WHAT INFORMATION TO MEASURE HOW TO MEASURE?
Paolo Rocchi
IBM - via Shangai 53, 00144 Roma, Italy
LUISS University - via Alberoni 7, 00198 Roma, Italy
procchi@luiss.it
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LUISS University
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What is Information?
Timeline of Information Theories (partial)
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The statistical theory of information by Fisher (1922);
The transmission theory of information by Hartley (1928);
The communication theory of information by Shannon (1949);
The semantic theory of information by Carnap and Bar Hillel (1953);
The utility theory of information by Karkevich (1960);
The cybernetic theory of information by Wiener (1961);
The algorithmic theory of information by Solomonoff, Kolmogorov (1965), and Chaitin (1977);
The descriptive information theory by MacKay (1969);
The semiotic/cybernetic theory of information by Nauta jr. (1970);
The economic theory of information by Marschak (1971);
The pragmatic theory of information by von Weizsäcker (1974);
The qualitative theory of information by Mazur (1974);
The living system information theory by Miller (1978);
The autopoietic theory on information by Maturana and Varela (1980);
The hierarchical information theory by Brookes (1980);
The logical theory of information by Tarski (1983);
The common-sense information theory by Derr (1985);
The dynamic theory of information by Chernavsky (1990);
The systemic theory of information by Luhmann (1990);
The general information theory by Klir (1991);
The physical theory of information by Levitin (1992);
The organizational information theory by Stonier (1994);
The independent theory of information by Losee (1997);
The social theory of information by Goguen (1997);
The purpose-oriented theory of information by Janich (1998) …….
LUISS University
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What is Information?
Theorists have come to a standstill
By contrast Engineers, Humanists, Technicians, Physicists,
Musicians, Physicians, Zoologists, Biologists, Jurists and
Many others usually assume:
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The sign has a physical base
That base stands for something
LUISS University
→ Signifier
→ Signified
3 /24
What is Information?
“... by using the shortest channel symbol, a dot, for the most common English letter E;
while the infrequent letters, Q, X, Z are represented by longer sequences of dots and
dashes.” (*)
(*) C.E. Shannon (1948). A Mathematical Theory of Communication. The Bell System Technical J., Vol. 27, p.5.
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LUISS University
4 /24
What is Information?
We cannot say what is information
We can say that a piece of information consists of two elements:
The Signifier
The Signified
And thus we can inaugurate a new strategy of research
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LUISS University
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How to Measure It?
We cannot say how to measure information
We can measure the components of a piece of information
How?
In Search of the Mathematical Definition of the Signifier
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LUISS University
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A Mathematical Definition for the Signifier
First Remark
A compound signifier consists of two or more
elementary signifiers
Example:
A
This letter is a compound signifier
that includes the following elementary signifiers:
Color = red,
Pich = 24,
Font = Arial,
Style = Italics,
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LUISS University
7 /24
A Mathematical Definition for the Signifier
First Remark
An elementary signifier can be detected by means of
a sensor, a perceptor, a probe, an instrument etc.
Here called ‘observer’
Examples: 4 sensors from a car (top); 3 biological perceptors (bottom)
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LUISS University
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A Mathematical Definition for the Signifier
First Remark
The whole perception process encompasses
several components of living beings
Knowledge Culture
Personality
Mind’s Upper Level
Perceptor
Mind’s Lower Levels
Nerves
Sense Organ
Perceptors
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LUISS University
9 /24
A Mathematical Definition for the Signifier
Second Remark
Various authors share the idea that sharpness is the
essential property of an item of information.
“The elementary unit of information” is “a difference which
makes a difference” (*)
(*) Bateson G. (2000) - Steps to an Ecology of Mind - University of Chicago Press.
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LUISS University
10 /24
A Mathematical Definition for the Signifier
Second Remark
As a matter of facts, lacking sharpness a sign disappears
Oxford
High contrast
Low contrast
No contrast
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LUISS University
11 /24
A Mathematical Definition for the Signifier
Any real object or event E is an elementary signifier if E
differs from an adjacent entity E* with respect to the detector
or observer R (*)
E NOT=R E*
When the inequality is false, there is no information
(see the bottom case in slide #11)
(*) P. Rocchi – Logic of Analog and Digital Machines – Nova Science, N.Y., (2013) revised edition.
http://www.edscuola.it/archivio/software/bit/course/book.html
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LUISS University
12 /24
A Mathematical Definition for the Signifier
In principle a mathematical model should:
Be useful to scientists,
Enhance our knowledge in the field.
1.
2.
The inequality makes a contribution to:
1. → Measure Information: Calculation of signals, redundancy, fuzziness
etc. (Full discussion
omitted here)
2. → Understand Information: We shall address five philosphical issues
here.
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LUISS University
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1. – How to Measure Digital Information
E NOT=R E*
Electronic engineers adopt two electrical values as signifiers:
E = V1 ; E* = V2
The inequality can rewritten in this way:
V1 ≠ V2
And thus
s = V1 − V2 ≠ 0
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LUISS University
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The inequality demonstrates that discrete signals are clear even in the
worst situations because they are separed by a certain distance s
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LUISS University
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2. - Understand Information
#1 The problem of analog vs digital:
Analog signals are close to Nature and more appropriate. Digital
signals are unreal and less authentic. (*)
The inequality demonstrates that digital signals are perfect, whereas the analog
are fuzzy.
The inequality disproves the above common philosphical opinion.
(Digital cameras provide pictures of higher quality than ancient analog pictures)
Fig – An analog signal
(*) Watzlawick P., Beavin J. H., Jackson D. D. (1967) - Some Tentative Axioms of Communication - In Pragmatics of Human Communication: A Study of Interactional
Patterns, Pathologies, and Paradoxes, W.W. Norton & Company, pp. 48-71.
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LUISS University
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2. - Understand Information
#2 The problem of perception fallacy:
Is perception fallacious?
Is perception innate or learned?
Is perception objective or subjective?
Perception is a straightforward mechanical action without any understanding or
intention in the present frame, by contrast the perception fallacy conundrum is an allincluding argument (see slide #9)
The problem of perception fallacy is an ill-posed question
Thus it can but have various solutions
(We mention: the disjunctive theory of perception, the sense-datum theory,
the intentionalist theory, and the adverbial theory)
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LUISS University
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2. - Understand Information
#3 Paradoxical problem: The Allies sealed several documents at the end of the
Second World War. Information disappeared for decades. At the end of the Cold
War those secret documents became available and information came into existence
once again. Those military papers died for four decades and then were resurrected.
Information can cease to exist and can come ‘back to life’ anew: this seems to
disprove the physical nature of information
Answer: The mathematical definition of signifier includes three elements.
The object E is a sign provided that R operates.
The status of signifier depends on R and is not absolute, in turn information is a
relativistic notion which justifies the large amount of theories
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LUISS University
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2. - Understand Information
#4 Paradoxical problem: During a conversation, people sometimes communicate
using a silent pause. The blank space between two lines in a text means to separate
the subject contents notably it expresses a distinctive message. Silence and blank
can be used to convey information. Immaterial signs seem to rebut the physical
origin of information.
Answer: The inequality can be inverted
E* NOT=R E
This entails that even E* is a signifier and can convey information. We take E* null
E* = 0
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LUISS University
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We obtain that the null element can inform people as long as this special signifier
contrasts with E
0 NOT=R E
The symbol zero demonstrates on the theoretical plane that
‘nothing’ is a potential vehicle of information
This conclusion does not imply that information has an hethereal origin
A bodyless sign does not deny the physical origin of information
A silence pause during a conversation is real
A blank line on the paper can be touched by the fingers
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LUISS University
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2. - Understand Information
#5 Paradoxical problem: Wiener writes; ‘If people always get the same signal, this
becomes inessential and nothing may be transmitted with the same result.’(*) and
discards the physicism of information.
Answer: De Saussure holds that there is no obliged relation between the signifier and the
signified. The object E stands for X and one can substitute E with a smaller or more
manegeable signifier. When one trasmits the same signal for a long time, obviously he
selects the silence in that the silence is the cheapest signifier to represent the intended
message X.
Sometiems people select a bodyless sign to convey information
Wiener’s conclusion is false
(*) Wiener N. (1961) - Cybernetics: Or the Control and Communication in the Animal and the Machine - 2nd edition, MIT Press and Wiley.
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LUISS University
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Concluding Comments
There is no consensus about the notion of information.
Instead there is general accord in the use of the semiotic
notions called signifier and signified.
Unfortunately those notions are used by intuition so far.
We suggest a pragmatic strategy of research to bridge the
gap placed amongst semiotics and the various disciplines.
We suggest a formal definition for the signifier and using
this equation one can provide insights in favor of
philosophers, and formal equations for engineering.
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LUISS University
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The mathematical definition of the signifier provides
formal answers to some vexed questions about
information:
#1 Digital signals are perfect instead the analog are fuzzy
#2 The perception fallacy conundrum is an ill-posed argument and therefore
has many solutions
#3 Information is a relativistic concept
#4 ‘Nothing’ is a potential vehicle of information which does not disprove the
physicism of information.
#5 People can select a bodyless sign to convey information
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LUISS University
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LUISS University
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