<HTML><BODY><p style="margin-top: 0px;" dir="ltr">Dear Joseph, <br> The Borsuk-Ulam theorem 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. <br> Until the sphere lies between your eyes and the light source, the lights you can see are two (and it is valid also for every objective observer), it's not just a trick of your imagination or a Kantian a priori. <br> Therefore, the link between topology and energy/information is very strong. If we just think the facts and the events of the world in terms of projections, we are able to quantitatively elucidate puzzling and counterintuitive phenomena, such as, for example, quantum entanglement<br> https://link.springer.com/article/10.1007/s10773-016-2998-7</p>
<p dir="ltr">Therefore, the 'eternal' discussion of whether geometry or energy (call it dynamics, informational entropy, or whatsoever) is more fundamental in the universe, does not stand anymore: both geometry and energy describe the same phenomena, although with different languages. In physical terms, we could say that geometry and energy are 'dual' theories, e.g., they are interchangeable in the description of real facts and events. <br><br><br><br></p>
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<p dir="ltr">--<br> Inviato da Libero Mail per Android</p>
</div>venerdì, 25 novembre 2016, 00:28PM +01:00 da Joseph Brenner <a href="mailto:joe.brenner@bluewin.ch">joe.brenner@bluewin.ch</a>:<br><br><blockquote id="mail-app-auto-quote" style="border-left:1px solid #85AF31; margin:0px 0px 0px 10px; padding:0px 0px 0px 10px;" cite="14800735500000025323">
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<div><font face="Arial" size="2">Dear All,</font></div>
<div><font face="Arial" size="2"></font> </div>
<div><font face="Arial" size="2">Pedro should be thanked already for this new
Session, even as we welcome Andrew and Alexander. The depth of your work
facilitates rigorous discussion of serious philosophical as well as scientific
issues.</font></div>
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<div><font face="Arial" size="2">In Pedro's note of 2016.11.24 there is the
following:</font></div>
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<div><font face="Arial" size="2">"<font face="Times New Roman" size="3">Somehow, the
projection of brain "metastable dynamics" (Fingelkurts) to higher
dimensionalities could provide new integrative possibilities for information
processing. And that marriage between topology and dynamics would also pave the
way to new evolutionary discussions on the emergence of the "imagined present"
of our minds."</font></font></div>
<div><font face="Arial" size="2"></font> </div>
<div><font face="Arial" size="2">What Pedro calls here "the marriage between
topology and dynamics" reminds one of the 'eternal' discussion of whether
geometry or energy (dynamics) is more fundamental in the universe. I just
suggest that there are alternative terms to focus on and describe the
interaction between topology and dynamics that are more - dynamic, and make an
emergence a more logical consequence of that interaction.</font></div>
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<div><font face="Arial" size="2">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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