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<p style="margin-top:0; margin-bottom:0">Hi FISers,</p>
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<p style="margin-top:0; margin-bottom:0">One simple (and may be too simple) way to distinguish between
<i>information </i>and <i>entropy</i> may be as follows:</p>
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<p style="margin-top:0; margin-bottom:0">(i) Define information (I) as in Eq. (1)</p>
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<p style="margin-top:0; margin-bottom:0"> I = -log_2(m/n) = - log_2 (m) + log_2(n) (1)</p>
<p style="margin-top:0; margin-bottom:0"><br>
</p>
<p style="margin-top:0; margin-bottom:0">where n is the number of all possible choices (also called variety) and m is the actual choices made or selected. </p>
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</p>
<p style="margin-top:0; margin-bottom:0">(ii) Define the negative binary logarithm of n, i.e., -log_2 (n), as the 'variety' of all possible choices and hence identical with Shannon entropy H, <span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">as
suggested by Wicken [1]. Then Eq. (1) can be re-writtens as Eq. (2):</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;"><br>
</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;"> I = - log_2(m)
- H (2) </span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;"><br>
</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">(iii) It is evident that
when m = 1 (i.e., when only one is chosen out of all the variety of choices available) , Eq. (2) reduces to Eq. (3):</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;"><br>
</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;"> I =
- H (3)</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;"><br>
</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">(iv) As is well known, Eq.
(3) is the basis for the so-called the "negentropy priniciple of Information" frist advocated by Shroedinger followed by Brillouin,and others. But Eq. (3) is clearly not a principle but a special case of Eq. (2) with m = 1. </span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;"><br>
</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">(v) In conlcusion, I claim
that information and negative entropry are not the same qualitatively nor quantiatively (except when m = 1 in Eq. (2)) and represent two opposite nodes of a fundamental triad [2]:</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;"><br>
</span></p>
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<p style="margin:0in;margin-bottom:.0001pt;background:white"><span style="font-family:"Calibri",sans-serif;color:black"> Selection <o:p></o:p></span></p>
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<span style="font-family:"Calibri",sans-serif;color:black"> H ---------------------------------------------------------------->
<b style="mso-bidi-font-weight:normal">I</b> <br>
(uncertainty before selection) <span style="mso-spacerun:yes">
</span> (Uncertainty after selection)<o:p></o:p></span></p>
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<p style="margin:0in;margin-bottom:.0001pt;background:white"><b><span style="font-family:"Calibri",sans-serif;color:black">Figure 1. </span></b><span style="font-family:"Calibri",sans-serif;color:black"> The New Jerseyator model of information (NMI) [3].<span style="mso-spacerun:yes">
</span>Since selection requires free energy dissipation, NMI implicates both information and energy.<span style="mso-spacerun:yes">
</span>That is, without energy dissipation, no energy, and hence NMI may be viewed as a self-organizing process (also called dissipative structure) or an ‘-ator’.
<span style="mso-spacerun:yes"> </span>Also NMI is consistent with “uncertainty reduction model of information.”
<span style="mso-spacerun:yes"> </span></span><o:p></o:p></p>
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<p style="margin-top:0; margin-bottom:0"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">With all the best.</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;"><br>
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<p style="margin-top:0; margin-bottom:0"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">Sung</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;"><br>
</span></p>
<p style="margin-top:0; margin-bottom:0"><span style="font-family: Calibri, Helvetica, sans-serif, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols; font-size: 16px;">P.s. There are experimetnal evidences
that informattion and entropy are orthogonal, thus giving rise to the <i>Planck-Shannon plane</i> that has been shown to distiguish between cancer and healthy cell mRNA levels. I will discus this in n a later post. </span></p>
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<p style="margin-top:0; margin-bottom:0">References:</p>
<p style="margin-top:0; margin-bottom:0"> [1] Wicken, J. S. (1987). Entropy and information: suggestions for common language. <i>Phil. Sci.</i>
<b>54</b>: 176=193. <br>
[2] Burgin, M (2010). <i>Theory of Information: Funadamentality, Diversity, and Unification</i>. World Scientific Publishing, New Jersey,</p>
<p style="margin-top:0; margin-bottom:0"> [3] Ji, S. (2018). <i>The Cell Langauge theory: Connecting Mind and Matter.</i> World Scientific Publishing, New Jersey. Figure 10.24.</p>
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