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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">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">http://www.mdpi.com/2078-2489/8/1/24</a><br>
Greetings to all--Pedro<br>
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<p class="MsoNormal"
style="margin-bottom:10.0pt;line-height:115%;mso-layout-grid-align:
none;text-autospace:none"><b><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><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%;mso-layout-grid-align:
none;text-autospace:none"><b><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><br>
</span></b><span style="mso-ansi-language:EN-GB" lang="EN-GB"><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), <o:p></o:p></span></p>
<p class="MsoNormal"
style="margin-bottom:10.0pt;line-height:115%;mso-layout-grid-align:
none;text-autospace:none"><span style="mso-ansi-language:EN-GB"
lang="EN-GB"><span style="mso-spacerun:yes"> </span></span><span
style="mso-ansi-language:#000A">y
= (A/(x + B^5)/(Exp(C/(x + B)) – 1)<span
style="mso-spacerun:yes">
</span>(1)<o:p></o:p></span></p>
<p class="MsoNormal"
style="margin-bottom:10.0pt;line-height:115%;mso-layout-grid-align:
none;text-autospace:none"><span style="mso-ansi-language:#000A"><span
style="mso-spacerun:yes"> </span></span><span
style="mso-ansi-language:
EN-GB" lang="EN-GB">where A, B and C are free parameters, x is
the class or the bin to
which<span style="mso-spacerun:yes"> </span>objects or
entities belong, and y
is the frequency [1, 1a].<span style="mso-spacerun:yes"> </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="mso-spacerun:yes"> </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).<o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB">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.<o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><o:p> </o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB">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="mso-spacerun:yes"> </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="mso-special-character:
line-break">
<!--[if !supportLineBreakNewLine]--><br
style="mso-special-character:line-break">
<!--[endif]--><o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><span
style="mso-spacerun:yes"> </span>y =
Ae<sup>– (x – </sup></span><sup><span
style="mso-ansi-language:#000A">μ</span></sup><sup><span
style="mso-ansi-language:EN-GB" lang="EN-GB">)^2/(2</span></sup><sup><span
style="mso-ansi-language:
#000A">σ</span></sup><sup><span
style="mso-ansi-language:EN-GB" lang="EN-GB">^2)</span></sup><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><span
style="mso-spacerun:yes">
</span>(2)<o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><o:p> </o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB">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="mso-spacerun:yes"> </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="mso-spacerun:yes"> </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="mso-spacerun:yes">
</span><o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><o:p> </o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><span
style="mso-spacerun:yes"> </span>I<sub>P</sub>
= log<sub>2</sub>
(AUC(PDE)/AUC(GLE))<span style="mso-spacerun:yes"> </span>bits<span
style="mso-spacerun:yes">
</span>(3)<o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB">or<o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><br>
<span style="mso-spacerun:yes"> </span>I<sub>P<span
style="mso-spacerun:yes"> </span></sub>= log<sub>2</sub>
[∫P(x)dx/∫G(x)dx]<span style="mso-spacerun:yes">
</span>bits<span style="mso-spacerun:yes">
</span><span style="mso-tab-count:2"> </span><span
style="mso-spacerun:yes"> </span>(4)<o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><o:p> </o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB">where P(x) and
G(x) are the Plackian
Distribution Equation and the Gaussian-Like Equation,
respectively. <br style="mso-special-character:line-break">
<!--[if !supportLineBreakNewLine]--><br
style="mso-special-character:line-break">
<!--[endif]--><o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB">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="mso-spacerun:yes"> </span><i>Planckian
information</i>
is primarily concerned with the <i>amount</i> (and hence the
<i>quantitative</i>
aspect) of information.<span style="mso-spacerun:yes"> </span>There
are
numerous ways that have been suggested in the literature for <i>quantifying
information</i> bedside the well-known Hartley information,
<st1:place w:st="on">Shannon</st1:place>
entropy, algorithmic information, etc [5].<span
style="mso-spacerun:yes">
</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="mso-tab-count:1">
</span><span style="mso-spacerun:yes"> </span>(5)<br>
biomedical, mental, linguistic, socioeconomic, cosmological,
or any <o:p></o:p></span></p>
<p class="MsoNormal"
style="line-height:115%;mso-layout-grid-align:none;
text-autospace:none"><span style="mso-ansi-language:EN-GB"
lang="EN-GB">other
processes that generate long-tailed histograms obeying the <br>
Planckian distribution equation (PDE).”<br
style="mso-special-character:line-break">
<!--[if !supportLineBreakNewLine]--><br
style="mso-special-character:line-break">
<!--[endif]--><o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB">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="mso-spacerun:yes"> </span>I_P is
related to the “organized complexity”
and S is realted to “disorganized complexity” of Weaver [6].<span
style="mso-spacerun:yes"> </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="mso-special-character:line-break">
<!--[if !supportLineBreakNewLine]--><br
style="mso-special-character:line-break">
<!--[endif]--><o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB">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="mso-spacerun:yes"> </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="mso-spacerun:yes"> </span><o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><o:p> </o:p></span></p>
<table class="MsoNormalTable"
style="margin-left:5.7pt;border-collapse:collapse;mso-table-layout-alt:fixed;
mso-padding-alt:0cm 5.7pt 0cm 5.7pt" border="0" cellpadding="0"
cellspacing="0">
<tbody>
<tr style="mso-yfti-irow:0;mso-yfti-firstrow:yes;height:.05pt">
<td colspan="3" style="width:478.8pt;border:solid black
1.0pt; mso-border-alt:solid black
.35pt;background:#EEECE1;padding:0cm 5.7pt 0cm 5.7pt;
height:.05pt" valign="top" width="638">
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><b><span
style="mso-ansi-language:EN-GB" lang="EN-GB">Table
1.<span style="mso-spacerun:yes"> </span></span></b><span
style="mso-ansi-language:EN-GB" lang="EN-GB">Two
different views on the entropy-information relation.<span
style="mso-spacerun:yes"> </span>I<sub>P</sub> =
the Planckian information, Eq. (8.11).<span
style="mso-spacerun:yes"> </span>D = disorder.<span
style="mso-spacerun:yes"> </span>AUC = Area Under
the Curve; PDE = Planckian Distribution Equation, (1);
GLE = Gaussian-like Equation, (2). </span><span
style="font-size:11.0pt;font-family:
Calibri;mso-bidi-font-family:Calibri;mso-ansi-language:EN-GB"
lang="EN-GB"><o:p></o:p></span></p>
</td>
</tr>
<tr style="mso-yfti-irow:1;height:.05pt">
<td style="width:95.75pt;border:solid black 1.0pt;
border-top:none;mso-border-top-alt:solid black
.35pt;mso-border-alt:solid black .35pt;
background:#EEECE1;padding:0cm 5.7pt 0cm
5.7pt;height:.05pt" valign="top" width="128">
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="font-size:11.0pt;font-family:Calibri;mso-bidi-font-family:
Calibri;mso-ansi-language:EN-GB" lang="EN-GB"><o:p> </o:p></span></p>
</td>
<td style="width:171.0pt;border-top:none;border-left:
none;border-bottom:solid black 1.0pt;border-right:solid
black 1.0pt; mso-border-top-alt:solid black
.35pt;mso-border-left-alt:solid black .35pt;
mso-border-alt:solid black
.35pt;background:#EEECE1;padding:0cm 5.7pt 0cm 5.7pt;
height:.05pt" valign="top" width="228">
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><b><span
style="color:#7030A0;mso-ansi-language:#000A">Schrödinger
(1944) </span></b><span
style="mso-ansi-language:#000A">[8]</span><span
style="font-size:11.0pt;
font-family:Calibri;mso-bidi-font-family:Calibri;mso-ansi-language:#000A"><o:p></o:p></span></p>
</td>
<td style="width:212.05pt;border-top:none;border-left:
none;border-bottom:solid black 1.0pt;border-right:solid
black 1.0pt; mso-border-top-alt:solid black
.35pt;mso-border-left-alt:solid black .35pt;
mso-border-alt:solid black
.35pt;background:#EEECE1;padding:0cm 5.7pt 0cm 5.7pt;
height:.05pt" valign="top" width="283">
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><b><span
style="color:#7030A0;mso-ansi-language:#000A">Ji
(2015) </span></b><span
style="mso-ansi-language:#000A">[1, 3]</span><span
style="font-size:11.0pt;
font-family:Calibri;mso-bidi-font-family:Calibri;mso-ansi-language:#000A"><o:p></o:p></span></p>
</td>
</tr>
<tr style="mso-yfti-irow:2;height:.05pt">
<td style="width:95.75pt;border:solid black 1.0pt;
border-top:none;mso-border-top-alt:solid black
.35pt;mso-border-alt:solid black .35pt;
background:#EEECE1;padding:0cm 5.7pt 0cm
5.7pt;height:.05pt" valign="top" width="128">
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:#000A">Entropy (S)</span><span
style="font-size:
11.0pt;font-family:Calibri;mso-bidi-font-family:Calibri;mso-ansi-language:
#000A"><o:p></o:p></span></p>
</td>
<td style="width:171.0pt;border-top:none;border-left:
none;border-bottom:solid black 1.0pt;border-right:solid
black 1.0pt; mso-border-top-alt:solid black
.35pt;mso-border-left-alt:solid black .35pt;
mso-border-alt:solid black
.35pt;background:#EEECE1;padding:0cm 5.7pt 0cm 5.7pt;
height:.05pt" valign="top" width="228">
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:#000A">S = k log D</span><span
style="font-size:
11.0pt;font-family:Calibri;mso-bidi-font-family:Calibri;mso-ansi-language:
#000A"><o:p></o:p></span></p>
</td>
<td style="width:212.05pt;border-top:none;border-left:
none;border-bottom:solid black 1.0pt;border-right:solid
black 1.0pt; mso-border-top-alt:solid black
.35pt;mso-border-left-alt:solid black .35pt;
mso-border-alt:solid black
.35pt;background:#EEECE1;padding:0cm 5.7pt 0cm 5.7pt;
height:.05pt" valign="top" width="283">
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:#000A">S = k log D</span><span
style="font-size:
11.0pt;font-family:Calibri;mso-bidi-font-family:Calibri;mso-ansi-language:
#000A"><o:p></o:p></span></p>
</td>
</tr>
<tr style="mso-yfti-irow:3;mso-yfti-lastrow:yes;height:.05pt">
<td style="width:95.75pt;border:solid black 1.0pt;
border-top:none;mso-border-top-alt:solid black
.35pt;mso-border-alt:solid black .35pt;
background:#EEECE1;padding:0cm 5.7pt 0cm
5.7pt;height:.05pt" valign="top" width="128">
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:#000A">Information (I)</span><span
style="font-size:
11.0pt;font-family:Calibri;mso-bidi-font-family:Calibri;mso-ansi-language:
#000A"><o:p></o:p></span></p>
</td>
<td style="width:171.0pt;border-top:none;border-left:
none;border-bottom:solid black 1.0pt;border-right:solid
black 1.0pt; mso-border-top-alt:solid black
.35pt;mso-border-left-alt:solid black .35pt;
mso-border-alt:solid black
.35pt;background:#EEECE1;padding:0cm 5.7pt 0cm 5.7pt;
height:.05pt" valign="top" width="228">
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><i><span
style="mso-ansi-language:#000A">- S = k log (1/D)<span
style="mso-spacerun:yes"> </span></span></i><span
style="font-size:11.0pt;
font-family:Calibri;mso-bidi-font-family:Calibri;mso-ansi-language:#000A"><o:p></o:p></span></p>
</td>
<td style="width:212.05pt;border-top:none;border-left:
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height:.05pt" valign="top" width="283">
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><i><span
style="mso-ansi-language:EN-GB" lang="EN-GB">I<sub>P</sub>
= log<sub>2</sub> [AUC(PDE)/AUC(GLE)]</span></i><span
style="font-size:11.0pt;
font-family:Calibri;mso-bidi-font-family:Calibri;mso-ansi-language:EN-GB"
lang="EN-GB"><o:p></o:p></span></p>
</td>
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<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><b><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><o:p> </o:p></span></b></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><span
style="mso-spacerun:yes">
</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="mso-spacerun:yes"> </span>However,<span
style="mso-spacerun:yes">
</span>Planckian information, I<sub>P<span
style="mso-spacerun:yes"> </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 <o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><o:p> </o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><span
style="mso-spacerun:yes"> </span>“Information can,
but entropy cannot, be
negative.”<span style="mso-spacerun:yes">
</span>(6)<o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><o:p> </o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB">Hence that <br
style="mso-special-character:
line-break">
<!--[if !supportLineBreakNewLine]--><br
style="mso-special-character:line-break">
<!--[endif]--><o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><span
style="mso-spacerun:yes"> </span>“Information is
not entropy.”<span style="mso-spacerun:yes">
</span>(7)<span style="mso-spacerun:yes">
</span><o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><span
style="mso-spacerun:yes">
</span><span style="mso-spacerun:yes"> </span><o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="mso-ansi-language:EN-GB" lang="EN-GB">I recommended in
[10] that Statement
(6) or (7) be referred to as the <b>First Law of Informatics</b>
(FLI).<span style="mso-spacerun:yes"> </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><o:p></o:p></b></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><b><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><span
style="mso-spacerun:yes">
</span></span></b><span style="mso-ansi-language:EN-GB"
lang="EN-GB">Another way
of supporting the thesis that <i>information </i>and <i>entropy</i>
are not
equivalent is invoke<span style="mso-spacerun:yes"> </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="mso-spacerun:yes"> </span></i>The
irreducible
triadic relation (ITR) can be represented as a 3-node network
shown in <b>Figure
3</b>.<span style="mso-spacerun:yes"> </span>The <i>communication
system</i>
of <st1:place w:st="on">Shannon</st1:place> is also
irreducibly triadic, since
it can be mapped to the sign triad as indicated in Figurer 3.<span
style="mso-spacerun:yes"> </span>Entropy (in the sense of
<st1:place w:st="on">Shannon</st1:place>’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="mso-spacerun:yes"> </span>Clearly, nodes and edges
are two different
classes of entities, consistent with FLI, Statement (7).</span><b><span
style="mso-ansi-language:#000A"><o:p></o:p></span></b></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><b><span
style="mso-ansi-language:#000A"><o:p> </o:p></span></b></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><b><span
style="mso-ansi-language:EN-GB" lang="EN-GB">Figure 3.<span
style="mso-spacerun:yes"> </span></span></b><span
style="mso-ansi-language:
EN-GB" lang="EN-GB">The isomorphism between <st1:place
w:st="on">Shannon</st1:place>’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="mso-spacerun:yes"> </span>The
arrows read “determines” or
“constrains”.<span style="mso-spacerun:yes"> </span><i>f</i><span
style="mso-spacerun:yes"> </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. <o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><b><span
style="mso-ansi-language:EN-GB" lang="EN-GB"><o:p> </o:p></span></b></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><b><span
style="background:white;mso-highlight:white;mso-ansi-language:EN-GB"
lang="EN-GB">References:</span></b><span
style="background:white;mso-highlight:white;mso-ansi-language:EN-GB"
lang="EN-GB">
<br>
<span style="mso-spacerun:yes"> </span>[1] J<span
style="color:#333333">i, S.
(2015). </span></span><span
style="color:#6AB446;background:white;
mso-highlight:white;mso-ansi-language:#000A"><a
href="http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vigier9.pdf"><span
style="color:#6AB446;mso-ansi-language:EN-GB" lang="EN-GB">PLANCKIAN
INFORMATION
(IP): A NEW MEASURE OF ORDER IN ATOMS, ENZYMES, CELLS,
BRAINS, HUMAN SOCIETIES,
AND THE COSMOS. </span></a></span><span
style="color:#333333;
background:white;mso-highlight:white;mso-ansi-language:EN-GB"
lang="EN-GB"> In: <i>Unified
Field Mechanics: Natural Science beyond the Veil of
Spacetime</i> (Amoroso,
R., Rowlands, P., and Kauffman, L. eds.), World Scientific,
New <st1:place w:st="on">Jersey</st1:place>, 2015, pp.
579-589).<span style="mso-spacerun:yes"> </span>PDF at </span><span
style="background:white;
mso-highlight:white;mso-ansi-language:#000A"><a
href="http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vigier9.pdf"><span
style="mso-ansi-language:EN-GB" lang="EN-GB">http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vigier9.pdf</span></a></span><span
style="background:white;mso-highlight:white;mso-ansi-language:EN-GB"
lang="EN-GB"><br>
<span style="mso-spacerun:yes"> </span>[1a] Ji, S. (2016).<span
style="mso-spacerun:yes"> </span>Planckian Information
(I_P): A Measure of the
Order in Complex Systems.<span style="mso-spacerun:yes"> </span>In:
Information and Complexity (M. Burgin and Calude, C. S.,
eds.), World
Scientific, New <st1:place w:st="on">Jersey</st1:place>. <span
style="mso-spacerun:yes"> </span><br>
<span style="mso-spacerun:yes"> </span>[2] Ji, S. (2012).<span
style="mso-spacerun:yes"> </span>Molecular Theory of the
Living Cell:
Concepts, Molecular Mechanisms and Biomedical Applications.<span
style="mso-spacerun:yes"> </span>Springer, <st1:place
w:st="on"><st1:state w:st="on">New York</st1:state></st1:place>.<span
style="mso-spacerun:yes">
</span>Chapters 11 and 12.<span style="mso-spacerun:yes"> </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="mso-spacerun:yes"> </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>
<st1:city w:st="on"><st1:place w:st="on">Vienna</st1:place></st1:city>,
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="mso-spacerun:yes"> </span></span><span
style="background:white;mso-highlight:white;mso-ansi-language:
#000A">............</span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="background:white;mso-highlight:white;mso-ansi-language:
#000A">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>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="background:white;mso-highlight:white;mso-ansi-language:
#000A"><br>
</span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="background:white;mso-highlight:white;mso-ansi-language:
#000A">S. Ji, 03/21/2017<o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="color:#222222;background:white;mso-highlight:white;mso-ansi-language:#000A"><o:p> </o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="color:#222222;background:white;mso-highlight:white;mso-ansi-language:#000A">--------------------------------------------------<br
style="mso-special-character:line-break">
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style="mso-special-character:line-break">
<!--[endif]--><o:p></o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="color:#222222;background:white;mso-highlight:white;mso-ansi-language:#000A"><o:p> </o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="color:#222222;background:white;mso-highlight:white;mso-ansi-language:#000A"><o:p> </o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="color:#222222;background:white;mso-highlight:white;mso-ansi-language:#000A"><o:p> </o:p></span></p>
<p class="MsoNormal"
style="mso-layout-grid-align:none;text-autospace:none"><span
style="color:#222222;background:white;mso-highlight:white;mso-ansi-language:#000A"><span
style="mso-spacerun:yes"> </span><o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
</o:smarttagtype>
<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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