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<p class="MsoNormal"><font face="Avenir" size="3">Dear colleagues,<o:p></o:p></font></p>
<p class="MsoNormal"><font face="Avenir" size="3"> </font></p>
<p class="MsoNormal"><font face="Avenir" size="3">Krassimir makes very important point that I would like to expand on.<o:p></o:p></font></p>
<p class="MsoNormal"><font face="Avenir" size="3"> </font></p>
<p class="MsoNormal"><font face="Avenir" size="3">It is vital to be aware under which assumption model/theory has been made. One might wish that this be accepted as a fundamental rule among researchers presenting their models – first declare fundamental assumptions
(preferably also implicit ones).<o:p></o:p></font></p>
<p class="MsoNormal"><font face="Avenir" size="3"> </font></p>
<p class="MsoNormal"><font face="Avenir" size="3">Only if we clearly understand the assumptions can we compare different models and approaches. What happens all too often is that this fundamental part is unclear and big discussions are taking place for no reason
as theories are built under different assumptions and refer to different domains, have different level of abstraction etc. but they are assumed to somehow give the same results.<o:p></o:p></font></p>
<p class="MsoNormal"><font face="Avenir" size="3"> </font></p>
<p class="MsoNormal"><font face="Avenir" size="3">For example if we make our models under assumption that light has corpuscular nature, we will see certain classes of phenomena. On the contrary, if we assume that it is a wave, we will see something else.<o:p></o:p></font></p>
<p class="MsoNormal"><font face="Avenir" size="3"> </font></p>
<p class="MsoNormal"><font face="Avenir" size="3">The same goes even here. We should see the assumptions and ask ourselves:<o:p></o:p></font></p>
<p class="MsoNormal"><font face="Avenir" size="3"> </font></p>
<p class="MsoNormal"><font face="Avenir" size="3">What does it imply if we assume that consciousness is a continuous function of reflected reality?<o:p></o:p></font></p>
<p class="MsoNormal"><font face="Avenir" size="3"> </font></p>
<p class="MsoNormal"><font face="Avenir" size="3">What does it imply if assume that consciousness is Euclidean n-space?<o:p></o:p></font></p>
<p class="MsoNormal"><font face="Avenir" size="3"> </font></p>
<p class="MsoNormal"><font face="Avenir" size="3"> </font></p>
<p class="MsoNormal"><font face="Avenir" size="3">With best wishes,<o:p></o:p></font></p>
<p class="MsoNormal"><font face="Avenir" size="3">Gordana<o:p></o:p></font></p>
<p class="MsoNormal"><font face="Avenir" size="3"> </font></p>
<p class="MsoNormal"><font face="Avenir" size="3"> </font></p>
<p class="MsoNormal" style="font-size: 14px; font-family: Calibri, sans-serif;"><o:p> </o:p></p>
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<div>_________________________________________________________</div>
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<div style="font-family: -webkit-standard;"><font size="2" face="Avenir-Book">Gordana Dodig Crnkovic, Professor of Computer Science</font></div>
<div style="font-family: -webkit-standard;"><font size="2" face="Avenir-Book">Vice Dean of Graduate Education</font></div>
<div style="font-family: -webkit-standard;"><font size="2" face="Avenir-Book">Department of Applied IT</font></div>
<div style="font-family: -webkit-standard;"><font size="2" face="Avenir-Book">Chalmers University of Technology & University of Gothenburg, Sweden </font></div>
<div style="font-family: -webkit-standard;"><font size="2" face="Avenir-Book"><a href="http://www.ait.gu.se/kontaktaoss/personal/gordana-dodig-crnkovic">http://www.ait.gu.se/kontaktaoss/personal/gordana-dodig-crnkovic</a>/ </font></div>
<div style="font-family: -webkit-standard;"><font size="2" face="Avenir-Book">School of Innovation, Design and Engineering, Mälardalen University</font></div>
<div style="font-family: -webkit-standard;"><font size="2" face="Avenir-Book"><a href="http://www.mrtc.mdh.se/~gdc" style="color: purple;">http://www.mrtc.mdh.se/~gdc</a>/</font></div>
<div style="font-family: -webkit-standard;"><font size="2" face="Avenir-Book">President of the International Society for Information Studies </font></div>
<div><font face="Avenir" size="2"><a href="http://is4si-2017.org">http://is4si-2017.org</a>/</font></div>
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<span style="font-weight:bold">From: </span>Fis <<a href="mailto:fis-bounces@listas.unizar.es">fis-bounces@listas.unizar.es</a>> on behalf of Krassimir Markov <<a href="mailto:markov@foibg.com">markov@foibg.com</a>><br>
<span style="font-weight:bold">Organization: </span>ITHEA<br>
<span style="font-weight:bold">Reply-To: </span>Krassimir Markov <<a href="mailto:markov@foibg.com">markov@foibg.com</a>><br>
<span style="font-weight:bold">Date: </span>Saturday 26 November 2016 at 18:23<br>
<span style="font-weight:bold">To: </span>FIS <<a href="mailto:fis@listas.unizar.es">fis@listas.unizar.es</a>><br>
<span style="font-weight:bold">Subject: </span>[Fis] Who may proof that consciousness is an Euclidean n-space ???<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 class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="DISPLAY: none"><math style="xmlns: "http://www.w3.org/1998/Math/MathML""><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle style="displaystyle: "true"" scriptlevel="0"><mi>f</mi><mo>:</mo>
<msup><mi><em>S<sup> <mrow class="MJX-TeXAtom-ORD"><mi>n</mi></mrow></sup><mo style="stretchy: "false"">→</mo>
<msup><mrow class="MJX-TeXAtom-ORD"><mi style="mathvariant: "double-struck"">R</mi></mrow></msup></em></mi></msup></mstyle></mrow><mrow class="MJX-TeXAtom-ORD"><mi><sup>n</sup></mi> </mrow><annotation style="encoding: "application/x-tex""></annotation></semantics></math></span></span><strong>is</strong>
<strong>continuous</strong> then there exists an <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="DISPLAY: none"><math style="xmlns: "http://www.w3.org/1998/Math/MathML""><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle style="displaystyle: "true"" scriptlevel="0"><mi>x</mi><mo>∈</mo>
<msup><mi>S</mi> <mrow class="MJX-TeXAtom-ORD"><mi>n</mi> </mrow></msup></mstyle></mrow><annotation style="encoding: "application/x-tex""></annotation></semantics></math></span></span> such that:
<span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="DISPLAY: none"><math style="xmlns: "http://www.w3.org/1998/Math/MathML""><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle style="displaystyle: "true"" scriptlevel="0"><mi>f</mi><mo style="stretchy: "false"">(</mo>
<mo>−</mo> <mi>x</mi> <mo style="stretchy: "false"">)</mo> <mo>=</mo> <mi>f</mi> <mo style="stretchy: "false"">
(</mo> <mi>x</mi> <mo style="stretchy: "false"">)</mo></mstyle></mrow><annotation style="encoding: "application/x-tex""></annotation></semantics></math></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"><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 style="face: "Times" size="4" newroman?=""><strong>continuous function</strong></font></a><font style="face: "Times" size="4" newroman?=""> 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 style="face: "Times" size="4" newroman?=""><strong>Euclidean
<i>n</i>-space</strong></font></a><font style="face: "Times" size="4" newroman?=""> ???</font></font></p>
<p><font style="face: "Times" size="4" face="Times New Roman" newroman?="">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>
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