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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.
<div class="ContentPasted0">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</div>
Baumgaertner, B., Floridi, L. Introduction: The Philosophy of Information. <i class="ContentPasted1">
Topoi</i> <b class="ContentPasted1">35</b>, 157–159 (2016). <a href="https://urldefense.com/v3/__https://doi.org/10.1007/s11245-016-9370-7__;!!D9dNQwwGXtA!SXg13tbkdIexlHicpgmmFoFwIcpgeHl3c2rgtD9HsQHuKRQodSQhjWMYAL-3r-YyBOXRc3vMzQUkPXSVFHs$" id="LPlnk776559">
https://doi.org/10.1007/s11245-016-9370-7</a><br>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Fis <fis-bounces@listas.unizar.es> on behalf of Loet Leydesdorff <loet@leydesdorff.net><br>
<b>Sent:</b> 23 January 2023 23:29<br>
<b>To:</b> fis@listas.unizar.es <fis@listas.unizar.es><br>
<b>Subject:</b> [Fis] definitions of information by Theil (1972) derived from Shnnon (1948); back to the basics?</font>
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<div>Theil (1972) pp. 1 and 2:</div>
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<b><i><span style="font-size:9.5pt; letter-spacing:0.45pt">1.1. </span></i></b><b><i><span style="font-size:9.5pt; letter-spacing:0.45pt">Information</span></i></b></p>
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<span style="font-size:10.5pt">Consider an event <i>E </i>with probability <i>p; </i>
the nature of the event is irrelevant. At some point in time we receive a reliable message stating that
<i>E </i>in fact occurred. The question is: How should one measure the amount of information conveyed by this message?</span></p>
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<i><span style="font-size:10.5pt; letter-spacing:-0.35pt">Information</span></i></p>
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<span style="font-size:10.5pt; letter-spacing:-0.1pt">Since the question is vague, we shall try to answer it in an intuitive manner. Suppose that
<i>p </i>is close to 1 (e.g., <i>p = </i>.95). Then, one may argue, the message conveys very little information, because it was virtually certain that
<i>E w</i>ould take place. But suppose that <i>p = .01, </i>so that it is almost certain
<i>E </i>will not occur. If <i>E </i>nevertheless does occur, the message stating this will be unexpected and hence contains a great deal of information.</span></p>
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<div align="justify"><span style="font-size:10.5pt; font-family:"Times New Roman",serif">These intuitive ideas suggest that, if we want to measure the information derived from a message in terms of the probability
</span><i style="font-size:10.5pt; font-family:"Times New Roman",serif">p </i><span style="font-size:10.5pt; font-family:"Times New Roman",serif">that prevailed before or to the arrival of the message, we should select a
</span><i style="font-size:10.5pt; font-family:"Times New Roman",serif">decreasing
</i><span style="font-size:10.5pt; font-family:"Times New Roman",serif">function. The function proposed by SHANNON (1948) is </span><span style="font-family:"Times New Roman"; font-size:10pt">when the probability prior to the message is zero) to 0 (zero information
when the probability is one).</span></div>
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</span></div>
<div align="justify"><span style="font-family:"Times New Roman"; font-size:10pt">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</span> <span style="font-family:"Times New Roman"; font-size:7pt"><sub>2</sub>
</span><span style="font-family:"Times New Roman"; font-size:10pt">2 = 1, and information is then said to be measured in binary digits or, for short,
</span><i><span style="font-family:"Times New Roman"; font-size:10pt">bits. </span>
</i><span style="font-family:"Times New Roman"; font-size:10pt">When natural logarithms are used, the information unit is a
</span><i><span style="font-family:"Times New Roman"; font-size:10pt">nit. </span></i></div>
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<div align="justify"><i><span style="font-family:"Times New Roman"; font-size:10pt">best, loet</span></i></div>
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</span></i></div>
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<p class="x_MsoNormal" style="line-height:normal"><b><font face="Times New Roman" size="1" style="font-size:9pt">_______________</font></b></p>
<p class="x_MsoNormal" style="line-height:normal"><b><font face="Times New Roman" size="1" style="font-size:9pt"><a href="https://urldefense.com/v3/__https://www.springer.com/gp/book/9783030599508__;!!D9dNQwwGXtA!UCpI3A8EWvaVDmOuc9hvIQ63G4mDCTSSAo-msd5Fp1s28PF75NWu969e_W5KiezGFeMPMGFtXsQLk0MTPOc$"></a>Loet
Leydesdorff</font></b></p>
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</font></b></p>
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<p class="x_MsoNormal" style="line-height:normal"><b style=""><font face="Times New Roman" size="1" style="font-size:9pt"><a href="https://urldefense.com/v3/__https://link.springer.com/book/10.1007/978-3-030-59951-5__;!!D9dNQwwGXtA!UCpI3A8EWvaVDmOuc9hvIQ63G4mDCTSSAo-msd5Fp1s28PF75NWu969e_W5KiezGFeMPMGFtXsQLLuhNS00$" style="">"The
Evolutionary Dynamics of Discusive Knowledge"</a>(Open Access)</font></b></p>
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<p class="x_MsoNormal" style="line-height:normal"><font face="Times New Roman" size="1" style="font-size:8pt">Professor emeritus, University of Amsterdam </font></p>
<p class="x_MsoNormal" style="line-height:normal"><font face="Times New Roman" size="1" style="font-size:8pt">Amsterdam School of Communication Research (ASCoR)</font></p>
<p class="x_MsoNormal" style="line-height:normal"><font face="Times New Roman" size="1" style="font-size:8pt"><a href="mailto:loet@leydesdorff.net" title="mailto:loet@leydesdorff.net" style="">loet@leydesdorff.net
</a>; <a href="https://urldefense.com/v3/__http://www.leydesdorff.net/__;!!D9dNQwwGXtA!UCpI3A8EWvaVDmOuc9hvIQ63G4mDCTSSAo-msd5Fp1s28PF75NWu969e_W5KiezGFeMPMGFtXsQLGpM1vg4$" title="http://www.leydesdorff.net/" style="">
http://www.leydesdorff.net/</a> </font></p>
<p class="x_MsoNormal" style="line-height:normal"><a href="https://urldefense.com/v3/__http://scholar.google.com/citations?user=ych9gNYAAAAJ&hl=en__;!!D9dNQwwGXtA!UCpI3A8EWvaVDmOuc9hvIQ63G4mDCTSSAo-msd5Fp1s28PF75NWu969e_W5KiezGFeMPMGFtXsQLaBGhTzQ$" style="background-color:rgba(0,0,0,0)"><font face="Times New Roman" size="1" style="font-size:8pt">http://scholar.google.com/citations?user=ych9gNYAAAAJ&hl=en</font></a></p>
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<font style="font-size:8pt"><font face="Times New Roman" size="1" style="font-size:8pt">ORCID:
<a href="https://urldefense.com/v3/__http://orcid.org/0000-0002-7835-3098__;!!D9dNQwwGXtA!UCpI3A8EWvaVDmOuc9hvIQ63G4mDCTSSAo-msd5Fp1s28PF75NWu969e_W5KiezGFeMPMGFtXsQLH5t9V6o$" style="">
http://orcid.org/0000-0002-7835-3098</a>; </font><span style="font-size:10pt"></span></font></p>
<span></span>
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