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<p>Hi Pedro,</p>
<p><br>
</p>
<p>Thanks for the excellent job done.</p>
<p><br>
</p>
<p>Sung</p>
<br>
<br>
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<hr tabindex="-1" style="display:inline-block; width:98%">
<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> Fis <fis-bounces@listas.unizar.es> on behalf of Pedro C. Marijuan <pcmarijuan.iacs@aragon.es><br>
<b>Sent:</b> Thursday, March 23, 2017 6:25 AM<br>
<b>To:</b> 'fis'<br>
<b>Subject:</b> [Fis] PLANCKIAN INFORMATION: A NEW MEASURE OF ORDER (From S. Ji)</font>
<div> </div>
</div>
<div>Note: what follows is an abbreviated text taken from the presentation.<br>
The whole file, too big for our list, can be found at fis web pages: <br>
<a class="moz-txt-link-freetext" href="http://fis.sciforum.net/wp-content/uploads/sites/2/2014/11/Planckian_information.pdf" id="LPlnk115894" previewremoved="true">http://fis.sciforum.net/wp-content/uploads/sites/2/2014/11/Planckian_information.pdf</a><br>
A very recent article developing similar ideas: <a class="moz-txt-link-freetext" href="http://www.mdpi.com/2078-2489/8/1/24" id="LPlnk891150" previewremoved="true">
http://www.mdpi.com/2078-2489/8/1/24</a>
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<a id="LPUrlAnchor_14902711066830.48986694996518865" href="http://www.mdpi.com/2078-2489/8/1/24" target="_blank" style="text-decoration: none;">Information | Free Full-Text | Waves as the Symmetry ...</a></div>
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In 1997, the author concluded that living cells use a molecular language (cellese) that is isomorphic with the human language (humanese) based on his finding that the ...</div>
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Greetings to all--Pedro<br>
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<p class="MsoNormal" style="margin-bottom:10.0pt; line-height:115%; text-autospace:none">
<b><span lang="EN-GB" style=""><font size="+2">What is the Planckian information ?</font></span></b></p>
<p><font face="Times New Roman"><b>S</b><b>UNGCHUL JI</b></font><br>
</p>
<p><i><font face="Times New Roman">Department of Pharmacology and Toxicology<br>
Ernest Mario School of Pharmacy<br>
Rutgers University</font></i><br>
<i><font face="Times New Roman"><a class="moz-txt-link-abbreviated" href="mailto:sji@pharmacy.rutgers.edu">sji@pharmacy.rutgers.edu</a></font></i></p>
<p class="MsoNormal" style="margin-bottom:10.0pt; line-height:115%; text-autospace:none">
<b><span lang="EN-GB" style=""><br>
</span></b><span lang="EN-GB" style=""><br>
The Planckian information (I_P) is defined as the information produced (or used) by the so-called Planckian processes which are in turn defined as any physicochemical or formal processes that generate long-tailed histograms fitting the Planckian Distribution
Equation (PDE), </span></p>
<p class="MsoNormal" style="margin-bottom:10.0pt; line-height:115%; text-autospace:none">
<span lang="EN-GB" style=""><span style=""> </span></span><span style="">y = (A/(x + B^5)/(Exp(C/(x + B)) – 1)<span style="">
</span>(1)</span></p>
<p class="MsoNormal" style="margin-bottom:10.0pt; line-height:115%; text-autospace:none">
<span style=""><span style=""> </span></span><span lang="EN-GB" style="">where A, B and C are free parameters, x is the class or the bin to which<span style="">
</span>objects or entities belong, and y is the frequency [1, 1a].<span style="">
</span>The PDE was derived in 2008 [2] from the blackbody radiation equation discovered by M. Planck (1858-1947) in 1900, by replacing the universal constants and temperature with free parameters, A, B and C.<span style="">
</span>PDE has been found to fit not only the blackbody radiation spectra (as it should) but also numerous other long-tailed histograms [3, 4] (see Figure 1).</span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style="">One possible explanation for the universality of PDE is that many long-tailed histograms are generated by some selection mechanisms acting on randomly/thermally accessible processes
[3]. Since random processes obey the Gaussian distribution, the ratio of the area under the curve (AUC) of PDE to that of Gaussian-like symmetric curves can be used as a measure of non-randomness or the order generated by the Planckian processes.</span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style=""> </span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style="">As can be seen in
<b>Figs. 1 (g), (i), (k), (o), (r) </b>and<b> (t), </b>the curves labeled ‘Gaussian’ or ‘Gaussian-like’ overlap with the rising phase of the PDE curves.<span style="">
</span>The ‘Gaussian-like’ curves were generated by Eq. (2), which was derived from the Gaussian equation by replacing its pre-exponential factor with free parameter A:<br style="">
<br style="">
</span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style=""><span style="">
</span>y = Ae<sup>– (x – </sup></span><sup><span style="">μ</span></sup><sup><span lang="EN-GB" style="">)^2/(2</span></sup><sup><span style="">σ</span></sup><sup><span lang="EN-GB" style="">^2)</span></sup><span lang="EN-GB" style=""><span style="">
</span>(2)</span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style=""> </span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style="">The degree of mis-match between the area under the curve (AUC) of PDE, Eq. (1), and that of GLE, Eq. (2), is postulated to be a measure of
<i>non-randomness</i> (and hence <i>order</i>).<span style=""> </span>GLE is associated with random processes, since it is symmetric with respect to the sign reversal of in its exponential term, (x - µ).<span style="">
</span>This <i>measure of order</i> is referred to as the Planckian Information (I<sub>P</sub>) defined quantitatively as shown in Eq. (3) or Eq. (4):<span style="">
</span></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style=""> </span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style=""><span style="">
</span>I<sub>P</sub> = log<sub>2</sub> (AUC(PDE)/AUC(GLE))<span style=""> </span>
bits<span style=""> </span>
(3)</span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style="">or</span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style=""><br>
<span style=""> </span>I<sub>P<span style=""> </span></sub>= log<sub>2</sub> [∫P(x)dx/∫G(x)dx]<span style="">
</span>bits<span style=""> </span><span style="">
</span><span style=""> </span>(4)</span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style=""> </span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style="">where P(x) and G(x) are the Plackian Distribution Equation and the Gaussian-Like Equation, respectively.
<br style="">
<br style="">
</span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style="">It is generally accepted that there are at least three basic aspects to information –
<i>amount</i>, <i>meaning, </i>and <i>value. </i><span style=""> </span><i>Planckian information</i> is primarily concerned with the
<i>amount</i> (and hence the <i>quantitative</i> aspect) of information.<span style="">
</span>There are numerous ways that have been suggested in the literature for <i>
quantifying information</i> bedside the well-known Hartley information, Shannon entropy, algorithmic information, etc [5].<span style="">
</span>The Planckian information, given by Equation (3), is a new measure of information that applies to the
<i>Planckian process</i> generally defined as in (5):<br>
<br>
“Planckian processes are the physicochemical, neurophysiological, <span style="">
</span><span style=""> </span>(5)<br>
biomedical, mental, linguistic, socioeconomic, cosmological, or any </span></p>
<p class="MsoNormal" style="line-height:115%; text-autospace:none"><span lang="EN-GB" style="">other processes that generate long-tailed histograms obeying the
<br>
Planckian distribution equation (PDE).”<br style="">
<br style="">
</span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style="">The Planckian information represents the degree of organization of physical (or nonphysical) systems in contrast to the Boltzmann or the Boltzmann-Gibbs entropy which represents the
disorder/disorganization of a physical system, whether the system involved is atoms, enzymes, cells, brains, human societies, or the Universe.<span style="">
</span>I_P is related to the “organized complexity” and S is realted to “disorganized complexity” of Weaver [6].<span style="">
</span>The organization represented by I<sub>P</sub> results from <i>symmetry-breaking selection</i>
<i>processes </i>applied to some randomly accessible (and hence symmetrically distributed) processes, whether the system involved is atoms, enzymes, cells, brains, languages, human societies, or the Universe [3, 4], as schematically depicted in
<b>Figure 2</b>. <br style="">
<br style="">
</span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style="">There is a great confusion in science and philosophy concerning the relation between the concepts of
<i>information</i> and <i>entropy</i> as pointed out by Wicken [7].<span style="">
</span>A large part of this confusion may be traced back to the suggestions made by Schrödinger in 1944 [8] and others subsequently (e.g., von Neumann, Brillouin, etc.) that
<i>order</i> can be measured as the <i>inverse of</i> <i>disorder</i> (D) and hence that information can be measured as negative entropy (see the second column in
<b>Table 1</b>).<span style=""> </span></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style=""> </span></p>
<table class="MsoNormalTable" border="0" cellpadding="0" cellspacing="0" style="margin-left:5.7pt; border-collapse:collapse">
<tbody>
<tr style="height:.05pt">
<td colspan="3" valign="top" width="638" style="width:478.8pt; border:solid black
1.0pt; background:#EEECE1; padding:0cm 5.7pt 0cm 5.7pt; height:.05pt">
<p class="MsoNormal" style="text-autospace:none"><b><span lang="EN-GB" style="">Table 1.<span style="">
</span></span></b><span lang="EN-GB" style="">Two different views on the entropy-information relation.<span style="">
</span>I<sub>P</sub> = the Planckian information, Eq. (8.11).<span style=""> </span>
D = disorder.<span style=""> </span>AUC = Area Under the Curve; PDE = Planckian Distribution Equation, (1); GLE = Gaussian-like Equation, (2).
</span><span lang="EN-GB" style="font-size:11.0pt; font-family:Calibri"></span></p>
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5.7pt; height:.05pt">
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style="font-size:11.0pt; font-family:Calibri"> </span></p>
</td>
<td valign="top" width="228" style="width:171.0pt; border-top:none; border-left:none; border-bottom:solid black 1.0pt; border-right:solid
black 1.0pt; background:#EEECE1; padding:0cm 5.7pt 0cm 5.7pt; height:.05pt">
<p class="MsoNormal" style="text-autospace:none"><b><span style="color:#7030A0">Schrödinger (1944)
</span></b><span style="">[8]</span><span style="font-size:11.0pt; font-family:Calibri"></span></p>
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<td valign="top" width="283" style="width:212.05pt; border-top:none; border-left:none; border-bottom:solid black 1.0pt; border-right:solid
black 1.0pt; background:#EEECE1; padding:0cm 5.7pt 0cm 5.7pt; height:.05pt">
<p class="MsoNormal" style="text-autospace:none"><b><span style="color:#7030A0">Ji (2015)
</span></b><span style="">[1, 3]</span><span style="font-size:11.0pt; font-family:Calibri"></span></p>
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5.7pt; height:.05pt">
<p class="MsoNormal" style="text-autospace:none"><span style="">Entropy (S)</span><span style="font-size:11.0pt; font-family:Calibri"></span></p>
</td>
<td valign="top" width="228" style="width:171.0pt; border-top:none; border-left:none; border-bottom:solid black 1.0pt; border-right:solid
black 1.0pt; background:#EEECE1; padding:0cm 5.7pt 0cm 5.7pt; height:.05pt">
<p class="MsoNormal" style="text-autospace:none"><span style="">S = k log D</span><span style="font-size:11.0pt; font-family:Calibri"></span></p>
</td>
<td valign="top" width="283" style="width:212.05pt; border-top:none; border-left:none; border-bottom:solid black 1.0pt; border-right:solid
black 1.0pt; background:#EEECE1; padding:0cm 5.7pt 0cm 5.7pt; height:.05pt">
<p class="MsoNormal" style="text-autospace:none"><span style="">S = k log D</span><span style="font-size:11.0pt; font-family:Calibri"></span></p>
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5.7pt; height:.05pt">
<p class="MsoNormal" style="text-autospace:none"><span style="">Information (I)</span><span style="font-size:11.0pt; font-family:Calibri"></span></p>
</td>
<td valign="top" width="228" style="width:171.0pt; border-top:none; border-left:none; border-bottom:solid black 1.0pt; border-right:solid
black 1.0pt; background:#EEECE1; padding:0cm 5.7pt 0cm 5.7pt; height:.05pt">
<p class="MsoNormal" style="text-autospace:none"><i><span style="">- S = k log (1/D)<span style="">
</span></span></i><span style="font-size:11.0pt; font-family:Calibri"></span></p>
</td>
<td valign="top" width="283" style="width:212.05pt; border-top:none; border-left:none; border-bottom:solid black 1.0pt; border-right:solid
black 1.0pt; background:#EEECE1; padding:0cm 5.7pt 0cm 5.7pt; height:.05pt">
<p class="MsoNormal" style="text-autospace:none"><i><span lang="EN-GB" style="">I<sub>P</sub> = log<sub>2</sub> [AUC(PDE)/AUC(GLE)]</span></i><span lang="EN-GB" style="font-size:11.0pt; font-family:Calibri"></span></p>
</td>
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</tbody>
</table>
<p class="MsoNormal" style="text-autospace:none"><b><span lang="EN-GB" style=""> </span></b></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style=""><span style="">
</span>As I pointed out in [9], the concept of “negative entropy” violates the <i>
Third Law of Thermodynamics </i>and hence cannot be used to define “order” nor “information”.<span style="">
</span>However,<span style=""> </span>Planckian information, I<sub>P<span style="">
</span></sub>, can be positive, zero, or negative, depending on whether AUC(PDE) is greater than, equal to, or less than AUC (GLE), respectively, leading to the conclusion that
</span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style=""> </span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style=""><span style="">
</span>“Information can, but entropy cannot, be negative.”<span style="">
</span>(6)</span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style=""> </span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style="">Hence that
<br style="">
<br style="">
</span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style=""><span style="">
</span>“Information is not entropy.”<span style="">
</span>(7)<span style="">
</span></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style=""><span style="">
</span><span style=""> </span></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-GB" style="">I recommended in [10] that Statement (6) or (7) be referred to as the
<b>First Law of Informatics</b> (FLI).<span style=""> </span>It is hoped that FLI will help clarify the decades-long confusions plaguing the fields of informatics, computer science, thermodynamics, biology, and philosophy.
<b></b></span></p>
<p class="MsoNormal" style="text-autospace:none"><b><span lang="EN-GB" style=""><span style="">
</span></span></b><span lang="EN-GB" style="">Another way of supporting the thesis that
<i>information </i>and <i>entropy</i> are not equivalent is invoke<span style="">
</span>the notion of <i>irreducible triadic relations</i> (ITR) of Peirce (1839-1914) [11], according to whom the sign (i.e., anything that stands for something other than itself) is irreducible triad of
<i>object</i>, <i>representamen</i> (also called <i>sign</i>) and <i>interpretant.<span style="">
</span></i>The irreducible triadic relation (ITR) can be represented as a 3-node network shown in
<b>Figure 3</b>.<span style=""> </span>The <i>communication system</i> of Shannon is also irreducibly triadic, since it can be mapped to the sign triad as indicated in Figurer 3.<span style="">
</span>Entropy (in the sense of Shannon’s communication theory) is one of the three
<i>nodes</i> and Information (in the sense of Peircean semiotics) is one of the three
<i>edges</i>.<span style=""> </span>Clearly, nodes and edges are two different classes of entities, consistent with FLI, Statement (7).</span><b><span style=""></span></b></p>
<p class="MsoNormal" style="text-autospace:none"><b><span style=""> </span></b></p>
<p class="MsoNormal" style="text-autospace:none"><b><span lang="EN-GB" style="">Figure 3.<span style="">
</span></span></b><span lang="EN-GB" style="">The isomorphism between Shannon’s communication system (<i>the source-message-receiver triad</i>) and Peirce’s semiotic system (<i>the object-sign-interpretant triad</i>), the “interpretant” being defined as the
effect that a sign has on the mind of an interpreter.<span style=""> </span>The arrows read “determines” or “constrains”.<span style="">
</span><i>f</i><span style=""> </span>= sign/message production, g = sign/message interpretation;
<i>h </i>= information flow, or correspondence. The diagram is postulated to be equivalent to the commutative triangle of the category theory [12], i.e., f x g = h.
</span></p>
<p class="MsoNormal" style="text-autospace:none"><b><span lang="EN-GB" style=""> </span></b></p>
<p class="MsoNormal" style="text-autospace:none"><b><span lang="EN-GB" style="background:white">References:</span></b><span lang="EN-GB" style="background:white">
<br>
<span style=""> </span>[1] J<span style="color:#333333">i, S. (2015). </span></span><span style="color:#6AB446; background:white"><a href="http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vigier9.pdf"><span lang="EN-GB" style="color:#6AB446">PLANCKIAN
INFORMATION (IP): A NEW MEASURE OF ORDER IN ATOMS, ENZYMES, CELLS, BRAINS, HUMAN SOCIETIES, AND THE COSMOS. </span></a></span><span lang="EN-GB" style="color:#333333; background:white"> In: <i>Unified Field Mechanics: Natural Science beyond the Veil of Spacetime</i> (Amoroso,
R., Rowlands, P., and Kauffman, L. eds.), World Scientific, New Jersey, 2015, pp. 579-589).<span style="">
</span>PDF at </span><span style="background:white"><a href="http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vigier9.pdf"><span lang="EN-GB" style="">http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vigier9.pdf</span></a></span><span lang="EN-GB" style="background:white"><br>
<span style=""> </span>[1a] Ji, S. (2016).<span style=""> </span>Planckian Information (I_P): A Measure of the Order in Complex Systems.<span style="">
</span>In: Information and Complexity (M. Burgin and Calude, C. S., eds.), World Scientific, New Jersey.
<span style=""> </span><br>
<span style=""> </span>[2] Ji, S. (2012).<span style=""> </span>Molecular Theory of the Living Cell: Concepts, Molecular Mechanisms and Biomedical Applications.<span style="">
</span>Springer, New York.<span style=""> </span>Chapters 11 and 12.<span style="">
</span>PDF at <a class="moz-txt-link-freetext" href="http:/www.conformon.net">http:/www.conformon.net</a> under Publications > Book Chapters.<br>
<span style=""> </span>[3] <span style="color:#222222">Ji, S. (2015). Planckian distributions in molecular machines, living cells, and brains: The wave-particle duality in biomedical sciences. <i>Proceedings of the International Conference on Biology and
Biomedical Engineering.</i> Vienna, March 15-17, pp. 115-137. Retrievable from </span><a class="moz-txt-link-freetext" href="http://www.inase.org/library/2015/vienna/BICHE.pdf">http://www.inase.org/library/2015/vienna/BICHE.pdf</a><br>
<span style=""> </span></span><span style="background:white">............</span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="background:white">See original file at:
</span><br>
<a class="moz-txt-link-freetext" href="http://fis.sciforum.net/wp-content/uploads/sites/2/2014/11/Planckian_information.pdf">http://fis.sciforum.net/wp-content/uploads/sites/2/2014/11/Planckian_information.pdf</a></p>
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<pre class="moz-signature" cols="72">--
-------------------------------------------------
Pedro C. Marijuán
Grupo de Bioinformación / Bioinformation Group
Instituto Aragonés de Ciencias de la Salud
Centro de Investigación Biomédica de Aragón (CIBA)
Avda. San Juan Bosco, 13, planta 0
50009 Zaragoza, Spain
Tfno. +34 976 71 3526 (& 6818)
<a class="moz-txt-link-abbreviated" href="mailto:pcmarijuan.iacs@aragon.es">pcmarijuan.iacs@aragon.es</a>
<a class="moz-txt-link-freetext" href="http://sites.google.com/site/pedrocmarijuan/">http://sites.google.com/site/pedrocmarijuan/</a>
------------------------------------------------- </pre>
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