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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>
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<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>
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<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>
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<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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