<div>Dear Joseph, </div><div>thanks a lot for the support! I appreciate it very much, now that I'm under fire!</div><div><br></div><div>I agree with you, with a sole difference, when you say "<span style="font-family: Arial; font-size: small;">within the same high overall energy level". Indeed, our approach predicts different energetic levels in different brain functional dimensions. </span></div><div><span style="text-align: justify; font-size: 10pt; line-height: 107%; font-family: "Times New Roman", serif;">A BUT topological approach, which states that mappings among every brain
signal and energetic information have the potential to be operationalized in fMRI and EEG studies. We will provide a proof-of
concept example, in order to demonstrate the feasibility of a BUT topological approach and its aptitude of providing very accurate testable
previsions. We have two mental states,
one standing for a symmetry, and another for a broken symmetry. Imagine that
the brain at rest displays a preserved symmetry, while the brain during a
visual task displays a broken symmetry. Our model sharply predicts the energetic
values for both the cases, either in EEG and fMRI series. </span><span lang="EN-GB" style="text-align: justify; font-size: 10pt; line-height: 107%; font-family: "Times New Roman", serif;">Indeed, according to BUT, a single microarea with
symmetry breaking (e.g., a primary visual area), necessarily
projects to TWO areas with preserved symmetry (e.g., a default mode network's area). The single area in lower dimensions and the two areas with matching description
need to display the same values of entropy. This allows us to recognize which
zones of the brain are correlated during symmetry breaks, e.g., during the
projective steps from higher to lower level of complexity, and vice versa.
Therefore, </span><span style="text-align: justify; font-size: 10pt; line-height: 107%; font-family: "Times New Roman", serif;">our framework is able to
predict the following hypothetical results: if we find, during a visual task,
say, three microareas with an entropy 1.08, we expect to find, during rest, six
or more microareas with entropy=1.08. In
sum, by knowing just the entropy values for each BOLD-activated or EEG brain subarea,
we are allowed to correlate two different brain states, e.g., a
lower-dimensional state with symmetry breaking
and a higher-dimensional state with preserved symmetries. </span></div><div>
<p class="MsoNormalCxSpMiddle" style="text-align:justify"><span style="font-size:
10.0pt;line-height:107%;font-family:"Times New Roman",serif;mso-ansi-language:
EN-US"><o:p> You can find further details in our manuscript (under review): </o:p></span></p><p class="MsoNormalCxSpMiddle" style="text-align:justify"><span style="line-height: 107%;"><o:p><font face="Times New Roman, serif"><span style="font-size: 13.3333px;">http://arturotozzi.webnode.it/products/a-topological-approach-assesses-brain-enthalpy-fre-energy-and-entropy/</span></font><br></o:p></span></p><p class="MsoNormalCxSpMiddle" style="text-align:justify"><span style="line-height: 107%;"><o:p><font face="Times New Roman, serif"><span style="font-size: 13.3333px;"><br></span></font></o:p></span></p><p class="MsoNormalCxSpMiddle" style="text-align:justify"><span style="line-height: 107%;"><o:p><font face="Times New Roman, serif"><span style="font-size: 13.3333px;">Ciao, and thanks again!</span></font></o:p></span></p><br><p class="MsoNormalCxSpFirst" style="margin-top:12.0pt;margin-right:0cm;
margin-bottom:12.0pt;margin-left:0cm;mso-add-space:auto;text-align:justify;
line-height:115%;mso-layout-grid-align:none;text-autospace:none"><span style="font-size: 14px; line-height: normal; text-align: start;"><font face="courier new, monospace"><b>Arturo Tozzi</b></font></span></p><p class="MsoNormalCxSpFirst" style="margin-top:12.0pt;margin-right:0cm;
margin-bottom:12.0pt;margin-left:0cm;mso-add-space:auto;text-align:justify;
line-height:115%;mso-layout-grid-align:none;text-autospace:none"><span style="line-height: 115%;"><font face="courier new, monospace">AA Professor Physics, University North Texas</font></span></p><p class="MsoNormalCxSpFirst" style="margin-top:12.0pt;margin-right:0cm;
margin-bottom:12.0pt;margin-left:0cm;mso-add-space:auto;text-align:justify;
line-height:115%;mso-layout-grid-align:none;text-autospace:none"><span style="font-size: 14px; line-height: normal; text-align: start;"><font face="courier new, monospace">Pediatrician ASL Na2Nord, Italy</font></span></p><p class="MsoNormalCxSpFirst" style="margin-top:12.0pt;margin-right:0cm;
margin-bottom:12.0pt;margin-left:0cm;mso-add-space:auto;text-align:justify;
line-height:115%;mso-layout-grid-align:none;text-autospace:none"><span style="font-size: 14px; line-height: normal; text-align: start;"><font face="courier new, monospace">Comput Intell Lab, University Manitoba</font></span></p><p class="MsoNormalCxSpFirst" style="margin-top:12.0pt;margin-right:0cm;
margin-bottom:12.0pt;margin-left:0cm;mso-add-space:auto;text-align:justify;
line-height:115%;mso-layout-grid-align:none;text-autospace:none"><font face="courier new, monospace"><a href="http://arturotozzi.webnode.it/" style="font-size: 14px; color: rgb(5, 68, 126); line-height: normal; text-align: start;">http://arturotozzi.webnode.it/</a><span style="font-size: 14px; line-height: normal; text-align: start;"> </span></font><br></p></div><br>
<br>
<blockquote>
----Messaggio originale----<br>
Da: "Joseph Brenner" <joe.brenner@bluewin.ch><br>
Data: 26/11/2016 21.05<br>
A: <tozziarturo@libero.it>, "fis"<fis@listas.unizar.es><br>
Ogg: Re: [Fis] Who may prove that consciousness is an Euclidean n-space ???<br>
<br>
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-->
<div><font face="Arial" size="2">Dear FISers,</font></div>
<div><font face="Arial" size="2"></font> </div>
<div><font face="Arial" size="2">At the risk of attracting the anger of all the
mathematicians in the group, I will agree with Arturo, <em>contra
</em>Krassimir. For a non-mathematician like me, a description of complex
dynamic processes such as consciousness and information can be partly
mathematical but need not involve proofs and their reduced logic.</font></div>
<div><font face="Arial" size="2"></font> </div>
<div><font face="Arial" size="2">The question I have is whether the field
description is itself necessary and sufficient and if incomplete, what is
missing. Perhaps it is my intuition that consciousness is both continuous and
discontinuous, and so is its opposite, unconsciousness, which still
involves high-level nervous functions. In my picture, antipodal points are
of little relevance compared to the
non-Euclidean multi-dimensionality of this dynamic opposition,
</font><font face="Arial" size="2">moving between identity and diversity, presence
and absence, clarity and vagueness, symmetry and dissymetry, within the same
high overall energy level. In any case, perhaps we can agree that everything
that is moving here is information!</font></div>
<div><font face="Arial" size="2"></font> </div>
<div><font face="Arial" size="2">Thank you and best wishes,</font></div>
<div><font face="Arial" size="2"></font> </div>
<div><font face="Arial" size="2">Joseph</font></div>
<blockquote style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<div style="FONT: 10pt arial">----- Original Message ----- </div>
<div style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><b>From:</b>
<a title="tozziarturo@libero.it" href="mailto:tozziarturo@libero.it">tozziarturo@libero.it</a> </div>
<div style="FONT: 10pt arial"><b>To:</b> <a title="fis@listas.unizar.es" href="mailto:fis@listas.unizar.es">fis</a> </div>
<div style="FONT: 10pt arial"><b>Sent:</b> Saturday, November 26, 2016 7:06
PM</div>
<div style="FONT: 10pt arial"><b>Subject:</b> Re: [Fis] Who may prove that
consciousness is an Euclidean n-space ???</div>
<div><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><font face="Arial" size="2"></font><br></div>
<p dir="ltr" style="MARGIN-TOP: 0px">Dear Krassimir, <br>Thanks a lot for your
question, now the discussion will become hotter!</p>
<p dir="ltr">First of all, we never stated that consciousness lies either on a
n-sphere or on an Euclidean n-space.<br>Indeed, in our framework,
consciousness IS the continuous function. <br>Such function stands for a gauge
field that restores the brain symmetries, broken by sensations. <br>Concerning
brain and gauge fields, see my PLOS biology paper:
<br>http://journals.plos.org/plosbiology/article?id=10.1371%2Fjournal.pbio.1002400</p>
<p dir="ltr">When consciousness lacks, the inter-dimensional projections are
broken, and the nervous higher functions temporarily disappear. </p>
<p dir="ltr">Concerning the question about which are the manifolds where brain
functions lie, it does not matter whether they are spheres, or circles, or
concave, or flat structures: we demonstrated that the BUT is valid not just
for convex manifolds, but for all the kinds of manifolds. <br>See our:
<br>http://onlinelibrary.wiley.com/doi/10.1002/jnr.23720/abstract?userIsAuthenticated=false&deniedAccessCustomisedMessage=<br></p>
<p dir="ltr">Therefore, even if you think that brain and biological functions
are trajectories moving on concave structures towards lesser energetic levels,
as suggested by, e.g., Fokker-Planck equations, it does not matter: you may
always find the antipodal points with matching description predicted by
BUT. </p>
<p dir="ltr">Ciao!</p>
<div id="mail-app-auto-default-signature">
<p dir="ltr">--<br>Inviato da Libero Mail per Android</p></div>sabato, 26
novembre 2016, 06:23PM +01:00 da Krassimir Markov <a href="mailto:markov@foibg.com">markov@foibg.com</a>:<br><br>
<blockquote id="mail-app-auto-quote" style="PADDING-RIGHT: 0px; PADDING-LEFT: 10px; PADDING-BOTTOM: 0px; MARGIN: 0px 0px 0px 10px; BORDER-LEFT: #85af31 1px solid; PADDING-TOP: 0px" cite="14801811490000025350">
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<div style="FONT-SIZE: 14pt; COLOR: #000000; FONT-FAMILY: 'Calibri'">
<p><font face="Times New Roman" size="4">Dear FIS colleagues,</font></p>
<p><font face="Times New Roman" size="4">I think, it is needed to put
discussion on mathematical foundation. Let me remember that:</font></p>
<p><font face="Times New Roman" size="4"></font> </p>
<p><font face="Times New Roman"><font size="4">The <b>Borsuk–Ulam theorem</b>
(BUT), states that every </font><a title="Continuous function" style="href: 'https://en.wikipedia.org/wiki/Continuous_function'"><strong><font size="4">continuous function</font></strong></a><font size="4"> from an
</font><a title="N-sphere" style="href: 'https://en.wikipedia.org/wiki/N-sphere'"><font size="4"><i>n</i>-sphere</font></a><font size="4"> into </font><a title="Euclidean space" style="href: 'https://en.wikipedia.org/wiki/Euclidean_space'"><strong><font size="4">Euclidean <i>n</i>-space</font></strong></a><font size="4"> maps some
pair of </font><a title="Antipodal point" style="href: 'https://en.wikipedia.org/wiki/Antipodal_point'"><font size="4">antipodal points</font></a><font size="4"> to the same point.
</font></font></p>
<p><font face="Times New Roman" size="4">Here, two points on a sphere are
called antipodal if they are in exactly opposite directions from the
sphere's center.</font></p>
<p><font face="Times New Roman" size="4">Formally: <strong>if</strong>
<span><span style="DISPLAY: none">f : <em>S<sup> n</sup> → R</em>
<sup>n</sup> </span></span> <strong>is</strong>
<strong>continuous</strong> then there exists an <span><span style="DISPLAY: none">x ∈ S n </span></span> such that: <span><span style="DISPLAY: none">f ( − x ) = f ( x )</span></span>.</font></p>
<p><font face="Times New Roman" size="4">[ </font><a title="https://en.wikipedia.org/wiki/Borsuk%E2%80%93Ulam_theorem" href="https://en.wikipedia.org/wiki/Borsuk%E2%80%93Ulam_theorem" target="_blank"><font face="Times New Roman" size="4">https://en.wikipedia.org/wiki/Borsuk%E2%80%93Ulam_theorem</font></a><font face="Times New Roman" size="4"> ] </font></p>
<p><font face="Times New Roman" size="4"></font> </p>
<p><font face="Times New Roman"><font size="4">Who may proof that
consciousness is a </font><a title="Continuous function" style="href: 'https://en.wikipedia.org/wiki/Continuous_function'"><font size="4"><strong>continuous function</strong></font></a><font size="4"> from
reflected reality ???</font></font></p>
<p><font face="Times New Roman"><font size="4">Who may proof that
consciousness is an </font><a title="Euclidean space" style="href: 'https://en.wikipedia.org/wiki/Euclidean_space'"><font size="4"><strong>Euclidean <i>n</i>-space</strong></font></a><font size="4">
???</font></font></p>
<p><font face="Times New Roman" size="4">After proving these statements we may
think further.</font></p>
<p><font face="Times New Roman" size="4"></font> </p>
<p><font face="Times New Roman" size="4">Yes, discussion is interesting but, I
am afraid, it is not so scientific.</font></p>
<p><font face="Times New Roman" size="4"></font> </p>
<p><font face="Times New Roman" size="4">Friendly regards</font></p>
<p><font face="Times New Roman" size="4">Krassimir</font></p>
<p><font face="Times New Roman" size="4"></font> </p>
<p><font face="Times New Roman" size="4"></font> </p>
<p><font face="Times New Roman" size="4"></font> </p>
<p><font face="Times New Roman" size="4"></font></p></div></div></div>
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<p>
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