tiin a documentrii/instruirii care s permit nu att acumularea indistinct, ct mai ales identificarea informaiei viabile. Conceput ca o nou metodologie integrativ, paradigma transversalitii ofer celor ce nva instrumentele necesare pentru a interpreta realitatea ca sistem logic de

institutions and brings essential changes at the level of the managerial thinking. We should think about projecting training systems with a reduced number of freedom degrees that should be much more easy to define, whose behaviour, even apparently messy, is regulated by this strange attractive feature that explains actually the functioning of the determinist chaos in education. Such a type of educational management should position education in the centre of all the future construction strategies.

4. For a Education that Connects in a Fractal Manner Life, Matter and Consciousness

The knowledge of organizing the ideas, the knowledge elements, the attempt to be loyal to the complexity may be the great challenges of this last century. Because as the fractal image is auto-generated progressively by successive iterations, having at its origins a simple equation, the equation based on the chaos logic and the complexity intelligence should help the ones who learn to build relationships between different epistemic levels bringing several disciplines in the same space in order to set free the knowledge from its known borders. The education thought in a fractal manner4 stimulates the operatory functions, the complexity elements, offering key-concepts, algorithmic schemes, action patterns etc. The teaching/learning will be interested not so much in contents (declarative knowledge), but mostly in methods and procedures of learning (meta-cognitive knowledge). At the same time with the data avalanche that was available on the great routes of information, we are about to impose a new science of documenting/training that could allow not so much the non-different accumulation, but especially the identification of the valid information. Conceived as a new integrative methodology, the transversality paradigm offers to the ones that learn the tools needed in



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semnificaii, ncurajndu-i s descopere, ntr-un context semnificativ pentru ei, ordinea implicit ascuns n profunzimile realului, real neles, n sensul teoriei cuantice, ca sum de interaciuni vehicualte de entiti mediatoare. Trebuind, de exemplu, s abordeze concepte de intergrani, ei se pot folosi de noiunile dobndite n cadrul tuturor materiilor colare. Explorarea, analiza i prezentarea informaiei nu mai sunt inute de barierele impuse disciplinelor tradiionale fragmentate, ineficiente n a surprinde, dincolo de o ordine discontinu a fenomenelor, ordinea profund subiacent, guvernnd evoluia realului. Demersul transversal, fr a minimaliza rolul disciplinelor, ofer, dimpotriv, subiectului (lucru absolut cardinal) percepia holotropic a universului ca manifestare a unui act de contiin trancendent. Pentru c, n absena acestei contiine care s mrturiseasc, prin intermediul subiectului, despre ea nsui, Fiina nsi este contestat. Este ceea ce confer un rost existenial nvrii, n sensul n care o alchimie misterioas face ca fiecare contiin reflexiv s devin prta la chipul totalitii transcendente, aa cum aceasta din urm le reflect pe toate. Spiritul nostru vine din profunzimi, situate mult dincolo de contiina personal. Cu ct subiectul cunosctor ptrunde mai adnc n miezul interconexiunilor, cu att se pro-duce apropierea lui de fundamentul universal care leag, fractal, viaa, materia i contiina. Realul este, potrivit teoriei cuantice, un ansamblu indivizibil unde totul este relaie/interconexiune, nct putem spune, asemenea lui Pearce, c spiritul uman reflect un univers care reflect spiritul. Fiindc nimic din ceea ce putem percepe n acest fel nu este eminamente real, n sensul vulgar conferit acestui cuvnt. Este ca i cum ne-am trezi n inima unei iluzii, care ne nconjoar cu un imens cortegiu de aparene i pe care, n mod aproape incontient, le identificm, n mod eronat, cu realitatea, ca urmare a unor sistematice deformri induse de o incontinent instruire monodisiciplinar.

order to interpret reality as a logic significations system, encouraging them to discover, in a context significant to them, the implicit order hidden in the deepness of reality, really understood, in sense of the quantum theory, as a sum of interactions spread by mediating entities. For example, by being forced to approach inter-border concepts, they may use the notions gained in frame of all the school matters. Exploring, analysing and presenting the information are not kept anymore from the borders imposed to the fragmented traditional disciplines inefficient in surprising, beyond a discontinuous order of the phenomena, a deep subjacent order, governing the evolution of reality. The transversal approach, without minimising the disciplines role, offers, on the contrary, to the subject (an absolute cardinal fact) the holotropic perception of the universe as a manifestation of a transcendent consciousness act. Because, in the absence of this consciousness that should confess by means of the subject about itself. The being itself is contested. It is what confers an existential role to learning, meaning that a mysterious alchemy makes each reflexive consciousness a part of the transcendent totality, as the last one reflects all of them. Our spirit comes from the deepness placed beyond the personal consciousness. The more the knowing subject gets into the middle of the interconnections, the more its closeness to the universal fundament that connects in a fractal manner life, matter and consciousness is produced. Actually, according to a quantum theory, reality means an indivisible ensemble where everything is relationship/interconnection so that we may say, just like Pearce, that the human spirit reflects a universe that reflects the spirit. Because nothing that we can perceive like that is eminently real in the vulgar meaning of this word. It is like we would get up in the heart of an illusion that surrounds us with an immense cortege of appearance that we unconsciously identify mistakenly with reality, as a result of certain systematic deformations



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Toate prejudecile legate de spaiu, de timp, de localizarea obiectelor, de cauzalitatea evenimentelor, tot ceea ce gndim despre caracterul separabil al lucrurile existente n univers, toate acestea i multe altele ne apar (dac nu cumva i sunt) ca o continu halucinie. O realitate stranie, profund, se ascunde sub aceste aparene, ca o uria, invizibil estur cosmic, cu totul altceva dect clasicul concept de materie, de fapt o vast gndire, pe care, iat, dup mai bine de o jumtate de secol, tiinele, deopotriv cu artele i miturile moderne, ncep s o neleag i ne invit la un nou gen de reflecie, altul dect cel con-sacrat prin tradiie. Realitatea observabil, deopotriv cu reflexele ei n contiina noastr, nu este dect un ansamblu de cmpuri i interconexiuni. Aceast ordine subiacent a realului, de unde rezult tot ceea ce perecepem, la limita simurilor, nu este, n ultim instan, dect manifestarea unui invariant global de simetrie, cum att de concis l-au denumit fizicienii, Educaia gndit fractal stimuleaz funciile operatorii, elementele complexificrii, oferind concepte-cheie, scheme algo-ritmice, pattern-uri de aciune .a.m.d. Predarea/nvarea se va interesa nu att de coninuturi (cunotine declarative), ct mai ales de metode i proceduri de nvare (cunotine metacognitive). O dat cu avalana de date, disponibil pe marile rute ale infomaiei, se impune o nou tiin a documentrii/ instruirii care s permit nu att acumularea indistinct, ct mai ales identificarea informaiei viabile.

Opacitatea la valoare i absena spiritului critic, care obstrueaz (inter)conexiunile productive, vor fi, probabil, obstacolele cele mai greu de escaladat ntr-o vreme n care tot ceea ce a conceput ingeniozitatea minii omeneti va fi mai devreme sau mai trziu accesibil pe ecran, iar formatul (mega)hipertext, modalitatea susceptibil de a deveni n timp o necesitate. Organizarea i ierarhizarea datelor, ntr-o concepie optim, suficient de intuitiv i ergonomic, care s-i permit

induced by an incontinent mono-disciplinary training. All the prejudices related to space, time, localizing objects, events causality, everything we think about the separable feature of the things that exist in the universe, all of these and many others seem to be (maybe they really are) a continue hallucination. A strange, deep reality hides under these appearances, like a huge, invisible cosmic tissue, totally different from the classic concept of matter, actually a vast thinking that after more than half a century the sciences, the arts and the modern myths start to understand and invite us to a new kind of reflection different from the one consecrated by tradition. The noticeable reality and also its reflexes in our consciousness is only an ensemble of fields and interconnections. This subjacent order of reality, from where results everything we perceive at the sense border is, in the last instance, only the manifestation of an invariant global of symmetry, as it was precisely called by the physicians. The education though in a fractal manner stimulates the operatory functions, the complexity elements offering key-concepts, algorithmic schemes, action patterns etc. Teaching/learning will represent an interest not only for the contents (declarative knowledge), but mostly on method and procedures of learning (meta-cognitive knowledge). At the same time with the data avalanche that was available on the great routes of information, we are about to impose a new science of documenting/training that could allow not so much the non-different accumulation, but especially the identification of the valid information.

The opacity to value and the absence of the critical spirit that obstructs the productive (inter)connections will probably be the most hard to climb obstacles in a time when everything conceived by the creativity of the human mind will be sooner or later accessible on the screen and the (mega)hypertext format, the way liable to become in time a necessity. Organizing and ranking the data in an optimal, intuitive



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utilizatorului-elev accesul rapid la informaia semnificativ, se vor dovedi, n acest caz obiective majore. Tot astfel cum, noile practici de lectur vor obliga pedagogia lecturii s produc noi strategii de consum cultural de natur s previn efectele destructurante (provocate fie de impunerea unui model cultural unic prin alienare, depersonalizare i omogenizarea stilurilor de gndire, fie de abandonarea reperajului comun i exacerbarea identitii), dar i s stimuleze instituirea unui nou mod de comunicare, de con-strucie colectiv a cunoaterii, prin schimbul de informaii, de experien i expertiz (Ann Goldgar, 1995). Nu se pune problema de a sanciona tehnologiile hipertextuale, care impun o lectur interactiv, inhibnd ineriile textului tradiional, ci dimpotriv, de a nva i a-i ajuta pe cei ce nva s le st-pneasc, pentru a prentmpina primejdia evazionist, substituirea realului cu fantasmele unei lumi himerice, asimilarea la ntmplare a informaiei (efectul autodidactului lui Sartre), informaia-drog, xenofilic i snoab etc, tot attea cntece de siren care adorm vigilena i anihileaz spiritul creativ. Posibilitile de deriv ale lecturii n modul hipertext sunt, cum se vede, la fel de numeroase ca i avantajele pe care ni le ofer. Pentru c, ntr-o civilizaie n care ecranul interconecteaz sute de milioane de oameni ntr-o vast reea neuronal, inconfortul de lectur generat de absena expertizei lecturii virtuale conduce la frustrare i irosirea inutil a resurselor de timp i intelectuale.

Prin urmare, nu ntmpltor se vorbete, n prezent, i se va vorbi, cu att mai mult, n viitor despre necesitatea unei educaii n timp fractal, ca o replic ferm ndreptat mpotriva unui nvmnt strict programat, divizat temporal, pe discipline i niveluri de colaritate, incompatibil cu abordrile de tip sistemic, inter i transdisciplinar, n genere bazate pe complexitate i logica haosului.

enough and ergonomic conception that would allow the pupil-user to have quick access to the significant information will prove to be major objectives in this case. In the same way as the new lecture practises will force the lecture pedagogy to produce new strategies of cultural consume liable to prevent the destructing effects (provoked either by imposing a unique cultural mode by alienating, depersonalization and homogenizing the styles of thinking, or by leaving the common spotting and exacerbating the identity), but also to stimulate the institution of a new way of communication, collective construction of knowledge, by exchange of information, experience and expertise (Ann Goldgar, 1995). We are not talking about sanctioning the hyper-textual technologies that impose an interactive lecture, inhibiting the inertias of the traditional text but, on the contrary, to learn and to help the ones who learn to dominate them in order to prevent the absentee danger, the substitution of reality with the ghosts of a chimerical world, assimilating at random the information (Sartres autodidact effect), the xenophile, snob drug-information etc, the same number of mermaid songs that put vigilance to sleep and annihilate the creative spirit. The deriving possibilities of the lecture in the hyper-text way are, as it is seen, as numerous as the advantages it offers us. Because, in a civilization where the screen interconnects hundreds of millions of people in a vast neuronal network, the lecture discomfort generated by the absence of the expertise of the virtual lecture leads to frustration and useless waste of the intellectual and time resources. As a consequence, nowadays, we do not talk and will not talk in future randomly about the necessity of an education in fractal time, as a firm line directed against a strictly programmed, timely divided on disciplines and school levels educational system that is incompatible with the systemic, inter and trans-disciplinary approaches generally based on complexity and on chaos logic.



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1 Atractorul straniu (strange atractor) este o figur definind ansamblul traiectoriilor unui sistem supus unei micri haotice, nvedernd o ordine ascuns, subiacent, un spaiu de faze n haosul determinist (non-aleatoriu). El posed o structur fractal, invariabil, indiferent de scara la care este privit. Termenul a fost, probabil, utilizat pentru prima dat ntr-un articol intitulat On the nature of turbulence, semnat de David Ruelle i Floris Takens. n prezent, exist perspective promitoare privind posibilitatea simulrii activitii neuro-dinamice a creierului uman, pornind de la noi ipoteze viznd teoria haosului i fractalii. Exist convingerea c pot fi, astfel, simulate, prognosticate i influenate, de o alt manier, actele de gndire, procesele psihologice complexe i, bineneles, sporite ansele educaiei. 2 Termenul fractal (din lat. fractus > ceea ce este spart, rupt, fracturat) a fost inventat de matematicianul B. Mandelbrot (The Fractal Geometry of Nature. W. H. Freeman and Company, 1982) pentru a desemna un tip de obiecte definite ca iregulate, diferite de figurile euclidiene precum dreapta sau cercul. Geometria fractal este, n fapt, o teorie abstract. Un fractal conine, la diferite niveluri, motivul unei forme ori funcii, al unei entiti date. Acest motiv recurent n interiorul unitilor mai mici, reproduce motivul unitii de ansamblu. Fractalii ajut la reprezentarea de obiecte naturale com-plexe : muni, nori, linii de coast fulgere, conglomerate galactice .a. Tot astfel, fractalii intervin n cadrul teoriei haosului determinist cu aplicaii n diverse domenii, ntre care i educaia n sensul n care fenomene de genul dinamicii educaiei pot fi descrise printr-o figur fractal. n demersul nostru, conceptul de fractal este folosit nu att n accepiunea sa mate-matic, ct mai ales n sens metaforico-filozofic 3 The strange attractive feature is a figure that defines the ensemble of the trajectories of a system liable to a chaotic movement, proving a hidden, subjacent order, a phases space in the determinist (non-aleatory) space. It owns a fractal, invariable structure, no matter the scale we regard it. The term was used probably for the first time in an article named On the nature of turbulence, signed by David Ruelle and Floris Takens. Nowadays, there are promising perspectives regarding the possibility to simulate the neuro-dynamic activity of the human brain, starting from new hypotheses related to the chaos theory and to fractals. There is the belief that we may be able to simulate, foresee and influence thus in another manner the acts of thinking, complex psychological processes and, of course, to increase the education chances. 4 The fractal term (from lat. fractus > that is broken, fractured) was invented by the mathematician B. Mandelbrot (The Fractal Geometry of Nature. W. H. Freeman and Company, 1982) in order to assign a type of objects defined as irregular, different from the Euclidian figures such as the straight line or the circle. Fractal geometry is actually an abstract theory. A fractal contains, at different levels, the reason of a shape or function, of a given entity. This recurrent reason inside the smaller unities reproduces the reason of the ensemble unity. The fractals help the representation of complex natural objects: mountains, clouds, lightening lines, galactic conglomerates etc. In the same way, the fractals interfere in frame of the determinist chaos theory having applications in different fields, between which there is also the education, meaning that phenomena such as the education dynamics may be described by a fractal figure. In our approach, the fractal concept is used not so much in its mathematical acceptation, but mostly in a metaphoric-philosophic meaning.

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Mihai_nebunu Teoria Haosului in Educatie