Systems theory

I501 – Introduction to Informatics

[email protected]://informatics.indiana.edu/jbollen/I501

Informatics and computing

Lecture 3 – Fall 2011


Systems theory






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.

This week






Informatics:a possible parsing

X-Informatics or Computational X

Informatics

Computer Science

Complex Systems

Data & Search

Data Mining

HCID

Social Informatics

Security

Bio-

Chem-

Geo-

Music-

Health-

towards problem solving beyond computing into the natural and social synthesis of information technology






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






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






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.






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?






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.






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]






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)






Equivalence classes






Equivalence classes






Equivalence classes






Compatibility classes

Not different in more than 2 categories.






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 papercompatibility relation:reflexive, symmetric, non necessarily transitive































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.






Interpretation-free relations

From Klir [2001]

Class of isomorphic abstracted systems• Systemhood properties 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






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:

realism2) 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, infectiousnessetc

http://en.wikipedia.org/wiki/Philosophy

http://en.wikipedia.org/wiki/Knowledge






Immersed in scientific currents of the last decade

http://www.scribd.com/doc/14805983/Streams-Systemic-Thinking






10 miles up:

http://www.art-sciencefactory.com/complexity-map_feb09.html






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 comments on systems science.

Ashby, introduction to cyberneticsAshby 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






Discussion questions

The importance of stupidity:

http://matt.might.net/articles/phd-school-in-pictures/






Next lecture: September 28

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. September 28

Note: September 19 we will have no readings – postponed until September 28

Date post:	22-Feb-2016
Category:	Documents
Upload:	joshwa
View:	70 times
Download:	0 times

Systems theory

Documents