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<P class=MsoNormal
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align=justify><SPAN style="FONT-FAMILY: ; LINE-HEIGHT: 14pt"><FONT size=4>Dear
Arturo, Gordana, Joseph, and FIS Colleagues,</FONT></SPAN></P>
<P class=MsoNormal
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align=justify><SPAN style="FONT-FAMILY: ; LINE-HEIGHT: 14pt"><FONT size=4>The
key to our current discussion I found in the newest work of Arturo (I have read
it before last letter of Arturo <IMG class="wlEmoticon wlEmoticon-smile"
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alt=Smile src="cid:6330F6660C6049859032E1080AF689DF@VaioMarkov">
):</FONT></SPAN></P>
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align=justify><SPAN style="FONT-FAMILY: ; LINE-HEIGHT: 14pt"><FONT
size=4></FONT></SPAN> </P>
<P class=MsoNormal
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align=justify><B><SPAN style="FONT-FAMILY: ; LINE-HEIGHT: 14pt"><FONT size=4>A
TOPOLOGICAL/ECOLOGICAL APPROACH TO PERCEPTION</FONT></SPAN></B></P>
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align=justify><SPAN style="FONT-FAMILY: ; LINE-HEIGHT: 14pt"><FONT
face="Times New Roman"><A
href="http://biorxiv.org/content/biorxiv/early/2016/11/11/086827.full.pdf"><FONT
size=4
face=Calibri>http://biorxiv.org/content/biorxiv/early/2016/11/11/086827.full.pdf</FONT></A>
</FONT></SPAN></P>
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align=justify><SPAN style="FONT-FAMILY: ; LINE-HEIGHT: 14pt"><FONT
size=4>or</FONT></SPAN></P>
<P class=MsoNormal
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align=justify><SPAN style="FONT-FAMILY: ; LINE-HEIGHT: 14pt"><A
href="https://www.researchgate.net/profile/Arturo_Tozzi/publication/310006296_A_TOPOLOGICALECOLOGICAL_APPROACH_TO_PERCEPTION/links/5827617808ae254c50832922.pdf?origin=publication_list"><FONT
size=4>https://www.researchgate.net/profile/Arturo_Tozzi/publication/310006296_A_TOPOLOGICALECOLOGICAL_APPROACH_TO_PERCEPTION/links/5827617808ae254c50832922.pdf?origin=publication_list</FONT></A></SPAN></P>
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<DIV style="FONT: 10pt tahoma">
<DIV><FONT size=4 face=Calibri></FONT> </DIV>
<DIV><FONT size=4 face=Calibri>What is important is that there exist a non
correct using of the topological theory (concretely the BUT).</FONT></DIV>
<DIV><FONT size=4 face=Calibri></FONT> </DIV>
<DIV><FONT size=4 face=Calibri>It is taken as an idea to explain the perception
when different stimulus create the same meaning in the
consciousness.</FONT></DIV>
<DIV><FONT size=4 face=Calibri>See the example with ambulance of Figure 5a
(visual and sound stimulus) which is connected to the same meaning on Figure 5b
(single point).</FONT></DIV>
<DIV><FONT size=4 face=Calibri></FONT> </DIV>
<DIV><FONT size=4 face=Calibri>But !!!</FONT></DIV>
<DIV><FONT size=4 face=Calibri></FONT> </DIV>
<DIV><FONT size=4 face=Calibri>BUT explicitly proof that (citation from
the Arturo’s paper):</FONT></DIV>
<DIV><FONT size=4 face=Calibri></FONT> </DIV>
<DIV><FONT size=4 face=Calibri>BUT states that, if a single point on a
circumference projects to a higher spatial dimension, it gives rise to two
antipodal points with matching description on a sphere, and vice versa
(<B>Figure 1A</B>) (Borsuk, 1933; Marsaglia, 1972; Matoušek, 2003; Beyer, 2004).
This means that the two antipodal points are assessed at one level of
observation in terms of description, while a single point is assessed at a lower
level (Tozzi 2016b), i.e., point location vs. point description. Points on a
sphere are “antipodal”, provided they are diametrically opposite (Henderson,
1996). </FONT></DIV>
<DIV><FONT size=4 face=Calibri>Examples of antipodal points are the poles of a
sphere. This means, e.g., <STRONG>that there exist on the earth surface at least
two antipodal points with the same temperature and pressure</STRONG>. BUT looks
like a translucent glass sphere between a light source and our eyes: we watch
two lights on the sphere surface instead of one. But the two lights are not just
images, they are also real with observable properties, such as intensity and
diameter.</FONT></DIV>
<DIV><FONT size=4 face=Calibri></FONT> </DIV>
<DIV><FONT size=5 face=Calibri><STRONG>i.e. the antipodal points have the same
characteristics !!!</STRONG></FONT></DIV>
<DIV><FONT size=4 face=Calibri></FONT> </DIV>
<DIV><FONT size=4 face=Calibri><STRONG>This is not valid for the sound and
vision with the same meaning!</STRONG></FONT></DIV>
<DIV><FONT size=4 face=Calibri></FONT> </DIV>
<DIV><FONT size=4 face=Calibri>Nevertheless, Arturo wrote <STRONG>very important
conclusion</STRONG> (citation):</FONT></DIV>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: normal; TEXT-AUTOSPACE: ; TEXT-INDENT: 0cm; mso-layout-grid-align: none"
align=left><FONT face=Calibri><FONT size=4><SPAN style="FONT-FAMILY: ">Gibson’s
work strengthens and brings to the front the <STRONG>primary question of “what”
is perceived</STRONG>, before questions of </SPAN><SPAN
style="FONT-FAMILY: ; mso-fareast-font-family: calibri; mso-fareast-theme-font: minor-latin; mso-ansi-language: en-us; mso-fareast-language: en-us; mso-bidi-language: ar-sa">mechanisms
and material implementation are introduced (Rao et al., 1997).
</SPAN></FONT></FONT></P>
<DIV><FONT size=4 face=Calibri></FONT> </DIV>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: normal; TEXT-AUTOSPACE: ; TEXT-INDENT: 0cm; mso-layout-grid-align: none"
align=left><FONT size=4 face=Calibri>Finally, I like the conclusion. My remark
is to be more precise when we use mathematical theoretical results.</FONT></P>
<DIV><FONT size=4 face=Calibri></FONT> </DIV>
<DIV><FONT size=4 face=Calibri>Friendly regards</FONT></DIV>
<DIV><FONT size=4 face=Calibri>Krassimir</FONT></DIV>
<DIV><FONT size=4 face=Calibri></FONT> </DIV>
<DIV><FONT size=4 face=Calibri></FONT> </DIV>
<DIV><FONT size=4 face=Calibri></FONT> </DIV>
<DIV><FONT size=4 face=Calibri></FONT> </DIV>
<DIV style="BACKGROUND: #f5f5f5">
<DIV style="font-color: black"><B>From:</B> <A title=joe.brenner@bluewin.ch
href="mailto:joe.brenner@bluewin.ch">Joseph Brenner</A> </DIV>
<DIV><B>Sent:</B> Saturday, November 26, 2016 10:05 PM</DIV>
<DIV><B>To:</B> <A title=tozziarturo@libero.it
href="mailto:tozziarturo@libero.it">tozziarturo@libero.it</A> ; <A
title=fis@listas.unizar.es href="mailto:fis@listas.unizar.es">fis</A> </DIV>
<DIV><B>Subject:</B> Re: [Fis] Who may prove that consciousness is an Euclidean
n-space???</DIV></DIV></DIV>
<DIV> </DIV></DIV>
<DIV
style='FONT-SIZE: small; TEXT-DECORATION: none; FONT-FAMILY: "Calibri"; FONT-WEIGHT: normal; COLOR: #000000; FONT-STYLE: normal; DISPLAY: inline'>
<DIV><FONT size=2 face=Arial>Dear FISers,</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>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 size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>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 size=2 face=Arial>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 size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>Thank you and best wishes,</FONT></DIV>
<DIV><FONT size=2 face=Arial></FONT> </DIV>
<DIV><FONT size=2 face=Arial>Joseph</FONT></DIV>
<BLOCKQUOTE
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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>
<DIV><FONT size=2 face=Arial></FONT><FONT size=2 face=Arial></FONT><FONT
size=2 face=Arial></FONT><FONT size=2 face=Arial></FONT><FONT size=2
face=Arial></FONT><FONT size=2 face=Arial></FONT><FONT size=2
face=Arial></FONT><FONT size=2 face=Arial></FONT><FONT size=2
face=Arial></FONT><FONT size=2 face=Arial></FONT><FONT size=2
face=Arial></FONT><FONT size=2 face=Arial></FONT><FONT size=2
face=Arial></FONT><FONT size=2 face=Arial></FONT><FONT size=2
face=Arial></FONT><FONT size=2 face=Arial></FONT><FONT size=2
face=Arial></FONT><FONT size=2 face=Arial></FONT><FONT size=2
face=Arial></FONT><FONT size=2 face=Arial></FONT><FONT size=2
face=Arial></FONT><FONT size=2 face=Arial></FONT><FONT size=2
face=Arial></FONT><FONT size=2 face=Arial></FONT><FONT size=2
face=Arial></FONT><FONT size=2 face=Arial></FONT><BR></DIV>
<P style="MARGIN-TOP: 0px" dir=ltr>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 size=4 face="Times New Roman">Dear FIS colleagues,</FONT></P>
<P><FONT size=4 face="Times New Roman">I think, it is needed to put
discussion on mathematical foundation. Let me remember that:</FONT></P>
<P><FONT size=4 face="Times New Roman"></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 size=4 face="Times New Roman">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 size=4 face="Times New Roman">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 size=4 face="Times New Roman">[ </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 size=4
face="Times New Roman">https://en.wikipedia.org/wiki/Borsuk%E2%80%93Ulam_theorem</FONT></A><FONT
size=4 face="Times New Roman"> ] </FONT></P>
<P><FONT size=4 face="Times New Roman"></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 size=4 face="Times New Roman">After proving these statements we may
think further.</FONT></P>
<P><FONT size=4 face="Times New Roman"></FONT> </P>
<P><FONT size=4 face="Times New Roman">Yes, discussion is interesting but, I
am afraid, it is not so scientific.</FONT></P>
<P><FONT size=4 face="Times New Roman"></FONT> </P>
<P><FONT size=4 face="Times New Roman">Friendly regards</FONT></P>
<P><FONT size=4 face="Times New Roman">Krassimir</FONT></P>
<P><FONT size=4 face="Times New Roman"></FONT> </P>
<P><FONT size=4 face="Times New Roman"></FONT> </P>
<P><FONT size=4 face="Times New Roman"></FONT> </P>
<P><FONT size=4 face="Times New Roman"></FONT></P></DIV></DIV></DIV>
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