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  1. Systems theory

  2. This week • Papers: • Klir, G.J. [2001]. Facets of systems Science. Springer. Chapters: 1 and 2 • Rosen, R. [1986]. "Some comments on systems and system theory". Int. J. of General Systems, 13: 1—3. • Ashby, W.R.[1956]. An Introduction to Cybernetics, Chapman & Hall, London, Chapter 1.

  3. Informatics: a possible parsing Health- HCID Security Geo- Data Mining Bio- Data & Search • towards problem solving • beyond computing • into the natural and social • synthesis of information technology Social Informatics Complex Systems Music- Chem-

  4. MACY meetings: • Norbert Wiener and Arturo Rosenblueth: • Goal-directed behavior and negative feedback (control) • Homeostasis and circular causality • In machines and biology • Automata Theory • Communication • The fundamental idea is the message, even though the message may not be sent by man and the fundamental element of the message is the decision” (Norbert Wiener) • Information and Communication Theory • Natural semiotics (McCulloch and others later get into Peircean Semiotics) • “functional equivalence” of systems (general systems) • Bio-inspired mathematics and engineering and computing/mechanism-inspired biology and social science

  5. What is systems science?a science of relations and a lesson for informatics? • How to define an interdisciplinary field • “systems science is what systems scientists do” • “systems science is that field of scientific inquiry whose objects of study are systems” • What are systems? (George Klir) • “a set or arrangement of things so related or connected as to form a unity or organic whole” (Webster’s New World Dictionary) • Systemhood properties of nature • Robert Rosen • Systems depends on a specific adjective: thinghood (cf. “setness” or cardinality) • Systemhood: properties of arrangements of items, independent of the items

  6. What is a system?(slightly more formally) • S = (T, R) • S: a System • T: a set of things • thinghood • R: a (or set of) relation(s) • Systemhood • Examples • Collections of books or music files • Are sets • But organizations of such sets are systems • E.g. alphabetically, chronologically, typologically, etc.

  7. What is a system, cont’d... • Organizational properties defined by relations • Same relation can be applied to different sets of objects or things • Systems science deals with organizational properties of systems independently of the items • Wiener’s functional equivalences • Separation only relevant for complex systems • What about Informatics? • Can we separate what pertains to informatics and what pertains to thinghood-based dsciplines?

  8. Systems science: cross-disciplinary • It is a scientific endeavor that contains • A body of knowledge~ (complex) relations • A methodology to acquire new knowledg, solve problems • A metamethodology: Methods and problem-solving capabilities are characterized and critically examined • Knowledge and methodology • Applicable to thinghood-based science • Equivalent organizations from different fields can be studied as a whole rather than as a subproblems in a specific field • Offers unifying principles in partnership with traditional science • Two-dimensional science for the information or postindustrial age • Examples • Control, Communication, information, dynamical systems, chaos, evolutionary systems, scale-free networks, modularity, robustness, information networks, search, Etc.

  9. What is a system: more formally • S = (T, R) • S: a System • T = {A1, A2, …, An} • A family of sets of things: thinghood • Cartesian Product • Set of all possible associations of elements from each set, i.e. all n-tuples • {A1 × A2 × … × An} • R: a (or set of) relation(s) • Subset of the Cartesian product of some set of sets: Systemhood • Many relations R can be defined on the same T From Klir [2001]

  10. Types of relations • Equivalence: (~exact same features) • Reflexive, • Symmetric, • transitive • Compatibility: (~synonyms) • Reflexive, • symmetric • Partial orderings: • Reflective, • anti-symmetric, • transitive (t1 >= t2) • Strict orderings: • anti-reflexive, • Antisymmetric, • transitive (t1 > t2)

  11. Equivalence classes

  12. Equivalence classes

  13. Equivalence classes

  14. Compatibility classes Not different in more than 2 categories.

  15. An example in bibliometrics: the scientific social system • System: science • Things: scientists • Relation: compatibility relation, e.g. co-authorship S = (T,R) T = {t1,t2, …, tk} R is subset or equal to T x T, R = {(ti,tj), …} defined as: has co-authored a paper compatibility relation: reflexive, symmetric, non necessarily transitive

  16. An example in bibliometrics: the scientific social system

  17. An example in bibliometrics: the scientific social system

  18. An example in bibliometrics: the scientific social system

  19. An example in bibliometrics: the scientific social system

  20. An example in bibliometrics: the scientific social system We have defined our system now. In fact, equivalence class of systems? - set of systems for which isomorphic relation establishes equivalence such that systemhood properties are preserved, for different set of things What would be in equivalence class of this system? • article networks, • social networks, • epidemiological networks? Scientific process of analysis and modeling continues, but now focused on system properties of equivalence class, not so much thinghood.

  21. Interpretation-free relations • Class of isomorphic abstracted systems • Systemhoodproperties are totally preserved under some suitable transformation from the set of things of one system into the set of things from the other system • Equivalence relation: Reflexive, symmetric, and transitive • Divide the space of possible systems (relations) into equivalent classes • Devoid of any interpretation! • General systems • Canonical examples of equivalence classes From Klir [2001]

  22. Constructivism vs. realism Issue situated in epistemology: “branch of philosophy concerned with the nature and scope (limitations) of knowledge.” Systems: two positions: 1) exist independent of observer and discovered from nature: realism 2) system do not exist in the real word, independent from of the human mind, but created by the decisions and distinctions that scientists make: constructivism OK, but how to choose between such constructions? Francis Heylighen (evolutinary perspective): - objective: distinctiveness ("difference that makes a difference”), invariance (to point of view, time, persons), controllability - subjective: utility, coherence, complexity, etc - intersubjective: formality, conformity, infectiousness etc

  23. Immersed in scientific currents of the last decade http://www.scribd.com/doc/14805983/Streams-Systemic-Thinking

  24. 10 miles up: http://www.art-sciencefactory.com/complexity-map_feb09.html

  25. Discussion questions • Klir, Facets of Systems Science: • - Think of two isomorphic systems based on partial orderings in your domain of interest • “constructivism”: summarize in your own words and speculate on relevance to education • Rosen, comments on cybernetics and systems science • Margaret Thatcher famously said: “There's no such thing as society... only individuals and families.” Frame that statement in Rosen’s comment on systems science. • Ashby, introduction to cybernetics • Ashby gives an example of the development of a rabbit ovum. Discuss the cybernetics point of view and juxtapose it to what Ashby calls the “older point of view”

  26. Complexity Lazebnik, Y [2002]. "Can a biologist fix a radio?--Or, what I learned while studying apoptosis". Cancer Cell, 2(3):179-182. Simon, H.A. [1962]. "The Architecture of Complexity". Proceedings of the American Philosophical Society, 106: pp. 467-482. Klir, G.J. [2001]. Facets of systems Science. Springer. Chapters: 3, 8, and 11. First assignment! Next lecture