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

[konstantin lidin]

Unfortunately, Shannon's definition can only be used in a very narrow class of cases. When we consider any process other than the transmission of a message from the inductor to the recipient, this definition does not work.
The most authoritative researchers of the philosophy of information admit that there is still no general definition. The concepts of information in different spheres differ significantly and cannot be combined into something commonly used
Baumgaertner, B., Floridi, L. Introduction: The Philosophy of Information. Topoi 35, 157–159 (2016). https://urldefense.com/v3/__https://doi.org/10.1007/s11245-016-9370-7__;!!D9dNQwwGXtA!SXg13tbkdIexlHicpgmmFoFwIcpgeHl3c2rgtD9HsQHuKRQodSQhjWMYAL-3r-YyBOXRc3vMzQUkPXSVFHs$ 
________________________________
From: Fis <fis-bounces at listas.unizar.es> on behalf of Loet Leydesdorff <loet at leydesdorff.net>
Sent: 23 January 2023 23:29
To: fis at listas.unizar.es <fis at listas.unizar.es>
Subject: [Fis] definitions of information by Theil (1972) derived from Shnnon (1948); back to the basics?

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() = log 2 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


_______________

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