Informatics
Systems theory
Informatics
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.
Informatics
Informatics:
a possible parsing
X-Informatics or
Computational X
HealthInformatics
HCID
Bio-
 towards problem solving
 beyond computing
 into the natural and social
 synthesis of information technology
Data &
Search
Security
Computer
Science
Social
Informatics
Data
Mining
Complex
Systems
Music-
Chem-
Geo-
Informatics
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
Informatics
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
Informatics
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.
Informatics
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 thinghoodbased dsciplines?
Informatics
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.
Informatics
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]
Informatics
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)
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Equivalence classes
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Equivalence classes
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Equivalence classes
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Compatibility classes
Not different in more than 2 categories.
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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
Informatics
An example in bibliometrics: the scientific social system
Informatics
An example in bibliometrics: the scientific social system
Informatics
An example in bibliometrics: the scientific social system
Informatics
An example in bibliometrics: the scientific social system
Informatics
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.
Informatics
Interpretation-free relations
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
From Klir [2001]
Informatics
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
Informatics
Immersed in scientific currents of the last decade
http://www.scribd.com/doc/14805983/Streams-Systemic-Thinking
Informatics
10 miles up:
http://www.art-sciencefactory.com/complexity-map_feb09.html
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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”
Informatics
Next lecture
 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!