I guess that's why black swan events magically and consistently lead to financial calamity when events supposedly more than two or three standard deviations from normal are considered to offer zero information.<div><br></div><div>Roy<br><br><div id="ymail_android_signature"><a id="ymail_android_signature_link" href="https://urldefense.com/v3/__https://go.onelink.me/107872968?pid=InProduct&c=Global_Internal_YGrowth_AndroidEmailSig__AndroidUsers&af_wl=ym&af_sub1=Internal&af_sub2=Global_YGrowth&af_sub3=EmailSignature__;!!D9dNQwwGXtA!S_JW2hPwStZUUyJlCSWG4Q9ArdkBcYE0kt6e8kPZwmHISXHSVdTWbktvoTi3WwDcJyGpN5OGd6RzX5j1cQgWsZ3jIYKk$">Sent from Yahoo Mail on Android</a></div> <br> <blockquote style="margin: 0 0 20px 0;"> <div style="font-family:Roboto, sans-serif; color:#6D00F6;"> <div>On Mon, Jan 23, 2023 at 10:30 AM, Loet Leydesdorff</div><div><loet@leydesdorff.net> wrote:</div> </div> <div style="padding: 10px 0 0 20px; margin: 10px 0 0 0; border-left: 1px solid #6D00F6;"> <div id="yiv4277838701">
<div><div>Theil (1972) pp. 1 and 2:</div>
<div>
<div id="yiv4277838701xffee1d4888fa460cb226666f8b0a0764" style="word-wrap:break-word;">
<p style="margin-top:14.65pt;line-height:14.4pt;vertical-align:baseline;" class="yiv4277838701MsoNormal"><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>
<p 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;" class="yiv4277838701MsoNormal"><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>
<p style="margin-top:7.3pt;line-height:11.65pt;vertical-align:baseline;" class="yiv4277838701MsoNormal"><i><span style="font-size:10.5pt;letter-spacing:-0.35pt;">Information</span></i></p>
<p style="margin-top:6.45pt;margin-right:0.05in;margin-bottom:0.0001pt;text-indent:0.1in;line-height:12.85pt;vertical-align:baseline;" class="yiv4277838701MsoNormal"><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>
</div><div><span style="font-size:10.5pt;font-family:New serif;"><br></span></div><div>
<span style="font-size:10.5pt;font-family:New 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:New serif;">p </i><span style="font-size:10.5pt;font-family:New serif;">that
prevailed before or to the arrival of the message, we should select a </span><i style="font-size:10.5pt;font-family:New serif;">decreasing </i><span style="font-size:10.5pt;font-family:New serif;">function. The function proposed
by SHANNON (1948) is </span><span style="font-family:New;font-size:10pt;">when the probability prior to the message is zero) to 0 (zero information when the probability is one).</span></div><div><span style="font-family:New;font-size:10pt;"><br></span></div><div><span style="font-family:New;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:New;font-size:7pt;">
<sub>2</sub>
</span>
<span style="font-family:New;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:New;font-size:10pt;">bits. </span>
</i>
<span style="font-family:New;font-size:10pt;">When natural logarithms are used, the information unit is a </span>
<i>
<span style="font-family:New;font-size:10pt;">nit. </span></i></div></div><div><i><span style="font-family:New;font-size:10pt;"><br></span></i></div><div><i><span style="font-family:New;font-size:10pt;">best, loet</span></i></div><div><i><span style="font-family:New;font-size:10pt;"><br></span></i></div><div id="yiv4277838701signature_old"><div id="yiv4277838701xd0f008326390429">
<div id="yiv4277838701x37dfff32a36b4410ad8e891fea6bb1b8">
<p style="line-height:normal;" class="yiv4277838701MsoNormal"><b><font face="Times New Roman" style="font-size:9pt;" size="1">_______________</font></b></p><p style="line-height:normal;" class="yiv4277838701MsoNormal"><b><font face="Times New Roman" style="font-size:9pt;" size="1"><a rel="nofollow noopener noreferrer" target="_blank" href="https://urldefense.com/v3/__https://www.springer.com/gp/book/9783030599508__;!!D9dNQwwGXtA!UCpI3A8EWvaVDmOuc9hvIQ63G4mDCTSSAo-msd5Fp1s28PF75NWu969e_W5KiezGFeMPMGFtXsQLk0MTPOc$"></a>Loet Leydesdorff</font></b></p><p style="line-height:normal;" class="yiv4277838701MsoNormal"><b><font face="Times New Roman" style="font-size:9pt;" size="1"><br></font></b></p><div id="yiv4277838701x37dfff32a36b4410ad8e891fea6bb1b8"><p style="line-height:normal;" class="yiv4277838701MsoNormal"><b style=""><font style="font-size:9pt;" face="Times New Roman" size="1"><a rel="nofollow noopener noreferrer" target="_blank" href="https://urldefense.com/v3/__https://link.springer.com/book/10.1007/978-3-030-59951-5__;!!D9dNQwwGXtA!UCpI3A8EWvaVDmOuc9hvIQ63G4mDCTSSAo-msd5Fp1s28PF75NWu969e_W5KiezGFeMPMGFtXsQLLuhNS00$" style="">"The Evolutionary Dynamics of Discusive Knowledge"</a>(Open Access)</font></b></p></div><div id="yiv4277838701x37dfff32a36b4410ad8e891fea6bb1b8"></div><p style="line-height:normal;" class="yiv4277838701MsoNormal"><font face="Times New Roman" style="font-size:8pt;" size="1">Professor emeritus, University of Amsterdam </font></p><p style="line-height:normal;" class="yiv4277838701MsoNormal"><font style="font-size:8pt;" face="Times New Roman" size="1">
Amsterdam School of Communication Research (ASCoR)</font></p>
<p style="line-height:normal;" class="yiv4277838701MsoNormal"><font style="font-size:8pt;" face="Times New Roman" size="1"><a rel="nofollow noopener noreferrer" ymailto="mailto:loet@leydesdorff.net" target="_blank" href="mailto:loet@leydesdorff.net" title="mailto:loet@leydesdorff.net" style="">loet@leydesdorff.net </a>; <a rel="nofollow noopener noreferrer" target="_blank" href="https://urldefense.com/v3/__http://www.leydesdorff.net/__;!!D9dNQwwGXtA!UCpI3A8EWvaVDmOuc9hvIQ63G4mDCTSSAo-msd5Fp1s28PF75NWu969e_W5KiezGFeMPMGFtXsQLGpM1vg4$" title="http://www.leydesdorff.net/" style="">http://www.leydesdorff.net/</a>
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</font></span><p style="line-height:normal;background-color:rgba(0,0,0,0);" class="yiv4277838701MsoNormal"><font style="font-size:8pt;"><font style="font-size:8pt;" face="Times New Roman" size="1">ORCID: <a rel="nofollow noopener noreferrer" target="_blank" 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><p style="line-height:normal;background-color:rgba(0,0,0,0);" class="yiv4277838701MsoNormal"></p></div>
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