[Fis] definitions of information by Theil (1972) derived from Shnnon (1948); back to the basics?

[Loet Leydesdorff]

Theil (1972) pp. 1 and 2:
1.1. Information

Consider an event E with probability p; the nature of the event is 
irrele­vant. At some point in time we receive a reliable message stating 
that E in fact occurred. The question is: How should one measure the 
amount of information conveyed by this message?

Information

Since the question is vague, we shall try to answer it in an intuitive 
manner. Suppose that p is close to 1 (e.g., p = .95). Then, one may 
argue, the message conveys very little information, because it was 
virtually certain that E would take place. But suppose that p = .01, so 
that it is almost certain E will not occur. If E nevertheless does 
occur, the message stating this will be unexpected and hence contains a 
great deal of information.


These intuitive ideas suggest that, if we want to measure the 
information derived from a message in terms of the probability p that 
prevailed before or to the arrival of the message, we should select a 
decreasing function. The function proposed by SHANNON (1948) is when the 
probability prior to the message is zero) to 0 (zero information when 
the probability is one).

The unit of information is determined by the base of the logarithm. 
Frequently 2 is used as a base, which implies that any message 
concerning a 50-50 event has unit information: h() = log2 2 = 1, and 
information is then said to be measured in binary digits or, for short, 
bits. When natural logarithms are used, the information unit is a nit.

best, loet

_______________

Loet Leydesdorff



"The Evolutionary Dynamics of Discusive Knowledge" 
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Amsterdam School of Communication Research (ASCoR)

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