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Information and Communication
Mathematical Models
Vasil Penchev
• Bulgarian Academy of Sciences: Institute for
the Study of Societies of Knowledge
• [email protected]
Thursday, October 8th, 18:15 – 19:00
Vilnius university: Faculty of Philosophy
Models of Communication:
Theoretical and Philosophical Approaches
Vilnius, 8-10 October 2015
“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
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
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
The philosophical formula of Shannon’s
mathematical theory of communication
A comment: Information is the mathematical
quantity, which can represented all stages of
communication as an ideal process of
calculation realizable in technical devices
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
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
The philosophical formula of Wiener’s
cybernetics
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
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
The philosophical formula of Habermas’s
theory of communicative 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
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)
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
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
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
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
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
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
Production
of information
in society
Utilization
of information
in technics
Understanding
A cell of memory
Com. 1
„0“
Com. 2
Communicative
action
Choice
Alternative 1
Alternative 2
„1“
Technical
action
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
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
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
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
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
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
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
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
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
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
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
Literature
I. Habermas’s Theory of communicative action
1. Habermas, J. 1984-1987 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. 2001 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.
Literature:
II. Information theory and cybernetics
1. Wiener, N. 1948 Cybernetics or control and
communication in the animal and the machine,
New York: J. Wiley: The Technology Press.
2. Shannon, C. 1948 “A mathematical theory of
communication,” Bell System technical journal,
27(3): 379–423; 27(4): 623–656.
3. Kolmogorov, A. 1968 “Three approaches to
the quantitative definition of information,”
International Journal of Computer Mathematics,
2(1-4): 157-168.
Dėkojame!
Thank you for your attention!