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CMLM’14
Complexity Management Literacy Meeting, Fiesole, 15 e 16 Novembre 2014
LIBRI CONSIGLIATI da VALERIO ELETTI
TRADUZI...
principale di un moto caotico è la sensibilità alle condizioni iniziali:
traiettorie nello spazio delle fasi che inizialme...
Un sistema dinamico continuo può essere descritto da un set autonomo
di equazioni differenziali di primo grado (...) Un si...
ne consentono lo studio e la classificazione tramite l'apparato
matematico.
Il caos si presenta essenzialmente sotto due f...
descrivendole come proprietà dell’organizzazione dei loro componenti.
(...)
L’autopoiesi può essere vista con l’ottica del...
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CM Literacy Meeting - Valerio Eletti, alcune voci del glossario del libro: "Lexicon of Complexity"

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Per il Complexity Management Literacy Meeting 2014, Valerio Eletti - Direttore Scientifico del “Complexity Education Project” dell’Università Sapienza di Roma, curatore della collana “I Quaderni della complessità” della Guaraldi e docente della Complexity Management School del Complexity Institute - ha presentato come Libri Consigliati

Lexicon of Complexity, di Fortunato Tito Arecchi e Alessandro Farini
Il Glossario dell'Auto-Organizzazione, di Francesco Trombetta
Come funziona il Caos. Dal moto dei pianeti all’effetto farfalla, di Ivar Ekeland

Published in: Education
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CM Literacy Meeting - Valerio Eletti, alcune voci del glossario del libro: "Lexicon of Complexity"

  1. 1. CMLM’14 Complexity Management Literacy Meeting, Fiesole, 15 e 16 Novembre 2014 LIBRI CONSIGLIATI da VALERIO ELETTI TRADUZIONE DALL’INGLESE DELLE CITAZIONI dal glossario di ambito fisico-matematico-epistemologico F.T. Arecchi, A. Farini, Lexicon of Complexity, Studio Editoriale Fiorentino, 1996 A1.p155 Sistema Un assemblaggio di parti che forma un intero unificato (def. Gen) Una collezione di particelle o di componenti che interagiscono tra loro: collezione che, allo scopo di studiarla o identificarla, può essere vista come un’entità fisica distinta (def. Fis-Chim) (da Academic Press Dictionary of Sciences and Technologies) A4.p72 Sistema caotico Chaos: Moto irregolare (non periodico) dovuto alla natura non lineare del sistema. Sebbene il moto caotico appaia irregolare e casuale, esso è regolato da equazioni deterministiche del moto, al contrario del movimento stocastico, influenzato dal rumore... (def. Mat) Chaotic (system): in riferimento alle proprietà di un sistema che esprime caos nel suo processo evolutivo nel tempo, (diciamo che) la caratteristica
  2. 2. principale di un moto caotico è la sensibilità alle condizioni iniziali: traiettorie nello spazio delle fasi che inizialmente sembrano sovrapposte, si separano in maniera esponenziale secondo tempi che vengono misurati in termini di “esponente di Liapunov” (n.d.r.: misuratore della divergenza fra le traiettorie: un valore positivo indica caos, uno negativo indica attrazione, cfr. Arecchi, p.116) (def. Mat) (da Korsch e Jodl, “Chaos”, Berlino 1994) A5.p79 Sistema Complesso Un sistema complesso è quello in cui le parti che lo compongono interagiscono in maniera talmente intricata da non essere prevedibile utilizzando equazioni lineari standard; ci sono cioè in gioco nel sistema così tante variabili che il suo comportamento globale può essere compreso solo come una conseguenza emergente dalla somma olistica delle miriadi di comportamenti presenti (embedded) al suo interno. E dunque l’approccio riduzionista non funziona con i sistemi complessi (...) l’intero è più della somma delle sue parti. (def. Gen) (da Levy S., Artificial life: the quest for a new creation”, NY 1992) Un sistema è complesso se lo possiamo descrivere in una varietà di modi diversi, ciascuno dei quali corrisponde a un distinto sotto-sistema. La complessità smette così di essere una proprietà intrinseca del sistema, diventando invece una funzione del numero delle diverse descrizioni che servono per descrivere queste interazioni. (def. Gen) (da Rosen, “Fundamentals of measurement”, North Holland 1978) A3.p87 Sistema dinamico Un sistema dinamico può essere definito come una “ricetta matematica deterministica” per il modo in cui si evolve nel tempo lo stato del sistema stesso. (da Ott, “Chaos in dynamical system”, Cambridge 1993)
  3. 3. Un sistema dinamico continuo può essere descritto da un set autonomo di equazioni differenziali di primo grado (...) Un sistema dinamico discreto può essere descritto da una mappatura iterata in cui x i+1 è funzione di xi (...) In generale, sistemi dinamici continui di dimensione n possono esser ridotti formalmente a una mappatura discreta di dimensioni n-1 (n.d.r.: rif. alla “sezione di Poincaré”, ovvero all’intersezione tra un’orbita periodica nello spazio delle fasi con un particolare sottospazio di minori dimensioni, per esempio intersezione tra le orbite in uno spazio 3d con un piano) (def. Mat) (da Thomson e Stewart, “A tutorial glossary of Geometrical Dynamics”, in IJBC, 1993) A2.p87 Sistema dissipativo Si chiama dissipativo un sistema dinamico che nel corso della sua evoluzione nel tempo vede ridursi i propri elementi volumetrici nello spazio delle fasi (...) La dissipazione è un prerequisito per l’esistenza di attrattori nel sistema (def. Mat) (da Korsch e Jodl, “Chaos”, Berlino 1994) Nota: molto chiara e illuminate la voce “Caos e complessità” scritta da Vinicio Pelino per l’Enciclopedia Italiana Treccani (www.treccani.it), che mette in relazione sistemi dissipativi, sistemi conservativi (tra cui gli hamiltoniani), complessità e caos. Eccone alcuni passaggi significativi: Il caos, nel linguaggio della fisica e della matematica moderna, identifica la situazione di impossibilità di stimare a priori con certezza il valore futuro delle grandezze che caratterizzano un sistema fisico in evoluzione. L'accuratezza finita della conoscenza dello stato iniziale del sistema determina l'impredicibilità, ossia l'impossibilità di determinare, dopo un tempo finito, lo stato futuro di esso. Sebbene l'evoluzione dinamica sembri assumere un aspetto casuale, l'esistenza di leggi deterministiche non lineari alla base di questi sistemi,
  4. 4. ne consentono lo studio e la classificazione tramite l'apparato matematico. Il caos si presenta essenzialmente sotto due forme. Nei sistemi conservativi, di cui quelli hamiltoniani sono un importante sottoinsieme, il volume nello spazio delle fasi si conserva nel corso dell'evoluzione temporale del sistema. Nei sistemi dissipativi, il volume decresce a causa di processi irreversibili, come per es. la viscosità o la conduzione termica. Per ambedue le classi di sistemi il caos è il risultato di successivi allungamenti e piegamenti degli elementi di volume dello spazio delle fasi. Il Sistema solare ha un comportamento caotico ed è un esempio di caos conservativo, più precisamente hamiltoniano, la turbolenza di un fluido viscoso come l'atmosfera, anche se infinitesima, costituisce un esempio di caos dissipativo. (...) Il concetto di caos trova vaste applicazioni in campo scientifico, soprattutto nello studio dei sistemi complessi. Ciò che accomuna un sistema complesso a un sistema caotico è la non linearità. In questa visione di complessità i sistemi caotici sono considerati un sottoinsieme dei sistemi complessi: la complessità si manifesta infatti sulla soglia della caoticità. http://www.treccani.it/enciclopedia/caos-e-complessita_(Enciclopedia-Italiana)/ A7.p63 Sistema autopoietico L’autopoiesi è un concetto introdotto da Varela e Maturana negli anni ’70 con lo scopo di cogliere le peculiarità distintive degli organismi viventi,
  5. 5. descrivendole come proprietà dell’organizzazione dei loro componenti. (...) L’autopoiesi può essere vista con l’ottica della auto-organizzazione (...) In questo modo passiamo da una visione del sistema come un oggetto che scambia e processa quantità fisiche a una visione del sistema come un oggetto che scambia e processa informazione. Un tale sistema può essere definito propriamente autopoietico se la struttura dei flussi di informazione al suo interno è tale per cui questi formano occasionalmente dei loop chiusi (questi loop chiusi di flusso informativo vengono chiamati “loop metastabili”). Gli elementi del sistema attraverso cui fluisce l’informazione di un loop chiuso possono essere visti come singole unità che mostrano proprietà emergenti rispetto al resto del sistema, che invece non possiede quelle specifiche proprietà. L’autopoiesi può essere un concetto molto utile in psicologia, in biologia e nelle scienze sociali, ma non bisogna mai dimenticare che sotto la struttura informativa c’è sempre una struttura fisica ben definita (rete, n.d.r.). Per la sua stessa natura il concetto di autopoiesi non ha alcun senso in fisica.

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