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<body><div>Theil (1972) pp. 1 and 2:</div>
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<div id="xffee1d4888fa460cb226666f8b0a0764" style="tab-interval:.5in;word-wrap:break-word">
<p class="MsoNormal" style="margin-top:14.65pt;line-height:14.4pt;mso-line-height-rule:exactly;mso-layout-grid-align:auto;punctuation-wrap:simple;text-autospace:ideograph-numeric ideograph-other;mso-line-break-override:restrictions;vertical-align:baseline;" xmlns="http://www.w3.org/TR/REC-html40"><b><i><span style="font-size:9.5pt;mso-bidi-font-size:12pt;letter-spacing:0.45pt;">1.1. </span></i></b><b><i><span style="font-size:9.5pt;mso-bidi-font-size:12pt;letter-spacing:0.45pt;">Information<o:p xmlns:o="urn:schemas-microsoft-com:office:office"></o:p></span></i></b></p>
<p class="MsoNormal" style="margin-top: 9.2pt; margin-right: 0.05in; margin-bottom: 0.0001pt; text-align: justify; text-indent: 0.1in; line-height: 12.1pt; vertical-align: baseline;" xmlns="http://www.w3.org/TR/REC-html40"><span style="font-size:10.5pt;mso-bidi-font-size:12pt;">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?<o:p xmlns:o="urn:schemas-microsoft-com:office:office"></o:p></span></p>
<p class="MsoNormal" style="margin-top:7.3pt;line-height:11.65pt;mso-line-height-rule:exactly;mso-layout-grid-align:auto;punctuation-wrap:simple;text-autospace:ideograph-numeric ideograph-other;mso-line-break-override:restrictions;vertical-align:baseline;" xmlns="http://www.w3.org/TR/REC-html40"><i><span style="font-size:10.5pt;mso-bidi-font-size:12pt;letter-spacing:-0.35pt;">Information<o:p xmlns:o="urn:schemas-microsoft-com:office:office"></o:p></span></i></p>
<p class="MsoNormal" style="margin-top: 6.45pt; margin-right: 0.05in; margin-bottom: 0.0001pt; text-indent: 0.1in; line-height: 12.85pt; vertical-align: baseline;" xmlns="http://www.w3.org/TR/REC-html40"><span style="font-size:10.5pt;mso-bidi-font-size:12pt;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.<o:p xmlns:o="urn:schemas-microsoft-com:office:office"></o:p></span></p>
</div><div align="justify"><span style="font-size: 10.5pt; font-family: "Times New Roman", serif;"><br /></span></div><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><div align="justify"><span style="font-family: "Times New Roman"; font-size: 10pt;"><br /></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></div><div align="justify"><i><span style="font-family: "Times New Roman"; font-size: 10pt;"><br /></span></i></div><div align="justify"><i><span style="font-family: "Times New Roman"; font-size: 10pt;">best, loet</span></i></div><div align="justify"><i><span style="font-family: "Times New Roman"; font-size: 10pt;"><br /></span></i></div><div id="signature_old"><div id="xd0f008326390429">
<div id="x37dfff32a36b4410ad8e891fea6bb1b8">
<p class="MsoNormal" style="line-height:normal;" xmlns="http://www.w3.org/TR/REC-html40"><b><font face="Times New Roman" style="font-size: 9pt;" size="1">_______________</font></b></p><p class="MsoNormal" style="line-height:normal;" xmlns="http://www.w3.org/TR/REC-html40"><b><font face="Times New Roman" style="font-size: 9pt;" size="1"><a href="https://urldefense.com/v3/__https://www.springer.com/gp/book/9783030599508__;!!D9dNQwwGXtA!UCpI3A8EWvaVDmOuc9hvIQ63G4mDCTSSAo-msd5Fp1s28PF75NWu969e_W5KiezGFeMPMGFtXsQLk0MTPOc$"></a>Loet Leydesdorff</font></b></p><p class="MsoNormal" style="line-height:normal;" xmlns="http://www.w3.org/TR/REC-html40"><b><font face="Times New Roman" style="font-size: 9pt;" size="1"><br /></font></b></p><div id="x37dfff32a36b4410ad8e891fea6bb1b8"><p class="MsoNormal" xmlns="http://www.w3.org/TR/REC-html40" style="line-height:normal;"><b style=""><font style="font-size: 9pt;" face="Times New Roman" size="1"><a href="https://urldefense.com/v3/__https://link.springer.com/book/10.1007/978-3-030-59951-5__;!!D9dNQwwGXtA!UCpI3A8EWvaVDmOuc9hvIQ63G4mDCTSSAo-msd5Fp1s28PF75NWu969e_W5KiezGFeMPMGFtXsQLLuhNS00$" style="">"The Evolutionary Dynamics of Discusive Knowledge"</a>(Open Access)</font></b></p></div><div id="x37dfff32a36b4410ad8e891fea6bb1b8"></div><p class="MsoNormal" style="line-height: normal;" xmlns="http://www.w3.org/TR/REC-html40"><font face="Times New Roman" style="font-size: 8pt;" size="1">Professor emeritus, University of Amsterdam </font></p><p class="MsoNormal" style="line-height:normal;" xmlns="http://www.w3.org/TR/REC-html40"><font style="font-size: 8pt;" face="Times New Roman" size="1">
Amsterdam School of Communication Research (ASCoR)<o:p xmlns:o="urn:schemas-microsoft-com:office:office"></o:p></font></p>
<p class="MsoNormal" style="line-height:normal;" xmlns="http://www.w3.org/TR/REC-html40"><font style="font-size: 8pt;" face="Times New Roman" size="1"><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$" title="http://www.leydesdorff.net/" style="">http://www.leydesdorff.net/</a>
<o:p xmlns:o="urn:schemas-microsoft-com:office:office"></o:p></font></p><p class="MsoNormal" style="line-height:normal;" xmlns="http://www.w3.org/TR/REC-html40"><a href="https://urldefense.com/v3/__http://scholar.google.com/citations?user=ych9gNYAAAAJ&hl=en__;!!D9dNQwwGXtA!UCpI3A8EWvaVDmOuc9hvIQ63G4mDCTSSAo-msd5Fp1s28PF75NWu969e_W5KiezGFeMPMGFtXsQLaBGhTzQ$" style="background-color: rgba(0, 0, 0, 0);"><font style="font-size: 8pt;" face="Times New Roman" size="1">http://scholar.google.com/citations?user=ych9gNYAAAAJ&hl=en</font></a></p></div><div id="x37dfff32a36b4410ad8e891fea6bb1b8"><span><font style="font-size: 8pt;" face="Times New Roman" size="1">
</font></span><p class="MsoNormal" xmlns="http://www.w3.org/TR/REC-html40" style="line-height:normal;background-color:rgba(0,0,0,0);"><font style="font-size: 8pt;"><font style="font-size: 8pt;" face="Times New Roman" size="1">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;"><o:p xmlns:o="urn:schemas-microsoft-com:office:office"></o:p></span></font></p><span>
</span><p class="MsoNormal" xmlns="http://www.w3.org/TR/REC-html40" style="line-height:normal;background-color:rgba(0,0,0,0);"></p></div>
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