1. Information and Communication
Mathematical Models

2. Vasil Penchev
Bulgarian Academy of Sciences: Institute for the Study of Societies of Knowledge
Thursday, October 8th, 18:15 – 19:00
Vilnius university: Faculty of Philosophy
Models of Communication:
Theoretical and Philosophical Approaches
Vilnius, 8-10 October 2015

3. “A mathematical theory of communication”
The concept and quantity of information are introduced by Shannon (1948) as a way and mathematical method for communication to be formalized as transmission and relation of messages
The communication is formalized as transmitting messages in channels
A general quantity of information measured in bits is introduced to describe mathematical both message and communication

4. About Shannon’s information
It is inverse to thermodynamic entropy
It depends both on the content and length of message as both are represented as mathematical functions
This implies that the content of communication is indirectly postulated as a stage or result of calculation to be representable as any mathematical function
Correspondingly, the length of message is the number of digits necessary for that function to be encoded

5. Noise and information in Shannon
Anything, which is not information, in Shannon’s mathematical theory of communication, is “noise”: Thus “noise” means both: - any change of information due to internal influence or the material realization of communication - any additional component of communication, which is not (or cannot be) reduced to information

6. Communication = Information
The philosophical formula of Shannon’s mathematical theory of communication
Communication = Information
A comment: Information is the mathematical quantity, which can represented all stages of communication as an ideal process of calculation realizable in technical devices

7. Wiener’s “cybernetics”
Wiener (1948), his colleague in MIT, used an analogical approach to define “cybernetics” as "the scientific study of control and communication in the animal and the machine“
In fact, this is a rather philosophical generalization of Shannon’s approach for the mathematization of communication:
Shannon
Wiener
Communication
Control & Communication
Machine
Animal & Machine

8. What information in Wiener is
So, information was understood as:
The “matter of control and communication”
Structured in units such as messages
Allowing of mathematical models general to the human being, the animal, the machine and even to any physical, chemical, and biological systems
Entropy as the quantity of disorder is opposite to that of information

9. The philosophical formula of Wiener’s cybernetics
Control
= Information
Communication
A comment: Information is the mathematical quantity, which can represented all stages of communication and control as a process of calculation realizable in technical devices, animals and even any systems

10. Habermas’s “Theory of communicative action”
Habermas (1981) introduced the model of communicative rationality based on communicative action
The information approach to communication reduces it to transmitting rational messages and thus any message to some ordering or “logic” of what is communicated:
The idea and corresponding ideal of communication is the collaboration for ordering nature, society, and the world in a rational way relevant to all communicators

11. The philosophical formula of Habermas’s theory of communicative action
Communication = Action
A comment: Communicative action suggests another kind of rationality, rationality in society (or social rationality). It is different from that rationality directed to nature for achieving human aims and objectivities

12. Habermas’s philosophical background
Though different, rationality in society and rationality to nature are similar anyway both being forms of rationality:
Rationality to nature is an infinite continuation of the finite human mind
Rationality in society is an discrete leap between two or more finite human minds (me ... others)
Thus, infinite continuation to nature should be similar to discrete leap within the finite of society (intersubective transcendentalism)

13. Information vs communication in Habermas
One and the same message can be and usually is interpreted rather differently by separate human beings
Nevertheless, it has an invariant base shared by all or many enough: This is the information of the message
It is not formal and yet less mathematical
Information is not identical to communication
Communication suggests discontinuity of information: Though information is one and the same, it is shared by different members of society

14. Communicative vs technical action I. Technical action
Technical action embodies certain information being an intention or plan in a material of nature creating an artefact such as a technical device, etc
Thus it continues the plan in a material object
Action is what leaps from the ideal into the material and links them over the gap of infinity

15. Communicative vs technical action II. Communicative action
Communicative action does not consider the Other as an object of nature, in whom to embody the message
It is directed to mutual understanding, in which it will reveal its information depending on that mutual understanding but independent of different interpretations
Its information is impossible without understanding and even does not exist before understanding
Thus information exists only in a society

16. Communicative as technical action
Though being so different, information in Shannon and Wiener and it in Habermas share a general and formal structure:
This is the unit of information, a bit in Shannon and Wiener, which is the elementary choice between two equally probable alternatives
This is the elementary communicative action sharing one and the same information in two individuals in the process of understanding

17. Technical as communicative action
One can think of any bit of information as a hidden communicative action preliminary accomplished in a society
Those bits of information are what are further embodied in the piece of nature for it to be modeled according to human intentions and plans
Thus communicative action is embodied in information being social understanding and concordance and only then that information is embodied in nature by technical action in turn

18. A generalized formula of information and action
Comment: the formula
elucidates that
information and
action incl. physical
action pass from each
to other
Therefore they should
share a common and
thus general
philosophical ground
Communicative
action
Information
Technical
action

19. Information Production of information in society Utilization
in technics
A cell of memory
Understanding
„0“
„1“
Com. 1
Com. 2
Technical
action
Communicative
action
Choice
Alternative 1
Alternative 2

20. The ground of communication
That ground might be choice and ordering
Thus any communicator is representative and represented by its participation in common ordering
Ordering is a result of choice
Information elaborated by understanding and communicative action is the quantity of choices and thus ability of ordering
The essence of technical action is the ordering in a certain pattern

21. Rational communication
However the model of rational communication interchanging information whether reduced to a mathematical formula or a result of understanding in a society is unable to represent and even imagine many other sides of communication as an aim and objectivity by itself
All other possible aspects of the messages and communication are either ignored or reduced to some obstacle or “noise” in the process of communication and ordering

22. Mathematics
The same approach of rational communication and information is relevant even to mathematics and its foundation:
Peano arithmetic, which is usually accepted as the ultimate element of mathematics is easily to be underlain by processes of information and calculation such as in a Turing machine
Even the completeness of the so generalized arithmetic can be proved using two or more Turing machines (a quantum computer)
That completeness corresponds to Gentzen’s or intuitionistic approaches for completeness

23. Choice as the base of rationality and mathematics
Then the quantity of information and thus the corresponding ideal of rational communication underlie mathematics by means of the concept of choice
Indeed the axiom of choice in mathematics allows of any even infinite or coherent class to be enumerated and thus reduced to a single Peano arithmetic
Furthermore it allows a Peano arithmetic to be chosen between two independent ones

24. Information as the quantity of choices
Information is interpreted formally as the quantity of elementary choices such as:
Bits (in the case of finite messages, series or sets): a bit is an elementary choice between two equally probable alternatives; or
Qubits, i.e. quantum bits (in the case of infinite ones): a qubit is that generalization of a bit referring to an elementary choice among an infinite set of alternatives
A qubit (after Kolmogorov’s algorithmic definition of information) is equivalent to a transfinite bit, i.e. to an elementary choice between two independent Peano arithmetic

25. After choice, or utilizing information
The ideal (and result) is well-ordering guaranteed by a relevant axiom or principle such as the axiom of choice or the well-ordering principle (theorem) equivalent to each other
The essence of technical action is implementation of a certain pattern equivalent to a series of choices, i.e. information
However that model for technical use is elaborated before that by communicative action in society, i.e. by the production of information in understanding

26. The inherent, but hidden link
One can deduce an inherent link between the mathematical models of communication, the concept of and quantity of information and Habermas’s “communicative rationality”
All those divide disjunctively the state before or after choice therefore postulating the choice itself
Then rationality can be separated from irrationality entirely within the choice and its mechanism, and rationality accepted the choice as granted somehow beginning after it

27. The ground of both rational communication and information
Production
of information
in society
The “black box”
of choice:
The ground of both rational communication and information
Communicative
action
Information
Technical
action
Utilization
of information
in technics

28. Rational communication and information in European tradition
All those are grounded on rational and empirical tradition in philosophy and especially in European philosophy
There exists:
The practice of separating rationality from irrationality disjunctively
Representing irrationality as some “black box”, e.g. that of choice
Postulating that “black box” as a an initial element of rationality

29. On that background
It tends to all different from the rational and ordered to be generalized and ignored as the “irrational”
Then, the irrational sides of communication can be studied only as obstacles and “informational noise” or as far they admit some rationalization by means of any more or less relevant model preferably mathematical

30. Conclusions: Shannon’s mathematical theory of communication,
Wiener’s cybernetics, and even
Habermas’s theory of communicative action
share the European approach of rationality to communication
Its essence consists in dividing the rational from the irrational, and then “bracketing” the latter as a “black box” and initial element for rationality

31. Literature
I. Habermas’s Theory of communicative action 1. Habermas, J The theory of communicative action. Vol. 1:Reason and the rationalization of society; Vol. 2: Lifeworld and system : a critique of functionalist reason, Boston: Beacon Press. 2. Habermas, J On the pragmatics of social interaction: preliminary studies in the theory of communicative action, Cambridge, Mass.: MIT Press. 3. Honneth, A., H. Joas (eds.) 1991 Communicative action: essays on Jürgen Habermas's The theory of communicative action, Cambridge, Mass.: MIT Press.

32. Literature:
II. Information theory and cybernetics 1. Wiener, N Cybernetics or control and communication in the animal and the machine, New York: J. Wiley: The Technology Press. 2. Shannon, C “A mathematical theory of communication,” Bell System technical journal, 27(3): 379–423; 27(4): 623– Kolmogorov, A “Three approaches to the quantitative definition of information,” International Journal of Computer Mathematics, 2(1-4):

33. Thank you for your attention!
Dėkojame!
Thank you for your attention!