[Fis] a definition of information

Dear colleagues,

It seems to me that one is able to draw some conclusions from the discussions of the last few weeks:

1. “Information” can be defined mathematically, i.e., without reference to a specific system. The advantage of using Shannon’s (1948) definition of information as uncertainty is its direct relation with the concept of probabilistic entropy. However, one can also use other definitions of information.

In answer to Syed’s question:

The expected information content of a distribution ∑ i pi is then

                              H = − ∑ i pi 2log pi

Using the 2log, the bit of information is then defined as the 50/50 case since:

                              H = − ½ 2log ½ − ∑ ½ 2log ½ = 1

In summary, information can be measured in bits of information.

2. “A difference which makes a difference” (Bateson) can be considered as “meaningful information.” Meaning, however, assumes a system. Information can only be meaningful for a system. Meaningful information (ad 2) is to be distinguished from information as uncertainty (ad 1). One cannot measure ‘meaningful information’ without the specification of a system of reference.

3. Meaning cannot be defined without reference to a system, but it can be defined at the level of general systems theory, notably as an operation of the system. Meaning can then be defined as the update value of the incoming information. When the update mechanism and the expected information content of the system are known, one is perhaps able to measure the meaningful information, that is, the mutual information between information processing and meaning processing. Meaning can only be provided by a system which is able to use the information content along its recursive axis for discarding the noise. Meaning, however, is provided with hindsight (ex post), while information processing goes with the arrow of time because of the second law. (Theil (1972, at pp. 59f.) has shown that the second law is valid for probabilistic entropy.)

4. Information gets specific meaning by specifying a system of reference. Biological meaning, psychological meaning, etc. can be considered as different expectations of communication because the update operations are different. In principle, each system of reference can thus provide us with a special theory of communication (that is, substantive theory).

5. Biological systems, for example, can provide meaning to information, but they cannot exchange the meanings thus generated among themselves in a next-order layer. The system would need language to develop meaning into codified meaning or knowledge that can be exchanged. Thus, biological systems are able to retain (that is, to reproduce) a first-order codification in the hardware, but not a second-order one of providing meaning with specified (that is, knowledge-based) meaning. Maturana, for example, carefully distinguished between the generation of biological observers within the networks and human super-observers who use the language of biology as a science for studying the biological processes.

6. The psychological system is expected not only to process meaning, but also to generate identity. Thus, the anticipation is towards hierarchical control at a center. Unlike the social system—which remains distributed by definition—the dynamics at the level of the individual identity can under conditions become historically fixed. The distinction can then also be identified.

7. Luhmann sometimes used the word “dividuum” for the distinction of the social system from an individuum. The social system can entertain all these degrees of freedom at the same time. Globalization of meaning can historically be realized when the processing of meaning is not only variable, but also differentiated in terms of the codes of the communication. The operation of this system can be discussed in terms of various forms of reflexivity (e.g., hyper-reflexivity and infra-reflexivity) and correspondingly in terms of different forms of meaning of the communication.

8. The problem of defining meaning is so difficult because scientific discourses themselves can be considered as social systems of communication. Thus, meaning can be specified with reference to the evolving system of communication as a participant and with reference to the system under study as an observer. (In sociology, Giddens (1976) has called this “a double hermeneutics.” One can also use the emic/etic distinction (Geertz, 1973).) The specification of meaning (and its derivatives at other levels like hyper-meaning, infra-meaning, etc.) requires the specification of one or more systems of reference. Otherwise, confusion can be expected to prevail.

With kind regards,

Loet

  _____

Loet Leydesdorff
Amsterdam School of Communications Research (ASCoR)
Kloveniersburgwal 48, 1012 CX Amsterdam
Tel.: +31-20- 525 6598; fax: +31-20- 525 3681
 <mailto:[email protected]> [email protected] ; <http://www.leydesdorff.net/> http://www.leydesdorff.net/

 
 <http://www.upublish.com/books/leydesdorff-sci.htm> The Challenge of Scientometrics ; <http://www.upublish.com/books/leydesdorff.htm> The Self-Organization of the Knowledge-Based Society
 
Received on Sat Feb 28 07:52:46 2004